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Tim,
Mistakes are easy to make. In order to cast a specific problem into my equations, one must first make sure all of the constraints on the data used to develop those equations are in fact fulfilled. Since the universe is everything by definition, and the mechanism by which we obtain the data is undefined by the fact that all information is processed by an unexaminable process, the constraints are valid automatically.
However, in the case of other problems, the data must first be mapped into a data set which does conform to those constraints.
For example, consider economic data. Just for the fun of it consider a data stream consisting of the stock prices on the New York Stock Exchange as the data input. The purpose being to write down the equations those prices must obey.
Well, we have some problems. We have information outside the set of numbers. Our analysis must include all that information or it should be recognized that the additional information is being ignored in the analysis. OK, we may still be able to do something useful. We can see the thing as bunch of numbers changing in time. My work should still yield equations which will capture the observed trends. (There are a lot of statistical models out there which do just that and people find them useful.)
Ah, there is another problem which must be handled. Prices are positive definite (no one pays you to take their stock off their hands). There is a trick to get around that problem. Instead of dealing directly with the prices, one can use x=log(p) instead. There is another problem in that the range of p is not at all infinite; however, that one can be ignored to the extent that we are essentially analyzing a case where p is continuous and can go to both zero and infinity. Those are common approximations made in economics anyway (i.e., few if any economists think about the consequences of money being finite and discreet). Remember, the unknowable data, constitutes trades going on that you cannot see (figments of your imagination inserted to make sense of the data you see).
So, making that single substitution, we can see what the ordinary physics equations become. It turns out that what one obtains is essentially most of the equations taught in the economics classes. Plus, some insights into the field.
I will leave the thing there as being no more than an example of what can be done along the lines you speak of. Remember, what I have developed are no more than the consequences of definition. That means that one must be very careful to define things in an orderly way as it is very easy to misunderstand your own definitions.
Have fun -- Dick |
