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Wednesday, February 04, 2009

value of analysis

What is the value of finding simple formulas to explain things?
Our minds, in the midst of this computerized landscape, sometimes seem small and insignificant.
If a program exists to simulate a system, what is the value of searching for simple ways of looking at it? One answer is that it cuts down on the number of cases one needs to simulate. Getting at the important parameters limits and sharpens the questions and makes on more effective at using the simulation. But what if one can somehow ask the computer to do this? To write such a nice interface to the code that new structures are created based on results from running the code.

The research topic I'm involved in has a funny history with computation. I think that some of the people involved in the early days had something against mathematical reasoning, and the slow process of analysis. One can try to guess at the reasons. Perhaps they'd observed too many mathematicians or theorists making grand statements on practical problems where the methods were simply inadequate and did not actually solve the problem. Or maybe they were not great analysts themselves and just trying to keep the power in their own hands. Regardless, the closing of the SSC precipitated a battle that is still going today between computation and analysis. There is excess on both sides. The theoretical structures one sees are overly grandiose. There are lie algebras and differential algebras and non-standard analysis and geometrical concepts such as tensors and fiber bundles. These are spoken of both with reverence and spite. Those who invoke such concepts either are trying to appease those theorists who they admire or prevent people from thinking critically and trap them into a self-serving view. Some of the original theorists had good motivations and indeed a broader set of questions they were looking at where such abstraction may have been helpful. On the computing side, one sees object oriented computing concepts such as polymorphism, linked lists, discrete algorithmic type approaches, control theory, optimization, SVD, model theory.
Viewing physics from an information theory, algorithmic approach. It sounds modern and laudable in some sense, but behind it is a desire to kill analysis.

This snake's nest of buggy concepts and software in the end often solves the problems good enough to get by. But one sacrafices understandability in entering this field. One speaks of minimizing terms and higher order calculations where exactly what kinds of objects these terms are members of and sometimes even what is meant by order is typically murky. It resembles a religious cult or a radical political group more than solid physics. But the rhetoric is getting old.
So I've gotten a bit specific here. I meant to try to explore the value of analysis. I feel that clear analysis is the only way out of this mess, but just what that means and whether it is adequate is not always clear.

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