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Dick Burkhart's avatar

My Ph.D. thesis was about the mathematics of quantum mechanics, specifically the Feynman Path Integral. But I was trying to use simpler math, such as asymptotic expansions and basic functional analysis to explain what Feynman was up to. Today many of the mathematical models being used are highly speculative and don't really help much, including string theory. Typically they appear to "explain" somethings but fail to explain others. Often they get too complex when trying to explain too many things.

There's a certain common phenomenon in mathematical models: You can "explain" almost anything by adding enough "degrees of freedom" (as in string theory) or other speculative assumptions. The big challenge, as Einstein understood, is to find relatively simple models to elucidate at least the key features of some complex phenomena. But such models, if they exist at all, may be difficult to create precisely because they defy intuition. The failures of economists, for example, are legendary because their simple and intuitive models just aren't up to the task of modeling the complexities of real-world economics. The good news is that the realms of intuition and common sense can often be extended by exploring new or different points of view. This why I support speculative physics as an exploratory tool but am slow to jump on the latest band wagon.

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