The rule about advance prediction is a rule of the social process of science—a moral custom and not a theorem. The moral custom exists to prevent human beings from making human mistakes that are hard to even describe in the language of probability theory, like tinkering after the fact with what you claim your hypothesis predicts. People concluded that nineteenth century evolutionism was an excellent explanation, even if it was post facto. That reasoning was correct as probability theory, which is why it worked despite all scientific sins. Probability theory is math. The social process of science is a set of legal conventions to keep people from cheating on the math.
Yet it is also true that, compared to a modern-day evolutionary theorist, evolutionary theorists of the late nineteenth and early twentieth century often went sadly astray. Darwin, who was bright enough to invent the theory, got an amazing amount right. But Darwin’s successors, who were only bright enough to accept the theory, misunderstood evolution frequently and seriously. The usual process of science was then required to correct their mistakes. It is incredible how few errors of reasoning Darwin14 made in The Origin of Species and The Descent of Man, compared to they who followed.
That is also a hazard of a semitechnical theory. Even after the flash of genius insight is confirmed, merely average scientists may fail to apply the insights properly in the absence of formal models. As late as the 1960s biologists spoke of evolution working “for the good of the species,” or suggested that individuals would restrain their reproduction to prevent species overpopulation of a habitat. The best evolutionary theorists knew better, but average theorists did not.15
So it is far better to have a technical theory than a semitechnical theory. Unfortunately, Nature is not always so kind as to render Herself describable by neat, formal, computationally tractable models, nor does She always provide Her students with measuring instruments that can directly probe Her phenomena. Sometimes it is only a matter of time. Nineteenth century evolutionism was semitechnical, but later came the math of population genetics, and eventually DNA sequencing. Nature will not always give you a phenomenon that you can describe with technical models fifteen seconds after you have the basic insight.
Yet the cutting edge of science, the controversy, is most often about a semitechnical theory, or nonsense posing as a semitechnical theory. By the time a theory achieves technical status, it is usually no longer controversial (among scientists). So the question of how to distinguish good semitechnical theories from nonsense is very important to scientists, and it is not as easy as dismissing out of hand any theory that is not technical. To the end of distinguishing truth from falsehood exists the entire discipline of rationality. The art is not reducible to a checklist, or at least, no checklist that an average scientist can apply reliably after an hour of training. If it was that simple we wouldn’t need science.
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Why do you pay attention to scientific controversies? Why graze upon such sparse and rotten feed as the media offers, when there are so many solid meals to be found in textbooks? Textbook science is beautiful! Textbook science is comprehensible, unlike mere fascinating words that can never be truly beautiful. Fascinating words have no power, nor yet any meaning, without the math. The fascinating words are not knowledge but the illusion of knowledge, which is why it brings so little satisfaction to know that “gravity results from the curvature of spacetime.” Science is not in the fascinating words, though it’s all you’ll ever read as breaking news.
There can be justification for following a scientific controversy. You could be an expert in that field, in which case that scientific controversy is your proper meat. Or the scientific controversy might be something you need to know now, because it affects your life. Maybe it’s the nineteenth century, and you’re gazing lustfully at a member of the appropriate sex wearing a nineteenth century bathing suit, and you need to know whether your sexual desire comes from a psychology constructed by natural selection, or is a temptation placed in you by the Devil to lure you into hellfire.
It is not wholly impossible that we shall happen upon a scientific controversy that affects us, and find that we have a burning and urgent need for the correct answer. I shall therefore discuss some of the warning signs that historically distinguished vague hypotheses that later turned out to be unscientific gibberish, from vague hypotheses that later graduated to confirmed theories. Just remember the historical lesson of nineteenth century evolutionism, and resist the temptation to fail every theory that misses a single item on your checklist. It is not my intention to give people another excuse to dismiss good science that discomforts them. If you apply stricter criteria to theories you dislike than theories you like (or vice versa!), then every additional nit you learn how to pick, every new logical flaw you learn how to detect, makes you that much stupider. Intelligence, to be useful, must be used for something other than defeating itself.
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One of the classic signs of a poor hypothesis is that it must expend great effort in avoiding falsification—elaborating reasons why the hypothesis is compatible with the phenomenon, even though the phenomenon didn’t behave as expected. Carl Sagan gives the example of someone who claims that a dragon lives in their garage. Sagan originally drew the lesson that poor hypotheses need to do fast footwork to avoid falsification—to maintain an appearance of “fit.”16
I would point out that the claimant obviously has a good model of the situation somewhere in their head, because they can predict, in advance, exactly which excuses they’re going to need. To a Bayesian, a hypothesis isn’t something you assert in a loud, emphatic voice. A hypothesis is something that controls your anticipations, the probabilities you assign to future experiences. That’s what a probability is, to a Bayesian—that’s what you score, that’s what you calibrate. So while our claimant may say loudly, emphatically, and honestly that they believe there’s an invisible dragon in the garage, they do not anticipate there’s an invisible dragon in the garage—they anticipate exactly the same experience as the skeptic.
When I judge the predictions of a hypothesis, I ask which experiences I would anticipate, not which facts I would believe.
The flip side:
I recently argued with a friend of mine over a question of evolutionary theory. My friend alleged that the clustering of changes in the fossil record (apparently, there are periods of comparative stasis followed by comparatively sharp changes; itself a controversial observation known as “punctuated equilibrium”) showed that there was something wrong with our understanding of speciation. My friend thought that there was some unknown force at work—not supernatural, but some natural consideration that standard evolutionary theory didn’t take into account. Since my friend didn’t give a specific competing hypothesis that produced better predictions, his thesis had to be that the standard evolutionary model was stupid with respect to the data—that the standard model made a specific prediction that was wrong; that the model did worse than complete ignorance or some other default competitor.
At first I fell into the trap; I accepted the implicit assumption that the standard model predicted smoothness, and based my argument on my recollection that the fossil record changes weren’t as sharp as he claimed. He challenged me to produce an evolutionary intermediate between Homo erectus and Homo sapiens; I googled and found Homo heidelbergensis. He congratulated me and acknowledged that I had scored a major point, but still insisted that the changes were too sharp, and not steady enough. I started to explain why I thought a pattern of uneven change could arise from the standard model: environmental selection pressures might not be constant . . . “Aha!” my friend said, “you’re making your excuses in advance.”
But suppose that the fossil record instead showed a smooth and gradual set of changes. Might my friend have argued that the standard model of evolution as a chaotic and noisy process could not account for such smoothness? If it is a scientific sin to claim post facto that our beloved hypothesis predicts the data, should it not be equally a sin t
o claim post facto that the competing hypothesis is stupid on the data?
If a hypothesis has a purely technical model, there is no trouble; we can compute the prediction of the model formally, without informal variables to provide a handle for post facto meddling. But what of semitechnical theories? Obviously a semitechnical theory must produce some good advance predictions about something, or else why bother? But after the theory is semi-confirmed, can the detractors claim that the data show a problem with the semitechnical theory, when the “problem” is constructed post facto? At the least the detractors must be very specific about what data a confirmed model predicts stupidly, and why the confirmed model must make (post facto) that stupid prediction. How sharp a change is “too sharp,” quantitatively, for the standard model of evolution to permit? Exactly how much steadiness do you think the standard model of evolution predicts? How do you know? Is it too late to say that, after you’ve seen the data?
When my friend accused me of making excuses, I paused and asked myself which excuses I anticipated needing to make. I decided that my current grasp of evolutionary theory didn’t say anything about whether the rate of evolutionary change should be intermittent and jagged, or smooth and gradual. If I hadn’t seen the graph in advance, I could not have predicted it. (Unfortunately, I rendered even that verdict after seeing the data . . .) Maybe there are models in the evolutionary family that would make advance predictions of steadiness or variability, but if so, I don’t know about them. More to the point, my friend didn’t know either.
It is not always wise to ask the opponents of a theory what their competitors predict. Get the theory’s predictions from the theory’s best advocates. Just make sure to write down their predictions in advance. Yes, sometimes a theory’s advocates try to make the theory “fit” evidence that plainly doesn’t fit. But if you find yourself wondering what a theory predicts, ask first among the theory’s advocates, and afterward ask the detractors to cross-examine.
Furthermore: Models may include noise. If we hypothesize that the data are trending slowly and steadily upward, but our measuring instrument has an error of 5%, then it does no good to point to a data point that dips below the previous data point, and shout triumphantly, “See! It went down! Down down down! And don’t tell me why your theory fits the dip; you’re just making excuses!” Formal, technical models often incorporate explicit error terms. The error term spreads out the likelihood density, decreases the model’s precision and reduces the theory’s score, but the Bayesian scoring rule still governs. A technical model can allow mistakes, and make mistakes, and still do better than ignorance. In our supermarket example, even the precise hypothesis of 51 still bets only 90% of its probability mass on 51; the precise hypothesis claims only that 51 happens nine times out of ten. Ignoring nine 51s, pointing at one case of 82, and crowing in triumph, does not a refutation make. That’s not an excuse, it’s an explicit advance prediction of a technical model.
The error term makes the “precise” theory vulnerable to a superprecise alternative that predicted the 82. The standard model would also be vulnerable to a precisely ignorant model that predicted a 60% chance of 51 on the round where we saw 82, spreading out the likelihood more entropically on that particular error. No matter how good the theory, science always has room for a higher-scoring competitor. But if you don’t present a better alternative, if you try only to show that an accepted theory is stupid with respect to the data, that scientific endeavor may be more demanding than just replacing the old theory with a new one.
Astronomers recorded the unexplained perihelion advance of Mercury, unaccounted for under Newtonian physics—or rather, Newtonian physics predicted 5,557 seconds of arc per century, where the observed amount was 5,600.17 But should the scientists of that day have junked Newtonian gravitation based on such small, unexplained counterevidence? What would they have used instead? Eventually, Newton’s theory of gravitation was set aside, after Einstein’s General Relativity precisely explained the orbital discrepancy of Mercury and also made successful advance predictions. But there was no way to know in advance that this was how things would turn out.
In the nineteenth century there was a persistent anomaly in the orbit of Uranus. People said, “Maybe Newton’s law starts to fail at long distances.” Eventually some bright fellows looked at the anomaly and said, “Could this be an unknown outer planet?” Urbain Le Verrier and John Couch Adams independently did some scribbling and figuring, using Newton’s standard theory—and predicted Neptune’s location to within one degree of arc, dramatically confirming Newtonian gravitation.18
Only after General Relativity precisely produced the perihelion advance of Mercury did we know Newtonian gravitation would never explain it.
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In the Intuitive Explanation we saw how Karl Popper’s insight that falsification is stronger than confirmation translates into a Bayesian truth about likelihood ratios. Popper erred in thinking that falsification was qualitatively different from confirmation; both are governed by the same Bayesian rules. But Popper’s philosophy reflected an important truth about a quantitative difference between falsification and confirmation.
Popper was profoundly impressed by the differences between the allegedly “scientific” theories of Freud and Adler and the revolution effected by Einstein’s theory of relativity in physics in the first two decades of this century. The main difference between them, as Popper saw it, was that while Einstein’s theory was highly “risky,” in the sense that it was possible to deduce consequences from it which were, in the light of the then dominant Newtonian physics, highly improbable (e.g., that light is deflected towards solid bodies—confirmed by Eddington’s experiments in 1919), and which would, if they turned out to be false, falsify the whole theory, nothing could, even in principle, falsify psychoanalytic theories. These latter, Popper came to feel, have more in common with primitive myths than with genuine science. That is to say, he saw that what is apparently the chief source of strength of psychoanalysis, and the principal basis on which its claim to scientific status is grounded, viz. its capability to accommodate, and explain, every possible form of human behaviour, is in fact a critical weakness, for it entails that it is not, and could not be, genuinely predictive. Psychoanalytic theories by their nature are insufficiently precise to have negative implications, and so are immunised from experiential falsification . . .
Popper, then, repudiates induction, and rejects the view that it is the characteristic method of scientific investigation and inference, and substitutes falsifiability in its place. It is easy, he argues, to obtain evidence in favour of virtually any theory, and he consequently holds that such “corroboration,” as he terms it, should count scientifically only if it is the positive result of a genuinely “risky” prediction, which might conceivably have been false. For Popper, a theory is scientific only if it is refutable by a conceivable event. Every genuine test of a scientific theory, then, is logically an attempt to refute or to falsify it . . .
Every genuine scientific theory then, in Popper’s view, is prohibitive, in the sense that it forbids, by implication, particular events or occurrences.19
On Popper’s philosophy, the strength of a scientific theory is not how much it explains, but how much it doesn’t explain. The virtue of a scientific theory lies not in the outcomes it permits, but in the outcomes it prohibits. Freud’s theories, which seemed to explain everything, prohibited nothing.
Translating this into Bayesian terms, we find that the more outcomes a model prohibits, the more probability density the model concentrates in the remaining, permitted outcomes. The more outcomes a theory prohibits, the greater the knowledge-content of the theory. The more daringly a theory exposes itself to falsification, the more definitely it tells you which experiences to anticipate.
A theory that can explain any experience corresponds to a hypothesis of complete ignorance—a uniform distribution with probability density spread evenly over every possible outcome.
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Phlogiston was the eighteenth century’s answer to the Elemental Fire of the Greek alchemists. You couldn’t use phlogiston theory to predict the outcome of a chemical transformation—first you looked at the result, then you used phlogiston to explain it. Phlogiston theory was infinitely flexible; a disguised hypothesis of zero knowledge. Similarly, the theory of vitalism doesn’t explain how the hand moves, nor tell you what transformations to expect from organic chemistry; and vitalism certainly permits no quantitative calculations.
The flip side:
Beware of checklist thinking: Having a sacred mystery, or a mysterious answer, is not the same as refusing to explain something. Some elements in our physics are taken as “fundamental,” not yet further reduced or explained. But these fundamental elements of our physics are governed by clearly defined, mathematically simple, formally computable causal rules.
Occasionally some crackpot objects to modern physics on the grounds that it does not provide an “underlying mechanism” for a mathematical law currently treated as fundamental. (Claiming that a mathematical law lacks an “underlying mechanism” is one of the entries on the Crackpot Index by John Baez.20) The “underlying mechanism” the crackpot proposes in answer is vague, verbal, and yields no increase in predictive power—otherwise we would not classify the claimant as a crackpot.
Our current physics makes the electromagnetic field fundamental, and refuses to explain it further. But the “electromagnetic field” is a fundamental governed by clear mathematical rules, with no properties outside the mathematical rules, subject to formal computation to describe its causal effect upon the world. Someday someone may suggest improved math that yields better predictions, but I would not indict the current model on grounds of mysteriousness. A theory that includes fundamental elements is not the same as a theory that contains mysterious elements.
Rationality- From AI to Zombies Page 117