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Saturday, June 12, 2010

The Mentaculus

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.



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

9 Comments:

Professor Blogger WHT said...

BTW, I highly recommend the movie.

12:10 PM  
Professor Blogger monkeygrinder said...

So - the canoe represents rationality, the river is chaos, and you simply wish to navigate the river without flipping the canoe?

More seriously, when you talk of rationality are you in fact talking about scientific materialism ala Descartes with his floating soul trimmed away?

Anyways, I'm not sure how I missed that movie I thought I'd seen em all. TIme tonetflix it.

2:39 PM  
Professor Blogger WHT said...

Watch the movie and you will see what the canoe means. Lots of people are discussing how rationality fits in. The title Serious Man is a clear example of this theme.
But YMMV, as all fiction is open to multiple interpretations.

4:08 PM  
Professor Blogger Step Back said...

Hi there WHT/Mobjectivist,

I recently re-saw Serious Man on cable TV.
It's definitely a disrespected movie that deserved more respect than it got from the mass audience.

I don't understand what you guys are talking about when bringing up the canoe dream and then focusing on "the canoe". Maybe, possible it is, that we need a Joseph and his multicolored robe to interpret this dream? Maybe the canoe represents a man-made artifice for helping Arthur escape from his troubles and his pre-ordained destiny (what was "meant to be") except that one can never escape the mighty hand of Ha-Shem? Apparently Ha-Shem appears in many strange and mysterious ways, including on the inner surfaces of the Goy's teeth. In the canoe escape dream, Ha-Shem appears in the form of the careless hunter neighbor who blows away Larry and Arthur's escape scheme.

The main take away I got from the Coen Brothers movie is the idea that "respected" people of so-called authority turn out to be quacks and the crazy people turn out to be the sooth seers.

Consider for example the case of the 3 rabbis. The "common sense" of the community is that the elder Rabbi Marshack is the wisest and most to-be consulted and respected of the 3 rabbis.

The youngest rabbi on the other hand (there is always an other hand in Jewish folklore) is supposedly the most foolish and least respectable. Arthur Gopnick and his so-called Mentaculus are also disrespected.

Indeed, when the junior Rabbi tells Physics Professor Larry Gopnick to look at the parking lot in order to see Ha-Shem, even we the audience come to think this junior rabbi is a real whack job.

But then, at the end of the movie, Ha-Shem does appear in the parking lot; in the form of a tornado. The junior rabbi was right all along.

2:07 AM  
Professor Blogger WHT said...

I didn't get the tornado/parking lot connection until now. that was aa loose end to me.

3:28 AM  
Professor Blogger Step Back said...

There are many subtext innuendos in the movie.

More to the point, we are treated to a family of supposedly religion abiding Jews. On the other hand they are all busy violating each and every rule in the 10 Commandments. The end of the movie (the tornado) may be seen as representing God's anger and vengeful wrath against those who have scorned his commandments.

Let's start with the Gopnick son and these of the 10 Commandments:
(http://en.wikipedia.org/wiki/Ten_Commandments)

1. Honor your father and your mother (F Troop)
2. You shall not steal. (the $20)
3. Do not have any other gods before me. (weed)
4. Remember the Sabbath day and keep it holy. (smoking on Bar Mitzvah day)

So you can quickly see by looking past the angle of, oh --he's just a normal teenager, that the Gopnick son is actually a spoiled and disrespectful brat. The Korean student gives Larry way more respect than does Gopnick's one son.

So Gopnick's son (deservedly?) gets the tornado --in the parking lot-- as the junior rabbi foretold.

BTW, I forgot --there were actually four (4) rabbis in the movie, not three. But as we know from Inception, the human brain cannot remember more than 3 things at a time.

9:10 AM  
Professor Blogger Step Back said...

Mazal Tov.

A Serious Man finally was replayed on cable TV.

So about the canoe crossing the river into Canada. Yes that scene.

The reason the canoe flips over is because Arthur Gopnick gets intentionally shot in the back by Larry's Nazi neighbor and therefore it is not chaos. It is intentional. On the other hand the scene relates to the basic adage about being careful regarding what one wishes for. It also relates to the entanglement principle of physics.

On re-viewing the film I realized that a great deal of it plays out in Hebrew and some in Yiddish. So those who do not know at least the first language are left out of some the subtle twisters.

In Rabbi Nachner's eulogy (the #2 rabbi) for the deceased Sy "Able"man, he mentions "Canada" as being a possible location for "Olam Ha Bah Ah" --the place where good Jews go after they die.

Larry's dream about taking his troublesome brother to Canada is therefore a twisted version of Cain and Able. It indicates that he subconsciously wants his brother dead and he makes an active move to that goal by pushing his brother beyond the "edge", from North Dakota and into Canada (to the metaphorical "Olam Ha Bah Ah").

Larry gets his wish. Arthur is indeed killed. But be careful if you are entangled with your brother in a Cain and Able kind of way because Ha Shem (God) sends Larry's Nazi neighbor in to do the killing. And after the Nazi kills Arthur, he shoots Larry. That's where the dream ends.

Humorously at the bottom of the credits in the movie, the Coen Brothers put in the line: "No Jews were harmed in the shooting of this movie."

p.s. The Blogging Mathematician gets it wrong here:
http://yabm.wordpress.com/2010/05/06/a-serious-man-and-a-beautiful-mind/

One has to freeze time and study it in slow motion to realize that Larry Gopnick derives the Higgs Boson here:
http://i124.photobucket.com/albums/p1/toddalcott/Mentaculus4.jpg

source site:
http://toddalcott.livejournal.com/288881.html?thread=5778545

2:32 AM  
Professor Blogger WHT said...

Classic. I figured there were all these other subtexts roaming around the movie.

10:22 AM  
Professor Blogger David said...

I was struck by how many times "Jesus Christ" was used as a curse word by these "devout" Jews. The irony in this film is thick.

2:38 PM  

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