[FOM] ordinal notations on wall st

Jeffrey Sarnat jeffrey.sarnat at gmail.com
Tue Jun 1 19:17:20 EDT 2010

On Mon, 31 May 2010, joeshipman at aol.com wrote:

> It's obvious that ordinals are what you need in game theory to
> represent ever-more complex versions of "I know that he knows that (I
> know X, He knows I know X, I know he knows I know X, ...)" which is
> just omega+2 as an ordinal, so if you have a war  between competing
> algorithms trying to outguess each other then this can be interpereted
> in the ordinals.

So basically you're speculating that they're making spectacular amounts of 
money from what amounts to a transfinite generalization of Vincini's 
reasoning in the battle-of-the-wits scene from The Princess Bride. I 
wonder: which ordinal corresponds to having spent the last few years 
building up an immunity to iocane powder?

My pet conspiracy theory is that the post was intended to draw attention 
to (what is in my opinion) an underappreciated branch of mathematics, 
although it certainly would be nice if there really were a fairy-godmother 
out there who magically bestows salaries unto proof-theorists in direct 
proportion to the size of the largest ordinal they can name. 
Ordinal-fairy, if you're out there, give me a call: a seven figure salary 
*might* be enough to tempt me away from my current postdoc if you were to 
ask nicely enough (although I do have to admit that, as a recently minted 
Ph.D. in computer science, I've only ever had reason to count as high as 
the Small Veblen ordinal thus far).


> But I can't believe that a competent mathematician and programmer who
> understands this concept and ordinal notations up to, say, Gamma_0 will
> gain any insight useful in financial practice from the more arcane
> systems of ordinal notations.
> -- JS
> -----Original Message-----
> From: Kenny Easwaran <easwaran at usc.edu>
> To: Foundations of Mathematics <fom at cs.nyu.edu>
> Sent: Sun, May 30, 2010 9:15 pm
> Subject: [FOM] ordinal notations on wall st
> Does anyone know anything about
> this?http://christianmarks.wordpress.com/2010/05/25/mathematical-logic-fi
> nds-unexpected-application-on-wall-street/Unfortunately, the post
> didn't have any links to examples of this, orany discussion of how it
> works, but somehow the idea of basing tradingstrategies on
> proof-theoretic ordinals, with companies trying to movefarther up the
> ordinal hierarchy to get better strategies, sounds justbarely within
> the realm of plausibility.If anyone can confirm that this is actually
> real, and not just made upby the blog author, that would be quite
> interesting.Kenny
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