The Mentaculus

• Update: Here is a real-life crazy Mentaculus man ⇦ Paul Vaughan is Arthur.

I saw the Coen brothers movie "A Serious Man" a few months ago. A definite period piece from the 1960's, it contrasted two scientists, one an academic and one a hapless amateur. The main protagonist, Larry Gopnick, a physics professor at what looks like a small liberal arts school in the Twin Cities (Macalester, Hamline maybe?), spends time teaching his students what look like elaborate mathematical derivations on a huge chalkboard. He has trouble dealing with some of his students on occasion:

Clive Park: Yes, but this is not just. I was unaware to be examined on the mathematics.
Larry Gopnik: Well, you can't do physics without mathematics, really, can you?
Clive Park: If I receive failing grade I lose my scholarship, and feel shame. I understand the physics. I understand the dead cat.
Larry Gopnik: You understand the dead cat? But... you... you can't really understand the physics without understanding the math. The math tells how it really works. That's the real thing; the stories I give you in class are just illustrative; they're like, fables, say, to help give you a picture. An imperfect model. I mean - even I don't understand the dead cat. The math is how it really works.

His academic colleagues want Professor Gopnick to publish articles at some point (with the implicit threat of not getting tenure). Gopnick's main problem lies in his rationality:

But his rigid framing of a cause-and-effect universe makes him indignant about lack of apparent cause ...

Gopnick's brother, the minor character of Uncle Arthur, takes the role of an almost savant numerologist, busy at work on a treatise called The Mentaculus. Filled with dense illustrations and symbology, it apparently functions as a "probability map" in what appears to spell out a Theory of Everything. It also apparently works to some extent:

We might guess that it makes no sense, but Arthur's "system" apparently "works" as intended, and he applies it to winning at back room card games.

Based on the events that eventually transpire, the theme of the movie essentially says that if you seek rationality, you will ultimately only land on random chance.

I consider myself a "serious man" as well. But do I have a variation of The Mentaculous buried in the contents of this blog?

I tried to make a probability map of all the applications and blog links that I have worked on relating to what I call entropic dispersion in the following table [full HTML]:



The math is how it really works. Perhaps I should publish. Yet blogging is too much fun. Perhaps I need to take a canoe trip.

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Good reads describing The Mentaculus of probability and statistics

1. "Dawning of the Age of Stochasticity", David Mumford

   From its shady beginnings devising gambling strategies and counting corpses in medieval London, probability theory and statistical inference now emerge as better foundations for scientific models, especially those of the process of thinking and as essential ingredients of theoretical mathematics, even the foundations of mathematics itself.

2. "Probability Theory: The Logic of Science", Edwin T. Jaynes
   

   Our theme is simply: probability theory as extended logic. The ‘new’ perception amounts to the recognition that the mathematical rules of probability theory are not merely rules for calculating frequencies of ‘random variables'; they are also the unique consistent rules for conducting inference(i.e. plausible reasoning) of any kind. and we shall apply them in full generality to that end.

3. "On Thinking Probabilistically", M.E. McIntyre
4. "The Black Swan" and "Fooled by Chance", N.N. Taleb