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Missile Defense

Technology has always found its greatest consumer in a nation's war and defense efforts. Since the last attempts at a "Star Wars" defense system, has technology changed considerably enough to make the latest Missile Defense initiatives more successful? Can such an application of science be successful? Is a militarized space inevitable, necessary or impossible?

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rshow55 - 10:34am Oct 12, 2002 EST (# 4825 of 4826)
Can we do a better job of finding truth? YES. Click "rshow55" for some things Lchic and I have done and worked for on this thread.

"I'm more clear now than Steve and I were in 1997 on the nonaxiomatic nature of the world of measurement that S-K fits into. Our work does not pertain to pure math, based on the conventional axioms alone, but requires some additional assumptions, which some might call axiomatic, and some might call acts of faith. Here are the formal “acts of faith” on which our derivation logically rests:

. I assume that parts of the physical world are representable by mathematics.

. I assume that there are arithmetical and dimensional rules that correctly represent these physical things.

. I assume that the parts of the physical world that can be described by correctly stated rules are self consistent, so that values that should be identical according to different computational sequences are identical.

. I assume that a valid system of physical description can represent any combined effects that occur by a permitted construction within the system.

"These assumptions may or may not seem self-evident. I personally feel that they are self-evident. Self evident or not, these assumptions are external to pure math as it is now practiced in the academy. Steve and I assumed these things implicitly, and I believe that some classical mathematical physicists, notably J.C. Maxwell, assumed something like these things.

"We also assumed that the world, rightly understood, was a consistent place - that the right derivations, based on the right assumptions, would in fact fit the evidence of correctly conducted and relevant experiments. This assumption is widely held, though logically baseless, and many feel it is plausible on Bayesian grounds. Scientists often act as if they believe this assumption.

"We also chose to give priority to our basic assumptions, even if the logic of our assumptions required us to discard or modify notations or conventions. . We assumed that that long established notations in mathematical and mathematical physics practice, including very old ones, could include hidden errors or oversimplifications. We assumed that when notations and procedures did not fit the requirements of our “acts of faith” above, we could question those notations and procedures. We also assumed that, after consideration, we could change them.

"Whether such changes are right or wrong in positive terms, they are socially awkward, and we knew it. To question standard notations, especially longstanding ones, is to question reflexes that are organic parts of the people who use these notations.

"Lipman Bers expressed some core facts about math, that make the social and conceptual difficulty of challenging notation clear:

" “What is the strength of mathematics? What makes mathematics possible? It is symbolic reasoning. It is like “canned thought.” You have understood something once. You encode it, and then go on using it without each time having to think about it.”

"What if the “something” that is “understood” is wrongly or incompletely encoded? What if that canned encoding was done hudreds of years ago, so that no one alive can easily think about the “something” that was encoded, apart from the symbolic encoding itself? Problems with such canned encodings ought not to be inconceivable, and should be discussable and testable. For some purposes, the discussions and testing may be best done with people involved who are not committed to the canned encoding under discussion.

"Encodings and usages that are sanctified by the passage of time may not have been carefully done in the first place. Cajori quotes Augustus de Morgan as follows:

“ Mathematical notation, like language, has grown up without much looking to, at the dictates of convenience and with the sanction of the majority.”

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