Re: definition of science

From: D. F. Siemens, Jr. <dfsiemensjr@juno.com>
Date: Sat Apr 30 2005 - 15:34:44 EDT

As I recall, I have noted that there are an infinite number of
theories/models. To expand, some of them will be exact matches (QM
alternates). Others will match up to a point (Whitehead and Einstein).
The impression I got is that some of the theories mentioned in the SciAm
article belonged in each of these categories--Dicke's in the latter.

Call it what you will, a particle is not a wave, and neither are
wavicles. A hole can be punched with a bullet or with a laser. But they
are not the same. My impression from outside is that the "particle"
theory and the "wave" theory give identical results for all computations.
However, some computations that are devilishly difficult in the one are
relatively simple in the other, but there are two theories for the same
results. The pair, because equivalent, are used as one by scientists.
Philosophers insist that equivalence is not identity. Scientists round
off and substitute linear approximations for nonlinear equations.
Mathematicians say it's wrong. This depends partly on the fact that
scientists have to measure, necessarily with limited accuracy, while
mathematicians submit to a perfect ideal. After measuring with limited
accuracy, scientists idealize their results. Empiricism has its
requirements, as do formalisms.
Dave

On Sat, 30 Apr 2005 01:41:02 -0700 "Don Winterstein"
<dfwinterstein@msn.com> writes:
DFS: Are you suggesting that only one mathematical model fits? ...

DFW: Einstein believed, as do I, that one is superior to all others.
Only experiment can decide. (Although, if you're Einstein, you can
apparently decide also on the basis of which theory has the simpler math.
 : ) ) RH Dicke also presented an alternative to Einstein's General
Relativity, as I recall. I think he wrote the SciAm article. But none
of the other versions have earned widespread acceptance.

DFS: Quanta may be approached either as particles or as waves, equivalent
theories. ....

DFW: There are different representations of the QM formalism (e.g.,
Dirac's bra & ket notation), but it's the same theory. Lots of people
would like a more "reasonable" theory, and I've heard of attempts, but no
one has yet improved on QM as we know it. As for waves and particles,
it's not that we're invoking different but equivalent theories but that
we're doing different kinds of experiments. Particles are also waves;
but when measuring them, some experiments detect particle-like behavior
and others wave-like behavior. It's called complementarity. Or don't I
understand what you're saying?

Don

----- Original Message -----
From: D. F. Siemens, Jr.
To: dfwinterstein@msn.com
Cc: asa@calvin.edu
Sent: Thursday, April 28, 2005 11:02 AM
Subject: Re: definition of science

Are you suggesting that only one mathematical model fits? After Einstein
presented his work, Whitehead came up with a different version. Not
liking Riemannian geometry, his was based on Euclidean. Eddington proved
that the two were equivalent on the four matters then recognized as
relevant. Later work disproved Whitehead's version of relativity because
of other matters. I recall an article in /Scientific American/ that
presented additional relativity theories, though it did not discuss the
calculus underlying them. Some apparently were equivalent to Einstein's
theories, while others were designed to be slightly different.

Quanta may be approached either as particles or as waves, equivalent
theories. I understand that two approaches to string theory were
demonstrated equivalent. In other words, the fit is multiple. Beyond
that, are four dimensions simple? What about 10 or 11? Is seeing a
matching pattern simple? Once seen, it's "obvious," of course. Then why
does it take brilliant people so long to see it? How many have an /annus
mirabilis/?
Dave
Received on Sat Apr 30 15:57:34 2005

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