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A Note On Rigor

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Posted by Paul R. Martin on May 13, 2002 16:04:16 UTC

Hi Richard,

***You claim rigor. I claim you connected to established science like the Dirac and Schroedinger equation by analogy. You derived something having the same form and stated it was the same. It's just an analogy.***

This may be parochial and myopic on my part, but, as I have said many times, I think that what everyone is missing about Dick's work, including Dick himself, is that the derivation of his fundamental equation is a work of pure mathematics. I claim it is a theorem.

If you look at the most powerful and impressive theorems of mathematics, they are commonly derived from a basis that is far removed from the ultimate application. (E.g. powerful Geometry theorems have come out of Number Theory). The way this is done in mathematics is through what mathematicians call isomorphisms. Isomorphisms are what you casually dismiss as "analogy". They may be "just" isomorphisms, but they are completely rigorous and very powerful.

I think if you read the book, "A Beautiful Mind", you would see what I mean. John Nash was a successful mathemetician in large part because he typically attacked difficult problems from a direction completely opposite of the traditional approaches for the subject of that particular problem. He would work up some seemingly completely unrelated theory, and then at the crucial point, would introduce an isomorphism that would relate his obscur approach to the difficult problem and it would yield. I think the book presents this process in a way that non-mathematicians can grasp. Of course, if you can grasp mathematics, I think the Galois theory if by far the best example of what I am talking about.

I am feeling rather frustrated at the moment because I realize that what I wrote has probably not convinced you or even shed any light on the question of rigor for you. But that's the way I see it, and I took a crack at it anyway.

Warm regards,

Paul

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