[time 84] Re: [time 82] discrete models, QM vs. GR

Stephen P. King (stephenk1@home.com)
Wed, 31 Mar 1999 21:46:58 -0500

Dear Ben,

        I just got of the phone with my friend Paul Hanna. He confirmed the
octonionic-relativity connection. We are will be working out the details
and I hope to post it here ASAP. He is not on-line... :)

Ben Goertzel wrote:
> One more comment. I am really in love with discrete physics models. Stripping away the
> fancy math and getting everything in terms of lattices and finite algebras
> is incredibly revealing. Remember, we can only test our theories up to finite precision
> anyway. If it's the case that the "magic" of continuous mathematics is needed to capture
> physical theories, that's wonderful, but it should be demonstrated rather than assumed. I
> know this is an eccentric view but I'm convinced it is correct. One can get straight from
> logic to discrete models, and I suspect that this is how the next physics revolution is going
> to work -- in synch with the computer revolution. The universe as bits!

        Have you read Wheeler's papers on "It from Bit"? Several people are
busy looking into this. I am convinced that that is a fundamental
principle hiding there. I again refer you to Pratt's ratmech.ps paper
(http://boole.stanford.edu/chuguide.html#ratmech); it and Wegner's
Interactive computing model paper
(http://www.cs.brown.edu/~pw/papers/math1.ps) contain ideas that IMHO
are pointing us to it! :)
> Now let me make this more concrete.
> Suppose we view the Standard Model as tony smith wanted to, as a discrete
> 8-D lattice
> This lattice isn't ~quite~ derivable from abstract algebra, because
> algebra just gives you a graph, not a graph with weighted links. I.e., the algebra does not give
> you the metric structure.

        Do we look at this quantum mechanically by thinking of an ensemble of
graphs, one for each possible way that the nodes can be connected?
> But, what is it that GR talks about? Precisely this metric structure, and
> how the massive elements in space affect it.

        Don't we need to consider how "this metric" is constructed by Nature? I
think that there is a mutation/selection mechanism at work, behind the
scenes as it were. Interestingly, mutation can be seen as a One -> Many
mapping and selection can be seen as a Many -> One mapping. What if
there is a symmetry or duality involved? From my discussion tonight with
Paul, I think that this will be fleshed out shortly, but as you say it
is just a crazy idea. ;)
> Perhaps we can view the two perspectives on the cosmos as follows:
> 1) the local perspective sees the links in the universe graph as having
> certain "standard" weights
> 2) the global perspective sees the feedback between the weights on the
> links and the entities (particles) living at the nodes of the graph
> This is a half-baked idea obviously, but ... ;)

        It tastes good to me! :) Could we think of this "feedback" as part of a
computational process that is "approximating" "absolute values of
quantum mechanical quantities x, p, "approximate" being understood as a
kind of average of quantum mechanical obscure values. Here is a kind of
contraction procedure of R^6 to R^4 by some compactification of a small
region into a point, in the expectation that the region would be quite
small compared to the classically recognizable region." Hitoshi's post
[time 72] ?
> GR basically says that space is curved more near a massive object. This
> means that mass is defined as that which makes weights smaller (makes a single link
> correspond to a smaller distance).

        This would connect easily to Hitoshi's explanation of time (and space!)
uncertainty. We still need to take Robert's latest ideas and plug them
in, there seems to be a Fourier transform like relationship between time
and space. There will also be ideas coming in from the octonion people!
> Even if these ideas are totally wrong, as is likely, they illustrate the
> kind of extremely simple framework I think needs to be adopted to get at the heart of things
> More later,
> ben

        That is what we need, ideas that could be wrong! :)



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