Re: definition of science

Dave Siemens wrote:

"As for QM, the earliest approach to quanta involved particles--Planck, Einstein, Bohr, Sommerfeld.... Since the historical development of theory is not all that important to practitioners, but solutions and applications are, you got the amalgamated approach."

The approach I got was for everybody, theorists and experimenters alike--and theorists certainly ought to know history. I'd argue that the early experimental and conceptual results led to QM but had little to do with the shape of current theory, which encompasses much more than those pioneers imagined at the time. Specifically, it says (as the result of considerable agony and argument) that all physical entities are both wave-like and particle-like. Current theory deals with such complementary properties of entities and doesn't bifurcate. QM is now your "amalgamated approach."

Anyway, it's been interesting and educational. Thanks.

Don

  ----- Original Message -----
  From: D. F. Siemens, Jr.<mailto:dfsiemensjr@juno.com>
  To: dfwinterstein@msn.com<mailto:dfwinterstein@msn.com>
  Cc: asa@calvin.edu<mailto:asa@calvin.edu>
  Sent: Sunday, May 01, 2005 4:18 PM
  Subject: Re: definition of science

  On the infinite number of models, we go back to the turn of the past century. French engineers were working on a project of designing devices to produce various motions, with the aim of having a specific plan to introduce to produce whatever motion their larger device needed. They hoped for a simple menu to solve engineering problems. A country engineer, Koenigs, presented a proof that any pattern of motion could be arrived at by an infinite number of different devices. I ran the paper down in /Comptes rendues/ some decades back, but do not remember the issue. Poincare expanded the proof in one of his books to cover any set of data that fall under the least action principle. Logico-mathematical models are more flexible than mechanical devices, which finishes the proof.

  As a practical matter for supercession, theorists have to produce theories that make different predictions. However, such replacement is not necessary. It may be enough to produce a more convenient version. I have noted that some recent proofs, Fermat's last theorem and the 4-color map problem, are appallingly long. A new approach leading to an elegant proof would not prove something new, but would be hailed. From a different angle, experimentalists won't know what to look for unless a theorist has produced a tentative map. Theorists can't know that they've produced something relevant until experimentalists can test it. Denigrating the alternate approach is quite silly, but very human.

  As for QM, the earliest approach to quanta involved particles--Planck, Einstein, Bohr, Sommerfeld. De Broglie devised a wave theory later, I think about 1923. I believe Schrodinger showed the equivalence of the two approaches a few years later. Since the historical development of theory is not all that important to practitioners, but solutions and applications are, you got the amalgamated approach.

  When I need to check out with my groceries, the several clerks are equivalent. Each one is equally skilled in scanning the items and taking my money. They are, however, not identical. Leibnitz held the theory of the identity of indiscernibles. But it does not seem to be a necessary principle. I may not, in mathematics, be able to distinguish between 3+1 and 2+2, but there is a difference between a fried egg and a 3-egg omelet and 2 2-egg omelets. Euclid's "Things equal to the same thing are equal to each other" holds in geometry, but not necessarily for comestibles.
  Dave
Received on Tue May 3 04:08:04 2005