The true Thomas Bayes

Rational or irrational?

Thomas Bayes was a Presbyterian minister.

Bayes’s first publication was a theological work, entitled Divine Benevolence ([Bayes], 1731). Since no author appears on the title page of the book, or anywhere else, it is sometimes considered to be of doubtful authorship. For example, the National Union Catalog of the United States ascribes authorship to Joshua Bayes. However, Thomas Bayes was the author of this work. Bayes’s friend, Richard Price refers to the book in his own work A Review of the Principal Questions in Morals (Price, 1948, p. 248) and says that it was written by Thomas Bayes. In Divine Benevolence Bayes was trying to answer the question of the motivating source of God’s actions in the world.

The essay dealt with how to handle the problem of evil in the world.  It is also believed that Bayes was an Arian.

That is from a D.R. Bellhouse paper (pdf), with a relevant pointer from Asher Meir.


It's priors all the way down.

It's interesting to speculate whether George Boole (of zeroes and ones logic) was inspired by non-Western thought. His father-in-law was George Everest, the surveyor-general of India (for whom Mt. E. is named), so he had personal connections to the land that came up with the idea of zero developed.

Everest was the uncle of Boole's wife, Mary, not her father. However, she claimed that indeed he provided an influence of Indian thought on Boole.

Interesting. Do you have a reference, or do you know what specifically was that influence of Indian thought over Boole?
Of course, it has to go beyond "the zero" because at the time of Boole (1815-1864), schoolboys and mathematicians were as familiar with the concept of zero that we today are, the concept of zero being well integrated in western mathematics since the late middle age (from Indian origin through Arabic mediation, as is well-known).

Also, I don't know much about the history of this part of math, but did Boole actually think of the two elements of his system as 0 or 1 rather than False and True? I have not checked, but my instinct would be that it is a more modern interpretation.

It's also interesting to speculate how much Indian thought is retconned imports from the western tradition from the Greco Bactrian kingdoms or later. Not that the Brahmins didn't come up with interesting stuff on their own, I've seen evidence they knew the Pythagorean theorem a thousand years before Christ, but are the similarities between the platonic and stoic traditions and the Hindu/Buddhist tradition coincidental, convergent or the result of diffusion.

Sailer, see Egglash's Ted:


And the most interesting thing I found out about it was historical. In the 12th century, Hugo of Santalla brought it from Islamic mystics into Spain. And there it entered into the alchemy community as geomancy: divination through the earth. This is a geomantic chart drawn for King Richard II in 1390. Leibniz, the German mathematician, talked about geomancy in his dissertation called "De Combinatoria." And he said, "Well, instead of using one stroke and two strokes, let's use a one and a zero, and we can count by powers of two." Right? Ones and zeros, the binary code. George Boole took Leibniz's binary code and created Boolean algebra...

Right. So Islam is (once again) the source of all knowledge - including integral calculus. I'm guessing you're an Evergreen State grad. Riot on dude. Riot on.

PS. There is no zero. Unless you believe it's meaningful to say that you're holding zero suns in your hand.

Oh, you are very much mistaken, Thanatos. My late mathematician father once gave a public speech, and a young woman asked him, "Professor Rosser, is zero a real number?" He replied, "One of the finest, my dear, one of the finest."

Not only is it a real number, but it is the only number that is both real and imaginary in and of itself, since of course complex numbers are both real and imaginary, but only as a result of adding a real number to an imaginary one.

As it is, Boole helped resolve the crisis in British algebra in the early 1800s, which substantially had to do with how to deal with both negative and imaginary numbers. But you cannot deal with either of them without recognizing the profound reality of zero.

Islamic mystics were not the only source of this tradition. The neo-Platonism that thrived in the Italian renaissance after the failed council of florence led to a renewed interest in the hermetic and neopythagorean traditions which were related to the alchemical tradition which had never died out completely in the east or Islamic world, where it was practiced by both muslims and non-muslims. And this was merely the culmination of an interest in alchemy and related magical fields that began with the reintroduction of a metalic money economy during the commercial revolution. Heavily indebted sovereign and bankers became easy marks for all kinds of mystical woo woo peddles who promised a perpetual money machine that could prevent the spontaneous liquidity crises that emerged with the rise of banking. A lot of this woo woo was built around the concept of microcosm of the macrocosm, which makes lots of room for fancy math. kabala is also an important and related part of the lye medieval mystic math mix.

Consider: I have five apples and give you four: how many do I have left? Now consider: I have five apples and give you five: how many do I have left?
So 0 is as much a number as 1 is.

Since when did you all become mathematical Platonists? Numbers have no reality in the world independent of units. When they have units, zero is only real as a privation, while others are real as enumerating them. The most important thing, though, is that none of these numbers are real whatsoever (and zero is even less real, since it can only be instantiated in reference to privation.)

A curious link between Bayes and Boole is that both were Unitarian in their theological views, with this a serious matter for Bayes, who was officially a Presbyterian minister. They differed in Bayes being a Newtonian while Boole was a Leibnizian, as noted by Sailer above. For Bayes, a motive for his theorem was a concern for how one progressed in the face of new events toward an understanding of God, and he had previously studied infinite series in his effort to defend Newton's calculus against the critidism by Bishop Berkeley that derivatives were simply ratios of "ghosts."

Did Bayes obtain his insight in spite of his religious beliefs or because of them? Likely the latter: he believed the universe is subject to well-defined physical laws (events are rational not random), laws created by God. In that sense God intervenes in our daily lives, not as an arbitrary act in response to prayer. Norman Maclean: "As for my father, I never knew whether he believed God was a mathematician but he certainly believed God could count and that only by picking up God's rhythms were we able to regain power and beauty."

John Marrant was born to free black parents in NY in 1755, shortly after his ordination in 1785 "A narrative of the Lord's wonderful dealings with John Marrant..a black" was published as black message sealed in a white envelope. His a·man·u·en·sis Rev Wiliam Aldridge, attests to his claim as a Christian and mediated the narrative. Only the fourth edition claims to have been "PRINTED for the AUTHOR." Absent the phrase "a Black" , nothing in the preface of the narrative indications Marrant was of African descent. Marrant's ethnicity is irrelevant to his conversion.

His Calvinist message, was ameliorationist toward slavery, whereas John Wesley, preached of emancipation or a more liberal, Arminian view.

That aspect of Bayes is almost certainly irrational. Maybe he didn't have the data or knowledge of how to apply his own theorem?

In fact, I read somewhere that Bayes developed his theorem as a way of refuting David Hume's famous critique of miracles.

re:"The essay dealt with how to handle the problem of evil in the world."

It's not hard to solve a problem that doesn't exist...

"Evil does not exist; once you have crossed the threshold, all is good. Once in another world, you must hold your tongue." —Franz Kafka

What we call "Bayesian inference" was mostly developed by Laplace.

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