I decided recently to take the plunge and fully immerse myself in Bayesian statistics. (Bayesian statistics, as relevant here, says that the best estimate of the chance of something being right or wrong requires the use of all available information.) A little poking around on the Internet suggested to me that the book to get was E. T. Jaynes’ Probability Theory: The Language of Science.

In Chapter 5, I encountered a convincing logical argument that, when applied to climate change, explains why people who think logically will draw different conclusions from the same evidence. This concept, I daresay, baffles most people, who assume that logic dictates identical conclusions from the same evidence.

Jaynes is discussing the published results of an ESP experiment in which the subject, Mrs Stewart, over a large number of trials, produced a success rate unexplainable by chance. I’ve modified the text to make it understandable to a non-Bayesian. When you read this, feel free to substitute “global climate catastrophe” or “man has zero effect on climate” for “ESP”.

“This kind of experiment can never convince me of the reality of … ESP; not because I assert [that ESP is impossible] dogmatically at the start, but because the verifiable facts can be accounted for by many alternative hypotheses (such as unintentional error in the record keeping, tricks by Mrs Stewart, withholding of data, or outright fabrication), every one of which I consider inherently more plausible than ESP, and none of which is ruled out by the information available to me.

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 [we think the likelihood] for deception is greater than that of ESP [being real], then the more improbable the alleged data are …, 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… The reader’s [perceived likelihood] for deception by all mechanisms must be pushed down below that of ESP.

It is interesting that Laplace perceived this phenomenon long ago. His Essai Philosophique sur les Probabilites (1814, 1819) has a long chapter on the ‘Probabilities of testimonies’, in which he calls attention to ‘the immense weight of testimonies necessary to admit a suspension of natural laws’. He notes that those who make recitals of miracles, ‘decrease rather than augment the belief which they wish to inspire; for then those recitals render very probable the error or the falsehood of their authors. But that which diminishes the belief of educated men often increases that of the uneducated, always avid for the marvelous.’

…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.”

What is more marvelous in climate change? The idea that man may have a catastrophic effect on the climate, or the idea that the climate system is too big for man to have much effect on it? If you find the former hard to believe, will you not think that scientists are wrong in their extrapolation of the state of the climate into the future? If you find the latter naive and implausible, will you not think that almost all contrarian articles have some fatal flaw in them?

In last week’s blog entry, entitled Idiots, I critiqued two essays on climate change, one from each side. Tell the truth to yourself: did you think it likely that one of the essay writers was making honest mistakes and the other was being dishonest? Was the honest one presenting the viewpoint you generally agreed with? Do you have any shred of evidence, aside from the essays themselves, that speaks to the honesty of the authors or whether one is more of an idiot than the other?

[Marvelously, after I had drafted the above paragraph but before this entry was posted, two commenters to “Idiots” proceeded to have a heated exchange on which writer was honest and which was dishonest!]

Next week, I’ll discuss how Jaynes explains that additional evidence can actually make logical people move farther apart rather than come to agreement.