From: plpaul
Subject: Re: Applications of Non-Associative Algebras?
Date: Mon, 28 Aug 2000 17:07:40 -0400
Newsgroups: sci.physics.research
Summary: [missing]
John Baez wrote:
> In article <39A6029A.3532@easyon.com>,
> James Gibbons wrote:
> >I was wondering if non-associative algebras have any physical
> >applications other than genetics? I seem to recall John Baez
> >said that physicists are starting to warm up to them.
>
> What are the applications to genetics?
There is a set of lectures by Worz-Busekros "Algebras in Genetics" Lect.
Notes in Biomath 1980. (o is o umlat). The basic idea is, I think,
inheritance is nonassocative using Punnet square and Hardy-Weinberg law.
cheers
pp
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From: Chris Hillman
Subject: Re: Applications of Non-Associative Algebras?
Date: Tue, 29 Aug 2000 09:38:50 -0700
Newsgroups: sci.physics.research
On Mon, 28 Aug 2000, plpaul wrote:
> John Baez wrote:
> > In article <39A6029A.3532@easyon.com>,
> > James Gibbons wrote:
> > >I was wondering if non-associative algebras have any physical
> > >applications other than genetics? I seem to recall John Baez
> > >said that physicists are starting to warm up to them.
> > What are the applications to genetics?
> There is a set of lectures by Worz-Busekros "Algebras in Genetics" Lect.
> Notes in Biomath 1980. (o is o umlat). The basic idea is, I think,
> inheritance is nonassocative using Punnet square and Hardy-Weinberg law.
I have heard that this idea was originally introduced by Claude Shannon in
his Ph.D. thesis! Supposedly it was later rediscovered by someone else,
but biologists are generally unaware that the creator of information
theory was the first to develop the application of modern algebra to
genetics, although I do know of someone at NIH who knows about Shannon's
precedence. I -don't- know, however, if geneticists really use this stuff
very much.
Hmmm... Aren't we talking about what I think algebraists might refer to as
"the simplest possible nontrivial Ore algebra"? Since the Hardy-Weinberg
law involves two noncommuting variables? Namely:
(p+q)(p+q) = p^2 + pq + qp + q^2
where pq =/= qp? There is certainly some interesting combinatorics (due
to Richard Stanley) associated with this particular algebra! Bell
curvewisely speaking :-/
Chris Hillman
Home Page: http://www.math.washington.edu/~hillman/personal.html
P.S.: I shouldn't be so coy--- the interesting combinatorics is Stanley's
beautiful proof of the unimodular nature (monotonic increase followed by
monotonic decrease) of each line in a sort of Pascal's triangle type thing
which comes up in the study of polytopes, and some related results. The
method of proof is probably more interesting than the results themselves.
[Moderator's note: sadly, I must repeat the other moderator's request
that discussions of mathematical genetics be taken elsewhere. - jb]
==============================================================================
From: plpaul
Subject: Re: Applications of Non-Associative Algebras?
Date: 29 Aug 2000 18:31:14 GMT
Newsgroups: sci.physics.research
hi,
here is the reference for "genetic algebras" Bulletin of AMS vol 34 #2 page 107
by Mary Lynn Reed "algebraic structure of genetic inheritance"
pp
[quote of original message deleted --djr]