May 9, 2005
On the discussion of data
regularity ŕ
On the Stephenson Cyber Attack
Taxonomy ŕ
Communication from Paul Werbos
Neuroengineering program at NSF, and dear friend…
to Paul Prueitt (and others)
Good morning!
Some friends of mine have recently asked me to re-examine some
important assumptions about physics. You and I, in different ways, have been
exploring some important possibilities -- but maybe we HAVE been missing
something. My goal here is to lay out a specific challenge that someone might
use to fill in the gap, to open the door to some new things which, IF TRUE,
would be very important to know about.
It starts with something small -- something which you, like I, may
have underestimated at first.
Deep in chapter 9 of a New Kind of Science, Wolfram claims in
effect, that his "causal network automata" (CNA) can regenerate the
predictions of the left-hand side of the Einstein equation. In other words, he
claims that the pattern of dynamics implied by the Einstein equations
(including nonlinear curvature effects) for regions of space in which T=0 is
reproduced exactly as an emergent statistical result from his very simple
models. (There is an analogy here to the way the heat equation represents
emergent behavior from lumpier small things...)
These models are so simple that it is hard to take them seriously.
Yet they are an EXAMPLE of the more general concept of ADAPTIVE CONNECTIVITY,
which will be truly essential to grapple with more effectively, if we ever want
to.... do several things. Engineering has taught us how essential it is to
start from a simple example, sometimes, in order to open the door to new
realms. (Then again, even Feynman played with the harmonic oscillator example a
lot... so it's not just engineering.) So even if we do not like these
particular models, maybe it would be important to explore further.
At first, Wolfram's claim
itself may sound uninteresting. But this also is an illusion, in my view.
**IF** adaptive connectivity could actually reproduce GR kinds of connectivity,
it suggests that the extension to handle gauge fields would not be so hard.
Wolfram doesn't have much of a clue about topology... but that could be filled
in. (For example, I can't help noticing that the class of bosonic theories
could be "approximated" on grids or even meshes, and that this would
allow a very quick way of making a partly-Wolfram-style model work to
regenerate the standard model. In effect, Wolfram's CNA provide an alternative
to John Wheeler's ancient tricks in "metrifying" a Lagrangian
system.)
**IF*** this should work, and if it ever passes discriminative
tests, it would be quite interesting. The idea of adaptive connectivity is a
key part of the idea of the universe as a kind of "great brain" or
"great mind." Adaptive connectivity would also be essential to any
hope of really large, really usable "nonlocal" effects in technology.
-
But -- there is a key hole here. There is one immediate obstacle
which is enough to block any serious pursuit of all this. The obstacle is that
Wolfram never really proved his claim about reproducing GR in the T=0 case.
(Things would look a WHOLE lot more interesting if he or anyone else ever
did.). We don't really know whether the claim is true or not. The challenge is
to find out. At
http://www.kurzweilai.net/articles/art0503.html?printable=1 a conversation is reported with
Wolfram. Wolfram DOES have observations
about the Ricci quantity which are well-argued and reasonable. His claim is not at all fanciful. And yet,
it isn't a proof. What's more... I do wonder about gravity waves. If ANY CNA (the ones he has thought about or
any variation) could really reproduce gravity
waves, as they should... then all of this could be a very interesting
start. But if not.. well. in that case
someone should publish an expose. One way or another... I would challenge
anyone in the gravity business to prove
or disprove the claim. Of Course,
Einstein's formulation may not be your favorite. But models based on adaptive
connectivity could offer some variety
as well..
--------
But I am not in the gravity business, and indeed, am behind on
bureaucratic duties. (My part of NSF doesn't
fund anything involving gravitational theory that I have ever heard
of... And of course nothing here represents NSF views...)
Best of luck,