Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] Digest Number 1236

On 16 Apr 2001 tuning@yahoogroups.com Paul Erlich wrote:

>
> Hi Stephen.
>
> >a category Douthett has extended into his particle physics
> >applications of ME.
>
> May I ask you what you mean by "particle physics" here, and what
> these applications are?
>

Hi Paul,

I know that this is one of those connections that sounds bogus at first
blush. And I, not being a physicist, have to be REAL careful with this
one so that it doesn't come off sounding less like a music-math-physics
connection and more like New Age gibberish. So the following is all with
the caveat: "as far as I understand it" and you can read the real story in
the pages of the Journal of Mathematical Physics.

I'm still hazy about exactly what KIND of microphysical systems Douthett
et al have applied maximal evenness to. Like many laymen, I have
difficulty dealing with abstract physical models -- I always want a
picture. Anyway, here goes....

The official area of physics this falls into is, within the physics trade,
actually called "statistical physics" as applied to large numbers of
particles displaying certain kinds of "behaviors." (Big tongue in cheek
on that last word, pace Jonjoe McFadden -- in this case "behavior"
involves the "pairwise interaction of spins on a lattice.") You'll recall
that in the 1991 Clough & Douthett article in JMT, they use a conceptual
model of ME that asks you to imagine a given number of electrons (say 7)
positioned in the same orbit and which are allowed only certain locations
(say 12). If, after placing one of the electrons at an "allowed" location
on the circular orbit, you are required to place the others "in such a way
that the charge equilibrium is disturbed as little as possible," you get
the good old ME pattern 2212221.

When I first read that, my reaction was really no more than "that's a
great analogy." Sure, I did some idle (novice) daydreaming about
deBroglie's insight from the quantization of vibrating strings, and
wouldn't it be cool if, and so on. For a non-physicist this is
Gurdjieff-Ouspensky stuff (irony intended). But I thought there couldn't
possibly be any REAL connection between a culturally and historically
ubiquitous scale structure and the behavior of charged particles via a
common mathematics. I was wrong.

Although I heard about it earlier than the first published article, I
think it's fair to say that the official birth of maximal evenness as a
mathematical model useful to physics came with the article entitled
"Energy extremes and spin configurations for the one-dimensional
antiferromagnetic Ising model with arbitrary-range interaction," by Jack
Douthett and Richard Krantz, published in Journal of Mathematical Physics
37 (7), July 1996, pp.3334-53. I also have a copy of Douthett's
Dissertation (University of New Mexico, 1999) entitled "The Theory of
Maximally and Minimally Even Sets, the One-Dimensional Antiferromagnetic
Ising Model, and the Continued Fraction Compromise of Musical Scales."
I've been told that Douthett continues to work with Krantz and other
physicists on applications, and I believe at least one other article has
come out in J.Math.Phys. I think last summer Clough and Douthett made a
"pop version" presentation of all this at the Bridges Conference in
Kansas, and they have a version coming out in a general interest science
journal soon.

In a nutshell, that's all I know (or think I know) right now. While I
continue to avoid jumping to conclusions about all this (as I would advise
everyone to do), nevertheless this connection makes me want to visit every
school board across the nation and ask them, in a not very polite way,
"Could you remind me once more why math and science are more important
than the arts?"

In this case at least, music has trumped physics in getting to the math
first.

Best,

Steve

Re: [tuning] Digest Number 1236

🔗Stephen Soderberg <SSOD@LOC.GOV>

🔗Stephen Soderberg <SSOD@LOC.GOV>