Another fun fact about Brouwer’s theorem is that it can be shown to be equivalent to the nonexistence of draws in the game of Hex.

Umberto Eco, “The Original and the Copy”, in Francesco J. Varela and Jean-Pierre Dupuy (eds), Understanding Origins, Kluwer Academic Publishers, 1992, pp.273-303.

Let us imagine the following:

In 1921 Picasso asserts that he has painted a portrait of Honorio Bustos Domeq. Fernando Pessoa writes that he has seen the portrait and praises it as the greatest masterpiece ever produced by Picasso. Many critics look for the portrait, but Picasso says that it has been stolen.

In 1945, Salvador Dali announces that he has rediscovered this portrait in Perpignan. Picasso formally recognizes the portrait as his original work. The painting is sold to the Museum of Modern Art, under the title ‘Pablo Picasso: Portrait of Bustos Domeq, 1921.’

In 1950, Jorge Luis Borges writes an essay (’El Omega de Pablo’) in which he maintains that:

1. Picasso and Pessoa lied because nobody in 1921 painted any portrait of Domeq.

2. In any case, no Domeq could have been portrayed in 1921 because such a character was invented by Borges and Bioy Casares during the forties.

3. Picasso actually painted the portrait in 1945 and flasely dated 1921.

4. Dali stole the painting and copied it (masterfully). Immediately afterwards, he destroyed the original.

5. Obviously the 1945 Picasso was perfectly imitating the style of the early Picasso and Dali’s copy was indistinguishable from the original. Both Picasso and Dali used canvas and colors produced in 1921.

6. Therefore the work in New York is the deliberate authorial forgery of a deliberate forgery of a historical forgery (which mendaciously portrayed a non-existent person).

In 1986 there is found an unpublished text of Raymond Queneau asserting that:

1. Bustos Domeq really existed, except his real name was Schmidt. Alice Toklas in 1921 maliciously introduced him to Braque as Domeq and Braque portrayed him under this name (in good faith) imitating the style of Picasso (in bad faith).

2. Domeq-Schmidt died during the blanket bombing of Dresden and his identity papers were destroyed in those circumstances.

3. Dali really rediscovered the portrait in 1945 and copied it. Later, he destroyed the original. A week later Picasso made a cop of Dali’s copy, then the copy by Dali was destroyed. The portrait sold to the MOMA is a fake painted by Picasso imitating a fake painted by Dali imitating a fake painted by Braque.

4. He (Queneau) has learnt all this for sure from the discoverer of Hitler’s diaries.

All the individuals involved in this story are now dead. The only object we have at our disposal is that hanging in the MOMA.

How is “… a universal price mechanism ..” [from p 226] different from a grand unified theory or theory of everything?

D Saari, “Mathematical Complexity of Simple Economics” discusses the dynamics of markets. Could this also be applied to the dynamics of energy econmics in general realtivity and quantum mechanics?

I have read Tamer Basar and Geert Jan Olsder, “Dynamic Noncooperative Game Theory (Classics in Applied Mathematics)”, [SCIAM]. I was very impressed by how they eventually came to use Pursuit-Evasion Games [chapter 8] to demonstrate this complicated mathematics for physical applications in various types of engineering.

I have read Bernd Heidergott, Geert Jan Olsder and Jacob van der Woude, “Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications (Princeton Series in Applied Mathematics) “. I was astonished to see how simplified game theory algebras can be using this form of dioid, k-algebra. There are various other forms such as Min-Plus [or Tropical] that heve even been extended from real to complex numbers.

Petri nets are used for graphing these powerful algebras. Nodes are used in lieu of vertices and arcs rather than edges. Form my perpsective these could be called “Node Operator Algebras” since they appear be so similar to Vertex Operator Algebras.

Petri nets also use transitions and tokens. The latter might be able to represent energy quanta.

Max-plus algebra, Wiki review:
http://en.wikipedia.org/wiki/Max-plus_algebra

Max-plus algebra:
http://www-rocq.inria.fr/MaxplusOrg
or
http://amadeus.inria.fr/gaubert/maxplus.html

Petri Nets:
http://www.informatik.uni-hamburg.de/TGI/PetriNets/

Algebra over a field:
http://en.wikipedia.org/wiki/K-algebra

Answer: whatever someone will give you in exchange for it, in goods or services.

Different people may arrive at different values. You are likely to accept those goods or services which you consider to be worth less than a dollar, and accept those goods or services which you consider to be worth more than a dollar.

The point is, different people will evaluate the dollar differently. Dollars are fungible; one is the same as another (as currency, one might be collectable to a numismatist).

John Armstrong is right, that two people can have “… assigned different values to the goods involved in the trade.”

As for a plausible theory of the economy in disequilibrium and how it moves to equilibrium, I was actually refering to a (limited) number of “economists” employing mathematical techniques borrowed from quantum mechanics or some other field of advanced physics trying to resolve that problem. I suppose they deserve some credit for trying, but whether e.g. the so-called isomorphism of “expected value” and “density matrix” is going to save the day, I doubt it …

And so is almost all other mainstream economic theories. I think this intellectual straightjacket is unfortunate.

Correction: (mainly U.S.) economists dreaming of the Nobel price who still suffer from the illusion that economics is on par with physics seem to take this “general equilibrium” stuff seriously.

If I value some collection of your goods more than a collection of mine, and similarly you value that same collection of your goods less than you do that same collection of mine, then we both benefit (in our own estimation) by trading. Nothing has been created or destroyed, but we both feel better off, since we assigned different values to the goods involved in the trade.