xorbie

I was recently thinking about the differences between math and science, and between the highly mathematical sciences and the less mathematical ones.

Take for example epidimiology. Basically, you analyze huge amounts of data and extract theories of causation. In theory, if you had an infinite amount of data, and some sort of way to analyze all this date, wouldn't you be able to extract a Grand Unifying Theory? And if one does not exist, wouldn't you at least be able to extract every singly possible physical law? Of course, you will never get an infinite set of date, but say we had one that was suffienctly enormous. Of course this field of math is not at all mechanistic, as in it does not describe the mechanism by which any of these laws operate and thus a purist might not be satisfied. Also, because you never understand the mechanism involved, and because the set of data is finite, there is a small (and it gets smaller as the data set grows) chace that you will be off.

This may be ugly, but it works. Paul Dirac noted that the most successful basic physical theory, quantum electrodynamics is also mathematically the ugliest... so there is not necessarily any corelation between "clean" or "beautiful" math and actual effective theories.

Now this may all be just a shortcut, but could it work?

DoubleDutchy

I guess the number of laws is potentially infinite. Gravity for instance is responsible for a host of phenomena in the physical world. If I have no clue to the underlying mechanism I could start formulating laws interrelating those phenomena and some regularity would always emerge. To sort out useful relations I need a theory first. (Be it a correct or an incorrect one).

jpbrooks

So epidemiology would be an example of a highly mathematical science because it draws inferences from huge amounts of statistical data.

AFAIK, there is no "procedure" for "extracting" a GUT (Grand Unifying Theory). So simply being able to analyze all the data with various theories is no guarantee for arriving at a GUT.

But how can every possible physical law be "extracted" in the absence of some kind of general theory that provides a complete description of the physical universe?

But how can the size of a "sufficiently enormous" data set be determined for a "model" of the entire physical realm?

I doubt it. Quantum Electrodynamics only unifies QM and Special Relativity. So it seems to be a long way from a GUT.