Re: Gauge theories in economics and physics

From: Jerzy Karczmarczuk (karczma_at_info.unicaen.fr)
Date: 08/27/04 

Date: 27 Aug 2004 07:10:25 -0400

Franz Heymann wrote:
> "Eric A. Forgy" <forgy@uiuc.edu> wrote in message
> news:3fa8470f.0408260841.52ce3477@posting.google.com...
>
> [snip]
>
>
>>Now, a "portfolio" of stuff can be thought of as an abstract vector
>>whose magnitude is the "value" of the portfolio. Each item in the
>>portfolio has it's own value and you can think of them as components
>>of a vector.
>
> This sounds remarkably like nonsense. The components of a vector are
> all orthogonal to one another. What does the concept of
> "orthogonality" mean in the present context?

I remind you politely that *vectors* can (or not) be orthogonal, *not*
their components. You may make vectors out of many things, e.g. shares,
money of different currencies, etc.
A vector in the Fock space contains sectors with zero, one, two, etc.
particles. Did you think about the meaning of orthogonality there? It
means simply incompatibility. The substrate of a computer program in its
symbolic form are vectors as well: compounds gathering all different
variables. "x" is one component, "y" is another. Adding "x"-es is adding
the same components, x+x=2x, but x+y is that and only that.
Please, turn your anger elsewhere. Many vector spaces have no metric...

> The magnitude of a vector can be determined from a knowledge of its
> components. How is this concept handles quantitatively in the
> presentcontext?

Now, this demands the knowledge of a concrete model of the space. In
a most primitive case this may be a 1-norm, the sum of component values,
at least when I have several different coins in my pocket, that's it.
Again, why getting so nervous?

> Have you ever read the nonsense written in sci.physics by George
> Hammond?
> Did the similarity between what you described here and the nonsense he
> described there ever strike you?

Now, this is unfair, and I wonder why the moderator didn't react. Mr.
GH bothers people with "scientific proofs of God", etc. here we see
a nice, even if lightweight analogy between two geometric models.
Economy, and even quantitative sociology are theories of dynamical
systems. There are problems of measuring, of stability, of probabilis-
tic reasoning with all, quite strong theorems which go with.

You have the Theory of Games, all the non-equilibrium stuff, etc.
Econophysics exists. Search Google. You will find at least 10000
pages.
http://www.unifr.ch/econophysics/
http://www1.elsevier.com/homepage/sak/econophys/index.html

I don't know whether the arbitrage can be formally defined as a
geometric concept in a formalized manner, but such an impolite
dismissal is hardly acceptable.

Perhaps you should also say a few harsh words addressed at John Baez
who dares to "marry" the categorical structures of quanta and general
relativity - apparently completely incompatible and worlds apart?
http://math.ucr.edu/home/baez/quantum/quantum.html

The best.

Jerzy Karczmarczuk