[GAP Forum] Conway Co2 group (fwd)

[Rudolf Zlabinger]

Dear Beth,

although this is outside the range of GAP Forum, here my basic ideas, yet in
an very intuitive and initial state, this is only a first possible and
speculative approximation:

Assume, that physical space is finite and consists of elements connected by
some kind of neighbourhood and thus can be modelled by finite graphs. Then
all possible physical structures can be modelled by graphs, whereas flat
space is a special structure only and physical objects, as particles,
emerging from flat space by their special structure, thus physical objects
and space are somewhat the same: graphs.

The symmetries of space and physical objects then would be given by groups,
and, as beeing finite, by finite groups..... Symmetries could be to some
extent "structure stabilizers" over the time and thus they could be the
primary constituent for objects, that could survive long enough to gain
physical "existence", the emergence I mentioned above. In such a way groups
could describe and classify emergent physical objects, for example the
stabile particles known, and not yet known.  (A "periodical system" of
particles?)

A thrilling example: Consider a full graph, where all vertices are fully
connected to each other. Lets assume, that lenght is a measure on the
minimal pathlengths between the vertices. Thus the object described by such
a graph would be a region of space of minimal diameter and maximal densitiy
and maximal symmetry and thus maximal stability, properties, that are, for
example, described for a black hole.....

A model like this could describe any structure, that, at the present, cannot
be handled by models used as yet....

I am fascinated by this idea, and, in order to develope it, I am now first
trying to get enough qualification in discrete mathematics. The next step
would be to gain some ideas and informations to "dynamic structures" ("time"
series of discrete structures).

thank you for your interest, best wishes, Rudolf Zlabinger


----- Original Message ----- 
From: "Beth Holmes" <bh at mcs.st-and.ac.uk>
To: <Rudolf.Zlabinger at chello.at>
Cc: "Steve Linton" <sal at mcs.st-and.ac.uk>
Sent: Sunday, April 16, 2006 3:52 PM
Subject: Re: [GAP Forum] Conway Co2 group (fwd)



Rudolf,

Hi.  I was interested to see that you want to apply group theory to
physics.  My own experience is mostly in computing with ATLAS groups, but
I am currently seeking physics problems that I can apply computational
algebra to.  If there is anything that you need any help with that wasn't
in Alexander's email, or any computations that GAP isn't sufficient for,
please get in touch as I am really keen to get involved with that sort of
thing.

Yours,

Beth Holmes

---------- Forwarded message ----------
Date: Fri, 14 Apr 2006 20:02:50 +0200
From: Rudolf Zlabinger <Rudolf.Zlabinger at chello.at>
To: Alexander Hulpke <hulpke at frii.com>
Cc: forum at gap-system.org
Subject: Re: [GAP Forum] Conway Co2 group

My longterm target is application of group theory, and, more general, the
further application of finite and discrete mathematics in basic physics. A
first approximation will be the automorphisms of graphs. I know, there is a
long way to go for me, but I think the effort will be worthwile. GAP will be
a valuable help to me for following my target.