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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 - 11:23am Sep 25, 2003 EST (# 13962 of 13965)
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.

Pure math, that we use instrumentally, is a "game" or "logical system" that is testable, consistent, and well defined in its own terms. The foundation of pure math is a few axioms, which may include those needed to define the integers, the arithmetical rules

a + b=b+a ...............................................ab=ba

a+(b+c)=(a+b)+c ....................................ab(c)=a(bc)

a(b+c)=ab+ac

and (sometimes for teaching convenience) Euclid's axioms and the geometrical notions these axioms convey. Pure math results can be verified by rules referred exactly to the axioms. It is as real as the game of chess.

What logical instruments do we have to CONNECT our measurements to pure math?

If there's a real world behind those measurements, and that seems exceedingly likely by now, that connection has to be something real, something specific.

If the real world is as mathematical as it appears to be, that connection has to be something of sharp mathematical precision.

That connection will have to be BEYOND the axioms of pure mathematics, which say nothing of the circumstances we measure. We won't be able to determine that connection axiomatically, no matter how mathematically precise it may be. We WILL be able to apply experimental math, and loop tests in particular, to our investigation of that connection.

Note: This is classical physics. Before possible difficulties in "higher" physics are addressed, it makes sense to deal with the logical requirements of classical physics and engineering.

Before the question

What logical instruments do we have to CONNECT our measurements to pure math?

can be asked clearly, one needs to answer another question, well beyond the axioms of pure mathematics.

A) How do we arithmetize our world? How do we measure, and how do we our express our measurements?

Clerk-Maxwell thought harder about that than anyone before Bridgman, and worked out dimensional notation standard to this day.

. . .

P. W. Bridgman spent much time elaborating on Maxwell's definitions and pointing out how necessary careful definition of measurement procedures actually was. It is one thing to express the dimensions of a quantity in standard units. It is another thing to define the measurement, and by doing so define what the quantity means. For instance, the units of torque and energy are identical, though torque and energy are entirely distinct physical ideas. Both have units of (Length^2..Mass)/time^2 . For both the energy and torque definition, there is geometrical information necessary to full definition, but not set out in the units. The unit definitions are encoded notations that achieve compactness but lose information.

The issues of measurement Maxwell, Bridgman and many others have discussed are ENTIRELY distinct from and unconnected to the axioms of pure mathematics. Bridgman pointed out that the world of measurement is a complicated and precise world.

The physical world of the measurable and the "meaningless game" of pure mathematics are distinct. There is no strict logic connecting them.

But with a little algebra, a connection between them seems to appear. That appearance has been taken for granted since Newton's time. D.C. Ipsen describes that algebra very clearly.

rshowalter - 05:16pm Jun 21, 1998 EST (#610 continues with a quote from Ipsen's fine book.

rshow55 - 11:27am Sep 25, 2003 EST (# 13963 of 13965)
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.

Here was the CENTRAL thing Bridgman knew about calibrating and perfecting a measurement instrument.

. THE INSTRUMENT HAD TO PASS LOOP TESTS.

Different cycles or trajectories, ending at the same place, should yield the same final reading. This is the same test surveyors have applied for centuries. This is a kind of test applied again and again in the making of precision tools. Bridgman didn't invent the loop test. But he showed by example and forceful argument how fundamental loop tests were, and insisted that people understand.

Here are two questions:

Do loop tests work at the interface between math and the measurable world?

Are there things like loop tests that work in discourse?

I've felt that these are important questions - felt that the answers to these questions have to be affirmative - and have been working - with lchic - to get these questions much clearer than they have been before.

There are good reasons to do that - and good reasons to do that here.

Reasons that involve with science - and all other issues where complex understanding is necessary.

Peace making is an example where these questions are important.

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