Oddly Influenced

What's up with quantum mechanics? (36 Views of Mount CritRat)

Sat, 30 May 2026 14:43:34 -0500

The critical rationalists disliked post-1925 quantum mechanics (QM) as much or more than they disliked Marxism. It’s not that QM wasn’t successful when judged against their methodology. It was. Theorists made dramatic predictions that matched later experimental results to an absurd degree of precision. Check. Anomalies were handled by adjusting or expanding the theory in ways that allowed new predictions that, in due time, survived attempts at refutation. Check. So the critical rationalists should have been happy, but they weren’t.

What’s the problem? In a word, it’s that QM is an instrumental theory, and those are the wrong kind of theories. In a draft of the final essay in this series, I used QM to explain instrumentalism, but then I thought of a better (or, at least, cuter and shorter) example.

Still, the QM story is interesting, so I present it as an optional supplement. As Abraham Lincoln didn’t actually say (of course), “People who like this sort of thing will find this the sort of thing they like.” It is in that spirit that I offer these words to you.

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About this series

The second quarter of the 20th century was an awkward time for theoretical physicists working on teensy entities. I’ll attempt to explain some of the issues, but I caution that I’m woefully unqualified to do so. I enrolled at CalTech intending to be a scientist, specifically: a physicist. I discovered I wasn’t smart enough, so I transferred to the University of Illinois, which at the time had a much better computer science department and was way cheaper. (Around $4000 a semester in 2026 dollars.)

It all has to do with causality.

Since at least Galileo, the assumption in physics has been that there is no action at a distance. An effect on something over there caused by something over here must have that causality carried from here to there by some thing (or things). Consider heat. Galileo wrote:

“Those materials which produce heat in us and make us feel warmth, which we call by the general name fire, would be a multitude of minute particles having certain shapes and moving with certain velocities. Meeting with our bodies, they penetrate by means of their consummate subtlety, and their touch which we feel, made in their passage through our substance, is the sensation which we call heat.”

Causality is contact, you might say. Kepler agreed. Quoting Wikipedia:

Kepler’s laws were developed based on a physical theory of planetary motion in which the Sun emitted magnetic fibrils which pulled the planets into orbits. The fibrils were somewhat elastic allowing non-circular motion driven by the inertia of the planets.

The Newton of the Principia also agreed, though he left undescribed what specifically was moving the planets:

“that one body may act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.”

Newton also wrote a book on Opticks. He had to confront the problem of what causes light’s remote effects. His solution was that light is formed of corpuscles (particles) – not dissimilar to Galileo’s minute particles of heat.

Newton’s approach fell out of favor in the early 1800s as experimental evidence came to favor a wave theory of light. But that doesn’t violate “causality is contact” because waves are waves in something (like an ocean). It’s the wave’s “medium” that does the pushing and pulling and contact.

The “something” that light waves are waves in was called the luminiferous aether, which is “an invisible and infinite material with no interaction with physical objects.“ Seems absurd, right? Insert here doubtless ignorant snark about dark matter or dark energy.

It turns out that the experimental evidence pushed against the existence of a luminiferous aether. Efforts to save the theory were put to bed in 1905 by special relativity, after which you could respectably consider light a wave in… um, nothingness? Let’s talk about something else, shall we?

We could talk about the photoelectric effect… except that – in the same year as special relativity – Einstein also explained the photoelectric effect by assuming that light is tiny packets of energy (photons).

So the situation in the early 20th century was that some experiments suggested light is particle-like: a photon has a definite position in space at a given time, and it follows a definite path. At the same time, other experiments pointed to a wave-in-nothing explanation: waves are present simultaneously at many points, with values at those points changing continuously over time. (Particles move; waves spread.)

Particle or wave? The question arguably came to a head around 1926. In September 1925, Heisenberg published a framework theory for quantum mechanics. In January of the next year, Schrödinger published a different theory. The two theories were in competition:

“For the main contestants, Heisenberg and Schrödinger, the issue at stake was which view could claim to provide a single coherent and universal framework for the description of the observational data. The choice was, essentially between a description in terms of continuously evolving waves, or else one of particles undergoing discontinuous quantum jumps.”

Great! We can see which theory survives experiment and thus resolve (at least for now) the particle-or-wave question. Unfortunately, in May of the same year, Heisenberg published another paper showing that the two approaches were equivalent. If I understand that correctly, the two theories would make all the same predictions, so no experiment can decide between them.

Meanwhile, other problems had been cropping up. One had to do with probabilities.

In “classical” physics, if you know the initial state of the system, you can predict its final state exactly. By that, I mean something like limits in calculus: the more precise your measurements of the initial state, the more precise your prediction will be. If a cue ball with a given mass and velocity (momentum) strikes the eight ball at a given angle, you know for sure whether the eight ball will go into the corner pocket (leaving aside friction, rips in the table’s fabric, how level the table is, yada yada yada).

However, the same is not true at the quantum scale. If a photon hits an electron and propels it into a detector’s screen, no matter what you know about the collision, you can’t predict where the electron will hit. The best you can do is calculate probabilities: it’s more likely to hit there than here. But what does it mean for a single cause to have in principle an infinite number of possible effects? (That is, measurement error isn’t the issue.)

To compound things, there are certain properties of the system that cannot be simultaneously known (complementarity). The most famous example is Heisenberg’s uncertainty principle: the more precisely you measure a particle’s position, the less you know about its momentum.

That seems tractable: just measure the position at one moment and the momentum at another, then work your way backward (using a billiard-ball style of reasoning) to the momentum the particle must have had at the moment its position was measured. Einstein proposed ingenious thought experiments for how you might know position and momentum at the same moment, but they never worked. The upshot, per Frescura and Hiley:

By using one particular piece of apparatus only certain features could be made manifest at the expense of others, while with a different piece of apparatus another complementary aspect could be made manifest in such a way that the original set became non-manifest, that is, the original attributes were no longer well defined.

I think “non-manifest” might mean that, once you’ve measured the momentum, the earlier measurement of position is useless in further calculations/predictions. But I don’t know, because I don’t have the math, and I think the upshot of the “quantum revolution” is that trying to use analogies with macroscope entities – even analogies as simple as “objects have at all times both a position and momentum” – to “picture” the quantum world – is a mug’s game. Frescura and Hiley again:

In the traditional view, it is assumed that there exists a reality in space-time and that this reality is a given thing, all of whose aspects can be viewed or articulated at any given moment.

Some people came to believe that view is wrong at the quantum level.

One experimental apparatus is intended to measure position, and another is intended to measure momentum. They will, independently, produce results – but that doesn’t mean there’s an entity, down there at the quantum level, that simultaneously possesses all the measurable properties. Konrad Hinsen comments: “Measurement requires interaction and thus changes the quantum state. If you measure the momentum of a particle, it has a new quantum state after the measurement, and in that state, position is undefined. It’s not just impossible to measure position and momentum at the same time. There is no possible quantum state in which position and momentum have well-defined values.”
Similarly, it’s meaningless to speak of a photon as being either a particle or a wave. Some apparatus will produce results compatible with a particle, some with a wave, but what’s measured isn’t really either, or both, or neither.
Until the electron is measured to have hit the screen, it’s meaningless to talk of its position. If you insist on talking about what the electron “is” before it hits the screen, what it is, is a probability distribution. (And what does that mean?)

Einstein came to accept the results of quantum mechanics, but he still wanted causality:

“[…] quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the ‘old one’. I, at any rate, am convinced that He [God] is not playing at dice.”

Einstein believed that there must be some sort of causal theory underlying QM that didn’t require “spooky action at a distance":

“Without doubt quantum mechanics has grasped an important fragment of the truth and will be a paragon for all future fundamental theories, for the fact that it must be deducible as a limiting case from such foundations, just as electrostatics is deducible from Maxwell’s equations of the electromagnetic field or as thermodynamics is deducible from statistical mechanics.”

But he was never able to find a causal theory “below” quantum mechanics that would generate its equations. I don’t believe anyone has.

In contrast to Einstein, other theorists gave up on causality, mostly adhering to the Copenhagen interpretation (really, the Copenhagen interpretation_s_). Per Wikipedia:

“Features common across versions of the Copenhagen interpretation include the idea that quantum mechanics is intrinsically indeterministic [and] that objects have certain pairs of complementary properties that cannot all be observed or measured simultaneously. Moreover, the act of ‘observing’ or ‘measuring’ an object is irreversible, and no truth can be attributed to an object except according to the results of its measurement.”

When it came to the quantum world, it seems most physicists gave up on the type of explanation that would have pleased Galileo (or Einstein). Some continued occasionally banging away at the metaphysical questions, but others preferred to “Shut up and calculate” (N. David Mermin, usually attributed to Feynman).

It’s possible this was a sociological or cultural thing. Physicists who hit their stride in the early parts of the last century had philosophical training and commitments different from younger physicists. Succeeding generations might have been more comfortable working on the “what” and leaving the “why” (the causality) to others. Konrad Hinsen again: “Action at a distance is perhaps no longer an issue for later physicists because they grew up with an atomic picture of matter. Distance zero doesn’t exist in the (sub-)atomic world. Interaction always happens at some distance, even among the constituents of an atom.” That’s weird to think of: not only is causality not contact, nothing ever comes into any contact with anything.

The critical rationalists think scientists shouldn’t have done that. As someone who benefits every day from applications of quantum mechanics – lasers, integrated circuits, MRI machines, electron microscopes, and whatnot – I’m happy that physicists have been metaphysically incorrect but instrumentally productive. But I have a more expansive view of what science is for than do the critical rationalists. (See the next essay.)

The incomplete API (36 Views of Mount CritRat)

Sat, 23 May 2026 16:29:16 -0500

It’s time – past time – to wrap this up. I’ve been focused on the question of why critical rationalist methodology didn’t prevent its proponents from making confident proclamations that were wrong. I’ve concentrated on matters of personality, habit, and bias that, to put it charitably, directed their attention away from important facts and classes of facts.

In this post, I’ll use an analogy from a reader to argue that the methodology is fundamentally too incomplete to be workable. I claim that even someone with the purest of intentions, best intuition, highest intelligence, greatest imagination, and best work ethic could not follow critical rationalism and contribute to the growth of science.

Attempts to apply critical rationalism outside science will fare no better.

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About this series

Mastodon user @interstar sent me this comment:

You are approaching this like an engineer asking “how might I implement a working model of a scientist?”, whereas Popper is more like the system architect designing an API or interface : “What’s the minimum contract something would have to support to still be a scientist?”

I don’t know if I agree with the characterization of me, but it’s certainly both fair and plausible. I’m also not sure that was Popper’s goal, but it’s definitely a useful lens on critical rationalism.

API?

This blog isn’t just for software people, so I’ll briefly explain what an API is. Skip this if you already know.

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An API is an Application Program Interface. The grouping of adjectives is ambiguous, so it’s clearer to call it an Interface for Application Programs (what we more often call “apps” today). Think of one set of code (the app) sitting on top of a barrier (the API). Below the boundary, some code provides services (such as reading and writing files) that are intended to be useful for all manner of apps. The API is not supposed to constrain (much) what apps are put on top of it. It just defines how any app with a particular need can get that need satisfied.

An API is described by two sets of names. The first names actions or “functions.” One such function might allow you to open a file for later use. An app might use it like this:

open_file("my file", ToRead)

open_file is the function name. The first argument ("my file") is the name of the file, and the second (ToRead) is some datum that tells whether the file is to be opened read-only, for writing but not reading, or both.

open_file’s two arguments are of different data types. A name of a file isn’t the same thing as a counting number is not the same thing as an indication of whether a file is ToRead, ToWrite, or ToReadOrWrite.

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The app’s author has to know (1) that open_file exists, and (2) what type of arguments it uses and in what order. That’s provided by documentation such as that in the sidebar, which will typically begin with information something like this:

open_file(FileNamed name, ForPurpose purpose)

The capitalized identifiers (FileNamed, ForPurpose) describe an argument’s type. The immediately following lowercase identifiers give the code that implements open_file names that it can use to refer to values passed down through the API. In one particular use of open_file, name might refer to “my file” and purpose to ToRead. The next use might give different values.

One more detail:

Let’s suppose there’s another function named transfer that transfers text from one open file to another. That function might “return a result.” That would look like this:

transfer(OpenFile from, OpenFile to, Count how_much) returns TransferResult
                                                     ^^^^^^^^^^^^^^^^^^^^^^

TransferResult can be casually described as one of:

“Everything went fine.” Whatever number of characters was intended to be transferred has been transferred.
“Only 5 of the intended 34355 characters made it.”
“You opened the from file wrong: it can only be written to, not read from.”
“You opened the to file wrong: it is read-only.”

That is all the computer science you need to know to understand the rest of this post.

A formative experience

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Somewhere around 1985 I was a junior programmer on a project to design and implement an API providing “real time services” to the Gould PowerNode Unix system. A main market for these computers was flight simulators – the kind that run in buildings filled with machinery, not the kind that runs on PCs.

Back then, the dominant rule-set for proper programmer behavior was the “waterfall methodology,” and our project followed it. The senior programmers were to design the API first. The physical form of the design was a set of short documents (“man pages”), one per function. Each man page started with a description of the function (like the ones for open_file and transfer in the optional section above). That strict definition of function names, argument types, and return value types was followed by natural-language text saying what the function did, how to use it, what the different possible return values meant, etc.

My main role on the project was to test the implementation. At that time, the conventional wisdom was that programmers couldn’t test their own code (find their own bugs). Since programmers of that era didn’t like testing anyway, they were happy to delegate the job to juniors like me. But there wasn’t an implementation to test yet – that would come after the design was finished and approved. So my job during the design “phase” was to write user documentation – to explain how to put the various functions together to accomplish some goal. An app will usually use more than one function from an API. Typically, a sequence of “calls” to different functions is needed to accomplish a particular goal.

My approach was to organize the document around one or more annotated examples. “If you want to do something like X with this API, here’s an annotated sample program that shows you how.” I couldn’t actually check if the examples worked until the implementation was finished, but I could get most of the documentation work done while I had nothing else to do.

While writing an example, I discovered an interesting problem (a bug in the design). There was a function in the API that took a magic Key value (something like a modern passkey). In at least my scenario, there was no way to produce that key. Thus, the task I was showing app programmers how to accomplish was in fact impossible.

Critical rationalism is like that

If I’m to think of critical rationalism as an API, I will, and say it’s an incomplete API like ours from the ’80s. So many entities are supposed to just appear, as with the Key argument that one function required and no function supplied. Experimental design: irrelevant to theory! Evaluating experimental results: hard in theory but someone else’s job in practice! Predictions: pure deductive logic suffices! Confirmations/refutations: simple binary values, no details needed! Collaboration: what does that have to do with anything?

The people I worked with in 1985 were fine people. The only one who I can actually picture in my mind was impressively smarter than me. But, if a methodology is equivalent to an API, what critical rationalism is missing makes it unable to accomplish actual science in the way the original as-designed SELUnix API would have been unable to support a flight simulator.

So who cares, and why should they?

As Konrad Hinsen has pointed out to me, I’m sort of smashing a gnat with a sledgehammer, since real scientists don’t actually follow the critical rationalist methodology and most everyone knows that. Scientists do what works, not what non-scientists tell them what to do.

Granted, but my career was in a field (software development) where it’s a cottage industry to take naive views of how other people do their jobs and then proclaim “we should be like them.” The very term “software engineering” is an example. It was a successful imposition of methodology supposedly used by Real Engineers – with, I think, inadequate consideration of what engineers actually do. As with the critical rationalists, a distaste for the squishy, non-logical, sociological parts of engineering meant that their comparisons of programming to designing and building bridges or intercontinental ballistic missiles were… fraught. Postscript: It’s been a while since I read the primary sources in software engineering. I have a feeling I’m maybe being unfair: they may have shown more concern for such matters than the (roughly contemporaneous) critical rationalists did. To get real work done, you had to pay attention to parts of the job they’d ignored and, realistically, at least bend the rules if not ignore some rules entirely. “This book is about doing testing when your coworkers don’t, won’t, and don’t have to follow the rules.” – Testing Computer Software (2/e), Kaner, Falk, and Nguyen, 1993.

The overall status of science has varied in the popular imagination. In my country (the USA), science’s reputation is currently at a low ebb. But there are still subcultures with high regard for science. I’m arguing that such science fans shouldn’t listen to people like the critical rationalists – they have a few useful ideas that you’ve already absorbed from the zeitgeist, combined with a bunch of abstract wankery you should ignore.

The hero's journey (36 Views of Mount CritRat)

Sun, 17 May 2026 17:33:45 -0500

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The image is of Alexander the Great. He won a lot of battles, aided by other soldiers, most notably his heavy cavalry (the Companions).

The critical rationalists are like historians who focus on the Great Men of history. When they see the history of science, they see the Alexander-equivalents – the Newtons, the Einsteins. They are uninterested in the common soldiers, and mostly uninterested in the scientific equivalent of the Companions. They do not see the full mosaic with all its participants:

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Thus – like Great Man historians – they miss a lot.

About this series – Sorry there’s no picture of Mt. Fuji, but the images above were too good not to use.

Here are some quotes:

“Why is Kuhn concerned to up-value Normal Science and down-value Extraordinary Science? This question is prompted by several considerations. First, Normal Science seems to me to be rather boring and unheroic compared with Extraordinary Science.” – John Watkins, “Does the Distinction Between Normal and Revolutionary Science Hold Water?”, Criticism and the Growth of Knowledge, 1970, p. 31.

“One has to appreciate the dare-devil attitude of our methodological falsificationist. He feels himself to be a hero who, faced with two catastrophic alternatives, dared to reflect coolly on their relative merits and choose the lesser evil.” – Imre Lakatos, “Falsification and the Methodology of Scientific Research Programmes,” Criticism, p. 113.

“But these marvellously imaginative and bold conjectures or ‘anticipations’ of ours are carefully and soberly controlled by systematic tests.” – Popper, The Logic of Scientific Discovery, 1959, p. 278.

“But the newly rising structure, the boldness of which we admire, is seen by the conventionalist as a monument to the ‘total collapse of science’, as Dingler puts it.” – Popper, Logic, p. 61.

“Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were, above a swamp.” – Popper, Logic, p. 94.

“Take Boltzmann: there are few greater scientists. […] But he was as far from a ‘normal scientist’ as anybody could be: he was a valiant fighter who resisted the ruling fashion of his day.” – Popper, “Normal Science and its Dangers,” Criticism, p. 54.

“To suggest such an idea required even greater courage than Prout’s; the idea crossed Einstein’s mind but he found it unacceptable, and rejected it.” – Lakatos, Criticism, p. 142.

“I believe that science is essentially critical; that it consists of bold conjectures, controlled by criticism, and that it may, therefore, be described as revolutionary.” – Popper, Criticism, p. 55.

I could go on, and I will, later.

Behold the scientist

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When Alexander the Great is lauded, it’s usually for how skillfully he applied his favored set of tactics. Against that, I present General Omar Bradley, who famously said, “Amateurs study tactics; professionals study logistics.” I’ve got nothing against hero worship, or studying the outsized characters of history, but when your entire methodology is a tactical methodology for the scientist equivalents of Alexander the Great, you miss the importance of other problems scientists must solve, ones akin to getting the right number of well-fed, disciplined-enough soldiers to the right place at the right time. To be fair, Alexander was also talented at strategy, but the Gen. Bradley quote I have leaves strategy out, so I did too. I’d argue strategy is intermediate between tactics and logistics on the sexiness/boldness scale.

The mass of common soldiers is vital to winning battles and wars, and I see no reason to ignore the role common scientists play in the big conflicts of scientific history. Recall that the critical rationalists adopt the philosophical habit (or conceptual metaphor) of comparing argument to conflict. You win intellectual battles by successfully attacking your opponent’s weak spot.

However, the critical rationalists think common scientists matter little to the progress of science. In fact, they are dangerous when they constrain the Great Men:

“Thus in Kuhn’s view scientific revolution is irrational, a matter for mob psychology.” – Lakatos, Criticism, p. 178.

“But the Kuhnian research programme contains a new feature: we have to study not the mind of the individual scientist but the mind of the Scientific Community. Individual psychology is now replaced by social psychology; imitation of the great scientists by submission to the collective wisdom of the community.” – Lakatos, Criticism, p. 179.

“In my view the ‘normal’ scientist, as Kuhn describes him, is a person one ought to be sorry for. […] I can only say that I see a very great danger in [the attitude of the such scientists] and in the possibility of its becoming normal (just as I see a great danger in the increase of specialization, which also is an undeniable historical fact): a danger to science and, indeed, to our civilization.” – Popper, Criticism, pp. 52-3.

I’ve already documented how limited is the role the critical rationalists allow to experimenters. But they talk even less about what I might call “minor theorists” – to the point that I don’t have an idea of what such people are supposed to do (except, I suppose, to work to become Great.)

An example

It’s characteristic of critical rationalist rhetoric that their stories skip nimbly from one scientific revolution to the next:

Newton published his theory of gravity in 1687.
- There was a dramatic confirmation in the form of the successfully predicted return of Halley’s comet (predicted in 1705, observed in 1758). Critical rationalists differ in whether it’s rational to care about a flashy confirmation like that. (Lakatos says it is; Popper says not.)
- The precession of the perihelion of Mercury is discovered in 1859. This violated a prediction (consequence) of Newton’s theory: that the axis of the ellipse Mercury traces around the sun will stay put. Turns out it doesn’t.
- Nothing much happens. People don’t abandon 172 years of gravitation (as Lakatos points out) “Theories grow in a sea of anomalies, and counterexamples are merrily ignored.” – Lakatos’s lectures on scientific method in For and Against Method, 1999, p. 99. .
Einstein produces a replacement theory of gravity in 1916. Notably, it explains the precession of Mercury. There’s a problem here for critical rationalists in that predicting a known fact isn’t novel or bold. A later elaboration allows such to count if “the hard core of the programme was not devised to explain it.” That seems weak to me: “Professor Einstein, do you state under oath that you never thought about Mercury whilst devising your scheme?” But Einstein gave two other bold predictions, so the point is moot.

What’s missing is anything anyone else did with Newton’s theory in the 220 years between Newton and Einstein. Consider the pendulum’s equation of motion. I think it’s an interesting case because it:

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… introduces two new entities to the Newtonian theory: the idea of a pivot point, and the distance from the pivot to the mass in question (the bob), and:
… uses Newton’s Laws to calculate a differential equation governing the motion of the bob, which unfortunately:
… is hard to solve. However, given an approximation that has negligible error given amplitudes of less than about twelve degrees, there’s a closed-form easy solution, which:
… supports Galileo’s earlier observation that a pendulum’s time-to-swing (period) is independent of how much you pull back the bob before you let it loose (amplitude).

So we have two new entities, one new equation, one approximation, and one significant piece of background knowledge explained (the independence of period). How does this fit in? It seems something that could be included in Newton’s overall theory or research programme. But where’s the refutation that prompts the addition? And does this new equation predict something new? We already knew about the constancy of the pendulum’s period.

This pendulum work is outside the critical rationalist methodology. It’s “puzzle solving,” which Popper looks down on:

“I do not know whether Kuhn’s use of the term ‘puzzle’ has anything to do with Wittgenstein’s use. Wittgenstein, of course, used it in connection with his thesis that there are no genuine problems in philosophy — only puzzles, that is to say, pseudo-problems connected with the improper use of language. If you’re interested in intellectual gossip with an admixture of serious topics, Wittgenstein’s Poker: The Story of a Ten-Minute Argument Between Two Great Philosophers (Wittgenstein and Popper) is an entertaining read. The incident described (Wittgenstein supposedly threatening Popper with a fireplace poker) predated what Popper wrote here. However this may be, the use of the term ‘puzzle’ instead of ‘problem’ is certainly indicative of a wish to show that the problems so described are not very serious or very deep.” – Criticism, p. 52, footnote 1.

Did Alexander the Great solve puzzles? Or did he conquer?

Cutting the Gordian knot

Well, actually, Alexander did solve puzzles. (Or were they problems by virtue of being worthy of his attention?) Famously, he solved the Gordian Knot with a bold stroke (literally: a stroke of his sword.)

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That image has appealed for centuries. Why? I think it’s Alexander’s quickness, decisiveness, and ability to just resolve the issue after all these years. “Let’s move on!”

(Would you watch a movie that showed Alexander patiently untying the Gordian knot over a period of several months?)

Part of the boldness the critical rationalists exalt is the ability to “strike to the heart of the matter,” to solve problems in a way lesser men were unable to see because of their timidity or lack of imagination.

I think it reasonable to say that Alexander’s solution to the Gordian Knot is simpler than the alternative. (After all, the expected solution – untying the knot – was so difficult no one had accomplished it.) But “simplicity” is another of those essentially contested concepts that no one will ever agree on.

Popper has a chapter on simplicity in The Logic of Scientific Discovery. He is not interested in different definitions of the word: “Nothing depends on the word ‘simplicity’: I never quarrel about words, and I did not seek to reveal the essence of simplicity.” – Logic, p. 131, addendum to the 1972 edition. (Good for him!)

What Popper is interested in is describing the underlying properties theorists are referring to when they say “this theory is simpler than that one.” He seems to claim that the more testable theory is simpler, He equates greater testability with “greater empirical content,” which means “they tell us more” – Logic, p. 128. and that such a simplicity is measured (approximated?) by the number of free parameters in equations. That is: consider some number of observed data points. There are an infinite number of equations that match (predict) those points. Of those equations, f(x, y) is simpler than f(x, y, z). I have a hunch that the critical rationalists' dislike for scientific fields that rely heavily on statistics (agronomy, social science) is partly that there are so many potentially-relevant variables that the scientists just give up and define an error or noise term that represents those variables. Thus they’re hiding within a single parameter many parameters they ought to be accounting for.

Because the critical rationalists are focused on formal languages (logic, mathematics) as the sine qua non of rationality, they tend to characterize theories in terms of the number of statements or equations:

“At the heart of any research programme is a ‘hard core’ of two, three, four or maximum five postulates. Consider Newton’s theory: its hard core is made up of three laws of dynamics plus his law of gravitation.” – Lakatos, For and Against Method, p. 103.

I think it’s better to think of the entities (or nouns, or parameters) in a theory. Newton’s research programme is better described as being essentially a set of entities like “force,” “mass,” and “acceleration,” together with the equations that link the terms together. That meshes with Popper:

“The new theory should proceed from some simple, new, and powerful unifying idea about some connection or relation (such as gravitational attraction) between hitherto unconnected things (such as planets and apples) or facts (such as inertial and gravitational mass) or new ‘theoretical entities’ (such as fields and particles).” – Popper, Conjectures and Refutations (5/e), p. 241, his emphasis.

The result is that adding the the entity (parameter) called “pivot point” to Newton’s theory complexifies it in an unaesthetic way. Consequently, psychologically, it makes the aggregate theory less appealing. The physicist Paul Dirac, who linked aesthetics tightly to truth, pointed out that Einstein’s general relativity is substantially more complicated than Newton’s theory but was still preferable because of its mathematical beauty. P.S. There’s an interesting podcast episode on Dirac. I would not have guessed he was trained as an engineer.

From this point of view, Great Scientists invent simple theories that lesser scientists then complexify with pendulums and pivot points and whatnot. The critical rationalists look away from that process because of their aesthetic preferences. They don’t talk about how the theory of the pendulum adds onto what Lakatos calls the “hard core” of a research programme.

Alexander didn’t cut the Gordian Knot and then fuss around looking at the relationship between sword strokes and different kinds of knots. He moved on. Methodologists of Great Men aren’t interested in what and who gets left behind to deal with the details.

Marxism again

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My claim throughout this “Mt. CritRat” series been that the critical rationalists have biases and prejudices and knee-jerk reactions that steer them away from seeing what they otherwise could. They’re wearing blinders, and their critique of Marxism as a science is an example.

Just as they seem uninterested in the theoretical events between the Newton of 1687 and the Einstein of 1916, they seem uninterested in the theoretical events between 1848 and 1917. That is – I claim – in part because they are biased to focus on the earliest expression of a Great Man’s theory; that is, on what Marx wrote circa 1848.

Marx made two bold predictions that I’ve discussed: the continued immiseration of the proletariat and the origin of the European revolution in the most advanced nations. He later complicated those predictions, apparently because he was trying to explain why the revolutions of 1848 fizzled. Marx adjusted his theory of immiseration and added a preliminary step (revolution in Russia) to his theory of history. The revolution was supposed to start in Russia, but that event was in turn supposed to prompt revolutions in the more advanced nations, who would then help Russia out as part of a pan-European revolution.

This is actually decent science in critical rationalist terms. A natural experiment (the failed 1848 revolutions) indicated problems in the theory. The theorist adjusted the theory and made two new predictions (if they’re savvy enough, the bourgeoisie can buy off the proletariat; and the revolution is most likely to happen in Russia because that’s the most vulnerable state.) Both predictions arguably proved out.

But if you skip 68 years of natural experiments and insist that history is a sharp revolutionary leap from one bold, simple theory to another, it’s easy to miss what actually happened. “Reality is that which, when you stop believing in it, doesn’t go away” – Philip K. Dick. Except that I’d replace “stop believing in it” with “stop paying attention to it.”

⊕ Who's responsible if a small child drowns in this pool?

Great men and simple theories are an attractive nuisance. We should keep that in mind, even if we’re not doing science, just looking for Big Names in Our Field to emulate or for simple methodologies to follow. People like Popper, Lakatos, me (and perhaps you) are suckers for that.

Waterfall science (36 Views of Mount CritRat)

Sat, 02 May 2026 17:10:03 -0500

Methodologies tell people how to do things: they describe steps in a process. A useful rule of thumb is that gotchas for a methodology cluster around the steps the methodologists aren’t interested in. The critical rationalists aren’t interested in experiments. They are Big Design Up Front, Command and Control people, and their methodology suffers because of it.

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About this series

My father (RIP) built houses. When he first went independent, people wanting a house would bring him an architect’s plans/blueprint, ask him how much building a house to match it would cost, then contract him to build it.

He hated architect’s plans, for two reasons that I remember:

Architects would include a feature designed in a way that was hard to build. That didn’t matter to Dad’s bottom line – he was good at estimating cost He was once off by one dollar in his bid to build a house. He got lucky, admittedly, on the things that are hard to predict, but an error of one part in maybe 40,000 (given prices of the time) is not bad. – but it offended him that his clients had to pay more for a feature that could be done just as well but more cheaply.
Architects tended to be detached from their client’s reality. I remember one time when Dad was building a house for a couple where the husband had a job that left him dirty at the end of the day, the way construction does. Such a person showers after getting home from work. A user-friendly house plan provides a “straight shot” from the garage to a bathroom with a shower. The architect’s design had the husband tracking dirt all through the house to get to the shower.

When Dad was successful enough, he simply stopped working with architect’s plans. If you wanted him to build you a house, you had to agree to collaborate with him as he drew the plans.

From this and my own later experiences in software, I’ve come to believe that abstract understanding fails unless combined with nitty-gritty implementation details. That applies to both the design of objects (like houses) and also design of methodologies.

With that context in mind, let’s talk about an experiment.

Solar neutrinos

The Homestake experiment tested a theory of how the sun works. It found fewer neutrinos than predicted. An adjustment or addition was made to a standard theory, and science marched on.

I could cast this as an example of how critical rationalists say science should work. At an abstract level, it is. At a concrete level, things get more interesting. I’m largely drawing on the description of the experiment in Dudley Shapere, “The concept of observation in philosophy and science,” Philosophy of Science, 49 (1982) pp. 485-525. Plus Wikipedia.

Although the scientists talked casually about “seeing neutrinos,” in the actual experiment what was observed was not neutrinos, but the number of clicks made by a glorified Geiger counter exposed to some very mildly radioactive argon gas. There’s a long chain of justification between “we counted X clicks in time Y” to “the sun produces neutrinos at such-and-so a rate.” Here are some of the links in the chain.

The argon gas fed to the detector was made by combining a very small amount of an unstable isotope of argon with a vastly larger number of off-the-shelf argon atoms. By “very small amount,” I mean that the experimental design estimated (based on theory) that a multi-day run of the experiment would produce around 200 atoms of radioactive argon. That number of atoms is not exactly easy to work with, hence the combination with enough argon that you can take advantage of known methods of working with gases.

Where did the radioactive argon atoms come from? From the highly unlikely but theoretically possible interaction of a neutrino and one isotope of chlorine. So unlikely is that interaction that you need a vast, vast, vast amount of chlorine to produce an estimated six atoms of argon per day. Fortunately, cleaning fluid (perchloroethylene) is mostly chlorine, and apparently it’s cheap enough that a mere 400,000 liters of it was estimated to contain enough of the right chlorine isotope.

Another problem was that neutrinos aren’t the only things that can convert chlorine to argon. Muons – found in cosmic rays – can too, but burying the fluid chamber 1,478 meters below the earth should have ensured that only a trivial number of muons reached it.

Alas, muons can also be created by the interaction of sulphur with fast neutrons (from radioactive decay of uranium in rock surrounding the fluid chamber), so they had to make sure the cleaning fluid wasn’t much contaminated with sulphur (less than one part per million).

Solving these and a few more problems led to an estimated one “spurious” argon atom every two days – 1/36th the expected sun-caused rate. They were very careful to avoid overcounting. But it turns out that overcounting wasn’t a problem because…

After all that careful setup (and more), only about 1/3 of the neutrinos predicted by theory were detected. There ensued debate about how to resolve what came to be called the solar neutrino problem.

One possibility was that the theory being tested – the standard solar model – had been refuted. But not so fast! That model is based on a simple formula for particle interactions:

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That says that a star works by smashing four hydrogen atoms together to produce a helium atom, two electrons, and two neutrinos. But there’s more to the process than a pretty formula. There are three different “pathways” from the starting state to the finished state, and how often each pathway is taken depends on the density and (especially) the temperature at the core of the sun.

Is it the formula that’s been refuted? Or hypotheses about the environment at the sun’s core?

Alternately, what about other parts of particle physics? The estimates for how often neutrinos interact with chlorine are derived from a theory of the weak interaction. Maybe what’s at fault is a misunderstanding of the weak interaction? (So that what was refuted was not what was being consciously tested, but a “nearby” theory?)

Or maybe neutrinos can decay and so only a third of them make it to earth?

Or what about chemistry? The argon atoms were collected by bubbling helium through the liquid in the chamber, then separating the argon from the helium with a charcoal trap. Maybe something went wrong there? For example, argon was chosen as the target atom because it’s a noble gas, one reluctant to participate in chemical reactions. But perhaps a new argon atom is born ionized and so can “stick” to a perchloroethylene molecule, in which case the helium trick wouldn’t work for that atom. Maybe 2/3ds of the argon atoms were missed for that reason? Or (in an alternate theory) maybe the new argon atoms are unavailable to the helium because they’re structurally “caged” in the molecules in which they were just created?

The anomalous results were detected in the early 1970s. Time passed, with people working on explanations like the above. By the time of Shapere’s paper – a decade later – matters were unresolved: Shapere 1982, p. 499, footnote 7.

The most serious possibility lies in the hypothesis of neutrino oscillations, which is being actively considered by physicists on other grounds. However, there remain grave doubts as to whether that hypothesis could really reduce the predicted neutrino flux to the observed level.

Neutrino oscillation holds (roughly) that neutrinos oscillate among three states as they move through space. Only one kind is energetic enough to have been detected by the Homestake experiment. The oscillation idea actually predates the Homestake experiment by a decade, but was untestable at that time. Homestake offered some weak confirmation for it (since the observed shortfall of 2/3 is consistent with it.)

It was not until 1984 that Herb Chen pointed out that heavy water could be used to address the question. After Atomic Energy of Canada Limited promised to lend experimenters CA$330,000,000 of heavy water and the owners of a really deep mine offered to lease part of it cheaply, the Sudbury Neutrino Observatory was set up. Per Wikipedia, in a mere sixteen years, Sudbury “provided clear evidence” that, um, failed to refute the conjecture of neutrino oscillation. Neutrino oscillation implies that neutrinos have mass, so this lack-of-refutation served as a (partial) refutation of the Standard Model of particle physics.

Evidence and methodology

This is roughly critical rationalism. Predictions were made. When they failed, theories were adjusted, and novel predictions resulted. More weight was given to confirmations of theory than Popper would have liked (though Lakatos would have likely approved of them as dramatic enough – akin to the return of Halley’s comet).

But notice the word “experiment” doesn’t appear in the previous paragraph. In both discussions of their methodology and case studies, the critical rationalists treat experiments as quick and conclusions as obvious. They don’t describe thirty-year sagas of people trying to figure out what a result means.

I shouldn’t be (too) unfair. Popper, in particular, devotes some time to things like the Duhem-Quine thesis. That’s the argument that any experiment that tests a theoretical prediction relies on a whole swath of “theories of the instrument.” It might be those theories that have been refuted, not the theory under test. There’s no principled, or rational, way to finger the culprit.

But having raised the issue, Popper drops it.

First, he appeals to “basic statements.” The Duhem-Quine thesis allows any attack you make on my theory of the instrument to be countered by my claim that your attack relies on a theory that itself is wrong. There is a recursive descent of theory-based claims and counter claims. Popper suggests that such claims can bottom out with basic statements: “Simple descriptive statements, describing easily observable states of physical bodies.“ Karl Popper, Conjectures and Refutations: the Growth of Scientific Knowledge) (5/e), 1989, p. 267.

But there’s a big gap between descriptions of the Homestake experiment’s tower of supporting claims and basic statements like that a counter clicked n times. No real argument conducted by actual humans will descend to basic statements, so this is a dodge that explains away a real problem rather than solving it.

Popper’s second gambit is what he calls “background knowledge”: Conjectures and Refutations, p. 238.

Almost all of the vast amount of background knowledge which we constantly use in any informal discussion will, for practical reasons, necessarily remain unquestioned; and the misguided attempt to question it all – that is to say, to start from scratch – can easily lead to the breakdown of critical debate. (his emphasis)

This is puzzling. Scientists are supposed to simultaneously relentlessly probe theories while at the same time just accepting the previously-established experimental background knowledge?

I don’t think you should adopt the mantle of “critical rationalism” if you choose what things it is rational to criticize. Is it perhaps that theories are objects of fascination to Popper whereas interpretation of experimental results is grubby and boring? Popper’s variant of Platonism describes three (metaphorical?) worlds. Per Wikipedia, World 1 is the physical world-states and world-processes that science studies – the physical world. World 2 is the realm of mental states and processes, such as sensations and thoughts. These arise only through biological processes. World 3 is ‘the products of thought’ as they float free of particular bodies – the world of culture or ideas. Critical rationalism is intended to regulate which ideas make it to World 3 by regulating the processes taking place in the bodies and minds of World 2. World 1 (the world in which neutrinos exist) is beneath Popper (metaphorically).

(OK, maybe I’m not so intent on being fair.)

Lakatos is even more dismissive of experiment. Whereas Popper seems to grant experimenters the right to interpret their results and so feed information to the theorist, Lakatos disdains experimenter judgment. I’ve already noted his claim (to Kuhn’s dismay) that the Balmer spectrum of hydrogen was entirely superfluous to the development of the Bohr atom: Lakatos claims the “positive [theoretical] heuristic” of the great particle theorists would have taken them to the same theories without the experimental evidence.

Moreover, Lakatos thinks that the great theorist ought to overrule the experimenter by insisting which theories of the instrument the latter is allowed: Criticism and the Growth of Knowledge, Lakatos & Musgrave (eds.) (1970) (full text), p. 130, footnote 5.

A classical example of this pattern is Newton’s relation to Flamsteed, the first Astronomer Royal. For instance, Newton visited Flamsteed on 1 September 1694, when working full time on his lunar theory; told him to reinterpret some of his data since they contradicted his [Newton’s] own theory; and he explained to him exactly how to do it. Flamsteed obeyed Newton and wrote to him on 7 October: ‘Since you went home, I examined the observations I employed for determining the greatest equations of the earth’s orbit, and considering the moon’s places at the times . . . ’ I find that (if, as you intimate, the earth inclines on that side [that] the moon then is) you may abate abt 20” from it.. .’ Thus Newton constantly criticized and corrected Flamsteed’s observational theories. Newton taught Flamsteed, for instance, a better theory of the refractive power of the atmosphere; Flamsteed accepted this and corrected his original ‘data’. One can understand the constant humiliation and slowly increasing fury of this great observer, having his data criticized and improved by a man who, on his own confession, made no observations himself: it was this feeling — I suspect — which led finally to a vicious personal controversy. (Italics Lakatos, I think; bolding mine.)

One imagines Lakatos swooping into Homestake like the XKCD physicist:

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He would probably swoop out again before coming to the necessary later realization:

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The consequences

The critical rationalists treat experiments as if they provide little more than one bit of information: confirmed or refuted. Popper allows that a refutation can point to which of the universal claims in the theory need revision or replacement, but also recommends that the theorist avoid confronting the refutation too directly. I failed to make a note of where I saw that advice, so I can’t provide a page number. I think it was in Conjectures and Refutations. I suppose he doesn’t want theorists tempted into a theory revision that just explains away a refutation without producing bold new predictions.

These rationalists do not allow for more information to flow from experiment to theory. For example, consider this statement from the Wikipedia article on neutrino oscillation:

Neutrino oscillation is of great theoretical and experimental interest, as the precise [measured] properties of the process can shed light on several properties of the neutrino.

That’s not a thing in the critical rationalist world. The idea of collecting a lot of information as a way to inform theoretical creativity goes unmentioned. Popper cites Einstein approvingly: Popper, The Logic of Scientific Discovery, (translation by the author of Logik der Forschung (1935), 1959), pp. 8-9 in the 2002 printing.

There is no logical path leading to [the highly universal laws of science]. They can only be reached by intuition, based upon something like an intellectual love of the objects of experience.

… but does not suggest that such intuition is obtained by groveling through either observed or experimental facts. I imagine he would disagree in principle with this comment on Darwin’s eight-year obsession with dissecting barnacles:

Darwin’s study of cirripedes, far from being merely a dry, taxonomic exercise, was a highly theoretical work that addressed several problems at the forefront of contemporary natural history.

Darwin mixed observation and theory in a way that reminds me of how test-driven design is simultaneously design, implementation, and testing, so tightly connected that it’s absurd to think of them as separate “phases.”

Such a mixing of theorizing and experiment was as foreign to the critical rationalists as mixing designing and building would have been to the architects my dad avoided. Theorists predict; experimenters check; and if the twain ever should meet, that’s a departure from methodological rationality.

It’s notable how much the critical rationalists point to the Newton of the Principia, but brush aside the Newton of the Opticks. That latter work…

… is largely a record of experiments and the deductions made from them, covering a wide range of topics in what was later to be known as physical optics.

Unlike the Principia, […] the stated propositions are demonstrated by means of specific, carefully described experiments. The first sentence of Book I declares “My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments.” (my bolding)

So when Newton was schooling Flamsteed on diffraction, he was doing so based on conclusions from his own experiments, which fact Lakatos characteristically doesn’t mention. Great theorist Newton fussing with prisms in Cambridge is as uninteresting as great theorist Darwin messing with barnacles.

That’s a core problem with critical rationalism: science relies on experiment. Everyone knows that. But the critical rationalists fall into the old, old trap of a binary hierarchy between abstraction and concreteness, theory and practice, architectural blueprints and the physical reality of houses and their occupants. That makes their advice fit badly with actual science and, I claim, would damage actual science if their methodology were followed.

Fortunately, as Peter Medewar wrote:

Most scientists receive no tutoring in scientific method, but those who have been instructed perform no better as scientists than those who have not. Of what other branch of learning can it be said that it gives its proficients no advantage; that it need not be taught or, if taught, need not be learned?

Actual scientists ignore what is still considered “the scientific method,” just as my dad ignored architects when their plans told him to do something stupid, just as programmers and software testers “in the trenches” ignored the methodologists as much as they could get away with.

I’m not saying that there should be no methodology of science, but rather that it should be more connected to the reality of the scientific practices that have been so surprisingly effective.

Marxism, again

If scientists were to really believe critical rationalism, they’d likely produce conclusions – frankly, embarrassing conclusions – like those I’ve documented for Popper and Lakatos’s proclamations about Marxism (here and here and here).

If you don’t believe observations (direct or indirect) of reality matter much, you won’t dig into the question of whether what you’ve gathered from your preferred sources – your “background knowledge” – actually happened. You become an ungrounded, unreliable narrator. That’s bad.

(The critical rationalist’s impoverished view of what theories actually are is more of a problem, but that’s a tale for another time.)

Science and the mirror of philosophy (36 Views of Mount CritRat)

Wed, 25 Mar 2026 14:50:13 -0500

The critical rationalists have the intellectual habits of philosophers. That biases their judgment of science and gives them a blinkered perspective on what scientists should be doing.

In this post: conflict as the path to ~~truth~~ confidence.

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About this series

Sociologist Randall Collins provides the epigraph for this post: The Sociology of Philosophies: A Global Theory of Intellectual Change, 2009, p. 728.

In the field of fundamental issues which is philosophical turf, creativity is tightly focused conflict boring in on problems until deep faults are found; around these reconceptualization takes place. In this sense Popper accurately recognized in falsification something central to intellectual life – perhaps not in actual histories of scientific discovery, but in the world of the philosophers that surrounded him.

Let’s explore that and see how that biases the critical rationalists' judgment.

Truth

The critical rationalists, being philosophers, are oriented toward truth. They want to speak true statements. The goal may be unachievable, but they still bend their efforts in that direction.

Traditionally (since Socrates), statements are about lofty concepts like temperance (Charmides), law (Minos), rhetoric (Gorgias), language (Cratylus), the Good (Philebus), justice (Crito), and so on.

These statements are universal. A true statement about language, say, would apply to all languages and all uses of words. Specific statements (“Children playing with puppies is an example of the Good”) are not of interest except insofar as they shed light on universal statements.

Scientists are presumed to have the same goals: to make universal claims about observable things (and processes) out there in the world. Such as this truth-valued claim: “Intestinal interoceptive dysfunction drives age-associated cognitive decline.” Specific observations such as “[We saw] Hydrallantois in a caprine doe” are not of interest unless they prompt further work that yields universal statements.

That is, Darwin’s eight years of concentrated work dissecting barnacles would not be valuable (to the critical rationalists) if it merely led to “a 4 volume monograph on the Cirrepedia, living and extinct – the authoritative text on barnacles then and probably still now.“ From “Darwin’s Barnacles.” Rather it’s valuable because “far from being merely a dry, taxonomic exercise, [it] was a highly theoretical work that addressed several problems at the forefront of contemporary natural history.“ From “Darwin’s Study of the Cirripedia.” This essay says the work was valuable for multiple reasons: as a standard reference work, as a way of perfecting Darwin’s understanding of taxonomy (both theoretically and technically), and for giving him a reputation as someone who sweats the details. That latter added credibility to his later claims about natural selection, ad hominem fallacy be damned.

This emphasis on universal statements means that the essence of science is the scientific theory, not experiment or observation.

Argument

At its worst, philosophy is something you do against an opponent. Your job is to take the most mean-minded interpretation you can of the other person’s view and show its absurdity. And repeat until submission. Philosopher Jonathan Wolff, quoted in Chris Bertram, “Against (most) aggression in philosophy.” I like the ambiguity: by “submission,” is he referring to submitting a paper? Or to the opponent submitting to your attack?

The philosophical tool for approaching closer to truth is argument, Collins' “tightly focused conflict boring in on problems until deep faults are found.” That’s hardly unique to philosophy, but Collins argues – drawing on the history of Chinese, Japanese, Indian, European, and American philosophy – that philosophy is where the “Argument is War” conceptual metaphor fits best. I speculate that philosophers are given to parasocial relationships with philosophers in their academic lineage. (Collins has much to say about such lineages – 881 pages worth, before appendices, endnotes, and indices.) So when a Kantian philosopher sees a utilitarian attack Kant’s ethics, it’s likely to get personal.

⊕ Some philosophical lineages. (Click to expand in a new tab.)

If the standard philosophical move is to attack a theory (ideally, even including your own), the same should be true of science. That is, forcing theories to change is the most valuable work a scientist can do. Some of that argumentation can be done at a purely theoretical (or logical) level. For example, the Bohr “solar system” model of the atom was criticized because it contradicted Maxwell’s equations of electromagnetism (as had some previous models).

Popper’s innovation was to focus on the experiment as an ally in the attack. Unlike in (most) philosophy, the physical world gets a say. That’s what experiments are for: to produce a credible counterexample to a universal theory, which the originator of the theory should use to make it stronger (to have more “empirical content”). Popper places great emphasis on the theorist making predictions to be checked by experiment, but I don’t see that it makes a difference if the prediction was made by someone else (like the experimenter) or even if the refutation is discovered by accident.

Lakatos differs from Popper in that he cares about confirmations, at least those of “bold” or “risky” predictions. As far as I’ve seen, Popper allows confirmations to play two roles. The first is moral support: “We need the success, the empirical corroboration, of some of our theories, if only in order to appreciate the significance of successful and stirring refutations.” The second is to help in “attributing our refutations to definite portions of the theoretical maze.” Both quotes from Karl Popper, Conjectures and Refutations: the Growth of Scientific Knowledge) (5/e), 1989, p. 243. I think it’s fair to think of those confirmations as attacks on a rival theory – to show it cannot predict what was just confirmed. Lakatos is fond of recounting how successful predictions force doubters into retreat. (He takes glee in how the French Academy was forced to give up on their opposition to Newton’s theory of gravitation when Halley’s comet appeared as predicted.) For and Against Method: Including Lakatos’s Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence, Motterlini (ed.), 1999, p. 99.

So?

“Intestinal interoceptive dysfunction drives age-associated cognitive decline” is a really interesting result from a series of experiments prompted by the question “Why are young mice housed with old mice ‘infected’ with the old mice’s weak memories?” The story of that research seems to be an example of something attributed to Isaac Asimov: Quote Investigator, as usual, ruins everything. There’s no evidence Asimov said it.

The most exciting phrase to hear in science, the one that heralds new discoveries, is not “Eureka!” but “That’s funny …”

The researchers wanted to know what was up with those mice, so they found out. They weren’t testing any theory in an attempt to refute it – or to confirm it, for that matter. They just did what the majority of scientists do: use theories to answer questions.

In a fairly detailed interview with the paper’s corresponding author, the interviewer says, “This is a study where, as I was reading it, I kept writing, ‘This is wild,’ in the margins.“ “Could boosting gut–brain communication prevent memory loss? A tale of microbes, memory, and our internal senses,” an interview with Christophe Thaiss. The link given is to a transcript, which is quite readable. The “this is wild” comment is at minute ~06:05. The critical rationalists wouldn’t have agreed, I think, because the study is merely what Thomas Kuhn called “normal science.” Which they didn’t care for. John Watkins: Criticism and the Growth of Knowledge, 1970, p. 27. (Full text.)

But I shall consider [Kuhn’s The Structure of Scientific Revolutions] from a methodological point of view, and methodology, as I understand it, is concerned with science at its best, or with science as it should be conducted, rather than with hack science.

and: ibid, p. 31.

Why is Kuhn concerned to up-value Normal Science and down-value Extraordinary Science? […] First, Normal Science seems to me to be rather boring and unheroic compared with Extraordinary Science.

Popper’s contribution to the same volume is titled “Normal Science and its Dangers.“ ibid, pp. 51-58. Quote is from p. 53. As I’ve mentioned before, he’s scathing:

The ‘normal’ scientist, as described by Kuhn, has been badly taught. He has been taught in a dogmatic spirit: he is a victim of indoctrination. […] I can only say that I see a very great danger in it and in the possibility of its becoming normal […]: a danger to science and, indeed, to our civilization.

I disagree. I think his vision of science is plodding and crabbed and – as an exclusive interest – only attractive to unattractive personalities. More importantly, it draws attention away from the world. Consider the critical rationalists' reaction to the facts of missing immiseration or the unexpected (to them) Russian revolution. Was it “that’s funny…”? No. They didn’t delve into the phenomenon, just turned to attacking (what they thought to be) the relevant Marxist theory. So they seem foolish to someone who looks even shallowly into what really happened.

To the critical rationalists, natural – or planned – experiments aren’t for casting light on reality; their value comes from making simple statements about theory. They treat experiments in science the same as thought experiments in philosophy. That’s the topic of the next post. (Or possibly the post after next.)

A swerve in the series: mental habits

Tue, 24 Mar 2026 11:18:28 -0500

If you’re one of those new-fangled believers in introspection, a good mental discipline is to ask if – how – your habits of thought predispose you to notice certain evidence and ignore other types.

The next set of posts will use the critical rationalists for case studies. Each will describe a habit they seem to exhibit, then link it to one or more blind spots. You may have similar habits and similar blind spots. I do.

Some psychologizing is inevitable, which the critical rationalists would hate. Oh well.

This series on the critical rationalists has gotten a bit scatterbrained – poorly structured. That’s because I started out thinking critical rationalism, while flawed, was useful as a checklist for things to look out for while making or evaluating arguments. My opinion has morphed – not suddenly – into something almost the opposite: critical rationalism makes it easier for people with certain habits of thought to indulge them and thus make their judgments less rational.

This shift makes it appropriate to take stock and establish a new direction.

The story thus far

I described critical rationality in Popper by example. It’s around then that I realized that the critical rationalists really botched their analysis of Marxism – and in a suggestive way. So I provided some background to their claims in Prelude to a discussion of some blind spots. Then I looked at two historical scenarios where Marxists were supposed to have behaved badly. I showed, I hope convincingly, that they actually hadn’t. See Blind Spot 1: Immiseration and the pair of posts Background: actually, Marxists were better than that and Blind Spot 2: Revolution.

I picked the Marxism example because their comments were intemperate enough to catch my attention and explaining what they got wrong was easier than, say, dissecting their equally intemperate comments about quantum mechanics after 1925. The Copenhagen interpretation “led to a defeat of reason within modern physics and to an anarchist cult of incomprehensible chaos.” Lakatos, Criticism and the Growth of Knowledge, 1970, p. 145. (Full text.) I hope to work more science-ey content (my lay understandings of quantum mechanics and neurobiology) into the examples.

The argument going forward

The whole point of a methodology is to steer people away from their own weaknesses. Why did the critical rationalists' own methodology fail them? They’re supposed to be good at this stuff! So why did they miss or ignore historical evidence that was readily available even in the 1970s? You could argue that critical rationalism is a tool for evaluating scientists' behavior, and that I’m using it to evaluate people evaluating scientists' behavior. And that’s a sort of type error. I don’t buy it. Critical rationalism is promoted as a general approach centered around the question “How would you know if you’re wrong?”

My claim is that critical rationalism is a methodology that amplifies certain mental habits that encourage people to drop away from rationality and indulge in their biases. Each of the next set of posts will look at a particular mental habit or tendency and describe how it makes critical rationalists “see what they want to see and disregard the rest.“ Quote is a reference to Simon and Garfunkel’s song “The Boxer,” which uses the verb “to hear” rather than “to see.”

So I’ll present a set of views of the same topic: critical rationalism’s flaws. On a whim, I’ll use as an overarching title “36 Views of Mount CritRat.” That’s an homage to Hokusai’s “36 views of Mount Fuji,” the most famous of which is “The Great Wave”:

⊕ Click to enlarge in new tab.

There won’t be 36 different posts (we all hope!), and the mental habit discussed in some of them won’t have much to do with the post’s illustrative image, but hey: boys just wanna have fun.

Blind spot 2: Revolution

Fri, 27 Feb 2026 17:52:51 -0500

In the last century, the critical rationalists laid out influential rules for how scientists should update or replace theories. As an example of bad behavior, they used the Marxists' reaction to the Russian Revolution of 1917. But their intellectual history of the period from 1848 to ~1925 was comically incomplete. Last time, I added more about what Marxists actually claimed and how they actually behaved.

But it’s still possible the critical rationalists came to a correct conclusion for invalid reasons. Given my more complete history, do I nevertheless agree Marxist theorists behaved badly?

A note on evidence

Marxist theorists have long had a weird cultural norm against saying Marx (or, later, Lenin) got it wrong. Their preferred rhetorical trope is to say that Marx was right all along, but earlier commentators (idiots all!) had misread him. So what an outsider would call a revised theory was actually portrayed as a better explanation or application of an unchanged theory.

It’s as if Einstein had said that Newton was right about gravitation, and his own general relativity was just an improved restatement of Newton. Well, it just isn’t. If he’d said it was, I wouldn’t be obliged to believe him in the face of the obvious.

Similarly, when Stalin says his theory of “socialism in one country” is a faithful interpretation of Lenin’s faithful interpretation of Marx, I’m not obliged to believe him.

The original set of predictions

In 1848, I’d characterize the relevant predictions derived from Marxist theory this way:

First (I’ll use tags like this to refer back to claims.): The first successful proletarian revolution would happen in one of the most industrialized countries. (Germany was perhaps most likely.)
Trigger: That revolution would trigger revolutions in other countries.
Support: New socialist states would support revolutions in other states.
Capitalists attack!: Such support would be necessary because the capitalist powers would gang up on revolutionary countries.
World revolution: Once the core imperialist European powers had transitioned, that would effectively be a world revolution (because Europe owned so much of the world).
Dictatorship of the proletariat: The result of a successful revolution would be a “dictatorship of the proletariat,” that being a transitional phase on the way to true communism. (I’ll say more about it later.)

There was a wave of attempted revolutions in 1848. Had one of them been in Russia, and had it succeeded, those events would have falsified prediction First. Since neither happened, it doesn’t. (The remaining predictions all depend on the first, so they’re moot.)

If the revolutions of 1848 didn’t refute First, did they confirm it? No, because:

Most of them failed. (Some would say all of them failed.)
The French version of an 1848 revolution perhaps succeeded. It did establish the French Second Republic. But that Republic lasted only four years. Does that little hiccup on the way from Emperor Napolean Bonaparte to Emperor Charles-Louis Napoléon Bonaparte really count as a success? Still, despite some proletarian involvement, I don’t think many would call it a proletarian revolution. In 1850, Marx described it as “complet[ing] the rule of the bourgeoisie by allowing, besides the finance aristocracy, all the propertied classes [not the workers] to enter the orbit of political power.“ “The Class Struggles in France, 1848 to 1850, Part I,” published in January, 1850. Note that this is two years before the Second Republic falls. (His italics.)

So Marxism’s predictions were neither falsified nor confirmed. As of 1850, they had not yet been tested.

A modification (a successor theory)

No later than 1877, Marx revised prediction First to something like this:

Russia first: The first potentially successful revolution will start in Russia.

Others remain unchanged – most notably that Russia’s revolution would Trigger other ones and those other revolutions would Support Russia.

A corollary to Support covers what happens if that support isn’t enough:

Russia fails alone: Without enough support from other (industrialized) proletarian states and revolutionary movements, Russia’s revolution would fail. There is no other path to success. I didn’t find a direct quote from Marx. But, for example, when the Russian revolution was in big trouble (1918), Rosa Luxemburg “believed the Bolsheviks' errors were a product of the fatal isolation of their revolution, and that its only salvation lay in a successful proletarian revolution in the West, especially in Germany.” – “Critique of the Russian Revolution.”

How does the Russian revolution stack up against this revised set of predictions?

Russia first: Confirmed.
Trigger: Confirmed by the Revolutions of 1917–1923.
Support: Moot. All the triggered revolutions failed. Or you could say “confirmed,” as every one of the zero successful revolutions supported Russia.
Capitalists attack!: Confirmed.
World revolution: Moot.
Dictatorship of the proletariat: It’s complicated. Hold that thought.

But, most importantly:

Russia fails alone: Falsified. Zero support certainly falls in the category “not enough support,” yet the government the revolution produced would last until 1991.

To a critical rationalist, there’s no shame in a falsified theory, so long as you react by adjusting your theory in a way that accounts for the anomaly and makes new predictions, preferably surprising ones.

Stalin’s revision

Stalin behaved according to the critical rationalist methodology. Building on some of Lenin’s modifications to Marxism, he created the theory of socialism in one country, which I’ll summarize as totalitarianism in service of speedrunning industrialization, guided by a vanguard party. It would allow the fledgling USSR to fend off the capitalists' inevitable covert subversion and, given enough time to prepare, to win an armed conflict. See Stephen Kotkin’s Stalin: Waiting for Hitler, 1929–1941 (2017) for how much Stalin anticipated an invasion from the West, specifically by industrial Germany. To him, fascism was just the government a capitalist system adopts under extreme pressure from the proletariat. So Germany had to destroy the USSR on behalf of capitalism, lest the USSR Support the upcoming proletarian revolution.

Stalin’s new theory replaced Russia fails alone with a new prediction: Totalitarian communism can survive. This was confirmed. OK, it was refuted in 1991, but fending off Germany in WWII is what critical rationalists would call confirmation of a low-probability prediction. There are arguments to be made here. How much of the failure of Operation Barbarossa was due to Hitler being so enamored of Blitzkreig that he left German troops unprepared for the kind of winter in Russia that Napoleon found so… awkward? And: the USA poured resources into Stalinist Russia during WWII. How much does that matter? Beats me! In fact, one of the themes of my next post will be (I hope) how the critical rationalists think weighing evidence is easy, when it’s not.

But what about the dictatorship of the proletariat?

Here’s a question that’s not as silly as it looks: did the Russian revolution actually succeed? Consider the Marxist prediction Dictatorship of the proletariat – which it is now time to define.

Engels described the Paris Commune of 1871 (a revolution that was pretty localized and only lasted two months) as the exemplar of the dictatorship of the proletariat. Here are some of its characteristics:

A government made up of proletarians (who would get paid workers' wages).
Proletarian guidance. Those proletarians would conceive of and implement the necessary changes to society. Other classes (like the petty bourgeoisie – think shop owners and lawyers) would look to them to chart the future.
Democratic governance and universal suffrage, which would lead to separation of Church and State, to replacing the police and armed forces with ordinary people rotating into and out of short-term service, and so on.

That is not very much like how revolutionary Russia turned out. Indeed, Lenin in 1906 redefined the dictatorship of the proletariate as follows:

[The] scientific term ‘dictatorship’ means nothing more nor less than authority untrammeled by any laws, absolutely unrestricted by any rules whatever, and based directly on force. Stalin was so bad that Lenin looks good in comparison, but Bertrand Russell was being charitable when he said his meeting with Lenin revealed Lenin’s “distinct vein of impish cruelty.”

Was this 1906 redefinition in response to the failed Russian revolution of 1905? If so, he did follow the critical rationalist methodology:

He reacted to an observation (“well, that revolution sure didn’t go well”) by adjusting the theory about what was required for a successful communist revolution (don’t allow any trammeling by laws).
His revised theory produced a revised prediction of the nature of post-revolutionary society that I’ll call Dictatorship by the vanguard party, ostensibly on behalf of the Proletariat.

This revised prediction came true. To Engels, the Russian Revolution failed to meet its core goal, the Dictatorship of the proletariat. Stalin completed the transition from Marxism to Marxist-Leninism. The new theory used the same phrase, but with a different meaning. That’s OK, I guess. Einstein did the same thing: his theory’s mass isn’t what Newton meant by the word.

Why did I grovel through a lot of Marxist thought I’m not particularly interested in?

I’ve thought for decades that Lakatos in particular had interesting things to say about how scientists decide whether to make the big career bet of jumping on a radical new theory. That is, I never believed he’d captured a set of rules for doing science. What he had were heuristics for persuading scientists, ones somewhat more realistic than Popper’s. I started this series wanting to recapitulate and improve on what I’d already written.

But as I reread the critical rationalists, I got increasingly annoyed by how much they were like me in my twenties. My favorite course in college was abstract algebra, and I was a vague sort of Platonist: I greatly favored the abstract over the concrete, and thinking over doing. In my profession, computer programming, I thought that the most abstract description of a program (the “specification”) was the most important. I taught a few courses at the University of Illinois, At that time, its computer science department was in something of a slump, and they allowed “industry types” like me to teach whatever we liked as long as we didn’t expect to get paid. and I remember telling students that my practice was to think about the program’s design (one level of abstraction above the code) until I couldn’t stand it any more, then I’d think about it some more, and finally the code would just pour out of me.

This was not long after I’d switched from programming to software testing. The thing about testing is that it’s relentlessly concrete, and I began to realize that the concrete is full of difficulty and subtlety and challenges – thinking at the abstract level is too easy. The death knell for my Platonism was probably reading philosopher of science Paul Feyerabend’s Conquest of Abundance: A Tale of Abstraction versus the Richness of Being, which is about what you lose when you drift off, ungrounded, into the realm of abstraction.

I believe Popper and Lakatos had temperaments much like mine of the ’80s. That led to a prediction: their methodology would be systematically blind to concrete matters. It would fall apart when it came to the interface between theory and the world.

Does it? I decided to look at their case studies and examples in more detail. Most are of scientists doing things right (perhaps with some bobbles along the way). I prefer to look at negative examples because they tend to make it clearer what’s important to the methodologist.

Their two favorite negative examples (dubbed pseudoscience) are psychoanalysis and Marxism. Of the two, it’s only for Marxism that they (both) point to one example of a prediction whose refutation was mishandled. So that’s what led me to the Marxist Internet Archive (and Wikipedia – that’s respectable nowadays, right?)

I hope this post and the one about the immiseration prediction show that the critical rationalists ignored way too much evidence when drawing their conclusions – a very Platonist thing to do.

If writers' block doesn’t finish its multi-year job and toss my moldering corpse onto the dustbin of history, Haha! A topical allusion to Trotsky: “A notable usage [of this phrase] was that of the Russian Bolshevik Leon Trotsky referring to the Mensheviks: “Go where you belong from now on – into the dustbin of history!” as the Menshevik faction walked out of the All-Russian Congress of Soviets.” – wikipedia I’ll next explain the omissions in the critical rationalist methodology.

Then (finally!), I hope to suggest how to use critical rationalism (with adjustments) when someone tries to convince you to risk your career on the Next Big Thing. (Vibe–I-mean-agentic coding waves from the CTO’s office.)

Background: actually, Marxists were better than that

Fri, 20 Feb 2026 17:44:03 -0500

As I’ve been documenting, philosophers of science Karl Popper and Imre Lakatos had harsh things to say about Marxists' response to the Russian Revolution of 1917. I think they were wrong, and wrong because they missed important changes to Marxist theory.

I have a teensy suspicion that not many of my readers will care about developments in Marxism between 1848 and 1917 and in the aftermath of the revolution, so I’ll separate that history out here.

Forthcoming:

Popper and Lakatos said their fictional history showed Marxist theoreticians breaking the rules of critical rationalism, their “methodology of scientific research programmes.” What does a more accurate history show?
Is there something about their methodology that biased them toward disregarding parts of the reality?

Disclaimer

As with my earlier post on blind spot 1, I have to start by saying that my understanding of Marxist theory is extremely shallow. In a way, that bolsters my case: if even I can see the problems with Popper and Lakatos' claims, imagine what someone who really understood Marxist theory and its history could do.

Nevertheless, I should warn you that this is yet another case of a techie who’s read a little bit about a topic and fancies he understands it. “I think, if you wrote a book, you fucked up, and it should have been a six-paragraph blog post.” – Sam Bankman-Fried, currently inmate #37244-510 at Terminal Island Federal Correction Institution. Railroaded by the booksellers cabal!

Prediction and observation

Both Karl Popper and Imre Lakatos claimed that Marxism “predicted that the first socialist revolution would take place in the industrially most developed society” (Lakatos). The Methodology of Scientific Research Programmes (Philosophical Papers: Volume 1), J. Worrall and G. Currie (eds.), 1978, pp. 4-5. The first unsquashed socialist revolution happened in 1917, in Russia – which was barely past feudalism and was no one’s idea of an industrial society. Consequently (they said), Marxism was a refuted scientific theory.

About the peasantry

The part of Marx’s theory in question is called stagism. Stagism held that it was necessary for feudal societies to change to ones dominated by the bourgeoisie (capitalists) before the proletariat (primarily factory workers) could have the revolution that established socialism.

You can’t have a class of factory workers until you have factories. To Marx, the proletariat is generated by the material conditions of industrial capitalism. The phrase “material conditions” signals that Marx is on one side of a philosophical debate between materialists and idealists. Materialists thinks the world of things and actions comes first and generates ideas, whereas idealists think the reverse. Marx focuses on how the new stuff that we need to keep living is created. These material conditions come in two kinds. The first is the means of production. That includes tools, techniques, factories, land, labor, capital, and so on. The second is non-voluntary relations between people or between people and things (relations of production). In a feudal society, the landowner has a relationship to the land (which he owns). The serf has a different relationship to that same land (that of a laborer). The serf and the landowner are also related: for example, if the serf wants to leave the land or get married, he must get permission from the landowner. These two kinds of material conditions determine society: political institutions, laws, culture, morality, which social classes exist and their character, and so on. Thereafter, the logic of capitalism will lead to the proletariat becoming poorer and more desperate until they attempt a revolution. That revolution might not succeed, but if it fails, another revolution will follow, and another, and… until one finally succeeds.

The reason the revolution would (tend to) happen first in an advanced industrial society is straightforward: that’s where the mass proletariat are. Can’t run a proletarian revolution without enough proletarians.

What Russia had was peasants, and Marxism had an uneasy relationship to the peasantry. In The Communist Manifesto, Marx and Engels write that the peasantry is doomed to “decay and finally disappear in the face of Modern Industry.“ Daniel Finn, “Marxism and the Agrarian Question,” Jacobin, 2024-08-07. And that’s what happened in the industrial nations. (In the United States today, around 1% of people live on farms.) Marx believed the vast majority of those displaced people would join the proletariat rather than ascend to the bourgeoisie. After swelling the mass of the proletariat, they could contribute to a successful revolution when things got bad enough.

In 1917, the Russian peasantry was 80-85% of the population. That sure doesn’t seem like enough proletarians for a revolution. (In contrast, the US farm population in 1920 was 26% of the total.) Germany and England – the industrial powerhouses of Europe – probably had similar numbers. That is, there were still lots of peasants. My dad was born in a peasant village in German East Prussia in 1920. They plowed their fields with oxen.

However, Marx allowed that an existing peasantry could be something of a “force multiplier” for the revolutionary proletariat. If the latter could get the former to revolt with them, the revolution could still work. Nigel Harris “The Revolutionary Role of the Peasants,” 1969-December. However, the proletariat would have to be firmly in charge because the material conditions of peasant life didn’t allow the development of a coherent and self-conscious class. Also, peasant goals stopped well short of what Marxists wanted. Peasants would be happy enough with land reform and political liberty; they aspired to the political position of the “petty bourgeoisie” (small businessmen, shopkeepers, lawyers, etc.) rather than a full-on socialist revolution. This attitude toward the peasantry was shared by Lenin. V. I. Lenin, “The Proletariat and the Peasantry,” 1905-11-12.

So, for Russian revolutionaries prior to the failed 1905 revolution and the (arguably) successful 1917 one, the question was not so much “are we a bourgeois society?” – clearly not – but “have we industrialized to the point where there’s a self-aware proletarian class who are angry enough or desperate enough to gamble on a revolution (and can get the peasantry to contribute their bodies to the cause)?”

Lenin and company said “yes.”

The scope of the revolution

Would Marx have agreed with these Russian revolutionaries? Well, as of 1877, in a letter, he declared: Kevin B. Anderson, “Marx on Communal Villages as Loci of Revolution, in 19th C. Russia & Beyond,” 2025.

All sections of Russian society are in complete disintegration economically, morally, and intellectually. This time the revolution will begin in the East, hitherto the unbroken bulwark and reserve army of counterrevolution.

Two years later, he wrote: ibid.

I am convinced that the explosion of the revolution will begin this time not in the West but in the Orient, in Russia.

But how does this square with stagism? Marx was not interested in what later came to be called “socialism in one country.” He was hoping that Europe would have a reprise of the revolutions of 1848, except this time successfully. None of the 1848 revolutions produced a socialist state, though Franch flipped from a constitutional monarchy to the Second Republic.

Marx’s theory was that socialist revolutions would spread. Each newly-socialist country would support not-yet-successful revolutions in others. Class solidarity would trump nationalism. World War I was a huge disappointment in that regard. The failure of cross-national working-class unity is actually, I think, a much better example of a refuted Marxist prediction. Russia’s revolution would trigger other revolutions, even while it was still in progress. It would become “the signal for a proletarian revolution in the West, so that both [sites of revolution] complement each other.“ Marx and Engels in the preface to the 1882 Russian-language edition of The Communist Manifesto. Thereafter, the more advanced nations could help the not-ready-yet Russia transition from semi-feudalism to socialism, leapfrogging bourgeois rule.

Coping with the aftermath

The Russian revolution of 1917 did indeed spark attempts at revolution in other countries, but they fizzled. My memory of reading Kotkin’s Stalin: Paradoxes of Power, 1878–1928 is that many of the Russian Bolsheviks realized they were in quite the pickle. There were no proper socialist states to support them in their very non-optimal situation, and it didn’t look like any would appear. Worse, the capitalist regimes were all around them and (as had been predicted) were acting aggressively to take down the barely established state. In 1918, if there was one thing both sides in World War I agreed on, it was that they needed to send troops and materiel to the non-Bolshevik side of the Russian Civil War that the revolution had kicked off.

Leon Trotsky wanted to double down on exporting the revolution (in order to midwife the needed supportive states), but Josef Stalin outmaneuvered him and solidified Soviet doctrine as socialism in one country. The USSR would go it alone.

In effect, Stalin said: “We are going to produce an advanced industrial state as fast as we can. We don’t have the material basis for a proper Marxist revolution, so we need to create one – and fast, before the capitalists destroy us.”

Props to a monster: it worked.

Structuralism

Wed, 04 Feb 2026 17:25:02 -0500

Structuralism was an intellectual movement most active a couple of decades after World War II, but I think it’s something people with a certain intellectual temperament gravitate to. I certainly did when I was younger, though I no longer do.

I need a short summary of it that I can refer to. I could just drop a link to Wikipedia or the Stanford Encyclopedia of Philosophy, but I want to highlight certain features that are important to how I think of it.

Structuralism in its modern form is commonly traced back to linguistics. From there, it came to influence the humanities, the social sciences, and mathematics. “The [Bourbaki] group is noted among mathematicians for its rigorous presentation and for introducing the notion of a mathematical structure, an idea related to the broader, interdisciplinary concept of structuralism.” – Wikipedia article on the French mathematicians that published under the name of Nicolas Bourbaki.

I’ll start with two frequently-used examples, one from literary analysis and one from anthropology, then add one from mathematics.

Analysis of fairy tales (humanities)

⊕

In the late 1920s, Vladimir Propp analysed 100 Russian folk tales to see what they had in common. He said that they were composed of combinations of 31 plot points. Here are some examples: Taken from “Propp’s Morphology of the Folk Tale”

1. Absentation: Someone goes missing
2. Interdiction: Hero is warned
…
12. Testing: Hero is challenged to prove heroic qualities
…
18. Victory: Villain is defeated
…
23. Arrival: Hero arrives unrecognized
…
31. Wedding: Hero marries and ascends the throne

You’ve likely read some folk tales that include those plot points. However, there are particular rules that must be followed:

In any given tale, between zero and 30 plot points may omitted – though a tale using all 31 would be wildly overstuffed, and a tale consisting of only, say, “Hero arrives unrecognized” wouldn’t be much of a story.
In a story, plot point m must occur before any plot point later in the list of 31. That is, once the hero arrives unrecognized (23), there’s no backtracking to testing the hero (12) or defeating the villain (18).

Propp doesn’t claim the people who create or retell folk tales consciously know the plot elements and the rules, only that they ended up using them. There’s also (as far as I know), no explanation of why those particular plot points or rules. His theory is purely descriptive.

Claude Lévi-Strauss was French anthropologist who applied structuralist ideas to anthropology. In chapter 4 of his 1958 book Structural Anthropology he described a structure underlying kinship systems in societies where marriage is implemented by one man giving a sister or daughter to another. He did this by looking at examples and trying to spot some sort of regularity.

One he found involved five people: a husband and wife, their son and daughter, and the wife’s brother (the son’s maternal uncle).

These people have relationships to each other, which he simplified as either “warm” or “cold.” For example, in some cultures, brothers and sisters aren’t allowed to be under the same roof at the same time. That’s a cold relationship. In others, brothers and sisters are so close they sleep in the same bed. Warm.

There are four relationships that matter: between husband and wife, father and son, brother and sister, and finally son and maternal uncle. Given the warm/cold dichotomy, that makes 16 possible combinations of warmth or coldness between the relevant people. But (Lévi-Strauss claims) such human cultures use only four, because of two rules:

The relationship of son to father must be the opposite of that between son and maternal uncle. If the society is one where the father gives orders to the son and expects unquestioning obedience, it will be the maternal uncle who’ll spoil the son with gifts and sooth his hurt feelings. Or if the father is indulgent, the uncle must be a stern law-giver.
The relationship between husband and wife must be the opposite of that between brother and sister. If husband and wife have a warm, friendly relationship, the son and daughter won’t. If the son and daughter sleep in the same bed, the culture might be one where the wife and husband only meet when the husband sneaks into her separate dwelling place for sex.

That given, a particular culture can be described by a picture like this:

⊕

Structuralist theories often lend themselves to good old node-and-edge diagrams, like the two above. The nodes name entities. Edges correspond to relationships.

I said “nodes name entities deliberately. Typically, a structuralist theory gives you little to no information about a node other than an arbitrary label. The oomph comes from the relationships. I’ll say more in a minute.

Groups (mathematics)

The mathematical concept of a group is structuralist. There are four entities: a set of things (integers, say, labeled G), two operations (+ and parentheses/grouping) and an identity (0). There are three formulae that mention those entities:

For all a, b, c in G, (a+b)+c = a+(b+c) (associativity)
0+a = a+0 = a (what the identity entity means)
Given an a, there exists a b such that a+b=0 and b+a=0 (negation)

Alternately, you could say there are three relationships that tie the entities together.

I don’t think I’ve ever seen a node-and-edge diagram for groups, but I offer this:

⊕

I suppose this does highlight that + is the… most important? most central? of the entities, as it participates in all the relationships.

Notice that actual numbers – the things being operated on – don’t appear in the diagram. That’s because groups apply to more than just numbers. For example, the three rules apply to the Rubik’s Cube group. What are numbers in arithmetic are rotations of one of the cube’s faces by some multiple of 90 degrees, the + operator means “then” as in “do rotation x, then do rotation y,” and the identity element is “rotate zero degrees.”

Assumptions of structuralism

Lévi-Strauss credited linguist Nikolai Trubetzkoy (1890–1938) with writing down four assumptions of structuralism. I harp on the second and fourth.

Conscious behavior (such as producing sentences) is supported by (or driven by) unconscious structures. So, more important than studying a language’s grammar is studying the underlying structures that control which grammatical rules you absolutely will find in a language, which rules might be found, and which definitely won’t be found.
What matters is relationships between entities, not properties of the entities themselves. The father’s character doesn’t matter in Lévi-Strauss’s theory of kinship; what matters is his relationship to his wife and to his son.

It’s actually better to think of relationships between relationships. So Lévi-Strauss is saying that the relationship between the mom-dad relationship and the sister-brother relationship is that they must be opposite.
The purpose of the work is to tease out the underlying structure. That’s a little circular: “structuralism is about structure.” So I’ll say what it means is that you should describe all the relevant relationships between entities and how the relationships relate to each other.
A structuralist theory must explain multiple real-world examples. Trobriand culture is matrilineal, and Tonga culture is patrilineal; Lévi-Strauss’s kinship rules work for both.

Applying structuralist theories

It’s possible to treat a model or a theory as an aesthetic object for contemplation, akin to the sun setting into the ocean or a dramatic thunderstorm in the mountains. But they’re usually used for solving problems.

The problems can be of various types. A theory can be used to generate new theories. Consider the simple pendulum:

⊕

Galileo discovered that the amount of time it takes for a pendulum to swing is independent of how far it swings (the amplitude), which makes it useful for keeping time. But that isochronism only works for small amplitudes. Some years later, aided by mathematics Galileo didn’t have (calculus), Huygens extended the theory of the pendulum to account for larger amplitudes. He also extended the theory from bob-type pendulums like the one above to “physical pendulums” where you can’t pretend all the mass is contained in a single point:

⊕

Along the way, he showed that you can flip such a pendulum, suspending it from the center of oscillation (below the center of mass, as shown above). The flipped version will have the same period, and the old pivot point will be the new center of oscillation, which is neat.

But theories are also applied to solve particular non-theoretical problems. The period of a pendulum depends on the acceleration of gravity (g). But that acceleration varies depending where on the earth you are (because the earth isn’t perfectly round and its surface is bumpy). So you can work backwards from a measured period to calculate the value of local gravitation (which is apparently useful to know for things like precise navigation and mapping).

⊕ Kater's pendulum (right)

And Huygen’s neat result for the physical pendulum allowed Henry Kater to create a very accurate pendulum for measuring gravitation.

I’m most interested in this sort of problem-solving, but pitfalls in structuralist theories can get in the way.

The details men don’t see

(That’s a labored reference to “The Women Men Don’t See” by Alice Sheldon, writing as James Tiptree Jr.)

I don’t know for sure, but I presume Propp was analyzing long-lasting folk tales (the Russian equivalents of the Brothers Grimm tales). Suppose I want to write my own tales that will last a couple of hundred years. What use would I make of Propp’s rules for folk tales? Because Propp’s theory isn’t causal (doesn’t explain underling mechanism), there are several possibilities:

Propp’s structuralist theory is a chance regularity in what was, after all, only 100 stories. If so, it has nothing to do with longevity. (Call this case no-causality.)
Longevity and the structure are both caused by some underlying phenomenon. Just because the phenomenon causes Propp’s rules to apply doesn’t mean that following the rules will cause the phenomenon – in which case, my rule-abiding tales wouldn’t be “sticky.” (side-effect)
Propp’s rules have some causal role in longevity, but it’s minor. He may have discovered the equivalent of the formula that describes the effect of large amplitudes on the period of a pendulum’s swing. That does allow you to fine-tune calculations of period, but such fine tuning is meaningless unless you’re already making use of the base property of isochronicity. That is, the problem’s really solved by something else. (minor-causality)
Propp has indeed identified a structure that is, by itself, a sufficient cause of longevity. (sufficient-causality)

I’d be willing to bet against no-causality and side-effect, but you’d have to give me pretty good odds to bet on sufficient-causality. Call me a pessimist, but my preferred bet would be that the truth is somewhere between minor-causality and sufficient-causality: that Propp’s rules aren’t enough by themselves to achieve my longevity goal. So it would be well worth my time to investigate other possibly causes of longevity before I put a lot of effort into writing.

My bias for over 40 years has been to focus such investigation on what a proposed explanation leaves out. Anything that draws your attention to certain aspects of a problem invariably draws your attention away from other aspects. Because structuralism is monomaniacal about relationships, that suggests two questions:

What’s important about the entities?

Not much information is given about the folk tale plot points. Consider “14. Acquisition: Hero gains magical item.” The text at the link reads:

The hero now acquires an item of some kind, often magical and usually being given by the donor as reward for passing the test. This may be potion, a weapon, and so on. The reward may also be more mundane, such as help from others or critical knowledge, but nevertheless is essential in helping the hero in completing the quest.

I have lots of questions.

What’s the difference between the tales that use a magical item and those that use a mundane one?
How often is it that the use of the item is straightforward, vs. how often there’s some sort of surprising twist? (I might be tempted to have the hero use the magical sword, crowbar-like, to pry up a manhole cover instead of using it in the expected way, but is that a modernist sort of irony that the target audience would think dumb?)
The hero and villain probably fit various stereotypes. What are they? (For example, in central Europe, a lot of stories involve a peasant who cleverly outwits someone with power. In “The Clever Peasant,” a Ukrainian folk tale, It’s a stretch to call Ukraine “central Europe,” but it seems most Ukrainians justifiably want to be as far in the direction away from Russia as possible. the titular peasant outsmarts a standoffish ruler. Notably, in this story, the peasant humiliates the ruler but hasn’t really changed the situation. The ruler still rules; the peasant is still subject to him. Sadly, that’s what’s so far happened with Putin, despite how the brave Ukrainians keep outsmarting him. In “The Peasant and the Devil,” a deal with the devil nets the clever peasant a nice treasure.)
And so on.

None of these are really about relationships, but the answers could be important for readers, if not for structuralist theory-makers.

What relationships are missing?

Whenever I see a diagram with all the arrows going in the same direction, I get suspicious, especially when the arrows represent time or importance. For a software development example, see “Oops! The Winston W. Royce Story. It’s a podcast episode, but there’s a transcript. Since there are no pictures, you might prefer a wikified version with diagrams. Here are two of the pictures (from Royce’s original). (You can click to enlarge in a new tab.) Propp’s structure of folk tales is linear in that way.

⊕ Bad

⊕ Better

⊕

What other types of arrows might there be? One that comes to mind links nodes with common settings or characters. What I want to focus on are back references.

Item: The Russian playwright Anton Checkhov is remembered for advice that’s come to be called “Checkhov’s Gun,” commonly quoted as “If in the first act you have hung a pistol on the wall, then in the following one it should be fired.”
Item: The callback is a common technique in standup comedy. You tell some jokes about a topic. You move on to other topics. Toward the end of your set, you make a new joke that refers to the original topic. People laugh harder when they notice the reference. The brick joke is a classic example, though weak because the first part isn’t actually funny.

For some reason, people like it when they are surprised by an unexpected reference to something set up earlier, especially when they didn’t predict that the setup was going to be used.

⊕ An obscure post-apocalyptic reference

So I, intending to write folk tales for the ages, should examine if and how existing successful tales used foreshadowing. They might not, since traditional tales are more about familiarity than surprise.

Which might lead me to think about comparing folk tales to epics like The Iliad. Both are from oral cultures, and presumably are tailored to be memorable. How does that work? I would want to use their tricks with my folk tales, for memorability in a post-literary world.

As I’m not actually going to write folk tales, I’ll stop describing how I’d prepare.

On diagrams

Structuralist theories (like Lévi-Strauss’s) lend themselves well to visualization with the good old-fashioned node-and-edge diagrams, as you’ve seen above.

Maybe it’s sour grapes, since I am practically aphantasic, being between 4 and 5 on the aphantasia scale:

⊕

⊕ Your metabolism is kludgy. Note that the drawing has imposed aesthetically-pleasing shapes on the underlying mess. That's telling, I think.

… but, while diagrams make theories easier to understand and apply, they make them harder to critique. As visual creatures, humans value aesthetic properties like symmetry, simplicity, repetition (with some variation), and the like. So we – especially of those of us who grew up in the thought collectives of mathematics and classic physics – give extra weight to a theory with an attractive diagram and are repelled by theories that look messy when drawn.

This is just one of those biases you should beware of. In fundamental physics and mathematics, influential people have believed that “Beauty is truth, truth beauty — that is all / Ye know on earth, and all ye need to know.“ Keats, “Ode on a Grecian Urn,” 1819. Maybe so, but are you doing pure – rather than applied – physics or mathematics? How much do you want to bet that your aesthetics apply to the problem at hand?

I think, playing the odds, you’ll be better off being suspicious when beauty is implied to be a criterion for acceptability or tolerability or truth.

The big takeaway

It’s good to know about structuralism. It’s better to know that structuralism is but one kind of theory/model/abstraction, one that often cannot stand alone. It’s best to know that all abstractions divide the world into two categories – the essentials and the ignorable details – and, in a particular situation, they’re likely to get the dividing line wrong.

Blind spot 1: Immiseration

Mon, 26 Jan 2026 17:30:37 -0500

According to Lakatos, Marxism predicted “the absolute impoverishment of the working class,” which didn’t happen. Marxists didn’t admit the mistake, kludged up some excuse, and moved on. See the previous post.

I think the story is more complicated, and it’s an example of how critical rationalists think experiments (natural or otherwise) and theories are way simpler than they actually are. As a result, their methodology (rule book) for science misleads.

I think it undeniable that the “industrial proletariat” in England or Germany are better off than in the days of the “dark satanic mills.” They’re less likely to starve, and a lot fewer children are getting mangled while using their nimble little fingers to clean industrial machinery. This is contrary to the thesis that the capitalist/haute bourgeoise class would squeeze the proletariat until the latter would have no choice but revolution.

That’s a refutation of Marxism, surely? Well, not so fast. In his Address of the Central Committee to the Communist League (1850), Marx is concerned about future attempts to “bribe the workers with a more or less disguised form of alms and to break their revolutionary strength by temporarily rendering their situation tolerable.”

I think it’s not unreasonable for a Marxist to claim that’s exactly what happened in the 20th century:

It’s a commonplace that the US President Franklin Roosevelt acted to “save capitalism from itself” in the 1930s. In that era, there was considerable debate about whether liberal democracy could compete with with the ascendent (supposedly more efficient) systems of fascism and communism. FDR demonstrated that it could. (He made a bold prediction that was confirmed.)
After World War II, it was common to worry that European countries (notably Italy and France) would tip into communism, so it can reasonably be argued that the widespread expansion of social welfare programs was Marx’s “bourgeois bribe” at scale.

So is the history of the 20th century a refutation of one part of Marxist theory or a confirmation of another? I don’t think it’s easy to tell. New predictions would be required to sharpen the question.

For example, if you believed that social welfare programs existed to placate the working classes by giving them a minimal share in the profits of capitalism, what would you predict would happen when communism became discredited as an option (with the fall of the Soviet Union)? I think you’d predict that there’d be less need to placate the workers, so the bribes would become smaller. US-centric predictions might be that (1) wealth disparities would increase…

⊕ source

⊕

(2) increased capitalist power would lead to a stagnation in the minimum wage and a decline in its inflation-adjusted value…

⊕ source

⊕

(3) union membership would decline along with worker leverage…

⊕ source

⊕

… and so on.

Experimentation

Let me put Marxism’s “immiseration” prediction in a more rigorous form. I’m following Lakatos’s recommendation: “The first stage of any serious criticism of a scientific theory is to reconstruct, improve, its logical deductive articulation.” Criticism and the Growth of Knowledge (1970) (full text) p. 128, followed by a particular re-articulation of a physical theory and the rather snarky comment “Physicists rarely articulate their theories sufficiently to be pinned down and caught by the critic.” I’ll return the snark by noting Lakatos’s critique of Marxist theory skips his own stage. I hope to show he would have benefited by following his own advice.

Over time, the proletariate’s average share (prol-share) of the nation’s absolute (not relative) wealth will decline. Plot it, and the line will persistently go down.
“Persistently go down” should be interpreted to allow for random fluctuations. Some years, there’s a bumper harvest of crops and the price of food goes down, so the prol-share will increase. That temporary bump shouldn’t count as a falsification. A plot of prol-share should use some sort of smoothing, a rolling average.
The end result of the persistent decline will be revolution.
Between the starting point of the experiment and the revolution, the bourgeoisie may “bribe” the proletariate to stave off the inevitable. Although many of the bribes – the right to unionize, for example – will only be indirectly tied to wealth, model them all as direct transfers (bribe-wealth). Then the graph of prol-share+bribe-wealth may have periods of longer-than-random stability or even increase, but this total at the moment of revolution will be less than the starting prol-wealth.

If I’m right in this formulation, this would be one possible observation of the inevitable course of history:

⊕

In this case, the bourgeoisie doesn’t bother bribing the proletariat, so things descend smoothly to revolution, as predicted.

But the following observation would also count as a confirmation of the theory:

⊕

Here, the bourgeoisie bribes the proletariat, but (inevitably) the dynamics of the capitalist mode of protection will undo the bribe, leading to an eventual decline to the revolutionary point.

But the following would falsify the theory, as the revolution happened with the proletariat less immiserated than they had been in the past:

⊕

The important thing is that you can’t distinguish between the latter two trajectories until the revolution. Popper was making the following observation to test the theory:

⊕

That is, his observation comes before the revolution (if any), and the data he has don’t suffice to distinguish between the confirming trajectory 2 and the falsifying trajectory 3.

By analogy, suppose a physicist predicts that all supernovae happen in stars of type X. You can’t judge the prediction for a particular star before it explodes.

In his The Open Society and its Enemies (1945), Popper asserts that the “development of mixed economies and welfare states in liberal democracies” falsified the Marxist prediction because such societies have “trade unions, legal protections, and political intervention.“ Quotes from the “Marx’s Prophecy” section of the Wikipedia article on Popper’s The Open Society, volume 2 (“Hegel, Marx, and the Aftermath”) rather than from Popper himself. I haven’t read the book, so I can’t pluck out direct quotes.

But this is asserting that the trajectory seen since WWII will continue ad infinitum. He is (whisper it) committing the sort of induction that his critical rationalism explicitly rules out. How is saying that a number of good years ensures all following years will be good any different than saying a number of white swans ensures all swans are white? You may say that the number of years without a revolution increases the chance the prediction is false, but – provided I understand Popper correctly – that’s not a move he allows himself.

That’s a logical error, yes, but I claim it’s based on a fundamental flaw in the methodology of critical rationalism: its proponents act as if experiments are easy. But they’re just not, especially on the cutting edge. Results are frequently ambiguous, and not just because the observable event hasn’t happened yet.

The book to read on this seems to be Peter Galison’s How Experiments End (1987), which I’m embarrassed to say I haven’t read. I have read his later Image and Logic: A Material Culture of Microphysics, 1997, which covers some of the same themes. Here’s a quote:

Textbooks do not tell you that groups of physicists gather around the table at CERN stamping OUT and IN on event candidates. This may be due to the persistent myth that, at least at the level of data-taking, no human intervention ought to occur in an experiment or, if it does occur, that any selection criteria should conform to rules fully specified in advance. But here, as everywhere in the scientific process, procedures are neither rule-governed nor arbitrary. This false dichotomy between rigidity and anarchy is as inapplicable to the sorting of data as it is to every other problem-solving activity. Is it so surprising that data-taking requires as much judgment as the correct application of laws or the design of apparatus? [My emphasis]

As if writing to Popper directly, Galison also claims:

In denying the old Reichenbachian division between capricious discovery and rule-governed justification, our task is neither to produce rational rules for discovery—a favorite philosophical pastime—nor to reduce the arguments of physics to surface waves over the ocean of professional interests. The task at hand is to capture the building up of a persuasive argument about the world around us, even in the absence of the logician’s certainty. [My emphasis]

By insisting on an unbridgeable gulf between “mob psychology" Lakatos’s term, but the sentiment is common among critical rationalists. In his “Response to my critics,” Kuhn writes “My critics respond to my views on this subject with charges of irrationality, relativism, and the defence of mob rule. These are all labels which I categorically reject […]” (Criticism and the Growth of Knowledge, p. 235) and rule-based science, the critical rationalists ignore how much of even the science they love best (physics) occupies that forbidden zone. Both Lakatos and Popper write little (that I’ve seen) about an essential activity of science: statistical analysis. Even in their lifetimes, results like p=0.03 and R²=0.14 were important to science. Galison’s Image and Logic describes how particle physicists gradually shifted from “image” (pictures of particle tracks and the like) to “logic” (counting and statistics). It seems to me that the critical rationalists got stuck thinking that all experimental observations are as easy as looking at a particle track in a bubble chamber, when they were even in their time becoming a vastly statistical affair. Lakatos is fond of putting ‘statistical techniques’ in scare quotes: “[…] adjustments may, with the help of so-called ‘statistical techniques’, make some ‘novel’ predictions and may […]” Criticism, p. 176 (my emphasis)

Moreover, experimental results don’t matter much. At its core, an experiment reveals one bit of information: Does the experimenter believe a prediction has failed? True or false? 1 or 0? I refer to the experimenter’s belief instead of using words like “confirmation” or “falsification” because the theorist has leeway to interpret the results. It is always logically possible to argue that the experiment is at fault rather than the theory, though Popper and Lakatos treat such cases differently.

For Popper, the process proceeds recursively. A logical claim about the experiment may be countered by a claim about the claim, which could lead to a claim about the claim about the claim. Popper allows the recursion to bottom out at “basic statements” – “simple descriptive statements, describing easily observable states of physical bodies”. Karl Popper, Conjectures and Refutations: the Growth of Scientific Knowledge (5/e)), 1989, p. 267 (Note the assumption that such simple observations are always available.) He allows the community of scientists to collectively decide that such basic statements are to be treated as true without further argument.

For Lakatos, scientists are always free to ignore anomalies if they choose. (However, if a theory persistently ignores all anomalies and also fails to be elaborated to create new predictions that are sometimes confirmed, scientists are rational to abandon it as going nowhere. Notice that Lakatos allows that what he calls a “degenerating” research programm may revive. That means the scientist is presented with a problem parallel to judging the immiseration of the proletariat. See the Lakatos entry in the Stanford Encyclopedia of Philosophy for an example. Search for “Flynn effect”.)

They both agree that an adjudicated falsification provides little to the theorist. Popper views theories as sets of universal statements. Falsifications and confirmations are useful because they allow us to “be reasonably successful in attributing our refutations to definite portions of the theoretical maze.“ Conjectures and Refutations, p. 243 Once that’s done, the theorist finds the fix by using his own genius and the internal logic of the theory, what Lakatos calls its positive heuristic: Criticism and the Growth of Knowledge, p. 135

The positive heuristic of the programme saves the scientist from becoming confused by the ocean of anomalies. The positive heuristic sets out a programme which lists a chain of ever more complicated models simulating reality: the scientist’s attention is riveted on building his models following instructions which are laid down in the positive part of his programme. He ignores the actual counterexamples, the available ‘data’. [The emphasis and scare quotes are in the original.]

That last sentence is quite striking. Elsewhere in Lakatos’s paper, he uses Newton’s gravitation (pp. 135-37) and “the Bohr atom” (pp. 138-54) as examples of the “relative autonomy of theoretical science” [his emphasis]: Criticism and the Growth of Knowledge, p. 137.

Which problems scientists working in powerful research programmes rationally choose, is determined by the positive heuristic of the programme rather than by psychologically worrying (or technologically urgent) anomalies. The anomalies are listed but shoved aside in the hope that they will turn, in due course, into corroborations of the programme. Only those scientists have to rivet their attention on anomalies who are either engaged in trial-and-error exercises or who work in a degenerating phase of a research programme when the positive heuristic ran out of steam.

We’ve come a long way from the observation that you can’t move from a set of examples to a universal statement (the problem of induction). The great scientists don’t actually need examples at all. In 1885, the Swiss experimenter Johann Jakob Balmer unveiled the empirical Balmer series of lines in the spectra of the hydrogen atom. Conventional histories present the Balmer series as something theorists needed to explain. Lakatos disagrees: Criticism and the Growth of Knowledge, p. 147

But the progress of science would hardly have been delayed had we lacked the laudable trials and errors of the ingenious Swiss school-teacher: the speculative mainline of science, carried forward by the bold speculations of Planck, Rutherford, Einstein and Bohr would have produced Balmer’s results deductively, as test-statements of their theories, without Balmer’s so-called ‘pioneering’. [Scare quotes his, as is the dismissive “ingenious Swiss school-teacher” – Balmer had a PhD in mathematics.]

… and: Criticism and the Growth of Knowledge, p. 187

The direction of science is determined primarily by human creative imagination and not by the universe of facts which surrounds us.

Kuhn, as a historian rather than a philosopher, was aghast: Criticism and the Growth of Knowledge, p. 246

Lakatos’s attempt to reduce science to mathematics, leaving no significant role to experiment, goes vastly too far. He could not, for example, be more mistaken about the irrelevance of the Balmer formula to the development of Bohr’s atom model.

… and devotes pages 256-259 of his response to contradicting Lakatos on the history.

Perhaps it’s just that I’m married to an experimentalist, but I’m with Kuhn. The degree to which critical rationalists disparage, downplay, and ignore what Kuhn called “normal science” and John Watkins called “hack science" Criticism and the Growth of Knowledge, p. 27 seems wildly disproportionate. I simply don’t believe successful science treats observations as occasionally-useful hints, nor do I think any methodology built on that can actually explain science’s successes. I think Hacking’s entity realism is much more plausible.

I think this attitude accounts for the apparent failure of either Popper or Lakatos to investigate the details of the history of the industrial revolution up to their present to determine how and to what extent it deviated from Marx’s predictions. You only need one bit of information, so how hard do you need to look to decide if that bit is 1 or 0?

I was surprised to realize that the critical rationalists, usually counted on the realism side of the Science Wars are actually close to the “social constructivist” faction, except that they point to logic and inspiration as the source of our descriptions of reality rather than sociology. For a highly opinionated history of the Science Wars from a realist perspective, see William Gillis, Did the Science Wars Take Place? The Political and Ethical Stakes of Radical Realism, 2025. For a “can’t we all just get along?” account, see Ian Hacking, The Social Construction of What?, 2000. You could argue that the Science Wars were sparked by Bruno Latour, Laboratory Life: The Construction of Scientific Facts, 1979. It’s a good read.

I suspect that working scientists, even pure theorists, are wise not to be so dismissive of experimental results.

Which theories and theorists count?

Let’s suppose that Popper and Lakatos never knew of Marx’s “bribe” prediction. They were both steeped in Marxism-Lenism in their youth, but maybe they never read “Address of the Central Committee to the Communist League,” and maybe Marx never mentioned that idea elsewhere.

And leave aside their problem with prejudging the evidence before the revolution.

There’s another problem in their use of their approach. Consider this story of correct methodological behavior:

Marx founded a Lakatosian research programme (although earlier socialists who influenced Marx might have something to say about that).
Both Lakatos and Popper say theories evolve over time, sometimes in response to refutations, other times because of their own internal logic. Moreover, both allow multiple theories to be “in play” at the same time.
So it’s entirely possible for variant theories to “fork off” from the mainstream development of Marxism. And it happened: Marx himself spent a lot of time warring with people who were Deliberately and Annoyingly Not Getting It. See the Origin Story podcast episode on “Karl Marx: the Fighter”
One such successor theory was social democracy which, over time, “went from a ‘Marxist revolutionary’ doctrine into a form of ‘moderate parliamentary socialism’.“ Wikipedia text, citing to Ian Adams, Political Ideology Today (2/e), 2001, p. 108. They ceased to predict proletarian revolution because the Marxian bribe could be extended forever.
In other words, their theory predicted “development of mixed economies and welfare states in liberal democracies” – just as Popper said had happened in the West (in large part because the social democrats, pushed by their theories, formed political parties to make it happen).
Therefore, what the critical rationalists present as a falsification of a predecessor theory is actually a confirmation of a successor theory.

Visually, here’s a family tree of Marxist theories:

⊕

A single observation has two different effects on two different theories:

⊕

This should be entirely normal: a newer theory should by definition have “greater empirical content” than an older one. Yet our critical rationalists don’t point to this as an example of what Lakatos would call a progressive research programme. Instead: they say Marxism (seemingly the whole tree of theories) is degenerating. What’s going on?

As I said in the last post, I’m bowing to the critical rationalists by not attributing their errors to their horrible experiences with Marxism-Leninism. Instead, I promised to use them to identify flaws in the methodology. I see two.

Critical rationalists act on the Great Man theory of science.

In their writing, science works because of individuals like Galileo, Newton, Einstein, Bohr, and other people named in popular histories of science. While there are many scientists who are not great, their careers are somewhere between uninteresting and pitiable. Watkins discounts Kuhn’s “normal science,” writing “methodology, as I understand it, is concerned with science at its best, or with science as it should be conducted, rather than with hack science.” (Conjectures and Refutations, p. 27) Popper: " In my view the ‘normal’ scientist, as Kuhn describes him, is a person one ought to be sorry for. […] [He] has been badly taught. He has been taught in a dogmatic spirit: he is a victim of indoctrination. […] As a consequence, he has become what may be called an applied scientist, in contradistinction to what I should call a pure scientist. (p. 52-3, italics in original.)

The case histories of the critical rationalists tend to be biographical. Newtonian physics is the story of Newton. Predecessor characters like Robert Hooke (who suggested to Newton that he break orbital motion into a straight-line tangent to the orbit and a radial motion toward the focus) are skipped, as are the contributions of later people to the theory. To me the histories read: There was Newton, who thought a bunch of amazing thoughts. Then there were a few big deal (“crucial”) experiments. Then not much happened for 200-some years. Then came Einstein.

Crucially, this focuses their analysis on the beginnings of research programmes, and away from the various elaborations and corrections. As a result, falsifying Marx – at the root of a tree of theories – is taken to falsify all the theories that followed.

Critical rationalists focus on subsets of theories.

Theories are sets of universal statements, but not all universal statements are the same. There are subcategories. Here’s the first.

Lakatos describes the founding theory of a research programme: For and Against Method: Including Lakatos’s Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence, Motterlini (ed.), 1999, p.103

At the heart of any research programme is a “hard core” of two, three, four or maximum five postulates. Consider Newton’s theory: its hard core is made up of three laws of dynamics plus his law of gravitation.

Popper describes the creation of a completely new theory (he doesn’t much use the phrase “research programme”): Conjectures and Refutations, p. 241

The new theory should proceed from some simple, new, and powerful unifying idea about some connection or relation (such as gravitational attraction) between hitherto unconnected things (such as planets and apples) or facts (such as inertial and gravitational mass) or new ‘theoretical entities’ (such as fields and particles). [his emphasis]

Theories grow by creating what Lakatos calls a protective belt of other universal statements or hypotheses:

⊕

The hypotheses accrete over time. They might be pure additions, or they might demand modifications to existing statements in the protective belt. But there won’t be changes to the hard core. Popper doesn’t specifically rule out changes to the hard core – he describes changes in even vaguer terms than Lakatos does – but I suspect it’s true. He implies – or I infer – that the need to do that would trigger the creation of a replacement powerful, simple, new, etc. theory – basically, starting over.

One type of protection is the purely defensive ad hoc hypothesis: one that explains away a falsification but doesn’t make any new, testable predictions. For Popper, that’s an immediate red flag: We USAnians never miss an opportunity to make a fußball metaphor. you’ve stopped being scientific. For Lakatos, it’s a yellow flag: if you keep doing it, the research programme will be seen as degenerating and scientists will rationally abandon it.

The other type of protection adds to the growth of knowledge by both protecting from an accepted falsification and also making new (preferably bold or unlikely) predictions (that, for the programme to stay progressive, must at least occasionally be confirmed).

Because the critical rationalists aren’t specific enough, I don’t know what else goes in the belt. For example, a theory of the pendulum is a logical consequence of Newton’s gravitation. And it’s been amply confirmed. Does its equation of motion go in the protective belt – protection from what? – or does it go somewhere else? It’s got to go somewhere, right?

My point? Critical rationalism focuses on the hard core and marks the rest as uninteresting. Perhaps it’s a matter only for those badly-trained applied scientists, not for the Great Man of Science or the later Great Men who will seek to explain his greatness. (Maybe that’s too snarky. Oh well.)

If you consider the immiseration of the proletariat to be part of the hard core of Marxism (or a prediction deductively derived from the hard core) and you want to evaluate whether the whole Marxist programme is a science or a pseudoscience, you’d naturally look to the original hard core, not to mushier derivative theories that make predictions that are less bold. After all, the social democrats were predicting a future much like the past, except getting better via the slow boring of hard boards.

And critical rationalists prefer to sing of warriors fighting dragons than of farmers fighting weeds, year after year.

Prelude to a discussion of blind spots

Wed, 21 Jan 2026 21:41:53 -0500

Like any methodology, critical rationalism (described in the previous post) has blind spots. Karl Popper’s and Imre Lakatos’s criticisms of Marxism cast those blind spots into high relief.

Each of the next two posts will look at one of their claims that Marxism made specific predictions (as a science should) but handled falsifications wrongly (unscientifically). Thus, they claim, Marxism started out as a science but degenerated into a pseudoscience.

This post provides background for the next two.

Here is what our two critical rationalists have to say.

Popper: Conjectures and Refutations, p. 217.

In some of [Marxism’s] earlier formulations (for example in Marx’s analysis of the character of the ‘coming social revolution’) their predictions were testable, and in fact falsified. Yet instead of accepting the refutations the followers of Marx reinterpreted both the theory and the evidence in order to make them agree. In this way they rescued the theory from refutation; but they did so at the price of adopting a device which made it irrefutable. They thus gave a ‘conventionalist twist’ to the theory; and by this stratagem they destroyed its much advertised claim to scientific status.

Lakatos: The Methodology of Scientific Research Programmes (Philosophical Papers: Volume 1), J. Worrall and G. Currie (eds.), 1978, pp. 4-5

Has…Marxism ever predicted a stunning novel fact successfully Never! It has some famous unsuccessful predictions. It predicted the absolute impoverishment of the working class. It predicted that the first socialist revolution would take place in the industrially most developed society. It predicted […] Thus the early predictions of Marxism were bold and stunning but they failed. Marxists explained all their failures […] But their auxiliary hypotheses were all cooked up after the event to protect Marxian theory from the facts. The Newtonian programme led to novel facts; the Marxian lagged behind the facts and has been running fast to catch up with them.

(I’ve emphasized the two predictions I’ll cover in the two posts.)

Disclaimer 1

I have no dog in this fight. I’m emotionally more of a Kevin Carson-style market anarchist than a Marxist. Since I don’t actually believe market anarchism is workable, I fall back on old-fashioned Millsian liberalism. I mention this to explain why my understanding of Marx and Marxism is shallow and haphazard compared to my reading of Lakatos and Popper, which could also be more thorough – had I world enough and time.

Disclaimer 2

It’s easy to attribute P&Ls distaste for Marxism to their personal histories. However, they would consider such psychologizing out of bounds, so I’ll play by their rules in the next two posts.

⊕ Not pictured: my calf in its mouth

But you may be curious about their personal history with Marxism (or, strictly, Marxism-Leninism / Stalinism). It gave them completely understandable reasons to lash out at Marxism in the same way that I’ve never been fond of German Shepherds since one caused me to get 36 stitches in my leg.

Here’s a bit from the Stanford Encyclopedia’s article on Popper (section 2):

His teenage flirtation with Marxism left him thoroughly familiar with the Marxian dialectical view of economics, class-war, and history. But he was appalled by the failure of the democratic parties to stem the rising tide of fascism in Austria in the 1920s and 1930s, and the effective welcome extended to it by the Marxists, who regarded fascism as a necessary dialectical step towards the implosion of capitalism and the ultimate victory of communism. [Emphasis mine.]

Or: Karl Popper at Wikipedia

[Popper] knew that the riot instigators were swayed by the Marxist doctrine that class struggle would produce vastly more dead men than the inevitable revolution brought about as quickly as possible, and so had no scruples to put the life of the rioters at risk to achieve their selfish goal of becoming the future leaders of the working class.

So Popper joins George Orwell (Homage to Catalonia) as someone unimpressed by Stalinism in practice and theory. Orwell wrote: “Why I write”

Every line of serious work that I have written since 1936 has been written, directly or indirectly, against totalitarianism and for democratic socialism, as I understand it.

Popper went further than Orwell and abandoned the “beautiful dream” of socialism, finding it inherently incompatible with individual liberty and democracy. It’s a bit amusing that he didn’t blame Lenin and Stalin so much as Plato, Hegel, and Marx for their “teleological historicism.” The guy aggressively wanted to live in his head.

Lakatos was younger than Popper and had an even worse experience with Stalin and then Khrushchev: Quotes from the Stanford Encyclopedia of Philosophy article on Lakatos.

But in the earlier and Hungarian phase of his life, Lakatos was a Stalinist revolutionary, the leader of a communist cell […]

Stalin took over Hungary, as Lakatos wanted, but then:

[Lakatos] was arrested in April 1950 on charges of revisionism and, after a period in the cellars of the secret police (including, of course, torture), he was condemned to the prison camp at Recsk. […] After his release from Recsk in September 1953 (minus several teeth), Lakatos remained for a while, a loyal Stalinist.

A few years after Stalin’s death (1953), Khrushchev made a famous speech (1956) denouncing Stalin’s cult of personality and its consequences. Hungary’s government was very Stalinist, so non-government Hungarians pursued “de-Stalinization” with vigor. “Not so fast,” said Khrushchev, and invaded to stop the popular revolt. So:

Lakatos left Hungary in November 1956 after the Soviet Union crushed the short-lived Hungarian revolution. He walked across the border into Austria with his wife and her parents.

One must forgive Lakatos for not viewing the Soviet Union and its intellectual influences favorably. “By their fruits ye shall know them.”

Popper by example

Mon, 19 Jan 2026 21:30:55 -0500

Given my goal for this series, I knew I’d have to explain more about the rules Karl Popper and Imre Lakatos think scientists should follow to be worthy of the name. Rather than smear the content throughout other posts, I’ve decided to put it all – well, most – in one place.

I’ve organized the post around the kind of running example I’ve wished my authors had given. They concentrate so much on justifying their rules that they explain them only in bits and pieces, not as a coherent whole.

This is a toy example, but I think it’s still useful.

Background

Popper and Lakatos devoted big parts of their careers to the so-called “demarcation problem": how can one distinguish science from pseudoscience? They each proposed sets of rules to characterize proper science. They call those sets of rules “methodologies.”

Popper’s methodology is called “critical rationalism,” and it’s close to the “scientific method” as taught in school.

Lakatos started out as an acolyte of Popper’s who came to see himself as extending and correcting Popper’s methodology. (Popper did not agree, to put it mildly.) Lakatos called his version “the methodology of scientific research programmes.”

I think their attitudes, assumptions, and rules are close enough that I’m going to call them both “critical rationalists” and use “critical rationalism” as the umbrella term. My explanation will use Popper’s version as its base, with Lakatos’s ideas presented as elaborations.

In what follows, highlighted words mark the first use of an important concept that I’ll use in later posts, but I also highlight for emphasis. Sorry about the ambiguity.

Sources, described

The entries on Karl Popper and Imre Lakatos at the Stanford Encyclopedia of Philosophy are good.

Criticism and the Growth of Knowledge, Lakatos & Musgrave (eds.), 1970. (full text). This is a collection of papers capturing discussion at a 1965 symposium where critical rationalists beat up on Thomas Kuhn for his The Structure of Scientific Revolutions (1962), ending with his somewhat bemused response. The Lakatos paper stands out as a solid description of his methodology. Paul Feyerabend’s paper stands out because it was a defense of Kuhn that I imagine had Kuhn thinking, “Paul, I appreciate the good intentions, but you. are. not. helping.” The Popper paper I thought was useful because it states bluntly things I realized had only been implied.

For and Against Method: Including Lakatos’s Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence, Motterlini (ed.), 1999. The transcripts of Lakatos’s lectures are good, concise, though often snarky explanations of both his and Popper’s ideas. (They are from after Popper repudiated Lakatos – in 1970 – and it shows.) The correspondence is a washout because Lakatos carefully filed away Feyerabend’s letters (typical) but Feyerabend used Lakatos’s letters as bookmarks and such (also typical), so not many survived. Feyerabend’s letters are long on gossip and low on ideas.

Conjectures and Refutations: The Growth of Scientific Knowledge (5/e), Karl Popper, 1989, is a collection of essays. I relied on the “Truth, Rationality, and the Growth of Knowledge” chapter, plus pages the index took me to. If you were to say I should have read the whole thing, I wouldn’t argue with you. Or reread. I bought it during my “it’s sinful to highlight books” phase, so I don’t know how much I actually read.

My example

Francis Williams (c. 1690 – c. 1770) was a Jamaican polymath. He’s most known for astronomy. But let’s assume that, like so many “natural philosophers,” he was also passionate about collecting and studying particular animals. In this case, birds. Specifically, swans.

And let’s suppose that, because he’d seen a lot of swans, he put forward a universal truth-valued claim:

Claim WhiteSwan:

All swans are white.

Critical rationalists would call this a theory, as it’s a collection (of size one) of universal claims.

Time passes. Williams receives a crate from Australia. In it, there are several odd animals, including what looks for all the world like a swan – except its feathers are black. What now of his universal statement?

He could change it to this:

Claim ExceptThisOne:

All swans are white.
Except for this one right here.

That’s obviously silly, but why? A critical rationalist would say:

A theory’s supposed to make predictions about the world. In the case of the WhiteSwan theory, that prediction is: “no matter where you look, you will never find a non-white swan.”
But ExceptThisOne makes the same prediction! No one will ever find a non-white swan, because the only one is already accounted for.
Equivalently, ExceptThisOne gives no hint about what anyone searching for swan specimens should do differently.

The rule is that you shouldn’t change or extend a theory unless the new version makes new predictions about the world. Anything else is an ad hoc change that was most likely made to protect the original theory against an inconvenient fact. It marks you as doing pseudoscience, not science. Explaining away, not explaining.

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Williams might also have had reasons to “contest the carcass.” It happens that the cover letter attached to the crate describes the specimen only as “a peculiar Antipodean swan.” Williams might say that the irregularity of the markings and the general condition of the corpse indicate the blackened color is in fact damage incurred during the long voyage from Australia, which involved all the usual perils of the Age of Sail: storms, being becalmed in the heat of the equatorial regions, constant lurching of cargo, occasional flooding of the hold, quite a lot of rats, sailors drinking the alcoholic tincture in which some specimens were kept, etc. I recommend Patrick O’Brian’s Aubrey-Maturin seagoing novels, often referred to as a combination of Jane Austen and Horatio Hornblower. All those events happened in the series. There was no actual European activity in Australia until the year Williams died, but work with me here.

Or Williams might, after dissecting the carcass, conclude that the bone structure is different enough from other species that the specimen doesn’t belong in genus Cygnus. It’s a non-white non-swan, so it doesn’t contradict the original WhiteSwan theory after all.

Again, my examples are far-fetched, but problems of interpreting experimental results abound, especially for cutting-edge theories. Did our expensive apparatus detect a superluminal neutrino or didn’t it? (And recall from an earlier post that the Eddington eclipse observations used “experimenter’s judgment” to reconcile three different measures of the deviation of starlight near the sun.)

The jargon is that “all observations are theory laden.“ Note that the word “observation” is used both for real observations like Williams looking at a bone during dissection and a physicist at CERN looking at a graph representing a statistical analysis of gazillions of particle collider events. I personally think the word “observation” underplays the challenges of interpreting experimental results, but critical rationalists tend to be dismissive of experimenters anyway.

⊕ An 'observation' of the Higgs Boson. Click to enlarge in a new window.

As a matter of strict logic, if a theory’s proponents want to shift discussion to a “theory of the instrument,” there’s no rational way to force them to shift it back. (After all, sometimes the problem is with the instruments, as was the case for the superluminal neutrinos.)

The irrational way to shift the discussion is for the community of people who care about the original theory (pro or con) to agree that enough people have failed to convincingly dispute the observation that the rest of us should just accept it and get on with our lives. That’s indeed what people do, and even Popper accepts that’s the best they can do.

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Because critical rationalism disallows an ad hoc amendment to a theory, Williams has to propose an amended theory that allows predictions of “novel facts” (Lakatos' term). Consider this amendment:

Claim AustraliaIsWeird:

All swans outside Australia are white.
Some swans in Australia aren’t white.

This might prompt a more concerted effort to look at Australian swans. But what’s the result?

Maybe people find black swans. But we already knew they exist: Williams has the carcass of one.
Maybe people don’t find black swans. Are they not looking hard enough? Was the swan Williams received the last black swan in Australia? (After all, there was a final passenger pigeon in North America and a final dodo in Mauritius.)

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The AustraliaIsWeird theory doesn’t seem very useful. It’s a “following the letter of the law rather than the spirit” sort of thing. A better revised theory would be:

Claim: HemispheresMatter:

All swans in the Northern Hemisphere are white.
All swans in the Southern Hemisphere are white, black, or some shade in between (combinations allowed).

At first sight, this doesn’t seem to add much. Nothing’s changed in the Northern Hemisphere, and we already knew there was a monochrome swan – it’s an exhibit in Williams' curiosity cabinet. But that’s a false impression because this is a toy example. Juxtapose it with real-world science:

The new swan theory is instructing naturalists to look elsewhere in the Southern Hemisphere than where (Williams assumes) they were looking: Australia. It’s not been unusual for theorists to tell experimenters to apply existing apparatus to a new “place” (a previously-ignored stretch of the electromagnetic spectrum, for example).
There’s no glory in finding a black swan any more, but a red swan… Naturalists will now be alerted to search for colored swans. That seems silly – it’s not like they wouldn’t have noticed a red swan before – but consider how particle physicists have spent the past century telling experimenters to build new accelerators to look for ever-more-exotic particles. They’re being told the equivalent of “learn to see a new color.”

Still, this is a bit boring, isn’t it? Suppose people search and no one finds a colored swan. Fine, we have more confidence that we can safely operate on the assumption that all swans are monochrome. Or instead suppose someone finds what will come to be called Dawn’s Turquoise Swan. Wow. Another non-white swan. Critical rationalists don’t favor the idea that a steady accumulation of small facts will add up to something important. I personally disagree.

Also, the theory gives no guidance for a more interesting question: why is there a difference in swan coloration between the two hemispheres? Suppose Williams ponders that, and jumps from it to another question: what else is different about the two hemispheres? Astronomy – Williams’s specialty – is sort of adjacent to meteorology, and that similarity reminds him that storms rotate clockwise in the Northern Hemisphere and anti-clockwise in the Southern, due to something called the Coriolis force. Perhaps something about the Coriolis force affects the balance of humours in the body. And that could interact with magnetism: while the direction of the Coriolis “push” flips when you cross the equator, north stays north…

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In due time, Williams persuades an English correspondent to read his paper “On the relationship between Mr. Coriolis’s force and migration of bodily pigments” at The Royal Society of London for Improving Natural Knowledge. In it, Williams lays out how the Coriolis force affects the humours, and how its direction (in relation to north) would produce a differential flow in those humours, and…

Such a paper could include multiple predictions:

“Animals near the equator have more variation in hue because…”
“The subtle shift in humours should also be detectable in the length of feather tubules, as length and color both rely on the balance of humours to…”
“Consider raising an animal in a pen whose floor has a slight but constant slant. Because of the off-center gravitational force, the following should be observed upon autopsy….”
“If a member of the Royal Society with a suitable estate were to raise generations of black Australian swans in England, he would notice a lightening of the feathers in descendants, akin to those trait changes achieved by successful dog and horse breeders, but without controlled mating.”
“White sheep shipped to Australia will gradually darken (possibly patchily).”

This theory produces predictions that no one has made before, and there are more of them than in the earlier version of the theory. More about nature will be revealed by checking them. More is better.

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Big is also better, specifically: big surprises. Suppose you were asked two questions:

“Did you hear that they found a black swan in Australia? So we’ve got black and white swans. What’s your guess for the odds of finding a colored swan somewhere in the world? You don’t have to give a number, just words like ‘high odds’ or ‘close to zero’ or whatever.”
“Every sheep breed imported from the Continent to England (and not cross-bred with other breeds) stays the same color over the generations (black or white). What are the odds that a herd of white sheep shipped to Argentina will darken?”

You’d probably find the latter less likely.

Critical rationalists prefer their theories to make bold predictions, such as Einstein’s prediction that the sun’s gravity would bend starlight passing near it, or Edmund Halley’s prediction (using Newton’s theory of gravitation) that a comet he’d been observing would reappear in 72 years at such-and-such a precise time and position. (Halley died before the return of his comet. In an astounding coincidence, our very own Francis Williams was one of the observers who confirmed Halley’s prediction. Williams was the first known Black “gentleman scientist” to (as was common among that sort) commission a portrait that alluded to his important observations, including Halley’s comet in the background.)

⊕ Click to enlarge.

My interpretation of the critical rationalists' reasoning is that an unsurprising prediction isn’t much help in distinguishing between rival theories. It wouldn’t be hard to come up with multiple theories for why some swans are red, but finding another reason for the bending of light near the sun would be quite a challenge.

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What a prediction predicts might be observed, or it might not.

Popper calls a prediction that doesn’t pan out a falsification. Provided the observation is credible, preferably replicated, etc., it kills the theory. If you’re a proper (rational) scientist, you’ll want to quickly repair or replace it. To delay that process is irrational, although practicalities may require it for longer than one would like.

If a prediction is confirmed, Popper doesn’t attach much weight to that: “Oh look, another white swan.” Confirmation only allows (or encourages) people to keep doing what they were going to do anyway: check other predictions. As far as I can tell, Popper treats confirmations of bold predictions no differently than boring ones.

Lakatos has a different attitude. He calls a prediction that doesn’t pan out an anomaly. (Note the more tentative, less judgmental language.) To him, “theories grow in a sea of anomalies, and counterexamples are merrily ignored.“ For and Against Method, p. 99. To Lakatos, it’s rational to continue working on the theory and hope someone else explains the anomaly later – maybe decades later (as with the perihelion precession of Mercury, which took 56 years to get explained).

Like Popper, Lakatos doesn’t care much about lesser (or “timid”) predictions, but he thinks scientists are rational to be wowed by the bold ones. For example: For and Against Method, also p. 99. The following quote is on the same page.

For about a hundred hears after Newton had proposed this theory (the Principia was published in 1687) the French Academy offered an annual prize for whoever refuted the theory. About a dozen prizes were actually awarded, and then something happened.

The something was that Halley’s prediction – that his comet would reappear at certain place in the sky at a certain time – was confirmed.

After that, the French Academy did not put out any more prizes for the refutation of Newton’s theory.

Popper would have been displeased with the French Academy for giving up because of a confirmation (and likely with all the English scientists who had been ignoring the dozen refutations).

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So, some key points:

Both of our critical rationalists agree scientists should eventually deal with anomalies, but they differ on the timing. Popper doesn’t allow many reasons for delaying, but Lakatos is happy with an indefinite delay.
A new or revised theory should produce new predictions, ones not made before. Popper further requires that a new theory should also explain everything the old theory did. Lakatos is not bothered if some of the observations the old theory explains aren’t explained in the new. They can remain as anomalies for the new theory until someone gets around to them.
Anomalies are more useful than confirmations because they drive further theoretical work. To Popper, confirmations might have some value by, for example, helping a theorist narrow down which theoretical claims a falsification implicates – but not much else. Lakatos thinks it’s a “metaphysical principle” (that is, one that’s not provable) that “highly falsifiable but well-corroborated theories are (in some sense) more likely to be true (or truth-like) than their low-risk counterparts.“ The quote isn’t Lakatos’s, but that of the author of The Encyclopedia of Philosophy article on Lakatos.

The Road to Lakatos

Tue, 09 Dec 2025 18:42:45 -0500

My next post is scheduled to be on Imre Lakatos’s “methodology of scientific research programmes.” I’m going to cast it as a failed attempt to make science rational that’s actually a good dissection of how scientists and people with a scientific temperament are persuaded (not-necessarily-rationally) to make big career bets.

But the question of why Lakatos was fixated on rationality makes for a good story. That’s this post.

Scientists have a right to feel smug.

Since the Scientific Revolution (~1543 - ~1687), science has progressed nicely. That is, scientists have figured out a way to spend extremely little time revisiting old controversies like phlogiston, spontaneous generation of animals, and the Ptolemaic universe. There are new controversies, to be sure, but rarely are they resurrected versions of older controversies. Moreover, the historical argumentation used in old controversies isn’t generally mined to get insight into today’s debates.

In contrast, philosophers (say) are always subject to getting sucked into more refined versions of skeptics' arguments from 2500 years ago. If you’re doing political philosophy, it’s still perfectly reasonable to refer to J.S. Mill’s On Liberty or Machiavelli’s Discourses on Livy. But college science courses don’t reach back to Newton’s Principia when teaching orbital mechanics or to Darwin’s On the Origin of the Species when teaching evolutionary biology.

Three methodologies

Naturally, when something works, people want to study how it works. What is it, exactly, that scientists are doing that accounts for the speed of their progress?

To oversimplify, this focus on method or methodology went through three overlapping phases:

Inductivism. The scientist worked by gathering observations and making generalizations from them. The generalizations were supposed to apply more broadly than the set of examples they came from. (Ideally, they would be universally true.)

Pretty much from the very beginning, people saw the problem with inductivism: if you see a bunch of white swans, and you induce that “all swans are right,” you’re going to get a nasty shock when someone presents you with a stuffed Australian black swan (Cygnus atratus). What was once universally true turns out to be true only of the swans of the northern hemisphere.
Waiting around for new examples and counterexamples is rather passive. It would be better to actively seek them out. The favored process became the hypothetico-deductive method. From observations (or wherever, really), you come up with a hypothesis. You should also come up with predictions of the form “I predict if someone sets up the following situation, they will observe thus and so.”

It’s called hypothetico-deductive because the predictions are supposed to flow from the hypothesis using only logical deduction, which is the only kind of logic that provides certainty. Induction over examples is still required, but at least part of the method provides certainty.

A classic example of the hypothetico-deductive method is Einstein’s theory of general relativity. Both his physics and Newton’s predicted a star’s light would bend as it passed near the sun, but a necessary consequence of Einstein’s theory would be bending twice that of Newton’s. So Einstein predicted that’s what one would see in a total solar eclipse. (It has to be total or the light of the sun would drown out the light of the star.) The experiment was tried, and Einstein’s amount of bending was observed. (Sort of.)

The hypothetico-deductive method proposed that a competition between hypotheses (like Newton’s and Einstein’s) should be decided by how well they were corroborated by predicted observations.
Falsificationism was due to Karl Popper, who wanted the scientific method to be still more stringent. He counseled that scientists should not consider a successful confirmation as giving more reason to believe in a hypothesis. Instead, what scientists should look for are falsified predictions: replicable counterexamples. (Popper was concerned with what he called the The Logic of Scientific Discovery, but there’s also a psychological angle: a person trying to falsify a hypothesis will probably come up with better experiments than someone merely trying to show the hypothesis works.)

If some random well-educated person talks about “the scientific method,” they’re most likely referring to Popper’s approach.

Motivations

Popper developed his approach in the early 20th century, which was a really weird half-century:

There was a pervasive sense of lost certainty. In mathematics, you had a crisis in foundations around the turn of the century. Freud’s The Interpretation of Dreams was published in 1899, so Freudianism was really hitting its stride, causing some distress to people who’d fancied themselves working according to the dictates of reason, not some weird, alien “unconscious.” Psychology had forked off from philosophy in the late 1800’s (James' The Principles of Psychology was 1890), and it too cast doubt on the philosopher’s cherished rationality. The Great War (World War I) was a crazy slaughter, started for no sensible reason, and ground on well beyond the point of rationality or sanity. (The US Civil War was a precursor of the Great War’s industrial-scale slaughter, and it had effects on American intellectuals that presaged those of the Great War.)

In an entirely human reaction, people doubled down on the quest for certainty and embraced dogmatism more than ever. I take Popper to be playing in that arena. He had produced The Logic of Scientific Discovery. Yes, scientific conclusions could never be as certain as logical deduction like:
```
  All men are mortal.     
  Socrates is a man.       
  Therefore, Socrates is mortal.
```
But the scientific method could be made logical, certain (dogmatic), and rational. That fit the tenor of the times.
This was also an era where increasing bureaucracy, credentialism, and specialization had formalized the definitions of professions and shifted authority about a profession from its practitioners toward outsiders. Drawing boundaries was important. No longer could the “gentleman scientist” (like Darwin) be accepted through a process of impressing people already in the charmed circle: there are rules that any scientist worthy of the name must follow.

This was called the “demarcation problem": how do you distinguish between science and non-science (pseudoscience, metaphysics)? Popper particularly had it in for Freudianism and “scientific Marxism.” His scientific method ruled them out because none of their predictions could be falsified. Proponents always gave some reason why a particular contrary observation didn’t count.

Lakatos

Imre Lakatos (1922-1974) was of the generation after Popper. He was a junior colleague of Popper’s at the London School of Economics (which had a philosophy of science department). He later broke from Popper because their ideas were incompatible.

He shared Popper’s disdain for Marxism despite having been a fervent Stalinist in his youth. Important milestones in his journey away from communism were:

The Hungarian secret police arrested him in 1950 for “revisionism,” tortured him, and threw him into a forced labor camp that was modeled after the Soviet Gulag.
He was, outwardly at least, still a loyal Stalinist, and it seems to have been discovering Popper that caused his final break with communism. He publicly repudiated Stalinism in 1956.

This was three years after Stalin’s death and probably after Khrushchev’s February 1956 not-so-secret speech denouncing Stalin’s purges and his cult of personality. So perhaps not so brave as it seems, but someone with his background must have known that a tide that’s turned once can always turn back.
And, indeed, the Khrushchev Thaw that promised less repression and censorship across the Soviet Union did not prevent it from invading Hungary later in 1956. Lakatos – along with about 250,000 other Hungarians – fled the country.

Lakatos also shared Popper’s opinion of Freudianism.

Proofs and Refutations

Lakatos' work on the history (“logic”) of mathematics nicely sets the stage for his later work.

⊕

His posthumous Proofs and Refutations is derived from his PhD work. It largely deals with the Euler characteristic which (as originally formulated) claims the following is true for all polyhedra: V means the number of vertices, E is the number of edges, and F is the number of faces.

2 = V - E + F

When Lakatos’s looked into the history of the Euler characteristic, he found that many people had proposed counterexamples. (“So what about this weird-ass three-dimensional structure? Do the vertices and edges and faces add up to two? They don’t, do they? Whatcha gonna do about that?)

Lakatos observed that mathematicians didn’t abandon the formula. Instead, they saved the formula using tactics Lakatos gave evocative names like “monster-barring” and “monster-adjustment.” That made them bad Popperians but, Lakatos observed, better mathematicians.

However Lakatos had, I think, a temperament that made him uncomfortable without rules. So things like “monster-barring” are, effectively, a list of rules about when it’s rational to break what you might call “first-level rules.”

The odd couple

Weirdly, Lakatos became great friends with Paul Feyerabend, who had quite the opposite temperament. That almost led to a great cooperative venture. Here’s the beginning of Feyerabend’s preface to his most famous book, Against Method:

In 1970 Imre Lakatos, one of the best friends I ever had, cornered me at a party. ‘Paul,’ he said, ‘You have such strange ideas. Why don’t you write them down? I shall write a reply, we publish the whole thing and I promise you – we shall have a lot of fun.’

Unfortunately, Lakatos died just before Feyerabend was to send him his draft, so only the Feyerabend part was ever published. Using examples, Feyerabend argued that Lakatos’s dream of rational rules and meta-rules would never work. Whatever rules you try to impose, great scientists will “cheat.” Moreover, they could not have achieved their greatness without breaking the rules.

Feyerabend was very much an “the end justifies the means” guy. Lakatos – perhaps because he was very much that kind of person in his Stalinist days “[The young] Lakatos decided that there was a risk that [a new member of his Marxist group] would be captured and forced to betray them, hence her duty, both to the group and to the cause, was to commit suicide. A member of the group took her across country to Debrecen and gave her cyanide.” source – seemed unwilling to go that far. There had to be good means that would, rationally, lead to good ends.

Postscript

Perhaps incorrectly and definitely simplistically, I think of Lakatos as being at the tail end of prescriptive philosophy of science: the quest for a way to do science that could be justified rationally from first principles. What came to be called “science studies” was more heavily influenced by sociology and anthropology than philosophy. It’s characterized by:

Less of a focus on Great Men (Galileo, Newton, etc.) and more on run-of-the-mill scientists.
Realizing that perhaps physics isn’t the model for all sciences. Maybe biologists weren’t just wanna-be physicists and had their own way of doing things that worked fine for them.
A greater focus on experimenters, whom pretty much everyone – Kuhn, Popper, Lakatos, Feyerabend – had brushed aside as mere mechanics.

All of this got caught up in the “science wars,” which were a silly offshoot of the silly culture wars that started in the 1980’s I documented some of the culture wars in a series on “political correctness.” 1984, 1987, 1990, 1991. Ironically, back then it was the culturally right that cast themselves as defenders of science and objective reality and the culturally left that were anti-science relativists. Though, as I say, the whole thing was silly. See Hacking’s The Social Construction of What? for a dissection of the science wars. Did the Science Wars Take Place? is an interesting (though more opinionated and intemperate than I’m comfortable with) take from an “a plague on both your houses!” anarchist. (Since the author doesn’t approve of the concept of intellectual property, there are ungated PDFs and ePubs at the site, in addition to the option to buy a hardcopy.) and seem unkillable.

I haven’t kept up with the field this century, but I found Godfrey-Smith’s Theory and Reality: An Introduction to the Philosophy of Science a good read.

Working backward from the theory to the observation

Wed, 03 Dec 2025 18:27:04 -0500

The recent death of Tom Stoppard, who cowrote the screenplay for “Shakespeare in Love,” reminded me of Dennis Overby’s Einstein in Love (2000). It’s a biography of Einstein during the two decades of his most groundbreaking work. In it, I found out that Eddington fudged the results of the famous experiment that was reported to have confirmed general relativity.

Three devices at two locations measured the deflection of stars near the sun during a solar eclipse. Einstein’s theory predicted a deflection roughly twice as large as predicted by Newtonian theory. Here were the results:

Device	Estimate of deflection	Data quality	Comment
Sobral telescope	1.98 ± 0.12	Best	Too high for both theories
Sobral astograph	0.86 ± ?	Next best	Close to Newton
Principe astrograph	1.61 ± ?	Worst	In the Einstein neighborhood

Eddington tossed the results closest to Newton, averaged the remaining two together, and got a results of “1.75, right on the relativistic mark.”

Well, gee, that seems bad. But Eddington turns out to have been right, as our phones demonstrate. “As predicted by Einstein’s theory, clocks under the force of gravity run at a slower rate than clocks viewed from a distant region experiencing weaker gravity. This means that clocks on Earth observed from orbiting satellites run at a slower rate. To have the high precision needed for GPS, this effect needs to be taken into account or there will be small differences in time that would add up quickly, calculating inaccurate positions.”

Here’s a longish quote from the book, with key sentences highlighted. At some point, I’ll use it as an example that comments on Imre Lakatos’s “methodology of scientific research programmes.”

In the end, Eddington and his crew had three sets of data from the three telescopes they had taken to the eclipse. By far the best plates were the ones exposed in the four-inch Irish telescope at Sobral. Measuring the seven stars on those seven plates gave a deflection of 1.98 seconds of arc, with an uncertainty of about 0.12 second. That was higher than Einstein had predicted, and taken alone would actually have cast severe doubt on general relativity. The next-best plates were from the Sobral astrograph. They showed many more stars, but heat from the sun had affected the mirror and blurred the images, and may even have affected the focus. The same analysis on these plates yielded a value for the deflection of 0.86, almost exactly the Newtonian prediction, but with a bigger uncertainty. Finally, there were the two plates from the Principe astrograph, shot through the clouds, with five blurry dumbbell-shaped stars on each. They were the worst quality of the lot. With only five stars, Eddington could not simply measure the images and solve an equation for the deflection. He had to engage in roundabout series of calculations: assume some amount of gravitational deflection, compute the other components contributing to the stars' displacements, and use those to recalculate the gravitational deflection, repeating the process until all the numbers were consistent. In such a manner he converged on a value of 1.61 seconds of arc for the gravitational deflection-very close to the Einsteinian prediction, especially when the rather large uncertainties were accounted for.

What, then, was the correct answer: 1.98, which was too high; 0.86, which was too low; or 1.61, which was just right, but unreliable? Was it an average of all three? Traditions and empires of the mind hung in the balance. The spread in the results should have been a big yellow caution sign that the experiment was flawed. Presumably there was only one right answer. Averaging the data from all three instruments, the philosophers and historians John Earmann and Clark Glymour have pointed out in a historical essay, would have led to an estimate of the deflection that was somewhere between the Newtonian value and the Einstein value, which was precisely what Eddington had reported to Lorentz in September. If Eddington wanted to exercise some judgment and keep only the best data—namely, that derived from the Sobral four-inch-then the answer would rule out general relativity.

As the American cosmologist Allan Sandage likes to say, quoting the British astronomer Sir Hermann Bondi, no experiment should be believed until it has been confirmed by theory. Bondi could have gotten that from Eddington. Eddington in 1919 already knew the truth: The truth was general relativity.

Eddington looked into the fuzzy forest of results and saw the trees leaning and he knew—or thought he knew—that there were only three choices for the amount of that lean. He threw out the Sobral astrograph, which had given the lowest number, and kept the other two. Their average was 1.75, right on the relativistic mark. General relativity was confirmed.

I can’t give page numbers because Google Books has plastered “Copyrighted material” over where the page numbers should be. This URL might get you to the text, though the search results when I just tried it don’t include the right page.

William James on pragmatism

Tue, 02 Dec 2025 17:46:50 -0500

In late 1906, William James gave a series of lectures on the topic of a newly coalesced philosophical approach that had come to be known as “pragmatism.” His second lecture was titled “What Pragmatism Means.” It starts with a story that illustrates what you might call the “pragmatic temperament.” I try to have that temperament myself.

SOME YEARS AGO, being with a camping party in the mountains, I returned from a solitary ramble to find every one engaged in a ferocious metaphysical dispute. The corpus of the dispute was a squirrel – a live squirrel supposed to be clinging to one side of a tree-trunk; while over against the tree’s opposite side a human being was imagined to stand. This human witness tries to get sight of the squirrel by moving rapidly round the tree, but no matter how fast he goes, the squirrel moves as fast in the opposite direction, and always keeps the tree between himself and the man, so that never a glimpse of him is caught. The resultant metaphysical problem now is this: Does the man go round the squirrel or not? He goes round the tree, sure enough, and the squirrel is on the tree; but does he go round the squirrel? In the unlimited leisure of the wilderness, discussion had been worn threadbare. Every one had taken sides, and was obstinate; and the numbers on both sides were even. Each side, when I appeared therefore appealed to me to make it a majority. Mindful of the scholastic adage that whenever you meet a contradiction you must make a distinction, I immediately sought and found one, as follows: “Which party is right,” I said, “depends on what you practically mean by ‘going round’ the squirrel. If you mean passing from the north of him to the east, then to the south, then to the west, and then to the north of him again, obviously the man does go round him, for he occupies these successive positions. But if on the contrary you mean being first in front of him, then on the right of him, then behind him, then on his left, and finally in front again, it is quite as obvious that the man fails to go round him, for by the compensating movements the squirrel makes, he keeps his belly turned towards the man all the time, and his back turned away. Make the distinction, and there is no occasion for any farther dispute. You are both right and both wrong according as you conceive the verb ‘to go round’ in one practical fashion or the other.”

Although one or two of the hotter disputants called my speech a shuffling evasion, saying they wanted no quibbling or scholastic hair-splitting, but meant just plain honest English ‘round’, the majority seemed to think that the distinction had assuaged the dispute.

This is a catchy example, but it doesn’t spell out how James was using what he calls “the pragmatic method.” So let me do that.

Here is the key question James wants you to ask:

What difference would it practically make to any one if this notion rather than that notion were true? If no practical difference whatever can be traced, then the alternatives mean [in practice] the same thing, and all dispute is idle.

What new facts would flow from the knowledge that the human did or did not go around the squirrel? To answer that, we need to consider the already-known facts. We know the human went around the tree. We also know that he never actually saw the squirrel, as it also went around the tree. Moreover, having seen squirrels, we know it didn’t fly around the tree; rather, it did the usual squirrel thing of clinging to the tree and moving sideways to keep the tree between itself and a possible threat.

That given, there are two possibilities:

If we believed that the human did go round the squirrel, our attention might be drawn to the fact that he traversed the points of the compass. But we already knew that because everyone agrees he went around the tree, and the squirrel is on the tree.
If we believed he didn’t go around the squirrel, we’d know that he’d never faced the squirrel’s back. But we already knew that, too, because we know how squirrels work.

So the pragmatist’s answer to the question “did he go around the squirrel?” is: who cares? The dispute is idle. Echoing the Rorty of the previous post, we can say we would simply like to change the subject – which James persuaded his companions to do.

In sum, the pragmatic method is:

In what respects would the world be different if this alternative or that were true? If I can find nothing that would become different, then the alternative has no sense.

Action

In the above, I focused on what additional knowledge is gained from interrogating the concept “around” (none). But pragmatists tend to focus on action rather than facts. James quotes Charles Sanders Peirce: “our beliefs are really rules for action.“ Peirce’s last name is pronounced like “purse” rather than “pierce.” That’s annoying, which is fitting, as my impression is that Peirce was a pretty annoying person, to his detriment. Kind of an “alpha geek” character. Nevertheless, I cherish my Peirce teeshirt. (Click to enlarge.)

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(Alternately, you could think of actions as creating new facts, which are then used to evaluate the usefulness of concepts.)

So the core question is “What would we do differently if we believed X than if we believed Y?” I once did a consulting gig with Ron Jeffries, and he asked that question when someone was arguing about the fundamentals of test-driven design (or something – it was twentyish years ago). The answer was, well, nothing, really, so we were able to move on. We came out to the company about once a month for a year. On numerous occasions, Ron demonstrated the difference between knowing something intellectually (as I did) and having internalized ideas to the point of automatically having the right reaction. I learned a lot. Thanks, Ron!

Truth

Pragmatism recommends believing in something when human experience (yours and others) shows it to be useful. So when it comes to essentially contested concepts – ones where there’s disagreement about what a word or idea means – our take on which idea is correct should be that it’s the one that provides what James calls “cash value.” The value can be determined by discussion of consequences of putting the concept into action or, better, by seeing what happens.

The pragmatists were greatly influenced by Darwinian evolution (still rather new at the time), so let’s analogize concepts to species. Both change over time to better fit the environment they’re used in. So, if the woodland argument about “around” had revealed that one side or the other actually did reveal new concrete facts or suggest new and useful activities, the concept of “around” should be extended to include that.

Where the pragmatists got controversial was in saying that’s all you need. “Giraffes have long necks” is true because believing that has useful consequences. “Giraffes invariably speak in iambic pentameter” is false because someone who believed it is going to run into problems when, say, interacting with giraffes. And that’s it for our knowledge of giraffes: there’s no Platonic essence of “giraffe” out there somewhere that defines it independently of human experience. Or, if there is, it’s inaccessible to us, so it has no cash value.

Making true statements be relative to the mere humans that use them produces some strong reactions. In his History of Western Philosophy, Bertrand Russell ended his chapter on James thusly:

But this is only a form of the subjectivistic madness that is characteristic of most modern philosophy.

And the following chapter, on the roughly contemporaneous pragmatist John Dewey, ends:

I am persuaded that this intoxication [thinking truth is not independent of humans] is the greatest danger of our time [1945], and that any philosophy which, however unintentionally, contributes to it is increasing the danger of vast social disaster.

Not a fan, I sense. I avoid the issue by considering the pragmatic method a social approach that should be more used, and leaving capital-T TRVTH to others.

There are more practical problems with pragmatism. Darwinism has the advantage of a pretty straightforward way of determining if a mutation is useful: does it persist through generations? Over time, does a larger and larger proportion of the population have it? The question of the fitness of a belief is much harder. It’s easy to go down a recursive rathole. A belief is judged by its usefulness, but what does “useful” mean? Arguing about the definition of one essentially contested concept using other essentially contested concepts is a mug’s game. Still, I believe it makes a decent heuristic.

Anecdote

Around the time I was reading up on pragmatism, I was hired to work on the testing part of the Rational Unified Process. At a meeting of three of us, there was an extended discussion of the meaning of the word “plan.” Already a budding pragmatist, I did not participate but just waited for it to be over. The discussion seemed interminable, but was probably less than an hour, possibly as short as half an hour.

After the two agreed they had resolved their differences, I said, in my usual gracious way, “You both think you agree now, but I guarantee you don’t.”

I was right, as subsequent discussion showed.

However, I’m certain (given later events) that at least one person had his love for abstract argumentation affected not the tiniest bit. As Peirce put it, “It is hard to convince a follower of the a priori method by adducing facts.“ Charles S. Peirce, “How to Make Our Ideas Clear,” Popular Science Monthly 12 (January 1878). I give a link to a PDF below. But perhaps this little essay will give people with a pragmatic temperament a method with some cash value.

If you want to learn more

The Stanford Encyclopedia of Philosophy’s article on pragmatism is only a click away. It complicates the picture I sketched and includes later developments. As philosophical summary articles go, it’s quite readable.

Louis Menand’s The Metaphysical Club is a good first book to read. The Metaphysical Club was the group of people who more-or-less invented pragmatism. So you get descriptions of the key players and how they developed and used their ideas. In addition to discussing the influence of Darwinian evolution, Menand focuses on how the US Civil War left a lot of intellectuals leery of absolute truths and doubting the usefulness of certainty.

James’s Pragmatism: A New Name for Some Old Ways of Thinking collects his lectures. It’s short, readable (making allowance for the style of the time), and out of copyright. It does spend time on controversies and people that mean nothing to the non-philosopher audience more than 100 years later. It works well as an audiobook. (Though it’s not read by the author, alas.)

Louis Menand also edited Pragmatism: a Reader, which is a good collection of papers. It includes Peirce’s paper that kicked it all off: “How to Make Our Ideas Clear.” Peirce is not as easy a read as James, but you’ve surely read much worse.

Rorty on pragmatism

Sun, 30 Nov 2025 17:47:59 -0500

I am, by nature and upbringing, dogmatic, but I fell in among bad companions earlier in my life – Lisp and Smalltalk programmers, certain philosophers of science, and the American Pragmatist philosophers. They made me better at my job of a software consultant.

Something that really struck me, way back when, was part of the Introduction to Richard Rorty’s Consequences of Pragmatism. I offer it to you, with a little light commentary.

Rorty is writing to other philosophers. A topic in philosophy is “When are you justified in saying something is capital-T True?” Pragmatists have their own theory of truth that I think the vast majority of philosophers disagree with. So here’s Rorty. Emphasis and paragraph breaks are mine.

Pragmatists think that the history of attempts to isolate the True or the Good, or to define the word “true” or “good,” supports their suspicion that there is no interesting work to be done in this area. It might, of course, have turned out otherwise. People have, oddly enough, found something interesting to say about the essence of Force and the definition of “number.” They might have found something interesting to say about the essence of Truth. But in fact they haven’t.

The history of attempts to do so, and of criticisms of such attempts, is roughly coextensive with the history of that literary genre we call “philosophy”—a genre founded by Plato. So pragmatists see the Platonic tradition as having outlived its usefulness.

This does not mean that they have a new, non-Platonic set of answers to Platonic questions to offer, but rather that they do not think we should ask those questions any more. When they suggest that we not ask questions about the nature of Truth and Goodness, they do not invoke a theory about the nature of reality or knowledge or man which says that “there is no such thing” as Truth or Goodness. Nor do they have a “relativistic” or “subjectivist” theory of Truth or Goodness. They would simply like to change the subject. (pp 1-2)

It is very freeing to realize that you don’t have to have an opinion.

(As an aside, Rorty is providing a strategy for working with what an earlier post called “essentially contested concepts.” The strategy is: derail the conversation into a more productive topic.)

But just changing the subject isn’t enough. The purpose of thinking is to successfully get around in the world. Controversies about essentially contested concepts, if resolved, typically “cash out” by guiding action. Wanting to change the subject doesn’t remove the need to make choices. So, in the absence of any firm notion of Truth or the Good, how do you decide what to do?

I’ll touch on that later with another catchy snippet, William James’s story of a squirrel. I’ll explain how OG Extreme Programmer Ron Jeffries used the point behind the snippet in a joint consulting gig we had.

Entity realism

Fri, 28 Nov 2025 16:35:13 -0500

An occasional controversy in science is whether some theoretical “entity” is really real, or just a mathematical/modeling convenience. Ian Hacking has an interesting and eminently pragmatic answer that goes under the name “entity realism.” I believe him.

The positron (positively charged electron) was originally theorized by Paul Dirac as an implication of Dirac equation, “a unification of quantum mechanics, special relativity, and the then-new concept of electron spin.”

But was it a real thing, or just a side-effect of the math? Four years later, C. D. Anderson produced this picture: ⊕ Anderson, Carl D. (1933). “The Positive Electron”. Physical Review 43 (6): 491–494. DOI: 10.1103/PhysRev.43.491. It is in the public domain, via Wikimedia Commons.

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The little track in the image curves as sharply as an electron would, but in the opposite direction.

However, that’s not a picture of a positron. It’s a picture of a trail of droplets in supersaturated alcohol vapor. Yes, the trail is consistent with the idea of an electron-but-with-positive-charge, but that’s only indirect evidence that there is a thing that’s a positron. Maybe there’s a different explanation?

That seems weird to us, but only because everything we’ve ever read assumes the positron is a real thing. Early on, the subject was much more debatable and debated. Another example is perhaps more intuitive. In 1917, Einstein introduced the cosmological constant Λ in his theory of general relativity. That was to be consistent with the evidence that the universe is “flat” (neither expanding or contracting). Later, it got removed (or set to zero). That was consistent with the then-dominant theory that the universe’s expansion was slowing down. However, it now appears that the expansion of the universe is accelerating, so Λ is back, baby, with a positive value. Fine. But is Λ a thing? If so, what kind of thing?

Philosopher of science Ian Hacking was aware of the issue: when are we justified in saying a postulated entity is real? Another example: is light a particle or a wave? Or is that a meaningless question? In his Representing and Intervening (2012) he describes chatting with some experimenters who were searching for “free quarks” (possible entities with 1/3 the charge of an electron). Their plan was to use a small niobium ball, cooled to superconducting temperature and given an electric charge. (Because of superconductivity, the charge would never decrease.)

Because of the charge, the ball could be suspended in a magnetic field then moved around by varying the field. Hacking takes it from there:

The initial charge on the ball is gradually changed, and […] one determines whether the passage from negative to positive charge occurs at zero or at ±1/3e. If the latter, there must be one loose quark on the ball. […]

Now how does one alter the charge on the niobium ball? “Well, at that stage,” said my friend, “we spray it with positrons to increase the charge or with electrons to decrease the charge.” From that day forth, I’ve been a scientific realist. So far as I’m concerned, if you can spray them then they are real. (p. 23)

That last sentence is a catchphrase for entity realism, part of a partial shift of philosophy of science toward paying more attention to experiment (vs. theory). Things are treated as real if they provide experimenters with “manipulative success.”

The way I think of it is that the purpose of science is to be able to do more and more sophisticated experiments that build on earlier experiments and their results. That makes the connection between science and engineering tighter: engineers and experimenters are both using science to build things. Where they differ is in the purpose: one is in support of more experiments, and one is in support of… things like cars that need support in order to cross a river. They also differ in the amount of repetition. Experimenters trade practicalities the way engineers do, but there’s a lot more bridge-building than cyclotron-building work. For practicality-sharing, see Fujimura, Crafting Science, Pickering (ed.) Science as Practice and Culture (which contains a shorter version of Fujimura), and Galison Image and Logic.

This is essentially an application of William-James-style American Pragmatism. Something is true if it can be practically and usefully applied: “the ultimate test for us of what a truth means is the conduct it dictates or inspires.” Is the positron real? A thing? Yes, because you can use it in experiments that have nothing to do with positrons, that aren’t about positrons. Things become real when they become tools.

In which I take on the binary

Thu, 20 Nov 2025 17:01:41 -0500

Human beans love thinking in binary oppositions. That is often way too crude for serious understanding and problem-solving. I offer a complex visual metaphor that might help you and others push against the binary reflex.

Reminders

A number of years ago, I made some “An Example Would Be Handy Right About Now” stickers.

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They were a punchy way of shifting a conversation that was going nowhere because people were fixated on airy abstractions and definitions of terms. By saying the slogan, I could (sometimes) shift the conversation to a discussion of particular concrete details. My experience as a software tester had taught me that even just searching for examples (and counterexamples) tends to make problems leap out at you.

I used to hand the stickers out to team members at consulting clients. Some put them on their laptops. When conversations got bogged down, someone could point to the sticker, say the “An example would be handy…” words, and the conversation would often shift. It’s funny that a laptop sticker would carry with it more authority than just the words of a tester. I can only echo the words of the narrator of “Bartleby, the Scrivener": “Ah Bartleby! Ah humanity!” I was told at least once that just mutely pointing at the sticker on someone’s laptop would do the work. As software researcher Warren Teitelman once said in reply to an audience question: “People need more often to be reminded than informed” (paraphrased from memory). The visual reminder was needed to kick people out of a conversational rut.

So let me develop a sticker-suitable diagram that might serve the same purpose for fruitless discussions that center on binary distinctions. My design skills are, to put it mildly, not great. If you want to do a better job – I’m sure you can – have at it. I hereby place all images on this page in the public domain, except for the images not due to me (noted at the end of the post). CC0 1.0 Universal “By marking the work with a CC0 public domain dedication, the creator is giving up their copyright and allowing reusers to distribute, remix, adapt, and build upon the material in any medium or format, even for commercial purposes.” I know, I know, it’s presumptuous to think anyone would want to, but a guy can hope, can’t he? If you want me to distribute your sticker, I will.

Binaries

Good/evil, left/right, mind/body, man/woman, child/adult, handsome/ugly, liked/disliked, loyal/traitorous, theory/experiment, academic/pragmatic, particle/wave, etc. etc. etc. Binary distinctions are a way of life for us. There are two key problems with that. To show the first problem, I’ll start with an easy target, the statistical binary significant / non-significant.

The reality is that a probability ranges from 0.0 to 1.0:

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However, scientific culture has decided that there’s a threshold for a statistically significant probability, the famous p < 0.05:

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That makes thinking easier. You don’t have to look at a p value of, say, 0.09 and interpret that number in the context of the experiment in order to make the practical decision of accepting that the measured effect is real (rather than random error), and thus potentially useful to build upon.

However, it’s not making thinking better, because you’re applying a distinction that doesn’t exist in nature. For purely pragmatic reasons, you’ve created a sharp binary, two different categories instead of a spectrum:

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Indeed, I’d argue that, in such cases, it’s more descriptive of the actual thinking to stop hinting at the underlying spectrum:

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I’ve labeled the circles “good” and “bad” because that’s the second of the two problems: we have a strong habit of assigning moral or emotional valence “Valence, also known as hedonic tone, is a characteristic of emotions that determines their emotional affect (intrinsic appeal or repulsion).” – Wikipedia I’ve recently become strangely fond of that word. “Salience,” too. to the two categories. Not only are the categories disjoint, one is better than the other. I’ve indicated that with the coloring and also by placing “good” higher than “bad.“ Humans tend to think of “up” as the direction of “good.” That’s why heaven is up. That’s why someone might leave their job to pursue a “higher calling.” And so on. See Lakoff and Johnson, Metaphors We Live By.

Come to think of it, the picture shown above suggests good declining into bad (since change happens in time, and time flows left to right for me, a native English writer). It’s more appealing to show progress rather than decline:

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That’s better.

In the jargon, one half of a binary distinction is “privileged” and the other is “marginalized.” Because of that, such distinctions are often called “binary oppositions,” building conflict into the morality play.

It’s not surprising or a problem, really, that scientists privilege statistical significance over non-significance: significance means they accomplished their goal, which is good.

But for other oppositions, things get more problematic:

mind/body
theory/experiment
academic/pragmatic
man/woman

There’s some debate, I understand, whether the direction “right” has historically been privileged over “left.” All I can say is that I remember my dad (born 1920) telling me his brother Richard was born left-handed. The schoolteacher in their small East Prussian peasant village forced Richard to write right-handed. Not for any practical reason that I recall, but just because that’s the right way to write, the right way for a person to be.

My claim is that binary oppositions often trick you into asking the wrong question. Consider the good/evil opposition. In life, the problem isn’t so often identifying whether x is good or evil but whether action x is a better choice than action y. The binary opposition reifies “To regard or treat (an abstraction) as if it had concrete or material existence.” evil, makes it a thing of its own, not an attribute of an action in a context. That leads to crude moral reasoning applied to situations where such is worse than useless.

I suspect such playing favorites is too innate to avoid. Maybe the best thing is to lean into it. For example, if you’re writing about typing in programming languages, and you personally wonder what’s wrong with people who prefer dynamic typing, maybe you should be explicit about your feelings with a diagram:

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Or maybe print your preferred term in green text and the other in red text. This will reveal to your reader that (1) you’re human, thus (2) biased, but that (3) you recognize it. More importantly, the silliness of doing so might make you reflect on whether you prefer your position because you’ve reasoned yourself into it or that you’ve reasoned yourself into it because it’s what you prefer. Interesting how smoothly that sentence makes a binary distinction between reason and preference, including tacitly implying that reason is the better of the pair. Note that the privileged/marginalized distinction is similarly artificial. That something is privileged is way less important than how privileged it is and the way that privilege manifests in practice.

Actions

Let’s move to another binary opposition: child/adult. In my country:

When it comes to drinking alcohol, you become an adult at age 21. (When I was in college, it was 19, except it was 18 next town over. There were more bars in that town.)
When it comes to voting, you’re an adult at 18. (It was 21 until people got upset 19-year-olds were adult enough to kill Vietnamese but not mature enough to be trusted with a vote.)
The age of consent (for sex) in my state (Illinois) is 17.
When it comes to driving, “adult” means 16.

If we think of a spectrum from child to adult, the lawmakers of the great state of Illinois have divided it up into hard-edged categories:

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However, all this isn’t worth much when it comes to thinking about the adult/child distinction. What underlies that diagram are the following notions:

Adults are responsible for their actions.
Amongst those actions are driving, consenting to sex, voting, working, and drinking alcohol. There are surely others, but these are ones worth legislating about.
A given child will become responsible for different actions at different ages.
Ideally, we’d allow a child to do something when he or she is responsible enough for that particular action. Since that’s impractical, we pick an easy-to-determine proxy (age) for the hard-to-observe characteristic of responsible-enough-for-X.

An attempt to roll these individual criteria up into a definition of what it means to be an adult presents all the problems I outlined in my post on essentially-contested concepts. That is, if adulthood is based on a combination of criteria, different people will weight them radically differently. To some, if you can hold down a job (age 14 in Illinois, with restrictions until 16), you’re for all practical purposes an adult. But some might retort that a 16-year-old in Illinois is adult enough to drive during the day, but not at night (between 22:00 and 06:00, but you get an extra hour on Friday and Saturday nights). Moreover, you can drive a car at 16, but you can’t rent one until you’re 21, except if you’re one of an enumerated list of exceptions, in which case it’s 18. Also, while you can have a job at 14, you can’t sign a contract until you’re 18. Evidently, there are many word-adjacent responsibilities that 16-year-olds aren’t ready for.

Others will focus on parenthood. Certainly someone responsible for a child ought to be an adult, so the age of consent should weigh heavily in determining whether someone is an adult. But in some states (not Illinois), age of consent depends on the age of your partner (so-called “Romeo and Juliet” laws). That is, you’re adult enough to have sex at 17 if, for example, your partner is 19, but not 25. Moreover, many men (at least) consider sex between a girl of 16 and an adult of 26 worse than between a boy of 16 and an adult of 26. Well, at least if the adult is a woman, where the reaction from men is fairly likely to be “I should have been that lucky!” A boy of 16 and a male of 25 is likely to get a very different reaction from those men.

The result of this is there’s no simple function is-adult? that takes an age and returns true or false. Any such function would have to weigh many variables. You might be dismissive and think “well, duh, lawyers like making complicated laws,” but such complexity is everywhere – it’s more common than the simple cases.

In practice the decision is unconscious, made via tacit knowledge (as in my story of the bright/dull cows) rather than an explicit calculation. All that matters is that you personally have some means of deciding adulthood that produces results consistent enough with those of the people whose opinions you care about (definitely including judges).

Let me represent that like this:

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We still have two distinct categories. Each of the circles represents some combination of factors that go into the tacit determination that a particular x belongs in one category or the other.

You may notice that each of the circle-clouds has one circle that’s largest. I’m following here what I think is the dominant view of categories in the human sciences (though not necessarily in philosophy):

Prototype theory is a theory of categorization in cognitive science, […] in which there is a graded degree of belonging to a conceptual category, and some members are more central than others. – wikipedia

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A common example is the category bird. For at least European and North American people, the prototypical bird is the small brown songbird. The more different a bird is from the prototype, the less “birdlike” it is. Ostriches are weird birds because you rarely see their wings, and they don’t fly.

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Penguins are even less birdlike – not only do they not fly, but their bodies are way more vertical than a songbird’s.

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Except that people often describe penguins as flying. They just use a different medium than air: water. How, then, should we weight the various kinds of flight against the verticality of posture? We usually evade the issue by just following the societal consensus of grouping all three animals under the category “bird.” Or, if we need to justify ourselves, we appeal to the authority of biology and its “tree of life” – which is a social move in itself. After all, biologists also have disputes about classification.

So let’s visually indicate the gradations of category membership by shading different circles differently:

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In this image, I’ve made the non-central examples a mixture of red and green, reflecting the possibility that there’s a linear gradient between “absolutely birdlike” and “not at all birdlike.” That’s not because it’s true but because I want people to have something to point at when saying, “Aren’t we linearizing something that’s more complicated?” That something is this:

⊕ All images can be clicked to enlarge them in a new tab.

I hope placing the simple linear spectrum in the context of the circle-clouds raises makes the question “linear or multi-dimensional?” more salient. Told you I was obsessed with the word. Something that’s more salient is more noticeable, more relevant in context. It stands out.

As a final addition, I place a different kind of cloud on the diagram:

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What this signals is that, yes, we’re bilaterally symmetrical and that does predispose us toward either/or thinking, but there are actually often more than two sides to an issue. By focusing on the big red and green clouds, perhaps you’re ignoring something important. If you focus too much on the binary distinction between plants and animals, you’re more likely to consider fungi as funny (penguin-like) plants rather than what they are: something completely different.

Wielding the sticker

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Suppose you’re in a meeting that’s getting bogged down in a way related to binary oppositions. ⊕ About this meme I like to think you might be able to say “Um, I think we’re making this mistake,” point to a part of the image, and explain what seems to be going wrong. I hope the sticker will convey enough authority that you can divert the argument into a more productive track.

Credits

My CC0 1.0 Universal license does not apply to these images:

The picture of the wren is in the public domain, but I didn’t put it there. It’s been more than 100 years since the author’s death. Wikipedia Commons page
The picture of the ostrich is by Nicor, CC BY-SA 3.0. Wikipedia Commons page
The picture of the penguin is by Bl1zz4rd-editor, CC BY-SA 4.0. Wikipedia Commons page

Note that it does apply to the “Example” sticker. If you love something, set it free.

Jaina seven-valued logic

Wed, 05 Nov 2025 19:19:54 -0500

Sometimes the answer to “is X true or false?” can only be a shrug. The answer might be unknowable, or perhaps unknowable without an impractical amount of work. Jaina seven-valued logic offers an interesting perspective on (or alternative to) the problem.

Consider the halting problem in computer science. The question is: “Can you write a program Oracle that takes any other program and answers whether that other program will halt for a given input?” (If not, it falls into an “infinite loop.")

The answer is: “no, you can’t.”

You can react to that answer in at least two different ways:

“Well, determining whether an arbitrary program will halt is impossible, so I’ll go do something else.”
“Okay, fine, there’s no universal answer, but what special cases can I write an Oracle to handle?”

The halting problem doesn’t prevent you from writing a perfectly useful Oracle that reports, for a given program:

“It will always halt, because it contains no loops.”
“It will definitely not halt on any input less than zero because of the way this loop right here at line 2383 is written.”
…
“Sorry, boss, you’ll have to do a lot of program-specific work to determine if the program might loop forever on some input. Does the answer really matter?”

This example shows why standard boolean logic is inadequate. We almost never, in daily life, solving today’s problems, care about ∀-claims (claims that are always either true or false). We care about specific examples, or classes of examples.

Ordinary true/false logic very radically simplifies the world into one where “dunno, beats me” is not an acceptable answer. That is unacceptable.

One alternative is Jaina logic. Crudely put, it has three basic truth values: true, false, and unassertible. (That last is the “beats me, boss” answer.)

However, Jaina logic is extra neat because it specifically includes context. The Jain use a Sanskrit word that can be translated as “from a certain standpoint” or “within a particular philosophical perspective.”

With that said, there are seven truth values in Jaina logic. My own rough gloss:

From a certain standpoint, P is true.
From a certain standpoint, P is false
From a certain standpoint, P is true. From another, it is false
From a certain standpoint, there’s nothing you can say about the truth or falsity of P
From a certain standpoint, P is true, but from a (different) standpoint, there’s nothing to say about P.
From a certain standpoint, P is false, but from a (different) standpoint, there’s nothing to say about P.
From one standpoint, P is true. From another, P is false. From another, there’s nothing to be said about P.

I find that a refreshing system, especially because it demands the question “from what standpoint?” It’s not something I use rigorously, but I find the “from what standpoint?” question a good one when confronted by confident claims about a Universal Truth.

Sources

Wikipedia

“Taking Perspective: the Jain Theory of Standpoints” - a podcast episode, but the page has a wealth of (non-clickable) links.

Hypertext 2: Zettelkasten

Thu, 30 Oct 2025 17:10:01 -0500

A Zettelkasten is a particular sort of hypertext document as well as a technique for creating it. My aim in this post is to give you an understanding of a Zettelkasten document – its parts and its whole – and, more importantly, show something of what it’s like to work with a Zettelkasten. A Zettelkasten will appeal to some people much more than to others, and I’d like you to be able to predict where you’d fall on that spectrum. Presenting vignettes of my own work (lightly fictionalized) is the means I’ve chosen.

Comparisons of the Zettelkasten to what I earlier called a “wiki traditional” hypertext document will come in a later post.

I’ve spent less than two months in near-daily Zettelkasten use. Which is not much time, especially since Niklas Luhmann (an originator of the technique) says, “The Zettelkasten needs a couple of years to reach critical mass.“ Niklas Luhmann, “Kommunikation mit Zettelkästen” (1981), translated by Sascha Fast. So why do I feel justified in writing this post?

It happens that when I’m emotionally and intellectually sympatico with a technology or work process, I have a knack for absorbing it and explaining it to outsiders, even while I’m still a novice myself. That is, I have a track record with this sort of thing that encourages me to be immodest in this case.
Novices have certain advantages in explaining to other novices, most notably that they remember what it’s like to be a novice. They have an advantage in knowing – viscerally – what novices need to know. For experts, the feeling fades.
Cunningham’s Law: “The best way to get the right answer on the Internet is not to ask a question; it’s to post the wrong answer.” With luck, I’ll learn faster as experts correct me.

If I whet your interest in Zettelcasten, let me recommend Bob Doto’s A System for Writing and Sönke Ahren’s How to Take Smart Notes. Doto’s book is more nuts-and-bolts. See also zettelkasten.de for various resources, including a forum. Those three sources by no means exhaust what’s available to you, but they’re what I’ve leaned on.

A bit of history

A Zettelkasten is a particular kind of hypertext document. The word literally means “note box” or “slip box,” because that was the physical manifestation of the original Zettelkasten: a set of some 90,000 note cards written by the German sociologist Niklas Luhmann over a period of 46 years. Luhmann isn’t the only person who used notecards. For example, the rough contemporary Hans Blumenberg had some 30,000 cards in his physical Zettelkasten. ("Ruminant machines: a twentieth-century episode in the material history of ideas", Daniela K. Helbig, 2019) But when people use “Zettelkasten” as a jargon word, they are usually referring to techniques descended from Luhmann’s practice. His preserved Zettelkasten looks like this:

⊕ Photo of Luhmann’s Zettelkasten is from Niklas Luhmann-Archiv and is licensed under CC-BY-NC-SA 4.0. Sourced from Tevin Zhang.

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The Zettelkasten was Luhmann’s tool for academic writing. He was ridiculously productive, writing over 70 books and nearly 400 articles. These were apparently not the result of a hack seeking to produce as many “least publishable unit" “In academic publishing, the least publishable unit […] is the minimum amount of information that can be used to generate a publication in a peer-reviewed venue, such as a journal or a conference. […] The term is often used as a joking, ironic, or derogatory reference to the strategy of artificially inflating quantity of publications.” – Wikipedia articles as quickly as possible: he made novel and interesting contributions to German-language sociology. He credited use of his Zettelkasten for both his productivity and originality.

I should note that the museum-preserved version of Luhmann’s Zettelkasten gives an overly sanitized picture of his physical working environment. Below, you see pictures of his office. (Click to enlarge.)

⊕ Screen shots from Niklas Luhmann - Beobachter im Krähennest. Thanks to Christian Tietze for the pointer.

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They show that he combined the traditional “piles of papers everywhere” style with his disciplined note-taking. You don’t have to be a paragon of orderliness to use a Zettelkasten. In fact, I believe a fairly high tolerance for disorder (of a certain sort) is required of a Zettelkasten user. The need to combine discipline and acceptance of disorder reminds me of Agile software development in the days before the industry took a giant Seeing Like a State sledgehammer to it, but that’s a comparison for another time.

Who is a Zettelkasten for?

A Zettelkasten is primarily a writer’s tool.

Its prototypical use is by someone who spends a fair amount of their life writing nonfiction long-form narratives (articles, blog posts, books, and so on).

The core purpose of a non-fiction narrative is to argue persuasively for one or more claims. The justification for a claim may be other subclaims, which must themselves be justified. This can presumably continue until it bottoms out in claims that won’t be justified (axioms, presumed axioms, and claims you want to avoid addressing because you’re not so sure of them).

You end up with something like a tree:

⊕ For all images, including those in this sidebar, you can click to enlarge into a separate tab.

The writing’s not finished until those claims are linearized into a sentence-after-sentence narrative, including adding a lot of connective tissue. How you organize the explanation – bottom up, top down, some combination – is up to you.

Good narrative writers use various devices to engage and persuade the readers. Those often require breaking the linear claim-by-claim structure to include implicit and, perhaps, explicit back links. That’s a fascinating subject, but it has nothing (I think) to do with the Zettelkasten, so I’ll say no more.

A Zettelkasten stores notes that the writer creates by reading various documents and writing down claims they want to remember. Later, some of those notes are reread and a selection of claims are used in a narrative.

Notes can also contain claims sourced to no one but the writer. That is, you’re allowed to have an idea, write it down on a note, and stash it for later use.

The writer typically makes no concessions to any other reader. The intended audience has one member.

Success criteria

An academic’s job is not to read old claims from a bunch of sources and repackage them in different combinations with a different order. Academics are supposed to invent new claims and argue for them.

New claims often come from juxtaposing claims that haven’t been so linked before. “If (1) fast feedback is important for design, and (2) testing can be thought of as providing not just bug reports but design feedback, then… (new) I claim testing can be done in a certain way that produces a tighter feedback loop.” (It’s both putting claims 1 and 2 together, and the devising of “the certain way” that make up the intellectual contribution.)

The creative process is not understood well enough to be mechanized, but it frequently involves some thinker having one or more claims active or “ready to mind,” adding a new claim to mind, and saying “Eureka!”

The Zettelkasten has to store claims as notes and retrieve them, and that needs to be reasonably easy. However, I’ll be bold and say that the main goal of a Zettelkasten is to be a serendipity machine. That is, it should make it more likely that the writer will, at some point, mentally juxtapose two or more notes and get a new idea.

The anatomy of a note

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The card boxes in the first picture look bigger than they are. The actual cards are A6 size, meaning 10.5 x 14.8 centimeters or 4.1 x 5.8 inches. You can’t write a whole treatise on an A6 card. Whatever you know will necessarily have to be spread over multiple cards. ⊕ Luhmann card numbered 83.2c2. It claims that “The meaning of cooperation is to be developed from the idea of performance.” I’ll talk about how such cards are organized later.

In the case of an electronic note, there’s no such constraint, but I think people generally favor making notes terse enough to be visible all at once. ⊕ Below: two of my cards

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The title

Luhmann used unique alphanumeric labels to identify cards. (More on that later.) Modern hypertext style encourages giving notes titles. Wiki-traditional titles are words or noun phrases – names of things (like Zettelkasten or Platonic Idealism or Karen Chekerdjian).

Zettelcasten titles are usually sentences, and usually what I think of as factual claims. Some of mine:

Concepts have fuzzy boundaries.
The brain has many action-oriented models.
Thinking hard doesn’t burn much more energy than just lazing around.
Derrida was entranced by recursion.

Note that titles aren’t necessarily passive-voice “to be” statements (“Bourbaki was a French collective of mathematicians”). They can be rather more active: “Human brains love either-or categories” or “Visual perception fluctuates.”

Titles (the claim the note makes) are to be atomic, about a single idea. There is no objective measure of a note’s atomicity. Since the Zettelkasten is for a single person, that person will form their own subjective understanding over time. For me, at this time, I think of a claim as atomic if I can imagine using it in its entirety within a narrative. If I’d have to leave behind part of what’s claimed, it’s really two claims that should go on different (probably hyperlinked) notes.

The text

At the moment you came up with the title, you have a pretty good idea of what you mean by it. But a Zettelkasten note might next be encountered a month, a year, a decade after it was written. It is very likely the title will not be enough to remind you of what you meant.

So you need to write more sentences about the claim. But it’s extremely likely you can’t write enough to be sure you’ll remember what you meant. Alternately, you could think of reading a note as causing you to re-generate a thought you’ve had before – or something close enough, anyway. If you tried, you’d spend all your time writing notes and no time using them.

So you’ll settle for a few sentences. Making the claims narrow – atomic – will help make them sufficient. Including links to related claims will also help jog your memory.

The links

Links in a note go to destination notes that make related claims. (Mostly.)

Because the titles of the destination notes are full sentences, and a link almost always shows the text of the destination’s title claim (as shown in the sidebar images above), it’s tempting to just list them in the body of the note:

Structuralism is a mental style

Neural clusters are self-reinforcing

Would you rather be correct or effective?

I have enough self-knowledge, though, to realize such sentences will not be enough when I revisit the note in a few months. I’ll need more context, more explanation of why I thought that claim was relevant to this one. So I add more text:

“If Structuralism is a mental style, does that push against understanding the sort of “order through fluctuation” described below?”

“Another is that clusters maintain state. (See Neural clusters are self-reinforcing). We know from distributed systems that maintaining replicas is expensive.”

“It’s true that chemistry is physically determined by the laws of physics, but is it useful to think of it that way? Would you rather be correct or effective?”

Note: going forward, I don’t want to cause confusion about when I’m talking about the title (text at the top of a note) and when I mean a link to a note with a particular title. So I’ll call the latter “title-links” and, when I can, I’ll show them highlighted as links, even though they aren’t actual links into my Zettelkasten. (They go to example.com.)

Important

Even given several sentences, I may still find the relevance of a link obscure later. So, when I figure it out, I change the note. This is not dissimilar from the advice I used to give programmers during my consulting days:

As you work on your current task, you’ll be browsing through existing code. Make note of what’s awkward about it – a function in the wrong place, a bad name, a function that does too many things, whatever bugs you. At the end of a task (twice a day, say) spend some time fixing some of those things – half an hour, say – before you move on.

Tweaking notes and adding links is the same as cleaning up code: constant modest improvement.

Labels

In a hypertext document, you just click on a link and poof you’re at a new note. Luhmann had to work with physical cards. How did he get from one card to the other?

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(This may seem irrelevant in the digital era, but bear with me.)

An inadequate solution would be to number the cards and keep them in order. Maybe you put some cards in sideways (portrait instead of landscape) every five thousand cards or so, numbered with the next card, to make searching for card 63821 easier. It wouldn’t be too hard to come close to 63821 if you know where card 65001 is, and then you’d need a few more tries to get to the target card.

The problem comes in adding new cards. What if you later have an idea very relevant to 63821? If your practice is to add cards to the end as you think of them, many cards will be far away from conceptually related cards, meaning following every link is going to be a search. Yuck.

But you’re certainly not going to add the new card as 63822, then increment the old 63822 and all cards following it.

Instead, you need a way of labeling cards that allows you to add a new one next to an old one without having to change old cards' labels. The solution is to establish a conceptual tree structure for the linear set of cards.

That is, imagine we start with a highly-interconnected graph:

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But now, certain links are treated specially by overlaying a tree structure (a spanning tree, roughly) over the free-form linking structure:

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This arrangement imposes two types of relationships on the graph. Nodes are related to their parent, and also to their siblings:

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The starting graph was just a mess. The ending graph is, well… As Luhmann puts it: “The entire note collection can only be described as a mess, but at least it is a mess with a non-arbitrary internal structure.“ Luhmann 1981, op. cit.

It’s easy to add new nodes to the graph (cards to the Zettelkasten) because the labels are hierarchical. When you add a new note, you conceptually add it as a new leaf to the tree:

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Its position gives you a unique label, and the label tells you where to put the new card in the card box. If you put related notes near each other in the conceptual tree, they’ll tend to be near each other in the Zettelkasten, as I demonstrate below. Technically, the tree is linearized into the card box with a pre-order depth-first search, which produces a topologically-sorted card order. Sounds way cooler than it is.

Adding notes (simplified version)

In this section, I’ll describe creating a Zettelkasten from scratch, showing how I decided where each note goes. This is a fictionalized version of what I actually did, but the titles and notes are real. I’ll pretend I was working with a physical card box, though I actually use Obsidian.

The first note

My first title was “We perceive events rather than snapshots.“ Lisa Feldman Barrett, “The theory of constructed emotion: an active inference account of interoception and categorization,” Social Cognitive and Affective Neuroscience, 2017. (Roughly, that means that the brain doesn’t constantly monitor perceptions. Rather, it treats the perceptual system as a sort of “smart peripheral” that it can ask to watch out for large-scale, compound perceptions – like when my hand is gripping a soda can firmly. When that happens, the Thinking part of the brain gets a notification of the event.)

Since this was the first entry, it got the label 1.1. (You’ll see why I used two digits later.) The figure below shows how I’ll represent the growing Zettelkasten. On the left is the conceptual tree (one node) and the contents of the card box (one card).

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The saga of note 1.1a

As a longtime computer programmer, there are certain distinctions I’m attuned to. One is between systems that require memory and those that don’t. Early ideas of perception had all the memory in the Thinking part of the brain. Later people like Barrett have pushed memory into the perceptual system. Using my field’s jargon, the pre-Barrett model of perception was of a pure function, but now it requires mutable state.

That seems worth writing down, so I created a new card and called it “Perception is stateful” (using the jargon of my field – remember, I’m only writing this for myself).

Where should I put it? Since this observation was derived from 1.1, it makes sense for the new note to be “below” 1.1 in the tree structure. Since it depends on 1.1 in a historical sense, it should depend on that note in the “to hang down” sense, har har.

There’s also a sort of part-whole relationship between “We perceive events rather than snapshots” and “Perception is stateful.” Any feature of perception (like the importance of events) demands something of perception’s implementation (like state), and we usually think of implementation as lesser than (“below”) features. In general, humans think higher things are better than lower things. There’s a reason heaven is up and hell is down, or that “the highest praise” is the best kind. See Metaphors We Live By, George Lakoff and Mark Johnson, 2003 (2/e).

Whatever my reason, the new note gets label 1.1a:

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The alternative would have been to make the new note a sibling. Let’s see an example of that.

1.1b vies for attention

Barrett has more to say about the perceptual system that’s worth recording. For example: “Perception proceeds in summarizing steps.“ The visual system is a good example. Inputs from the neurons in your retina get special processing to detect lines, edges, and basic orientations. The output of such processing gets fed to other areas that make summaries like “what objects are there in the scene?” and “what’s in front and what’s in back?”.

Summarizing is part of the mechanism for distilling perceptions into events, so it seems it should be somewhere below 1.1. Perhaps below 1.1a? But it’s not really a part of 1.1a’s claim that perception is stateful. The new claim is related, but not dependent. So I choose to make it 1.1b:

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The leftward arrow in the tree diagram reflects the relative positions of 1.1a and 1.1b in the imaginary card box. The arrows aren’t really needed, but I think they make the tree structure look nicer in this explanation.

1.1a1 joins the chat

Consider someone “in the zone” on a programming project or video game, who keeps on even as their bladder or stomach (or wrists) are complaining bitterly. ⊕ Not I would know anything about that, oh no indeed.

The brain has evidently decided that coding is more important than peeing. But does that mean the bladder is constantly sending “30% full,” “40% full,” “80% full” events that are being ignored? Some brain scientists think not. Instead, the brain implements “coding is more important than peeing” by telling the perceptual system (technically, the interoceptive system) to forward no bladder events until it’s at the “Dude, I’m way overfull and about to let go!!!” level.

The brain isn’t ignoring that the bladder is nearly full: it literally doesn’t notice.

So we have a perceptual setting that’s being tuned from outside the perceptual system. The new setting persists until changed. That means memory/state, again. Which suggests a new card below 1.1a – it elaborates on that card’s idea of state.

What to title it? Well, the brain’s adjustment only happens in certain contexts. The one that seems most relevant is what Mihali Csikszentmihalyi called “flow.“ “a state of concentration or complete absorption with the activity at hand and the situation. It is a state in which people are so involved in an activity that nothing else seems to matter.” – Wikipedia

That seems like a nice card title: “Flow involves tuning of perceptual levels.” Here it is:

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Browsing

The tree is now complicated enough that we can pretend to use it.

Suppose you’ve arrived at 1.1b, “Perception proceeds in summarizing steps,” for whatever reason. You don’t need an explicit link to know that its parent has label 1.1 and that there’s a sibling labeled 1.1a – the labeling scheme tells you that much.

You don’t know there’s a 1.1a1. But you can just flip to the card before 1.1b and look. The previous card will always be the last card in the 1.1a subtree (which might be 1.1a itself, but isn’t in this case).

Thus far, there aren’t more cards to the right of 1.1b. But if there were, you wouldn’t know if the first one was 1.1c or something else: perhaps 2.1. But all you have to do is flip the current card in the other direction and look.

In practice, when you arrive at a card in a new part of the Zettelkasten, you’re going to flip over its adjacent cards (in both directions), just to see if there’s anything interesting there. You’ll keep flipping as long as you keep being interested. Basically, you examine nearby subtrees until you get bored.

Electronic tooling makes that somewhat easier. For example, I took a few notes on a podcast episode that claimed that the concept of freedom evolved as a reaction to a new kind of widespread slavery. If I wanted to revisit that, I could ask my tool to show me the subtree:

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… and I can examine the nearby notes by clicking instead of flipping.

1.2 butts in

At some point, I started making other notes about the brain, starting with “The brain is associative.“ “Associationism is a theory that connects learning to thought based on […] the organism’s causal history. […] In its most basic form, associationism has claimed that pairs of thoughts become associated based on the organism’s past experience.” – Stanford Dictionary of Philosophy. I’m an associationist, which is why I think new ideas come from “juxtaposing” (or making an association between) two or more older ideas. Where should that go?

Let’s imagine we’re using a physical card box.

The new card doesn’t belong to the subtree under 1.1, since those claims are all about perception. Still… perception is something the brain does, and I’m claiming “maintaining associations” is another thing the brain does. So it makes sense to name the new note 1.2, thus putting it “next to” 1.1.

For fun, I’ll flesh out the 1.2 subtree with some of my other notes, producing this structure:

⊕ Remember, you can click to enlarge.

Location markers

It looks like the 1.X series of notes have turned into “where I put a bunch of claims about the brain.” It’s easy to remember that fact, given that so far there’s nothing but 1.X cards, but (as I write) I’m already up to 18.X. So pretend my Zettelkasten is both physical and far more mature, and that the brain claims were actually found in 13.1, 13.1a, 13.2, and so on. It might be handy to mark where those brain cards start:

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I’m not sure if Luhmann used such markers. Note that the brain note is labeled 13. I can do that because I follow Bob Doto’s suggestion (in A System for Writing) of making the topmost nodes of the form N.n.

I do something similar, which is a full note or long page that provides a rough grouping of all the top-level notes. Here’s the beginning:

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I don’t want to give the impression that the full note provides a nice categorization of all my topics. Remember: a Zettelkasten is “a mess with a non-arbitrary internal structure.” So, in the sidebar, you can see that the 4.x root notes are divided into two chunks, each labeled with a vague-ish group name. You can also see that I’m unconvinced that there are easily-labeled themes to the 5.x or 6.x groups or even, really, that there’s a distinction between them.

That’s OK. I’m not trying to “carve nature at its joints.“ The term is from Plato’s Phaedrus. When dividing a carcass, it’s easier to use a cleaver at the joints than in the middle of the bone. Similarly, when dividing nature into categories, there are natural dividing lines. I join with others in thinking that idea (or the equivalent desire for categories to have clear in-or-out conditions) is attractive but bogus. See Women, Fire, and Dangerous Things: What Categories Reveal about the Mind by George Lakoff, or The Big Book of Concepts by Gregory Murphy. This list of top-level title-links is just a convenience I mostly use to search for where to put new notes. (There will be more about searching and browsing in the next major section.)

22.1 upsets the apple cart

I read Csikszentmihalyi’s Flow: The Psychology of Optimal Experience some decades ago, and I probably still have it around somewhere in the house. Suppose I decide to reread it and take notes this time. Suppose the first resulting card is titled “Flow is complete absorption in an experience.” I would add it to the graph as follows:

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There’s a problem. I already mentioned “flow” in card 1.1a1. It now seems as if that card would better belong in the 22.1 hierarchy.

What do I do with it?

I do not move it. That’s not so much because putting a gap into the sequence of cards will be annoying and possibly confusing. It’s more because having a card disconnected from the “flow” tree is a benefit, not a problem. I’ll talk about that in the next major section. (Almost there!)

For the moment, I want to emphasize that adding a new card is not like adding a new species to a taxonomic tree. If you want to add a new species of trilobite to the fossil record, you know it will go within class Trilobita. It’s got big compound eyes, so it goes into the Phacopida (“lens face”) order. Its rather boring body places it in genus Flexicalymene. It’s different from the other known species of that genus, so you name it with a latinate version of your favorite childhood pet and call it a day. Don’t @ me, scholars of cladistics and the subtleties of biological classification. I know it’s not that simple. That it is, in fact, hard to impose a useful tree structure over an irredeemably messy world. Zettelkasten, in my interpretation, doesn’t much try. It embraces the mess.

Adding notes to a Zettelkasten is not trying to build a conceptual hierarchy.

Adding and using notes (creative version)

I’m interested in a particular intellectual approach called structuralism. People explaining it, especially in the context of literary criticism, will often use an example from Russian fairy tales. So it’s unsurprising my first note on the topic had the following text: I originally read this claim in Jonathan Culler, Structuralist Poetics: Structuralism, Linguistics and the Study of Literature, 2002.

Russian fairy tales are constructed from linearly-organized event types

This is the work of Vladimir Propp. [wikipedia link] He gives an ordered list of 31 events or situations, such that:

In a story, event m must occur before any event later in the list of 31. (No backtracking.)

Events may be skipped.

So the process of storytelling might be selecting a sequence of plot points – 2, 4, 5, 10, 18, 30 – which are then elaborated.

(This card is perhaps too wordy, containing facts I’d be unlikely to forget. That’s because I copied most of it from a draft podcast script about structuralism. I’m hoping extracting notes from the draft script will help me over the hump of turning it into a final script.)

The next step is to decide where to put it. I know structuralism is a new topic for my Zettelkasten, so it will likely be a top-level note. I could just give it an unused “major number” (19) and label the note 19.1. But that would leave it disconnected from other top level notes. Maybe I can find a top-level note that would make a good sibling?

When I look through the list of top-level title-links, I see this:

4.1 is intriguing. Clicking on the link shows this paragraph:

The claim here is that humans are built for listening to stories, so a persuasive narrative will have a “timelike” structure in addition to a logical structure.

Comparing that to “Russian fairy tales are constructed from linearly-organized event types,” I can see a loose connection: both are about a vague concept of “story,” and both are about sequences of events in time. So I’ll put my new note in the 4.x hierarchy. Since there’s already a 4.2, the new note will be labeled 4.3.

I could leave the link between the two implicit, but my habit is to document which sibling caused my decision, and perhaps why I thought I cared. (That latter is the same elaboration I might do for any title-link within a note.) So the top of the new note looks like this:

⊕ Click to enlarge.

Now that there’s a link from 4.3 to 4.1, there’s a question of whether it’s worth adding an explicit back link from 4.1 to 4.3. It’s not strictly necessary, since:

If I’m doing serious work with any claim, I should scan its siblings, just as a normal practice.
Obsidian makes it trivial to view the titles of all the notes that link to a given note.

So I only add explicit reverse title-links if it would be useful to expand on their text. In this case I chose not to. If I ever use the connection between the two, maybe I’ll change my mind.

But just adding a note isn’t the point

The act of adding a note would ideally prompt me to include relevant title-links in its text. Maybe there’s something useful to say about the (implicit) connection between the new 4.3 and the earlier 4.2? As it turns out, nothing came to mind after a brief scan of 4.2.

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But what’s more important is that looking at “nearby” notes can generate new ideas (and, thus, new notes). Because it was easy, I glanced at titles of the notes below 4.1. I found these two interesting:

4.1b: Narrative is about management of surprise
4.1c: Narrative has implicit back links.

Although these notes are directed to non-fiction narratives, it occurred to me that Propp’s model of fairy tales reads like a small child’s idea of a story: “and then this happened, and this happened, and then this other thing happened.” B-o-r-i-n-g.

If your only guide to writing Russian fairy tales was Propp’s model, you’d very likely write a bad one, because you’d be missing so much about what makes stories engaging.

That seems worth noting, so I created a new note, “Propp only included forward links in his model,” with title-links to the 4.1b and 4.1c claims. That was a matter of less than a minute. The new note automatically appeared in my “to be processed later” Inbox, so I was finished with it for now. No stopping a task in the middle to go off and finish a subtask for me, no sir – that way lies madness. In the software business, this is called “yak shaving.” The Mind Collection gives an example: “Imagine it’s your weekend and you sit at home trying to finish writing that important report for work. Your laptop battery dies so you need to fetch the charger from the office. You don’t have a key, though, so you call a colleague. He’s happy to help but he’s at his son’s basketball game. […] This is how you end up eating burgers and fries with a visibly proud dad and his son.”

I also decided to put a link to that new card on the original Propp note:

⊕

What I’d done made me think about structuralism more generally. I realized the other go-to introductory example of structuralism, Lévi-Strauss’s model of kinship, also has that feel of “as simple as possible and, in fact, maybe even simpler.“ “In every field of inquiry, it is true that all things should be made as simple as possible – but no simpler. (And for every problem that is muddled by over-complexity, a dozen are muddled by over-simplifying.)” – Sidney J. Harris

So I drafted a note titled “Structuralism tends toward minimalism” to elaborate on later. That’s more of a hypothesis than a solid claim. If I ever decide to use it in a proper narrative piece, I’ll do some more reading.

In sum, when writing notes, your goal should not just be to record the new claim, but to explore for a little while to see if somehow-related claims give you new ideas.

This production of new ideas is why I call Zettelkasten a “serendipity machine.” I’m thinking of “machine” in the sense of the basic machines of physics – the inclined plane, the pulley, and so on. They make tasks you could already do easier to do, and make possible tasks that would otherwise be beyond your abilities.

The task in question is being creative by bashing different ideas together. I’m already pretty good at making connections between disparate topics, but my Zettelkasten thus far seems to be making me better.

Other lists of title-links

It would be silly to be a stickler for a rule that every note must be a distinct claim. Early on, I felt the need to add summary notes, like this one:

Simmelian numbers

3 is the lowest number for social structures

ca. 7-10 – The maximum group size for a multi-sided conversation

30 is a formality threshold for speakers

75 is the breaking point for cult implosion

…

This is a collection of numbers and ranges that keep cropping up in sociology (at least according to Randall Collins).

When a source provides me a list of claims (like Ostrom’s nine principles for designing a commons) Ostrom’s career demolishes Hardin’s “Tragedy of the Commons.” Hardin is my go-to example of a theorist boldly asserting the flat impossibility of something people do all the time. But I digress. it would be silly not to copy it into the Zettelkasten.

These notes live in the same trees as those whose titles are claims. Ostrom’s note happens to have label 8.1, but it could also have been buried more deeply.

In addition to such notes, I also follow Luhmann in having a separate set of pointers from keywords to relevant notes. Here is a sampling of mine:

⊕

Note that it’s rather a hodge-podge. There are names of concepts or abstractions, like… Concept and Abstraction. There are whole technical fields, like Cybernetics. There’s technical jargon like Degeneracy (biology) or Bricolage. There’s even flat-out slang, like Grok (not shown).

I label the entire collection of such notes “Jargon” because I don’t want to give the impression (to myself) that I’m somehow Capturing the Platonic Essence of, say, “Aesthetics.” A Jargon note is humbler: just some annotated title-links to notes that have some relevance to a word or phrase. Here’s the Aesthetics note:

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When I create a new note, if I think it’s especially relevant to aesthetics (and if I remember I have a Jargon note with that title), I put an Aesthetics title-link on it. (This is like adding tags in many hypertext systems, including Obsidian.) That link automagically means a title-link to the note appears in the Inbox section of the Aesthetics note. At my leisure, and if it suits my fancy, I can pluck the title out of the Inbox and add a little context.

When searching for where to put a note (and finding some notes it should link to), I’ll occasionally use the Jargon notes in addition to my list of top-level title links. I also sometimes use full-text search.

I think what I’m calling Jargon notes have some important characteristics:

You create them when they’re convenient, not according to any fixed rule. If you want to get fancy, they emerge in the moment out of the complex interactions between a Zettelkasten and its human.
They strike a personal balance between discoverability and serendipity. You want to find particular notes easily, but not so easily that you don’t benefit from chance juxtapositions thrown up by your search. I expect the balance will depend a lot on the quirks of each person’s memory. (Mine seems to be worse than Luhmann’s was.)

My understanding is that Luhmann would sometimes browse his Zettelkasten with no fixed goal in mind. I can imagine such browsing as both throwing up juxtapositions but also maintaining his feel for the structure of his semi-structured mess. Memories are generally strengthened when they’re retrieved, so random browsing can avoid over-remembering frequently-accessed claims at the expense of forgetting the less-used ones.

Trails

A narrative, I said at the start of this post, starts as a linearized sequence of claims, possibly rearranged for purposes of narrative effectiveness. That actually echoes something from the very beginning of hypertext as a concept.

Vannevar Bush administered much of the government-funded research and development for the United States during World War II. He played a significant role in establishing postwar support for basic research. And he was the first popularizer of hypertext, in a 1945 popular magazine article. “As We May Think” The Atlantic Monthly, July 1945. One thing he emphasized there was associative trails, echoing in metal and optics what’s present in the brain:

The human mind […] operates by association. With one item in its grasp, it snaps instantly to the next that is suggested by the association of thoughts, in accordance with some intricate web of trails carried by the cells of the brain. It has other characteristics, of course; trails that are not frequently followed are prone to fade, items are not fully permanent, memory is transitory. Yet the speed of action, the intricacy of trails, the detail of mental pictures, is awe-inspiring beyond all else in nature.

He imagined users of his hypertext device, dubbed a “memex,” creating physical instantiations of mental trails:

The owner of the memex, let us say, is interested in the origin and properties of the bow and arrow. […] He has dozens of possibly pertinent books and articles in his memex. First he runs through an encyclopedia, finds an interesting but sketchy article, leaves it projected. Next, in a history, he finds another pertinent item, and ties the two together. […] Thus he builds a trail of his interest through the maze of materials available to him.

And people would purchase trails:

Wholly new forms of encyclopedias will appear, ready-made with a mesh of associative trails running through them, ready to be dropped into the memex and there amplified. […] The patent attorney has on call the millions of issued patents, with familiar trails to every point of his client’s interest. The physician, puzzled by its patient’s reactions, strikes the trail established in studying an earlier similar case, and runs rapidly through analogous case histories […]

There are trails in our modern hypertext documents, but they’re generally implicit. When reading Wikipedia, you can make your own trail, but there’s no tradition of making such trails permanent, something you could give to someone else. I think Bush vastly underestimated the importance of the “connective tissue” – narrative technique – that has to be added to a list of links to make it something people will read and benefit from. Writing this post would have been so much easier if I could have just dumped a list of claims onto you. Instead I spent a lot of time on the ordering and grouping of those claims, the tone of my exposition, and so on. That you’ve read this far suggests that was time well spent. Or that you’re made of more patient stuff than most.

But, since the purpose of a Zettelkasten is to support narratives – that is, trails of claims – its owner can make notes containing trails, notes that will be fleshed out into a proper narrative. (I can make a trail that’s meaningful to me much more easily than one that’s meaningful to some target audience.)

For example, I found it useful to preserve this trail:

What persuades scientists persuades us

Narrative is about management of surprise

Persuasion requires telling a persuasive story

… which I’ve titled “What’s the relationship of a Lakatos-style novel confirmation to narrative surprise?” Someday I can flesh that out into an essay or part of an essay. (I should probably add some text to the bare links before I forget what I had in mind.)

Note two things:

A trail is another list of title-links that provides a window into the full document.
Harvesting title-links for a trail will very likely provoke new claims because of the juxtaposition of old ones. Or it might suggest new topics to read up on.

A peculiar summary message

I took notes in exactly one class in college. (Abstract Algebra, I think.) I have since dabbled in note taking and note-taking tools off and on. Zettelkasten is the first one that seems at all likely to stick. Why?

A Zettelkasten document is “a mess with a non-arbitrary internal structure,” and I enjoy messing with that mess. It’s fun making linkages and especially fun when two notes spawn a new one.

Luhmann has a metaphor for that. He refers to the Zettelkasten as a communication partner. His “Kommunikation mit Zettelkästen,” linked above, is translated as “Communications with Zettelkastens.” In that paper, he speaks of “we”: “We (me and my Zettelkasten) obviously tend to think of systems theory […]” or “After 26 successful years with only occasionally difficult teamwork, we can report […]”.

Luhmann describes what’s needed for his Zettelkasten partner to keep holding his interest. The two words that stand out to me are “surprise” and “randomness”:

The Zettelkasten must be able to surprise by, metaphorically, advancing an unexpected claim. You don’t want a conversation where the Zettelkasten only ever repeats back to you what you told it last month.
Randomness is a mechanism that leads to surprise. It’s not that you don’t know what you’ll get when you ask the Zettelkasten about the claim on card 17.a3b8; it’s more that the Zettelkasten has the “yes, and” attitude. “A rule-of-thumb in improvisational comedy that suggests that an improviser should accept what another improviser has stated (‘yes’) and then expand on that line of thinking (‘and’)” – Wikipedia As you browse around (whether with a goal in mind or randomly), the mechanism should be such that you frequently think – at least glancingly – about the implications of two notes you’ve never looked at together (or haven’t for a long time, but your learning since then may interact with those past claims in new ways).

But that seems uncomfortably grandiose. Less imposingly, I think that for me, possibly for Luhmann, perhaps for other users of Zettelkasten, at least some of its appeal is that frobbing is fun.

Huh?

“To frob” is computer programmer jargon from the 1970s. As described in the Jargon File: “The original Jargon File was a collection of terms from technical cultures such as the MIT AI Lab […]” – wikipedia. A version edited by Guy Steele was published in 1983 as The Hacker’s Dictionary and was roughly this version. A later edition, The New Hacker’s Dictionary, seems to be widely considered by old-timers (including me) to have gone wildly astray.

Usage: frob, twiddle, and tweak sometimes connote points along a continuum. ‘Frob’ connotes aimless manipulation; twiddle connotes gross manipulation, often a coarse search for a proper setting; tweak connotes fine-tuning. If someone is turning a knob on an oscilloscope, then if he’s carefully adjusting it, he is probably tweaking it; if he is just turning it but looking at the screen, he is probably twiddling it; but if he’s just doing it because turning a knob is fun, he’s frobbing it.

⊕

⊕ Public Domain, 1793I’m sensing the feeling of frobbing as I work with my Zettelkasten. It’s fun to bounce ideas around. So, as Abraham Lincoln didn’t actually say: “People who like this sort of thing [playing with ideas in a generative way] will find this [Zettelkasten] the kind of thing they like.”

Comments? As part of my move to resurrect the Republic of Letters, I’ve established an email address you can use to reach me. Include a first-line salutation to me, “Brian Marick” (honorific optional), and I will reply as soon as the packet boat brings your missive to me.

Bright and dull cows (2025 remix)

Sun, 19 Oct 2025 10:01:12 -0500

Back in 2002, I published an article about how people learn “tacit knowledge,” using as an example how students of veterinary medicine learn a diagnostic category.

I’ve gotten a lot of mileage from that example over the years (in speeches and such), and I’d like to update the article, because there were some aspects I missed back then.

The topic

Veterinarians like to classify animals along three axes as a high-level overview. These axes are:

Is the animal bright or dull?
Is it alert or depressed?
Is it responsive or unresponsive?

Veterinary students are trained to accurately answer those questions. That is, for a given cow, a veterinarian trained at (say) Illinois will give the same answers as one trained at Ft. Collins.

How is that consistency achieved? The following is the training procedure as described to me by my wife, Dawn, who did such training for many years.

(Note: the description below has minor procedural differences from how things are done nowadays, but I don’t think any of them matter for this topic.)

Background

At the University of Illinois College of Veterinary Medicine, students spend their last year “rotating” through the various clinical services the teaching hospital offers. A rotation is two weeks long. That means that, every other Monday, all the students currently “on clinics” in the Food Animal section move to some other section (like Anesthesia or Exotic Animal Medicine), and a new batch of somewhere around six to ten students arrives.

Those students are there to soak up hands-on training. The existing cases “in the ward” are divided up among the new arrivals, and each new patient that arrives is also assigned to a student.

A good deal of the hands-on training is done by two or so interns or residents. These are people who’ve completed their Doctorate in Veterinary Medicine but are there to gain more experience (both hands-on and academic). They will demonstrate procedures to the students (on actual patients) and watch as the students try their hands at medicine. (“You’re going to have to push that syringe harder; remember, you’re punching through leather.")

There are, at a given time, one or two “clinicians” responsible for all these people. They are faculty members whose job includes spending some fraction of their time on clinics. Dawn was one of those people, and spent 50% or more of her time on clinics.

Clinicians, day to day, do the same sort of demonstrating and watching as residents and interns do. The difference is that clinicians have greater knowledge, experience, and responsibility if something goes wrong.

The setting for all this training is what looks like a large warehouse room: high ceilings, cinder block walls, various bulky machinery like headgates. The picture below shows the ambiance.

⊕

Training

The ward has a day-to-day routine.

Students arrive first. They look at their cases. For each case, they write up a SOAP (Subjective/Objective observations, Analysis, and Plan). As the name implies, the SOAP consists of observations of the patient’s state, the student’s interpretation of what that means disease-wise, and the student’s plan for what to do that day.

One thing that will be noted down in the SOAP’s subjective observations is whether the patient is bright or dull.

The attending clinician (Dawn) will wander onto the ward at some later, leisurely hour (0800, for example) and lead everyone in morning rounds. That means that everyone gathers around a stall to hear the student present the case.

For some reason, students tend to err on the side of judging a dull animal to be bright. Say the first student (nowadays most likely a “she”) does that. Dawn would correct her, saying (perhaps) “No, that cow’s dull. See: she’s not cleaning her nose.“ Cows clean their noses with their tongues. It’s weirdly charming. Here’s a video.

You can imagine the students furiously memorizing a rule:

NOT cow-cleaning-nose => dull

Then the group moves to the next stall. Let’s say this cow is bright, but her student has marked her as dull in the SOAP. So:

Dawn: No, this cow is bright.
Student: But she’s not cleaning her nose! You just said…
Dawn: But her ears are perky.

You can imagine students creating a new ruleset:

NOT cow-cleaning-nose AND NOT ears-perky => dull
cow-cleaning-nose => bright
ears-perky => bright

This process continues with other animals and during other rotations. Eventually, the students get good enough at evaluating bright vs. dull. What’s interesting is that, by then, they’ve lost the rules. What was once effortful and algorithmic is now perceptual and automatic. They can see things you and I do not.

My reflections and conclusions

I think it likely that this ability to perceive dullness is built on something innate. I bet most parents know the experience of looking at a child and thinking “She’s getting sick.” In my recollection, it’s something about the eyes. I suppose that innate ability is repurposed in veterinarians.

However, Dawn points out that students have trouble identifying dull cows until they’ve seen enough healthy (that is, bright) cows, which argues (I think) against my claim.
One might believe that the students have accumulated a good suite of rules and simply apply them unconsciously. That is, “losing the rules” means losing awareness of the rules, not the rules themselves. But that’s an assumption – a belief system, really – not an evidence-based conclusion. I choose to credit the self-reporting of experts.
I don’t imagine that Dawn, when challenged about why a cow is bright, accesses a rule like perky-ears => bright. Rather, her brain is scrambling to invent an answer, latches onto something that seems salient, and presents that as the reason. But it’s an output of the decision mechanism, not a part of it.
I further suspect that perky-ears => bright is not presented so much an explanation as a way to get the “why? why? why?” portion of the student’s brain to shut up while some other brain mechanism does the actual learning.

That is, the lesson of “Look at her ears. They’re perky” is more about making the ears salient for perception than it is about building mental categories of ear-types.

Essentially contested concepts – a catchy idea without a catchy name

Tue, 14 Oct 2025 20:15:44 -0500

What does it mean to be a good Christian? How do you decide whether something someone made is art or not art? If you say you’re practicing Agile software development, and I say you’re not – that you’re missing the point – where do we go from there?

The answer to the last question, in my experience, is: nowhere, and fast. But we don’t have that problem with questions like “is that tree an elm?” or “is light a particle or a wave?” Why not?

I recently stumbled across a paper that tries to answer that question. Since I’m exploring using a Zettelkasten method for writing nonfiction narratives, I thought it’d be useful to turn the notes I took on it into a blog post.

What’s in this for you? Understanding “essentially contested concepts” might save you some time that would otherwise be spent fruitlessly – or alert you to a different way to learn what you think.

The paper is “Essentially Contestable Concepts,” by W. B. Gallie, from 1956. There’s also a Wikipedia article, but I don’t like it much.

I should warn you that this is my elaboration of Gallie’s idea, infected by my own particular quirks and beliefs. I don’t think an expert would think I’m wildly wrong, though.

Concepts with value

People have been arguing about what characterizes a good Christian for over 2000 years, and there’s still widespread disagreement. In comparison, the question of whether light is best described as a particle or a wave has been settled, and quite speedily (relatively speaking).

The reason is that light wouldn’t be a better thing if it were a particle instead of a wave (or vice versa). And only a vanishingly few people would think saying “Um, that’s actually an elm, not an oak” is intended to make them think worse of the poor tree.

That’s very much not the case for statements like “she’s not a real Christian” or “you call that art?” Essentially contested concepts are strongly tied up with ideas of value. If something fits within the concept, it’s good. If it doesn’t, it’s bad.

To repeat the philosopher Richard Rorty: Contingency, Irony, and Solidarity, p. 73

All human beings carry about a set of words which they employ to justify their actions, their beliefs, and their lives. These are the words in which we formulate praise of our friends and contempt for our enemies, our long-term projects, our deepest self-doubts and our highest hopes.

Rorty referred to that set of words as a person’s final vocabulary – not, I have to say, the greatest coinage ever.

Essentially contested concepts aren’t, analytically, exactly the same concept as a final vocabulary (I don’t think), but there’s a lot of overlap, especially the centrality of value or emotional reaction. Even something as inconsequential as the way you do software development is freighted with value. You can see that from the very word “Agile”: of course my team is Agile. What’s alternative? We’re torpid? I’m not saying that associating an approach to a word with positive connotations is what makes “being Agile” a term of praise. I’m saying the pre-existing opinion that such approaches are good made it natural to label them with a word like “agile,” especially since the previous jargon was “lightweight methods,” and “lightweight” (at least in American English) signals disapproval.

Concepts with history

Gallie’s origin story for an essentially contested concept starts with exemplars or foundational examples. For Christianity, the most important exemplars are Jesus, as described in the Gospels, and the apostles, perhaps especially as described in Acts. No one would say that Christ behaved in an unchristian way. Moreover, when faced with a moral problem, “What would Jesus do?” is an entirely normal approach to solving it.

Similarly, when discussing whether a piece of music is art or not, reference will be made to characteristics of pieces (most) everyone agrees are exemplary: “you can see this piece is in a tradition dating back to Haydn and his innovations in the classical style.”

Agile, as a concept, was also built from exemplars. The Chrysler Comprehensive Compensation System was that for Extreme Programming (and Agile in general). Ken Schwaber used his first Scrum project as an exemplar in his training. In my own consulting, I told stories of how the “Scrum master” and product owner for a particular Scrum team acted.

But concepts don’t remain stable. The associated approaches, problem-solving techniques, and ways of thinking change over time as the concept is applied to new circumstances. What it meant to be a Christian changed as the faith moved from being a Jewish splinter group to the state religion of a mighty empire. Jesus and the Apostles didn’t face the question of what it means for the leader of a Roman army to be Christlike. The Apostle Paul didn’t need to invent Just War theory because he wasn’t personally faced with reconciling “thou shalt not kill” or “Prince of Peace” to inevitable civilian deaths.

And “Agile” weathered the shift from custom in-house apps to shrink-wrap software and web deployment without (we thought) changing in a fundamental way – just as my father’s understanding of the concept “hammer” didn’t change as the handles shifted from smooth wood to plastic with an especially grippy surface.

Parts

So far, essentially contested concepts don’t seem much different from any old concepts. My sense is that tying concepts to exemplars was somewhat unusual in 1956, but it’s pretty commonplace today. It’s called prototype theory, which originated with Eleanor Rosch around 1971. Two semi-popularizations are Women, Fire, and Dangerous Things (1987) and the whimsically titled Big Book of Concepts (2002). Here’s an example of prototype theory: when I was growing up, Playboy publisher Hugh Hefner presented as the prototypical bachelor, and his characteristics (very into high-fidelity stereos and jazz, etc.) were those of the prototypical bachelor. Before Hefner, the prototype was different. Some time after him, it seemed to become the typical reader of Maxim magazine (which I am surprised to find still exists). I have no idea who the prototypical bachelor is now. One possible difference between prototype theory and what Gaille describes is that his concepts are described as being derived from prototypes, whereas the “bachelor” example shows that concepts have prototypes, ones that can change while the concept stays stable (enough).

Gaille zeroes in on a key property of the essentially contested concept: it has structure, it contains parts. Consider Agile. It almost definitionally has four parts, four values:

[W]e have come to value:

Individuals and interactions over processes and tools

Working software over comprehensive documentation

Customer collaboration over contract negotiation

Responding to change over following a plan

That is, while there is value in the items on the right, we value the items on the left more.

Christianity has its parts, too. There’s the red-letter parts of the Gospels (Jesus' quoted words), perhaps especially the Sermon on the Mount. There’s the Book of Revelation. There’s the Apostle Paul’s letters explaining doctrine to far-flung congregations. There are parts of the Old Testament that have been retained, and others that have been superseded. And so on.

The key thing about the parts is that different people emphasize different parts. That doesn’t mean they reject some of the parts: they just don’t pay as much attention to them.

When Martin Luther translated the Bible into the vernacular, he was pretty dubious about the value of the Book of Revelation. Modern Protestant US evangelicals give it much, much more weight, frequently treating it as advice for navigating the near future.
There’s been a long debate within Christianity about whether people should pay more attention to Paul (“For we maintain that a man is justified by faith apart from works of the law”) or James (“So too, faith by itself, if it does not result in action, is dead”).
Was Jesus a woke soy boy (Sermon on the Mount) or a manly avenger (Revelation, killing a fig tree, the moneychangers in the temple, in the lineage of David)?
Was Christ primarily a fulfillment of the Old Testament or did He primarily represent a New Covenant?
Both the Old and New Testament have a lot to say about supporting the poor and mostly negative things to say about the rich. But there are passages that suggest faith will be rewarded here on earth, not just in the afterlife, which is appealing to those not thrilled with the verse “go, sell your possessions, and give the money to the poor, and you will have treasure in heaven.”

The important thing here is that choosing one side of a controversy doesn’t reject the other side. A Paulite doesn’t deny the book of James, but rather feels that Paul is more essential to Christianity, so the people who disagree are missing something they oughtn’t.

Agile has had a similar (though less consequential!) dynamic. As a consultant, I found that teams who resonated most to “individuals and interactions” were quite different from those focused on “working software.” I’d say the latter teams were generally more Agile, but that’s because I share their priorities. Individuals and interactions matter, but (in the words of someone who didn’t want to be cited) “sooner or later, at the end of the day, someone has to sit down and write some damn code.”

Moreover, I’ve seen a perhaps-subtle but important difference between teams that interpreted “Customer collaboration” as directed toward end users (outside the company) vs. toward company management. I’d say early Agilists tended to be people with something of a “problem with authority,“ Weirdly, given how things have turned out, early Scrum was much more aggressive toward management than, say, Extreme Programming. coupled with something of a protective attitude toward the users. Being “relentlessly focused on business value” was something of a later development (an evolution of the concept of Agile) that I personally felt became overemphasized. (And it’s become especially awkward in this age of enshittification, where business value tends to be actively opposed to end user value.)

Are you bristling a little at my implication that teams nowadays let “the suits” push them around? Well… welcome to the world of the essentially contested concept.

But more importantly, notice that we both (probably) agree on two principles:

We should be responsible for what our work does for (or to) our customers.
We’re being paid to produce value for the business, not code.

What differs is where we place our emphasis. That means:

Arguments about whether a particular team is Agile, or a particular person is a Christian, come down to arguing about who’s got the right emphasis (even if we often don’t realize that’s what we’re arguing about – always a recipe for a productive conversation).
So arguments about essentially contested concepts have the form “of course you should care about both A and B, but you should care about B more than A.” That’s a hard argument to make because we’re talking about preferences. People don’t adopt preferences because they were reasoned into them, and it’s hard to reason someone out of a position they weren’t reasoned into.
Especially if those preferences are themselves a final vocabulary or an essentially contested concept. My favoring the end user is tied to a fundamental belief that you should take the side of the person with less power. My disfavoring of management is because of my vaguely anarchist belief that relations of domination – “you have to do this because I tell you so” – are typically unjust. That led me to describe Agile as being, importantly, “team-scale anarcho-syndicalism.” That resonated with at least some prominent early Agilists.

But people can change

The dominant understanding of how scientists make decisions is “falsifiability”: you should provisionally believe in a scientific theory so long as it survives experimental tests. In a slogan: a theory can never be proven, but it can be disproven. The wikipedia description. Falsifiability is primarily due to Karl Popper and his Logic of Scientific Discovery. His description is more subtle than I’ve presented it, but still (I think) wrong for the reasons given below.

The philosopher of science Imre Lakatos observed that real scientists don’t behave like that. For example, the Astronomer Royal of Britain regretfully informed Isaac Newton that his new theory of gravitation was inconsistent with the measured movement of the moon. Refutation!

However, Newton failed to abandon his theory. Instead, he invented a new theory – of optics – and told the Astronomer Royale that if he used the new theory to adjust previously-recorded observations, he’d see that the adjusted numbers would match Newton’s earlier theory.

It turns out the numbers were closer, but still off. I don’t know if that was known in Newton’s time. The point is that, when it did become known, no one did anything about it. The puzzle remained, mostly ignored, until it was discovered that the moon’s center of mass is offset from its geometrical center, which explained the discrepancy.

Lakatos observed that it’s pretty rich to be saying that Isaac Newton wasn’t doing science right. I described Lakatos' ideas in an ancient blog post, “Imre Lakatos and Persuasion.” The main text is his The Methodology of Scientific Research Programmes. There’s a concise and good description in For and Against Method.

It turns out that scientists adopt new ideas not because of a lack of refutation, but because of the presence of an impressive (“novel”) confirmation. In the case of gravitation, the doubters conceded when Edmund Halley predicted the return of the comet that now bears his name to a previously-inconceivable degree of precision.

I believe that a pleasurable surprise at seeing something put to effective use motivates more than just scientists.

Anecdote: once I was consulting for a financial services firm. The team was having a meeting wrestling with some questions about how a new feature for some internal software should behave. The meeting was going nowhere, slowly, when I suddenly said something like, “Wait. The users of this software are sitting, what? 100 feet? 200 feet? – from where we are right now. Why don’t we just ask them?”

We did. It turned out what the users actually would be happy with was way simpler than what the team had been planning to deliver. The old design was scrapped, a fun design session happened, and everyone left happy.

Two observations:

I demonstrated the practical value of emphasizing the end user in one’s thinking, and I like to think that shifted the team’s understanding of Agile in my direction. All without argumentation.
It was because of what “parts” of Agile I consider more important that I reflexively looked to the user when solving problems. So, while I’m more of a “working software” guy, I used a particular bias to spark the right kind of interaction with the right individuals.

Yay me! (I omit the story of when proposing a more ambitious version of the same idea got me abruptly ejected from a consulting gig. That was less fun.)

Should we stop arguing?

Gallie says not. (You were expecting a philosopher to come out against argumentation?)

When I argue with you about Agile, or Christianity, or Art, my goal may be to convince you, but the practical effect is to help me zero in on the parts of the concept, to understand them better, and to learn how to put them to better use in my own activities. If I’m alerted to how important serving the user is to me, I’ll figure out how to do it better.

Gaille has other observations about argumentation. I find them less convincing, so I’ll let you read his paper for yourself.

The stirring conclusion

I don’t know that I have one. Maybe I can offer the same advice people give to writers: show, don’t tell. Instead of decreeing that someone else is or isn’t a Christian, concentrate on being visibly Christian yourself, according to your own understanding. If people see you as someone worthy of emulation, they’ll adjust their own (possibly tacit) understanding of that essentially contested concept.

Always ask what your abstraction has abstracted away

Wed, 08 Oct 2025 10:25:50 -0500

A little lesson from Wikipedia.

(Note: fear not. The second installment in the hypertext series is coming along. It’s long.)

There’s a psychology concept called “social proof.” Wikipedia Roughly, it means that people are more likely to do X if they know other people are doing X, even if that’s irrational.
It and other cognitive biases, Wikipedia became quite an intellectual fad this century as Kahnemann and Tversky’s “Heuristics and biases” “The Many Schools of the Great Rationality Debate”, Jared Peterson. research programme made it into the business-books-section-of-the-airport-bookstore.
Wikimedia sometimes puts fundraising blurbs on their pages. They invariably point out how few people donate: “… fewer than 1% of readers give.”
This is the opposite of what social proof would predict. Many, many people have apparently pointed this out to the Wikimedia people, who note “The online fundraising team has tested, dozens of times, removing this fact from our materials. Our donation rate drops when we try.” Wikimedia 2018/2019 fundraising report
The amusing thing is how many people felt the need to correct the fundraisers based on what they’d read of a generalization based on tests done on undergraduates in highly artificial conditions.

Note: I closed the tab that inspired this post, and have forgotten who deserves credit. Maybe Jared Bernstein? UPDATE: It was Bernstein, in Psychology Experiments Are Gardens, Not Digsites

Hypertext 1: Wiki traditional

Mon, 22 Sep 2025 16:10:45 -0500

Hypertext documents vary a good deal, so statements beginning “Hypertext is…” are likely to obscure more than they reveal. In three posts, I’ll discuss the dominant style (“wiki traditional”), one that flips the emphasis (“Zettelkasten”), and how well two metaphors (“garden” and “rhizome”) work for each. My premise is that if you understand what you’re doing when you write a particular kind of hypertext, you’ll do it better.

An exemplar

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Although I’m tagging the first type “Wiki traditional,” I’ll actually use a book as my exemplar. That book is A Pattern Language: Towns, Buildings, Construction by Christopher Alexander and colleagues. Although it sits before me as a printed book, it’s hypertext in that it consists of a number of discrete titled texts organized non-linearly, connected with links.

The book contains 253 numbered texts (called “patterns”) to be used by people constructing towns and buildings. The texts are usually several printed pages long. Each text has a numbered title, ranging from “1. INDEPENDENT REGIONS” to “253. THINGS FROM YOUR LIFE.” Because the book is a paper document, a text links to another text by mentioning its title. Here’s an example of a sentence containing two links: Titles, such as those at the head of a pattern’s text, have the numbers first, whereas link text puts the numbers last. The numbers-first style makes scanning for a matching number easier, and the numbers-last reads better in blocks of text with multiple links.

The maximum is a cottage – like a TEENAGER'S COTTAGE (154), or an OLD AGE COTTAGE (155) […]

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To follow the first link, you could go to the table of contents, which lists patterns in numerical order, to find the page number of pattern 154, or (more likely) you’d note that you’re reading text “141. A ROOM OF ONE'S OWN,” which means that 154 is not much deeper in the book. So you flip over a hunk of pages, look at the top of the page you’re now at, which reads “158. OPEN STAIRS,” then page back a bit until you get to 154.

The most common title is a noun phrase like the ones above. Some are more abstract, like “190. CEILING HEIGHT VARIETY,” but they’re still “noun focused.” Even ones like “208. GRADUAL STIFFENING” or “63. DANCING IN THE STREET” use gerunds: that is, verbs acting as nouns. There are exceptions, like “40. OLD PEOPLE EVERYWHERE” and “205. STRUCTURE FOLLOWS SOCIAL SPACES,” but they’re scarce. Overall, the titles refer to places (more generally: “things”) and the texts talk about how to create such things.

The overall structure is what I’ll call “roughly hierarchical with two way links.” The idea is that you, the reader, want to learn how to construct something. Let’s suppose you’re a city planner who’s been given the job of reconstructing an unhappy neighborhood to make it better for the people (a “subculture”) who live there. You’ve read 31. PROMENADE, whose summary reads:

Each subculture needs a center for its public life: a place where you can go to see people, and to be seen. (emphasis in the original)

That seems a useful place to have, but how do you design it? When I went to Bologna many years ago, it was rather charming to watch little old people promenading around a public square just outside my hotel. So maybe you want one of those. To learn about it, you can follow a link to 61. SMALL PUBLIC SQUARES. There actually isn’t a direct link from 31. PROMENADE to 61. SMALL PUBLIC SQUARES – you get there indirectly via 30. ACTIVITY NODE – but let’s ignore that. I suspect omitting the direct link was a mistake. It’s hard to keep track of backlinks manually.

61. SMALL PUBLIC SQUARES has a discussion of what makes public squares work. After that, there are suggestions for possible (or mandatory) constituent parts:

[…] build buildings around the square in such a way that they give it a definite shape […] BUILDING FRONTS (122), STAIR SEATS (125); and to make the center of the square as useful as the edges, build SOMETHING ROUGHLY IN THE MIDDLE (126)…

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You can follow those links to further decompose the parts into subparts. For example, 126. SOMETHING ROUGHLY IN THE MIDDLE recommends that the something have a SITTING WALL (243).

So the structure around 61. SMALL PUBLIC SQUARES looks like this:

⊕ All images can be clicked to see a larger version in a new tab.

As p. xii puts it:

Each pattern is connected to certain “larger” patterns which come above it in the language; and to certain “smaller” patterns which come below it in the language. The pattern helps complete those larger patterns which are “above” it, and is itself completed by those smaller patterns that are “below” it.

Notice that the things described can be abstract (an “activity node”) or concrete (a wall to sit on).

Generally, if a text links to another text, that other text will link back. For example, 125. STAIR SEATS (linked to from 61. SMALL PUBLIC SQUARES) begins:

… we know that paths and larger public gathering places need a definite shape and a degree of enclosure, with people looking into them, not out of them – SMALL PUBLIC SQUARES (61), POSITIVE OUTDOOR SPACE (106), PATH SHAPE (121). Stairs around the edge do it just perfectly; and they also help embellish FAMILY OF ENTRANCES (102), MAIN ENTRANCES (110), and OPEN STAIRS (158).

There can also be side links between two parts at the same “level” whose designs influence each other. For example, 65. BIRTH PLACES points sideways to HALF-HIDDEN GARDEN (111) and GARDEN WALL (95). You can can think of these links as saying: “If you choose to include a birth place, the mother’s desire for privacy when strolling with the child increases the desirability of a half-hidden garden or garden wall.” Side links emphasize the importance of iterating the mutual design of places when they’re at approximately the same level of scale.

That covers the parts out of which a particular hypertext document was built. But what of the end result? The introduction describes the individual patterns and the whole assemblage with words like “whole”, “coherent,” “alive,” “the core of the solution,” “clarity,” “complete,” “the heart of all possible solutions,” “essential,” “invariant property,” “properly,” “deep and inescapable,” “well-formed,” “true,” “profound,” “totality,” “human,” “natural,” “joyful,” “archetypal,” and “deeply rooted in the nature of things.”

That is, A Pattern Language fits into two long-standing intellectual/emotional worldviews: Platonism and structuralism.

Platonic idealism

Plato’s Theory of Forms holds that there are two “worlds.” One is the one we perceive, which is incomprehensibly complex. The other contains “Forms” or “Ideas” that cannot be perceived but only understood rationally. They are timeless, unchangeable, absolute, non-physical – choose your adjective – essences that are “behind” the world we see. For example, there are many triangles, but they are all reflections or emanations of a single, eternal and perfect Triangle. Emotionally, the Triangle is more real than any individual triangle.

Mathematics is the rational study of some of those Forms. As Davis and Hersh put it in The Mathematical Experience, as of 1981 the official word on mathematics, post-Hilbert, was that mathematics is formalist. That is, math is the study of the results of transforming sequences of symbols using a set of rules, without regard to what the symbols represent. “[Mathematics is] not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess.” – Alan Weir, 2014 However, they also say that working mathematicians are nevertheless secret Platonists: a commutative semigroup is a real thing, somewhere “out there.”

Alexander’s rhetoric of “the core,” “the heart,” “archetypal,” and “deeply rooted” is straight-up platonism. 61. SMALL PUBLIC SQUARE is a real thing that can be implemented or instantiated well or poorly (and any individual public square has no effect on the reality and unity and properties of the Ideal PUBLIC SQUARE).

This platonism is true both of individual patterns and the entire document. After all, the companion book is called The Timeless Way of Building. (My emphasis).

Structuralism

Structuralism is a methodology for inquiring about and describing human thought that seems so natural to STEM people like myself that it’s weird to think there could be any other way to do those things. Nevertheless, it only became thought of (in the West) as a distinct school of thought in the early-to-mid 20th century.

Broadly, you might be a structuralist if you thrill to diagrams like the following:

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That’s my redrawing of anthropologist Claude Lévi-Strauss’s analysis of kinship relationships in female-donating societies. These are societies where marriage is formed when one man gives his sister or daughter to another man. I won’t explain the diagram except to say that he discovered that if a relationship between a particular pair of family members is “warm,” a different relationship must be “cold.” In the image, because mom and dad have a cold relationship, brother and sister must have a warm one.

In Lévi-Strauss’s Structural Anthropology, he credits the linguist Nikolai Trubetzkoy with writing down structuralism’s four basic principles or “moves.“ Structuralism originated in linguistics and then spread to other fields like literature, anthropology, and even mathematics (via the Bourbaki collective). My paraphrase follows, with what I want to emphasize in bold.

Conscious behavior (such as producing sentences) is supported by (or driven by) unconscious structures. More important than actually studying a language’s grammar is studying the underlying structures that control which grammatical rules you absolutely will find in a language, which rules might be found, and which definitely won’t be found.
What matters is relationships between entities, not properties of the entities themselves. The father’s character doesn’t matter in Lévi-Strauss’s theory of kinship; what matters is his relationship to his wife and his son.
The purpose of the work is to tease out the underlying structure. That’s a little circular: “structuralism is about structure.” So I’ll say what it means is that you should describe all the relevant relationships and how the relationships relate to each other. In the case of Lévi-Strauss, that means discovering rules like “mom-dad relationship must be the opposite of brother-sister.”
A structuralist theory must explain multiple real-world examples. Trobriand culture is matrilineal, and Tonga culture is patrilineal; Lévi-Strauss’s kinship diagrams work for both.

Reading backwards from (4) to (2), I argue that A Pattern Language is a product of a structuralist investigation. A large number of examples were boiled down to a set of 253 rules (or patterns) that could be used to create a variety of new examples that would exhibit properties of liveness, completeness, etc. That covers points (4) and (3).

(2) is not as strong. The entities are texts with titles like 180. WINDOW PLACE or 98. CIRCULATION REALMS, and most of the words in the text are used to explain what the title means and how to achieve it. That’s a focus on entities, not on relationships.

However, the links are given some weight, especially because they’re typed. That is, the reader is informed (or can easily infer) what she’ll get if she follows one. For example, you know that links at the beginning of a pattern point upward from a part to larger wholes. Downward and sideways links are generally found at the end of the pattern. And the words surrounding a link describe why the reader might want to follow it. Here, for example, is the end of 116. CASCADE OF ROOFS:

Make the roofs a combination of steeply pitched or domed, and flat shapes – SHELTERING ROOF (117), ROOF GARDEN (118). Prepare to place large rooms in the middle – CEILING HEIGHT VARIETY (190). Later, once the plan of the building is more exactly defined, you can lay out the roofs exactly to fit the cascade to individual rooms; and at that stage the cascade will begin to have a structural effect of great importance – STRUCTURE FOLLOWS SOCIAL SPACES (205), ROOF LAYOUT (209)….

These words hint at the relationships between places (or entities), so I’ll say A Pattern Language exhibits structuralism.

Influence

The original wiki was created by Ward Cunningham, someone quite familiar with A Pattern Language, and it had many of the same properties (such as a preference for noun-phrase titles).

That wiki in turn influenced later wikis like Wikipedia. Here are similarities and differences between Wikipedia and A Pattern Language:

Wikipedia is also about things. Here are three random Wikipedia pages:

Peter Coleman (sailor)
Saltash with the Water Ferry (a landscape painting)
Ridazolol, a drug.

From the Saltash page, you can follow the following inline links: landscape painting, Joseph Mallord William Turner, a bunch of links to descriptions of places like the English Channel and Devon, a English political category (county town), the concept seaside resort, and so on.

Noun phrases all over the place.

Wikipedia also mixes levels of abstraction. The first sentence of the Peter Coleman entry reads “Peter J. Coleman is an American competitive sailor.” Coleman is a concrete example of a general (platonic) category.

Pages also strive for completeness. There’s not a second Wikipedia page titled “More facts about Peter Coleman,” any more than A Pattern Language has a 117. MORE STUFF ABOUT ALCOVES.

The entire document pushes toward completeness. That’s inherent to the whole idea of an encyclopedia. The original encyclopedia, the Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, par une Société de Gens de lettres was “a collaborative collection of all the known branches of the arts and sciences of the 18th century French Enlightenment” (my emphasis). Its goal was “to create a method of systematizing and organizing all legitimate information and knowledge as well as make easier and more efficient the unearthing of more knowledge.”

Links are similarly typed in the sense that a reader will know what’s coming when she clicks on a link. As with A Pattern Language, it’s the surrounding words that gives the clue. For example, the link from Peter Coleman to competitive sailor is an is-a link. The next three links are equally predictable: “Peter and his brothers Paul Coleman and Gerard grew up in Larchmont, New York close to Horseshoe Harbour…”

Wikipedia is more completist than platonic. I’m not sure you can avoid platonism when you’re defining a noun phrase, but it’s notable that Wikipedia authors are happy to include information that Plato would in no way consider part of the essence or Ideal Form of, say, the German Shepherd. Such as this:

The Orthopedic Foundation for Animals found that 19.1% of German Shepherds are affected by hip dysplasia.

Is hip dysplasia part of the essence of Shepherd-dom? (Platonism has a lot of trouble with properties that are not either/or, true/false.)

Wikipedia is only shallowly structuralist. Structuralism favors minimalism (as does Platonism): it’s not enough to describe entities and their relationships; ideally, you want a minimal set.

In contrast, I very much believe that the Wikipedia style of writing hypertext (the one I use myself in my own wikis) consists of writing a sentence without caring about hypertext, and then saying to yourself “Ooh, I should change these few words into a link.”

The difference?

A Pattern Language and Wikipedia are pretty similar, but I think a reason for their differences is important:

Wikipedia is truth-presenting, whereas A Pattern Language is goal-directed.

A Pattern Language expects its audience to want to design. The main reason I’m so fond of A Pattern Language is that, once upon a time when Dawn was out of town, I used it to redesign our front room, using patterns like Window Place and Circulation Realms and Light on Two Sides. And it worked! (How often can you say that about something you read in a book?) By “work,” I mean that a space that both family and guests at parties avoided became a place people gravitated to. It’s going on three decades, and I still spend hours every day in my Window Place.As a result, many of the its links are obligatory – if you want to build something, you have to follow links from wholes to parts (and, sometimes, parts to adjacent parts), all the way down to 240. HALF INCH TRIM and 246. CLIMBING PLANTS.

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⊕ Public Domain, 1793In contrast, it’s perfectly possible to read a Wikipedia page without following any links, assuming you have a good enough understanding of the related topics that links point to.

Next: Zettelkasten

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A proposal to resurrect the Republic of Letters

Sat, 06 Sep 2025 18:26:05 -0500

I propose resurrecting the old-time Republic of Letters to encourage more thoughtful writing.

“The Republic of Letters was the long-distance intellectual community in the late 17th and 18th centuries in Europe and the Americas. It fostered communication among the intellectuals of the Age of Enlightenment.” – wikipedia

Many names you’ll recognize were participants in the Republic of Letters. For example, Gottfried Wilhelm Leibniz, perhaps the last true polymath, wrote tens of thousands of letters.

A great deal of important thinking was done through such correspondence. For example, Leibnitz and Samuel Clarke exchanged five letters apiece as they refined differing positions on Newtonian mechanics. (There would have been more, but Leibnitz died.) You can read them in Clark’s 1717 book, A Collection of Papers, Which passed between the late Learned Mr. Leibnitz, and Dr. Clarke, In the Years 1715 and 1716.

Was the Republic of Letters so fantastically successful because the authors lucked out by being alive at the beginning of the modern age, when there was so much low-hanging fruit to harvest? Or was there something about the affordances “In design, affordance […] refers to possible actions that an actor can readily perceive.” – wikipedia My claim is that the ancient letter-writing infrastructure nudged people away from unproductive activities (shitposting, snark) toward productive ones (inventing calculus).of that particular form of communication that fertilized creativity? I suspect so.

Given that I’m unhappy with all the modern varieties of “collective sense-making” available to us now, perhaps an experimental revival is in order.

I haven’t researched the topic deeply yet, I have two books on order: The Republic of Letters: A Cultural History of the French Enlightenment, Dena Goodman, and Impolite learning: conduct and community in the Republic of Letters, 1680-1750, Goldgar.but I’m struck by some likely-important factors:

Letters took a long time to get to their recipient (how long, on average, I don’t know yet). This removes the pressure on the recipient to reply promptly – the sender isn’t waiting on you.
Perhaps as a result, letters are fleshed out. Dr. Clarke’s fifth reply starts as follows:

As Multitudes of Words are neither an Argument of clear Ideas in the Writer, nor a proper means of conveying clear Notions to the Reader; I shall endeavour to give a distinct Answer to this Fifth Paper, as briefly as I can.

You can see what “briefly” means by clicking the link above. He’s being thorough. (To be fair, the ancients had very different ideas of brevity than we do.)
(I think) replies were more in the nature of blog posts inspired by the sender than quoting little bits of the letter and then addressing each as a separate unit, making for no kind of coherence. (The dreaded “fisking" Fisking: “A rebuttal to an article or blog made by quoting its content in sections and refuting each section individually.”that originated in email replies and polluted the “blogosphere" “The blogosphere is made up of all blogs and their interconnections. The term implies that blogs exist together as a connected community.” – wikipedia back in the day.)
The letters weren’t broadcast, they were person to person. That’s not to say copies weren’t made. I expect letter senders kept copies (especially if they employed clerks to make fair copies of the letters) and I believe it was not uncommon to attach a copy of a letter from person X in a letter to person Y.

I think there’s a difference between personal communication and a broadcast medium like a blog because a personal communication encourages a thoughtful response, whereas blog comments encourage off-the-cuff, underthought remarks – often with the clickbait snark that typifies our corrupt age.

So here’s what I imagine.

I write an email to you, but I send it to republic@ofletters.net. The body of the text begins with “Esteemed email@example.com”.
An app of some sort will download such letters and assign them a randomly-generated delivery date.
On that date, the letter is sent to you. (I’m inclined to ignore the original Subject in favor of “Republic of Letters: Missive from sender@example.com”, with the original subject tossed into the body of the letter. Closer to what I imagine would be Leibnitz’s experience getting a letter from Clark.
That’s all. No archiving, for example. Future historians will have to grovel through a modern Leibnitz’s email folders, just like today.

I think this would be simple to implement, using Fastmail to handle that email address, just as it does marick@exampler.com.

This actually doesn’t need an app at all. It could just be implemented by adapting a convention of a recognizable Subject and a promise by everyone to roll a die and not read the email for that number of days. Maybe that would work just as well.

What do you think? It would be most appropriate to comment by sending me mail to marick@exampler.com.

Oddly Influenced

What's up with quantum mechanics? (36 Views of Mount CritRat)

The incomplete API (36 Views of Mount CritRat)

API?

A formative experience

Critical rationalism is like that

So who cares, and why should they?

The hero's journey (36 Views of Mount CritRat)

Behold the scientist

An example

Cutting the Gordian knot

Marxism again

Waterfall science (36 Views of Mount CritRat)

Solar neutrinos

Evidence and methodology

The consequences

Marxism, again

Science and the mirror of philosophy (36 Views of Mount CritRat)

Truth

Argument

So?

A swerve in the series: mental habits

The story thus far

The argument going forward

Blind spot 2: Revolution

A note on evidence

The original set of predictions

A modification (a successor theory)

Stalin’s revision

But what about the dictatorship of the proletariat?

Why did I grovel through a lot of Marxist thought I’m not particularly interested in?

Background: actually, Marxists were better than that

Disclaimer

Prediction and observation

About the peasantry

The scope of the revolution

Coping with the aftermath

Structuralism

Analysis of fairy tales (humanities)

Kinship structures (social science)

Groups (mathematics)

Assumptions of structuralism

Applying structuralist theories

The details men don’t see

On diagrams

The big takeaway

Blind spot 1: Immiseration

Experimentation

Which theories and theorists count?

Prelude to a discussion of blind spots

Disclaimer 1

Disclaimer 2

Popper by example

Background

Sources, described

My example

The Road to Lakatos

Three methodologies

Motivations

Lakatos

Proofs and Refutations

The odd couple

Postscript

Working backward from the theory to the observation

William James on pragmatism

Action

Truth

Anecdote

If you want to learn more

Rorty on pragmatism

Entity realism

In which I take on the binary

Reminders

Binaries

Actions

Wielding the sticker

Credits

Jaina seven-valued logic

Sources

Hypertext 2: Zettelkasten