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Re: [ProgSoc] Programming! Code!



On Tue, 2006-10-17 at 00:09 +1000, Christian Kent wrote:

> On Mon, 16 Oct 2006, Roland Turner wrote:
> 
> > I've not been tempted to dig into group theory yet. My present algebraic
> > struggle is Grgin's Algebra of Quantions. The premise appears absurd:
> > stop looking for different physics to unify quantum and relativistic
> > physics, instead use a different kind of number (the quantion). The
> 
> Whoa, that's so new-fangled that it's not even on Google yet, let alone 
> Wikipedia.  You have to find a few bookstore extracts just to see it 
> mentioned, or his name.

It is indeed new-fangled. What Grgin is working on is so far out of left
field that he essentially had to wait until he had retired before he
could work on it. He encountered quantions a decade ago (and, as an
"algebra with no known purpose", it's been known for far longer), but no
funding body would provide a grant to work out something that isn't a
clear extrapolation of existing work, so he shelved it for years. He's
now put the ideas together in a self-published book which was previously
difficult to obtain, although I note that Amazon now offers it[1].

My copy came from an ex-colleague who happens to be married to the niece
of one of Grgin's high-school friends (IIRC). While I was visiting said
ex-colleague in Frankfurt in January, he showed me this book that he'd
been given on a "you may be interested" basis, but which he found was
over his head. Needless to say I was fascinated, and have the good
fortune to be able to make slightly more sense out of it, so he gave it
to me.

> Give us a review, when you're ready.

Heh, nine months on and I'm less than a third of the way through it;
don't hold your breath. This may actually take me longer to read than
Hofstadter's Goedel Escher Bach did.

I suspect that part that I've read what will, for me, be the most
interesting part of the book anyway. Rather than leaping into the
maths/physics, he spends about 100 pages on epistemological concerns; if
you're going to spend years of your life working on something, it's
desirable to have some reason to believe that there's some probability
of a worthwhile outcome. For working academics this is largely solved by
working only on projects that funding bodies will make grants for, but
when you're in uncharted territory, what then? Well, it turns out that
if _any_ algebraic unification is possible, then quantions are it. He
doesn't merely postulate this, he proves it formally. This has a
resonance with Einstein's work on general relativity; it was clear
fairly early that it was an all-or-nothing proposition, that no part of
the general theory of relativity could be changed without bringing the
entire edifice down (erm, what, E = mc^2 + k?). This is in stark
constrast to the vast majority of theories in use today which were
developed by incremental improvement over decades from some early good
approximations. The point for Grgin is that it is likely that this
theory will, within his lifetime, either run up against contrary
experimental evidence, or be accepted _as-is_ by the scientific
community.

> (I've come to hate the way all 
> maths-topic pages on Wikipedia seem to be immune from the easy-to-read 
> style pervasive on the rest of the site).

Well, some of the ideas that mathematicians work with are intrinsically
difficult...

BTW, if you're interested in something of the flavour of what quantions
are, have a look at Wikipedia's article on quaternions[2]. The rules for
multiplying quantions are similar, but not the same. The important
difference is that while quaternions abandon commutativity (ab != ba)
and retain inverses (apart from a particular distibguished number, every
quaternion has an inverse; the analagous property of real numbers is
that, apart from zero, every number has a reciprocal), quantions instead
retain commutatity while abandoning inverses and therefore division.

Grgin's point of departure was to realise (!) that division was not, in
fact, neccessary for physics, but that commutativity was indispensible.
(e.g. The forementioned two-body problem, which comes up _everywhere_ in
physics: when determining elements of the gravitional fields around two
bodies A and B, multiplication of their masses is required and the field
is the same whether you brought A to place where B was or brought B to
the place where A was.) Armed solely with this realisation and "Zovko's
interpretation" which maps hilbert space onto the quantions (instead of
onto complex numbers), somehow, the rest is pure mathematics. Zovko's
interpretation is the _only_ physical postulate required; large tracts
of the rest of physics can then be derived as theorems by
straightforward (!) algebra.

If this plays out, the boundary between physics and mathematics will
need to be redrawn; much (most?) of what we currently call physics will,
in fact, be mathematics.

- Raz

1: http://www.amazon.co.uk/exec/obidos/ASIN/1420840363
2: http://en.wikipedia.org/wiki/Quaternion


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