Friday, December 02, 2005
Center of Excellence Proposal
à
The Taos Institute
(on the possibilities)
[bead thread on curriculum
reform]
Ballard’s
communication on information theory advance
à [258]
Hi, folks!
I note that Paul Prueitt asked me to comment only on the quantum claim that Dick Ballard makes.
I did notice that claim. I do not have sufficient information in hand to make strong assertions about whether the claim about the theory itself is true or false. One cannot properly draw strong conclusions about a theory without seeing what the theory is, in practical terms. Most likely, it would take some time to evaluate the theory.
It sounds as if the proposed theory is a member of a fairly large set of proposed theories or proposed theory development efforts, which I think of as "its from bits" or "digital universe" theories. I have gotten into long discussions about other members of that class. The book Moving Mars by Greg Bear is worth reading (and fun, an inexpensive sci fi paperback).
The most intriguing possibility that I know of on those lines resulted in a challenge I posed to some leading mathematicians, not ever responded to:
Good morning, folks!
Maybe the last thing you need right now is a new intellectual challenge, on top of all the ones you already have!
But, .... -- I remember our discussions here at NSF over coffee a few weeks ago. In ADDITION to the various funding issues... you have looked very closely at the Wolfram stuff. It is possible that you and ..(edited).. have a deeper real understanding of his type of models than anyone else on earth. And so you may be the people on earth best equipped to answer the next most important mathematical question about that work, in its relevance to physics. (If you don't have time... well.. you could write up the challenge in some kind of visible note to the readers of your journal.)
As you know, Wolfram does not only discuss cellular automata (CA). In chapters 5 and 9 of NKS, he talks about CA-LIKE models with variable or adaptive connectivity, not all systolic. The difference between systolic versus general connectivity is important, of course, in neural networks. Last week, Robert Kozma showed me two new papers he has in press with Freeman on "neuropercolation" models that might be important to the issue of how to get performance LIKE general connectivity WHEN one is constrained to the hardware realities we normally face in nanoelectronics.
But -- even if we learn how to live within the constraints of nearest-neighbor connectivity in computing... still we understand that general, nonlocal connectivity offers enormous power, if it is possible.
Could it be that the ultimate laws of physics also offer VARIABLE or ADAPTIVE or GENERAL connectivity?
Maybe, maybe not. We certainly do not see adaptive connectivity yet. General relativity and CA-type models of physics based on general relativity STILL ARE LIMITED to nearest-neighbor connections. They allow a variation of the weights in these connections, but that is all. Nothing nonlocal.
Perhaps the ultimate laws of physics are perfectly local, in the end. BUT SINCE WE DO NOT REALLY KNOW.. it is important to develop the mathematical tools that would allow us to find out, someday, in case there is some real nonlocality.
Some would claim that quantum field theory itself is nonlocal; this is not true, but you have heard that story already.
BUT: WOLFRAMS's type of "TOY MODEL" of gravity **REALLY DOES** include non local connectivity. If his model does what he claims it does, in chapter 9, it would be an important first step in allowing us to understand and evaluate nonlocal connectivity in general.
SO HERE IS THE CHALLENGE:
To prove or to disprove what Wolfram claims about his toy model (or to revise the toy model to make the claim true).
Wolfram argues that his emergent "causal network" automata result in a pattern of connectivity in space-time exactly the same as what general relativity predicts in the absence of a source term (in the case T=0). He claims it yields curvature, the scalar Ricci quantity, exactly the same as general relativity. Thus he claims that the Einstein equation, like the heat equation, can be derived as an emergent result of something more discrete in nature. As with the heat equation, the predictions would be highly nontrivial if clamped to interesting boundary conditions. BUT: could it really reproduce gravity WAVES, for example? Could it produce the entire 4-by-4 curvature field and metric as an emergent phenomenon? No one knows. Wolfram claims he has unpublished arguments to show this, but no one knows.
So there it is. If any of these variable connectivity models works, it should be easy enough to create a variable-connectivity version of the entire standard model of physics -- a unified model of physics -- by attaching the kinds of fields I propose in hep-th 0505023 (at arxiv.org, 2005 section) to the space-time points of the Wolfram model. Would it be a true model? I have no idea. But it would be an interesting alternative. The work needed to analyze and test it might be very useful, even if the model itself breaks down in the end.
So that's all.
By the way, I would **NOT** challenge either of you to answer some of the more immediate, large questions that I raise in hep-th 0505023. The reason is that they require a very different flavor of mathematics. Wave phenomena and PDE are important BOTH to the "Wolfram+" are AND to the hep-th area -- but knowledge of PDE is not enough for either area. The Wolfram+ area also requires knowledge of these discrete automaton systems (knowledge which you have and I don't). The hep-th area requires knowledge of field operators -- and that's where I have put more of my own time, so far.
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Additional comments:
1. I have had lots of good contacts with these folks on other issues in the meantime.
2. It is not accurate to say that lack of finiteness is a necessary consequence of continuum theories. At a minimum, it is well known that some superstring theories are finite. But I haven't yet persuaded a good real analyst -- ideally, someone in the school of Walter Strauss (Brown U., I think) -- to take on that challenge either. There are so many sources of paralysis, from bureaucracy to vested interests to legitimate fears of possible abuse.
3. One might imagine that fuzzy or RBF (Radial Basis Function) kinds of representations might be similar to solitons as a way of getting rid of things like the infinite self-repulsion of the electron not only in QED but in classical Lorentzian electrodynamics.
Does Ballard’s information theory do something categorically equivalent?
Discussion about this à [261]
4. I have a certain natural suspicion of any claim to automatically predict everything about the nuclear forces and gravity, based on "only" the information content seen in QED plus some universal elegant principles. It looks to me as if nuclear forces and gravity do contain some additional very fundamental information content -- at a minimum, some new parameters. But Grand Unified Theories have been tried, and I should not jump to conclusions.
5. I have not yet seen what I would consider a really credible theory in this class, despite having chased many, many claims of that sort.