Quantum game theory and Keynesian Economics

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The commonly accepted quantum theory can be used to predict optimal outcomes in social phenomena, i.e. the economy. To bad, we (i.e. the government) obviously doesn't use it to set financial policy.

Every year thousands of introductory economics students are made to accept as valid one of Keynes's lasting inversions of classical economics, namely the proposition that saving may be a private virtue, but is a public vice. According to Keynes, a community that seeks to increase its rate of saving would end up impoverishing itself and actually saving less, but the community that increases its consumption at the expense of saving would end up being richer and saving more. This proposition, frequently stated in macroeconomics textbooks as the "paradox of thrift," arises mainly from Keynes's definition of saving to include the hoarding of cash, contrary to the classical definition and language of the marketplace, but has received little recognition or criticism as such.

The classical theory of growth against which Keynes proposed his paradox of thrift argument simply states that economic growth is determined by the rate of saving or capital accumulation. The greater the amount saved out of income, the more capital goods, land, and labour services can be bought or hired for production.

Up until recently the decision of who is correct has been primarily the domain of politicians who select the economist that sets the fed's policies to encourage or discourage savings through manipulating the prime rate, tax laws, and other such tools of the politician.

Physics and mathematicians have been silently developing concepts of Quantum game theory. Quantum game theory is being applied to economic theory for proving optimal strategies in decision theory. (I'll spare you the reading through physics equations: SAVE!)

If Quantum game theory sounds like something out of Star Trek, that's because there is a made up series. This episode is sometimes known as the "Meyer's Penny" by quantum game theorist. It can be found in the book "A Beautiful Math" by Tom Siegfried. (To bad we can't get our politician to read the bills they vote for, suppose getting them to read this book would be classified as a quantum impossibility.)

Well, we can't do much about the politician till the next election. But till then, before you make your next major investment: if you use an advior ask your investment adviser if they are familiar with Quantum game theory. If you use software ask the vendor if the software analysis is based on Quantum game theory, if not get one that is.

Best starting point I can think of if you want to learn more about this subject is the paper Quantum Game Theory in Finance you can skim past the math and read the text.

Chomsky v Shannon

There is a whole lot of literature on Chomsky and generative grammar. There is also quite a bit written on Claude Shannon's Information Theory and the development of stochastic linguistics. On this subject I just read a really great paper that outlines the arguments by Chomsky against statical models in linguistics and computational linguistics in particular. Please read the paper in its entirety at http://www.vinartus.net/spa/95c.pdf by Steven Abney.

My favorite is the argument by Chomsky, (sorry Steve you missed this point in your paper), because Chomsky in essence by making his argument disproves himself. Here is the snippet in the form from Chomsky, Noam (1957). Syntactic Structures. The Hague/Paris: Mouton. pp. 15.

1. Colorless green ideas sleep furiously.
2. Furiously sleep ideas green colorless.

It is fair to assume that neither sentence (1) nor (2) (nor indeed any part of these sentences) had ever occurred in an English discourse. Hence, in any statistical model for grammaticalness, these sentences will be ruled out on identical grounds as equally "remote" from English. Yet (1), though nonsensical, is grammatical, while (2) is not.

If you just read the above you are an English speaker so both (1) and (2) are now in your experience, they are both indeed now part of the English discourse. Thus Chomsky actually disproves himself on that point.
Furthermore, since Chomsky wrote the sentences, the probability is not zero, and not even remotely zero. Wikipedia seems to that that (1) has enough informational value that there is even has a wiki page dedicated to the sentence, you can follow the link. In fact any nonsensical set of words that Chomsky would written for (1) and (2) with would also have a non-zero probability of occurring in a sentence. Secondly, since it is used as part of an argument it now contains information, (even though independent of the argument (1) and (2) may not have informational content) they have grammatical value. And anything that that any English speaker would replace (1) and (2) with in that argument would give the same results. So therefore, the Markov approach would actually work with a non zero probability since the 'grammaticalness' of the sentences is established by their use in the argument. And (2) is thus gramatical although grammatically undecipherable by generative grammar rules.

Hence, in any statistical model for grammaticalness, these sentences will be ruled in on identical grounds as equally "proximate" English.

Aside from my argument, Steven Abney's paper does a great job of explaining why Chomsky’s arguments do not bear at all on the probabilistic nature of Markov models only on the fact that they are finite-state, and that Chomskys arguments are not by any stretch of the imagination a sweeping condemnation of statistical methods.