E. T. Jaynes

A Correction Regarding Laplace

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A few years ago, I quoted Stanley Jaki on an episode supposedly involved Laplace:

Laplace shouted, “We have had enough such myths,” when his fellow academician Marc-Auguste Pictet urged, in the full hearing of the Académie des Sciences, that attention be given to the report about a huge meteor shower that fell at L’Aigle, near Paris, on April 26, 1803.

I referred to this recently on Twitter. When another user found it surprising that Laplace would have said this, I attempted to track it down, and came to the conclusion that this very account is a “myth” itself, in some sense. Jaki tells the same story in different words in the book Miracles and Physics:

The defense of miracles done with an eye on physics should include a passing reference to meteorites. Characteristic of the stubborn resistance of scientific academies to those strange bits of matter was Laplace’s shouting, “We’ve had enough of such myths,” when Pictet, a fellow academician, urged a reconsideration of the evidence provided by “lay-people” as plain eyewitnesses.

(p. 94)

Jaki provides no reference in God and the sun at Fatima. The text in Miracles and Physics has a footnote, but it provides generic related information that does not lead back to any such episode.

Did Jaki make it up? People do “just make things up“, but in this case whatever benefit Jaki might get from it would seem to be outweighed by the potential reputational damage of being discovered in such a lie, so it seems unlikely. More likely he is telling a story from memory, with the belief that the details just don’t matter very much. And since he provides plenty of other sources, I am sure he knows full well that he is omitting any source here, presumably because he does not have one at hand. He may even be trying to cover up this omission, in a sense, by footnoting the passage with information that does not source it. It seems likely that the story is a lecture hall account that has been modified by the passage of time. One reason to suppose such a source is that Jaki is not alone in the claim that Laplace opposed the idea of meteorites as stones from the sky until 1803. E.T. Jaynes, in Probability Theory: The Logic of Science, makes a similar claim:

Note that we can recognize the clear truth of this psychological phenomenon without taking any stand about the truth of the miracle; it is possible that the educated people are wrong. For example, in Laplace’s youth educated persons did not believe in meteorites, but dismissed them as ignorant folklore because they are so rarely observed. For one familiar with the laws of mechanics the notion that “stones fall from the sky” seemed preposterous, while those without any conception of mechanical law saw no difficulty in the idea. But the fall at Laigle in 1803, which left fragments studied by Biot and other French scientists, changed the opinions of the educated — including Laplace himself. In this case the uneducated, avid for the marvelous, happened to be right: c’est la vie.

(p. 505)

Like Jaki, Jaynes provides no source. Still, is that good enough reason to doubt the account? Let us examine a text from the book The History of Meteoritics and Key Meteorite Collections. In the article, “Meteorites in history,” Ursula Marvin remarks:

Early in 1802 the French mathematician Pierre-Simon de Laplace (1749-1827) raised the question at the National Institute of a lunar volcanic origin of fallen stones, and quickly gained support for this idea from two physicist colleagues Jean Baptiste Biot (1774-1862) and Siméon-Denis Poisson (1781-1840). The following September, Laplace (1802, p. 277) discussed it in a letter to von Zach.

The idea won additional followers when Biot (1803a) referred to it as ‘Laplace’s hypothesis’, although Laplace, himself, never published an article on it.

(p.49)

This has a source for Laplace’s letter of 1802, although I was not able to find it online. It seems very unlikely that Laplace would have speculated on meteorites as coming from lunar volcanos in 1802, and then called them “myths” in 1803. So where does this story come from? In Cosmic Debris: Meteorites in History, John Burke gives this account:

There is also a problem with respect to the number of French scientists who, after Pictet published a résumé of Howard’s article in the May 1802 issue of the Bibliothèque Britannique, continued to oppose the idea that stones fell from the atmosphere. One can infer from a statement of Lamétherie that there was considerable opposition, for he reported that when Pictet read a memoir to the Institut on the results of Howard’s report “he met with such disfavor that it required a great deal of fortitude for him to finish his reading.” However, Biot’s description of the session varies a good deal. Pictet’s account, he wrote, was received with a “cautious eagerness,” though the “desire to explain everything” caused the phenomenon to be rejected for a long time. There were, in fact, only three scientists who publicly expressed their opposition: the brothers Jean-André and Guillaume-Antoine Deluc of Geneva, and Eugène Patrin, an associate member of the mineralogy section of the Institut and librarian at the École des mines.

When Pictet early in 1801 published a favorable review of Chladni’s treatise, it drew immediate fire from the Deluc brothers. Jean, a strict Calvinist, employed the same explanation of a fall that the Fougeroux committee had used thirty years before: stones did not fall; the event was imagined when lightning struck close to the observer. Just as no fragment of our globe separate and become lost in space, he wrote, fragments could not be detached from another planet. It was also very unlikely that solid masses had been wandering in space since the creation, because they would have long since fallen into the sphere of attraction of some planet. And even if they did fall, they would penetrate the earth to a great depth and shatter into a thousand pieces.

(p.51)

It seems quite possible that Pictet’s “reading a memoir” here and “meeting with disfavor” (regardless of details, since Burke notes it had different descriptions at the time) is the same incident that Jaki describes as having been met with “We’ve had enough of such myths!” when Pictet “urged a reconsideration of the evidence.” If these words were ever said, then, they were presumably said by one of these brothers or someone else, and not by Laplace.

How does this sort of thing happen, if we charitably assume that Jaki was not being fundamentally dishonest? As stated above, it seems likely that he knew he did not have a source. He may even have been consciously aware that it might not have been Laplace who made this statement, if anyone did. But he was sure there was a dispute about the matter, and presumably thought that it just wasn’t too important who it was or the details of the situation, since the main point was that scientists are frequently reluctant to accept facts when those facts occur rarely and are not deliberately reproducible. And if we reduce Jaki’s position to these two things, namely, (1) that scientists at one point disputed the reality and meteorites, and (2) this sort of thing frequently happens with rare and hard to reproduce phenomena, then the position is accurate.

But this behavior, the description of situations with the implication that the details just don’t matter much, is very bad, and directly contributes to the reluctance of many scientists to accept the reality of “extraordinary” phenomena, even in situations where they are, in fact, real.

Settled Issues

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In chapter 5 of his book Probability Theory: The Logic of Science, E. T. Jaynes discusses ESP:

I. J. Good (1950) has shown how we can use probability theory backwards to measure our own strengths of belief about propositions. For example, how strongly do you believe in extrasensory perception?

What probability would you assign to the hypothesis that Mr Smith has perfect extrasensory perception? More specifically, that he can guess right every time which number you have written down. To say zero is too dogmatic. According to our theory, this means that we are never going to allow the robot’s mind to be changed by any amount of evidence, and we don’t really want that. But where is our strength of belief in a proposition like this?

Our brains work pretty much the way this robot works, but we have an intuitive feeling for plausibility only when it’s not too far from 0 db. We get fairly definite feelings that something is more than likely to be so or less than likely to be so. So the trick is to imagine an experiment. How much evidence would it take to bring your state of belief up to the place where you felt very perplexed and unsure about it? Not to the place where you believed it – that would overshoot the mark, and again we’d lose our resolving power. How much evidence would it take to bring you just up to the point where you were beginning to consider the possibility seriously?

So, we consider Mr Smith, who says he has extrasensory perception (ESP), and we will write down some numbers from one to ten on a piece of paper and ask him to guess which numbers we’ve written down. We’ll take the usual precautions to make sure against other ways of finding out. If he guesses the first number correctly, of course we will all say ‘you’re a very lucky person, but I don’t believe you have ESP’. And if he guesses two numbers correctly, we’ll still say ‘you’re a very lucky person, but I still don’t believe you have ESP’. By the time he’s guessed four numbers correctly – well, I still wouldn’t believe it. So my state of belief is certainly lower than −40 db.

How many numbers would he have to guess correctly before you would really seriously consider the hypothesis that he has extrasensory perception? In my own case, I think somewhere around ten. My personal state of belief is, therefore, about −100 db. You could talk me into a ±10 db change, and perhaps as much as ±30 db, but not much more than that.

The idea is that after Mr. Smith guesses 7 to 13 numbers correctly (when by chance he should have a probability of 10% of guessing each one correctly), Jaynes will begin to think it reasonably likely that he has ESP. He notes that this is his subjective opinion, saying, “In my own case,” and “My personal state of belief.”

However, Jaynes follows this up by stating that if this happened in real life, he would not be convinced:

After further thought, we see that, although this result is correct, it is far from the whole story. In fact, if he guessed 1000 numbers correctly, I still would not believe that he has ESP, for an extension of the same reason that we noted in Chapter 4 when we first encountered the phenomenon of resurrection of dead hypotheses. An hypothesis A that starts out down at −100 db can hardly ever come to be believed, whatever the data, because there are almost sure to be alternative hypotheses (B1, B2,…) above it, perhaps down at −60 db. Then, when we obtain astonishing data that might have resurrected A, the alternatives will be resurrected instead.

In other words, Jaynes is saying, “This happened by chance,” and “Mr. Smith has ESP” are not the only possibilities. For example, it is possible that Mr. Smith has invented a remote MRI device, which he has trained to distinguish people’s thoughts about numbers, and he is receiving data on the numbers picked by means of an earbud. If the prior probability of this is higher than the prior probability that Mr. Smith has ESP, then Jaynes will begin to think this is a reasonable hypothesis, rather than coming to accept ESP.

This does not imply that Jaynes is infinitely confident that Mr. Smith does not have ESP, and in fact it does not invalidate his original estimate:

Now let us return to that original device of I. J. Good, which started this train of thought. After all this analysis, why do we still hold that naive first answer of −100 db for my prior probability for ESP, as recorded above, to be correct? Because Jack Good’s imaginary device can be applied to whatever state of knowledge we choose to imagine; it need not be the real one. If I knew that true ESP and pure chance were the only possibilities, then the device would apply and my assignment of −100 db would hold. But, knowing that there are other possibilities in the real world does not change my state of belief about ESP; so the figure of −100 db still holds.

He would begin to be convinced after about 10 numbers if he knew for a fact that chance and ESP were the only possibilities, and thus this is a good representation of how certain he is subjectively.

The fact of other possibilities also does not mean that it is impossible for Jaynes to be convinced, even in the real world, that some individual has ESP. But it does mean that this can happen only with great difficulty: essentially, he must be convinced that the other possibilities are even less likely than ESP. As Jaynes says,

Indeed, the very evidence which the ESP’ers throw at us to convince us, has the opposite effect on our state of belief; issuing reports of sensational data defeats its own purpose. For if the prior probability for deception is greater than that of ESP, then the more improbable the alleged data are on the null hypothesis of no deception and no ESP, the more strongly we are led to believe, not in ESP, but in deception. For this reason, the advocates of ESP (or any other marvel) will never succeed in persuading scientists that their phenomenon is real, until they learn how to eliminate the possibility of deception in the mind of the reader. As (5.15) shows, the reader’s total prior probability for deception by all mechanisms must be pushed down below that of ESP.

This is related to the grain of truth in Hume’s account of miracles. Hume’s basic point, that an account of a miracle could never be credible, is mistaken. But he is correct to say that the account would not be credible unless “these witnesses are mistaken or lying” has a lower prior probability than the prior probability of the miracle actually happening. His mistake is to suppose that this cannot happen in principle.

Something like this also happens with ordinary things that we are extremely sure about. For example, take your belief that the American War of Independence happened before the Civil War. You can imagine coming upon evidence that the Civil War happened first. Thus for example suppose you found a book by a historian arguing for this thesis. This would be evidence that the Civil War came first. But it would be very unpersuasive, and would change your mind little if at all, because the prior probability of “this is a work of fiction,” or indeed of “this a silly book arguing a silly thesis for personal reasons” is higher.

We could call this a “settled issue,” at least from your point of view (and in this case from the point of view of pretty much everyone). Not only do you believe that the War of Independence came first; it would be very difficult to persuade you otherwise, even if there were real evidence against your position, and this is not because you are being unreasonable. In fact, it would be unreasonable to be moved significantly by the evidence of that book arguing the priority of the Civil War.

Is it possible in principle to persuade you to change your mind? Yes. In principle this could happen bit by bit, by an accumulation of small pieces of evidence. You might read that book, and then learn that the author is a famous historian, and that he is completely serious (presumably he became famous before writing the book; otherwise he would instead be infamous.) And then you might find other items in favor of this theory, and find refutations of the apparently more likely explanations.

But in practice such a process is extremely unlikely. The most likely way you could change your mind about this would be by way of one large change. For example, you might wake up in a hospital tomorrow and be told that you had been suffering from a rare form of amnesia which does not remove a person’s past memories, but changes them into something different. You ask about the Civil War, and are told that everyone agrees that it happened before the War of Independence. People can easily give you dozens of books on the topic; you search online on the matter, and everything on the internet takes for granted that the Civil War came first. Likewise, everyone you talk to simply takes this for granted.

The reason that the “one big change” process is more likely than the “accumulation of small evidences” process is this: if we want to know what should persuade you that the Civil War came first, we are basically asking what the world would have to be like in order for it to be actually true that the Civil War came first. In such a world, your current belief is false. And in such a world it is simply much more likely that you have made one big mistake which resulted in your false belief about the Civil War, than that you have made lots of little mistakes which led to it.