Some intriguing
material from ID physicist Rob Sheldon has recently appeared on Uncommon Decent
(See here.*1). He addresses the
question of whether or not a bottom-up
universe will generate life and comes to the conclusion it won’t. By bottom-up
I think the idea is that each part of the cosmos only responds to its immediate
locality; that is, in terms of my “node” model of the universe, each node only
signals its immediate neighbors and responds in a way consistent with certain
“localized” physical equations*2. In contrast, in a top-down universe nodes will react to
their total environment directly; that is, without need for the kind of signal
continuity whereby widely separated nodes can only communicate with one another via a
relay system that involves intermediate nodes passing the signals on.
Sheldon’s reasoning
in favour of a top down universe goes along these lines:
Random searches
obey the diffusion equation of which the Gaussian distribution is a solution.
The latter expands with a velocity given by v = x/sqrt(t) which implies an
expansion that slows with time. He therefore implies that this kind of search
is too slow to be useful. (Incidentally this slow communication associated with
the Gaussian is an issue that arose in my theory of gravity – see equation 10.5
on page 73 of Gravity and Quantum Non-linearity)
So, Sheldon goes
on to think about non-random searches – in particular of the “Levy flight” kind
where the random walk step size has a power law form – that is, the size of the
step has a distribution a bit like the distribution of crater sizes on the
moon. This kind of search is faster, but it is non-local. This non-locality in
Levy flight arises because nodes that are not adjacent must directly signal one
another without using the relay system of intermediate nodes.
My criticism of
these otherwise worthy ideas is that we need to take into account the quantum mechanical
analogy of the diffusion equation, namely the Schrodinger equation; here the signaling
is local and yet the wave solutions disperse linearly
with time; (i.e. much more rapidly than random walk) this is probably because, as I have pointed out in my Melencolia I series, quantum signaling cancels
out huge swathes of randomness. However, this in itself doesn't necessarily
rule out non-locality – for if the wave function literally collapses (as a opposed
to appears to collapse through
decoherence) then non-locality is still
on the agenda. Quantum signalling simply tells us that searches don't need to be non-local to be effectual in seeking significant configurations, but more to the point is the question of how we select what is found by our quantum search;
for, I submit, the cosmos has a general “cognitive structure” of seeking, rejecting and selecting. That selections are occurring is, I propose, evidenced
by literal discontinuous jumps of the wave function. But the big question is: What selection criteria do we need to input in
order to get the cosmos to do its strong anthropic principle job of generating
life? It is this selection procedure that, I’ll hazard, introduces nonlocality.
One of the
fallacies of the North American IDists is their attack on a straw man version
of the cosmic generation of life. This version doesn't take cognizance of the tripartite cognitive structure of seek, reject and select,
but rather thinks in terms of the physical regime as specially chosen in a preordained
way to generate life using a procedural (or "imperative") paradigm of computation rather than a
declarative paradigm; in the imperative paradigm the problem has effectively been solved in advance - front loading is the term used to describe it, I think. (See IDist’s VJ Torley’s views here as an example of this fallacy). Declarative computation is not
on North American ID agenda, partly, I suspect, because they have unconsciously taken on board a procedural
concept of “mindless natural forces”. They simply don’t see the cosmos as a cognitively
active search; but then neither do the "procedurally" minded atheists with whom
they contrast and compare themselves.
For standard evolution to work, configuration space must be reducibly complex. This means that the physical regime must be so chosen that the class of self-maintaining structures forms a connected set joined by such thin fibrils (or channels) that ordinary diffusion is able to search it successfully. But presumably in such a case so much computational effort would be required to find the right physical regime in the first place that in effect the problem solution has been solved in advance by "front loading" it into the physical equations *3. Given that many an evangelical atheist bases their anti-theist beliefs on a standard view of evolution this must be the mother of all ironies!
For standard evolution to work, configuration space must be reducibly complex. This means that the physical regime must be so chosen that the class of self-maintaining structures forms a connected set joined by such thin fibrils (or channels) that ordinary diffusion is able to search it successfully. But presumably in such a case so much computational effort would be required to find the right physical regime in the first place that in effect the problem solution has been solved in advance by "front loading" it into the physical equations *3. Given that many an evangelical atheist bases their anti-theist beliefs on a standard view of evolution this must be the mother of all ironies!
Relevant links:
Configuration space:
The Melencolia Series
Configuration space:
The Melencolia Series
On Quantum
Decoherence
Footnotes
*1 Sheldon is a
man worth keeping an eye on, but I find his politics far too right wing for me;
he used to run a blog on Townhall!
*2 Localized
physical equations don’t use “fractional differentials”. An example of "fractional differentials" arises in the
kind of procedure seen in the following rather bogus looking method of attempting
to derive a relativistic quantum equation using canonical substitutions:
(From Quantum Mechanics II, Landua 1996)
*3 Actually it is not clear whether or not such reducibly complex sets have a mathematical existence.
2 comments:
Mostly way over my head I'm afraid, but fascinating. I thought I was keeping up until this point:
"My criticism of these otherwise worthy ideas is that we need to take into account the quantum mechanical analogy of the diffusion equation, namely the Schrodinger equation; here the signaling is local and yet the wave solutions disperse linearly with time"
What does it mean that they disperse linearly in time, and why is it significant? Must one study the Schrodinger equation to understand?
Hi Dimwoo, thanks for the comment.
The Schrodinger equation implies solutions where the envelopes expand very quickly in a way proportional to time. This contrasts very much with the slow expansion of the Gaussian bell shaped envelopes whose expansion slows up with time.
The reason for the fast expansion of the Schrodinger wave envelopes is probably because the wave signalling has the effect of canceling out a lot of random backtracking. This contrasts with Gaussian envelopes where inefficient backtracking slows things down.
Thus Quantum signalling is an excellent search mechanism if you are looking for organisation.
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