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Very Interesting Thoughts, Mike, And Furthermore...

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Posted by Paul R. Martin on May 6, 2003 15:40:07 UTC

Hi everyone,

Yes, it's good to be back. It's even better to see Dick's paper is still being discussed. It's better yet to see that Dick's skill at attempting to explain his ideas in language to the rest of us is improving (I think his response to Tim was excellent). And, yes, life has been good to me but has kept me very busy.

On "absolute reality". Mike did an excellent job of framing what I wanted to say about this. Too much of our discussions have gotten all balled up over the use of the word 'reality'. As you know, Harv, I supported your suggestion that we use 'R1' as the symbol denoting Dick's arbitrary "set of numbers". But, as you have consistently failed to see, such a choice makes no difference in the results of Dick's formal development. It only makes a difference in how people interpret his results, and what he says, if they haven't put in sufficient effort in trying to understand the formal result.

Let me try to run a comb through this mess in order to tease out some distinctions that I think are confusing a lot of people.

First, there is the vernacular notion of 'reality' that everyone seems to have in his/her head. That is, "whatever is real", or "whatever exists", or "whatever is". It would be hard to get an agreement among people of exactly what kinds of things, and exactly what particular things, belong in the set of "real" things according to each persons notion, but as for the notion of "reality" itself, I don't think there would be that much disagreement among people if they could only articulate what they mean by "real", "exist", or "be".

That "reality" is what Science tries to investigate and explain. And, as Mike so eloquently pointed out, Science needs to refine the notion with respect to the level of abstraction from which one is to consider any particular member or subset of the set of "real" things. In this regard, if the adjective 'absolute' is stuck on the front of the word 'reality', a new source of confusion is introduced because the notion of 'absolute reality' might mean different things to people who would otherwise agree on the meaning of 'reality' by itself. (Keep in mind I am still discussing the first notion which I called the "Vernacular notion".)

Secondly, there is the formal notion of the term 'reality' as defined in Dick's paper (read this as 'R1' if you like, Harv). Even though the term was chosen to be suggestive of interpretions of his final result, that is incidental and has nothing to do with the formal conclusions derived from the math on the basis of this definition of 'reality', among other things. Think of it this way: Statisticians talk about "populations" in their work. If they happen to be talking about a particular study in which a set of real people had been sampled, it would be appropriate to ask them "Exactly what people comprise your population?" But if they happen to be talking about a theorem of statistics which includes the term 'population' it wouldn't make much sense to ask them that same question. Similarly in Probability Theory, the term 'Universe' is used in a formal sense to mean the entire set of elements under consideration. It would be a severe stumbling block in the way of understanding Probability Theory if you insisted that the use of the term 'Universe' be specifically related to the Universe studied by Astronomers.

Now, what happens when we stick the adjective 'absolute' on this second, formal, notion of 'reality' as defined as "a set of numbers"? To start with, we know, by definition, what we mean by 'reality': we mean a completely unspecified and arbitrary set of numbers. So, what would we mean by 'absolute reality' in this context? Well, I suppose we could mean "an absolutely, completely, unspecified, arbitrary set of numbers". Or, to make it stronger, "a perfectly, absolutely, completely - without exception - arbitrary, unspecified, set of numbers that could be of any size, configuration, pattern, derivation, level of specificity, without constraints, or other qualifications or preconceived limitations, or anything else that you could think of for that matter".

I don't think it adds anything.

As for Monday morning quarterbacking - You are pretty demanding, Harv. Dick stumbled on his fundamental equation after a considerable amount of work and in his opinion at that time, he thought it was remarkable that such a set of formal constraints could be found on an arbitrary set of numbers. If we stop the clock there, and if I imagine that I were told of that result, I am sure that I would tell him the same thing I tell him now. I would say, "Dick, I'm no expert, but from what I know, I think you have discovered a new theorem of Probability Theory!" But, I wasn't there then. If you were there then, Harv, you would ask him, "Dick, do those constraints tell us the rules of football?" Dick would say, "Well, ...no.", and you would dismiss his result with a polite snort.

Start the clock again. Five years or so after that discovery, and after five years or so of work on that differential equation, Dick was able to find solutions to his equation which turned out to be most of the laws of Physics (The rules of football, baseball, and soccer). Now, you come along and ask him "But what about Basketball? And what about the scores of next week's games?"

From my point of view, and from my knowledge of math, any differential equation that hairy and which has solutions as hairy as Maxwell's, Einstein's, and Schroedinger's equations, is likely to have several more solutions. You are right that it is a lot easier to check out a solution than it is to discover one. So, (and I don't know if this was Dick's method or not) you could guess, for example that Schroedinger's equation might be a solution, and try it and see. To find a solution that has no precedent, is a lot tougher, but it in no way means that such solutions don't exist.

To make that last point a little clearer, Harv, consider difference in the level of difficulty between these two questions: (1) What are the factors of 28,203? and (2) Is 237 a factor of 28,203? It is pretty clear that the monday morning help you get from (2) makes (1) a whole lot easier.

Your criticism of Dick is that in spite of what he has achieved, the discovery of the fundamental constraint, and the discovery that most of Physics is bound by that constraint, he hasn't done enough work in finding novel solutions to his equation.

My response is that it is time to pass the baton. Dick is an old man. He should be credited for what he has done and he should be relieved by a set of young, energetic, mathematicians and physicists who should step up and carry on that new work.

Finally, for anyone who cares, my email address has changed. My new one is prmartin@paulandellen.com

Also, to see what takes up a lot of my time, check out www.paulandellen.com

Warm regards,

Paul

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