Money and Mathematics

Well, I am hoping that nobody reading this posting steals any of these ideas, but, anyway, here is a thought I have been mulling for a while:

Money and mathematics seem to have a lot in common. I don't mean that both fields involve numbers, or addition and subtraction. Rather, I mean that the underlying theory of both fields is very similar, and that by studing the nature of mathematics, one can also learn about the nature of money, and, of course, vice versa.

For instance, in the history of American money, there have been attempts to disconnect the value of a dollar from the value of gold, or of silver, and so, in effect, ungrounding the definition of a dollar. But why has this disconnection caused people to become nervous? The reason, I think, is that when a dollar is not defined in terms of gold, people suddenly aren't sure what a dollar *is* anymore. Before the ungrounding of money, in theory, an American citizen could walk into a federal bank and exchange his paper money for the equivalent amount of gold. A paper dollar was a place holder, a substitute for a precious metal. In fact, in just the same way that a person can exchange a check for cash, people used to be able to exchange cash for gold. But if the value of a dollar does not depend on gold, then what are dollars? Do they have value anymore? The whole notion of money is suddenly called into question.

The same concerns, I think, have popped up in the realm of mathematics. For a long time, the exact definition of each of the natural numbers -- 1,2,3, and so on -- was not known. The natural numbers are the currency of mathematics, so if these entities were not completely understood, then, for all mathematicians knew, the entire set of theorms that depended on the natural numbers might be in doubt. Mathematics depended on making sure that the natural numbers had the properties people commonly believed they had. So, in the early twentieth century, Bertrand Russell and Alfred Whitehead tried to define numbers and basic mathematical operations like addition and subtraction in terms of the rules of reasoning, which are more or less certain. They didn't succeed, but I want to stress that, in this case, as well as in the realm of money, the notion that the basic entites should be strictly defined seems very important.

(I am sure I have made many mistakes in the above posting, so if you see any, please let me know.)