Tuesday, September 09, 2014

Declarative Cognition vs. Procedural Cognition.

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!

On Quantum Decoherence

*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.


dimwoo said...

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?

Timothy V Reeves said...

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.