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Missile Defense

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lunarchick - 12:29pm Jan 10, 2003 EST (# 7564 of 7569)

Canonicity

rshow55 - 12:55pm Jan 10, 2003 EST (# 7565 of 7569)
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.

The word is used in mathematics, too.

Let me get a reference, from a fine book edited by a wonderful man (I don't know whether he's alive or dead) who was an utterly aware Nazi war criminal . . . just a minute.

At some levels, I love the guy. Not at others - but on balance - Stanford was right to value him, and so was the McGraw-Hill book company.

Just a minute or two -- I'll find it.

rshow55 - 01:18pm Jan 10, 2003 EST (# 7566 of 7569)
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.

The man I had in mind is W. Flugge, Professor of Engineering Mechanics, Stanford University, and editor-in-chief of the HANDBOOK OF ENGINEERING MECHANICS - - I have the 1962 edition - and I treasure it - it is a classic. Flugge was a very senior, young engineering star in military aeronautics, at all levels, in Nazi Germany. - - Flugge's HANDBOOK is wonderful, and has good examples of canonical equations - which are transforms from one perspective, in one set of variables - to a fully consistent other perspective, in related but different variables. One where you can jump back and forth, and keep track of the information that is perserved, and the information that is lost. That handbook has some examples of canonical transforms of equations of dynamics.

. .

But I like the form of this passage better: (from the Handbook of Applied Mathematics Carl E. Pearson, ed, 1974 Van Nostrand)

8.44 Canonical Transformations

In preparation for the discussion of a technique of historical interest in dynamics we set down the essential ideas concerning canonical transformations , and in so doing show yet another interpretation of the Hamilton-Jacobi equation.

Consider a dynamical system governed by a Hamiltonian, i.e., a set of 2n ordinary differential equations derived from a Hamiltonian function

(equation, not important for this particular purpose, which is to express form - here)

such that

(specific condition, not important for this particular purpose, which is to express form - here)

(specific condition, not important for this particular purpose, which is to express form - here)

The reader is reminded that this is a severe restriction on the generality of the dynamical (or other application) system, and excludes, for example (specific class of problems - in this case, those involving damping)

We seek a transform from the values qi, pi and t to a new set q1*, pi*, t with the property that the Hamiltonian form of equations ( - -- - _ ) is preserved.

( more detail )

rshow55 - 01:27pm Jan 10, 2003 EST (# 7567 of 7569)
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.

You can sometimes put the same facts and known relations into two different frames of reference - sometimes according to different kinds of variables - and problems indeterminant in one frame may be much more convenient in another. IF you know enough to go back and forth from the perspectives.

If one set of people like one approach, and the another the other - they can agree on everything where the answers actually match - and things closely enough related (the things that can matter for action) - - even when approaches are very different (for instance, as different as black and white) - from some perspectives.

If you can trace the logic - you can use data taken from different perspectives to rule out some things in some "models" - . If people agree on the rules - they can come to new agreements about facts - sometimes enough to switch each other to fully compatible perspectives in every way that matters for a particular case.

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