Saturday, October 11, 2014

Dembski and Felsenstein: Part I

In the above video William Dembski gives us a digest of his mathematical work and what it means for evolution. It attracts the notice of Joe Felsenstein on Panda’s thumb and also PZ Myers who quotes Felsenstein. Myers seems too jaded and tired to engage the video properly and so hands the issue over to Felsenstein after declaring Dembski as “still wrong”.

Felsentein does give Dembski a fair hearing and that’s what Dembski deserves: In Dembski we are not taking about the abrasive and judgmental fundamentalist lunatic fringe: In my view Dembski has done some worthy work, work that deserves proper scrutiny. Moreover, Dembski, to me at least, always comes over as a nice reasonable guy who is not going to threaten anyone with divine judgment if they don’t agree with him. Unfortunately the creation question has been blighted by fundamentalist crank science and the resultant polarisation hasn’t helped the cause of evangelical moderates like Dembski.  

Between them Dembski and Felsenstein both provide some great food for thought, a veritable intellectual feast in fact. However, my overall assessment of the situation is that Dembski and Felsenstein are talking past one another: In the final analysis Dembski is talking about mathematical generalities and Felsentein more about biological specifics (as one might expect from, respectively, a mathematician and biologist). As I have said before on this blog, Dembski’s mathematical points are irrefutable, but they are very general and they don’t directly address the specifics raised by Felsenstein. But the social backdrop is that the Intelligent Design vs. atheism debate has set up such a strong polarizing field that even someone like Dembski will be demonized.

Dembki’s Video:
Twenty seven minutes into the video Dembski throws up a quote by Stuart Kaufamnn which includes the following statement:

Where did those well-wrought fitness landscapes come from such that evolution manages to produce the fancy stuff around us? No one knows.

Yes, the giveness of the requisite fitness landscape is a critical and enigmatic feature of evolution: The fitness landscape is the equivalent of my connected sets of stable organisms : Viz: for evolution to work the class of stable structures must form a continuously connected set in configuration space…. but not only that, the number of ways these structures can be slightly altered must be limited enough for the jump to the next stable structure to not be swamped by the number of possible changes that destabilize the structure. Taken together these two conditions of connectedness and limited “modification linkage", allow conventional evolution to diffuse through the class of organic structures.* Let me just say in advance that over the course of several years I have toyed with the idea of the kind of fitness landscape that would facilitate evolution, but I now doubt that the right landscape has a mathematical existence – I will say more about this in due time.

It is the rightness of the fitness landscape that is the essential abstract structure that would have to guide the standard evolutionary search. If we are to arrive at a working version of evolution we must first get this structure right; or as Dembski expresses in computational terms we must search for the search. The self-maintaining structures of biology are extremely rare in the huge space of absolute possibility; to locate these structures in relatively few algorithmic steps implies an algorithmic starting point that is itself of an extreme rarity (and by implication, also of extreme improbability); in terms of absolute possibilities the smooth fitness landscapes that would render evolution viable are themselves extremely rare beasts. On this point Dembski is irrefutable; in fact he quotes Paul Nelson who says that evolutionary theory fills one hole by digging another (31:20). Moreover, as Dembski hints, people seem unable to see this enigmatic entity of the fitness landscape. This is probably because it is an abstract object which exists in mathematical space as a background controlling structure and this is not easily seen or imagined. In as much as the requisite “fitness landscape” is itself a very rare structure Demsbki’s mathematical point about the projection of one seeming improbable outcome onto another is - I say it again -  irrefutable:  (See also here, here  and here)

Dembski doesn't just provide food for thought for evolutionists; he also says something that ought to pique the interest of the North American dualist ID movement. At 32:30 he says this

So many ID arguments look for discontinuity in the evolutionary process (as opposed to the chance of finding a result given the method of search )…[they] look for evidence for discontinuity.
But I’m going to give you evolution and common ancestry but what I’m interested in is the probability of success using this method of search

At this stage Dembski is neither attacking evolution nor common ancestry; rather he is concerned with the initial “information” required to get standard evolution to work as a process. In the above quote Dembski contrasts his approach with the dualist IDists who are enthralled by the thought of “magical” looking discontinuities existing in natural history. However, I’m not sure whether Dembski is just putting on his evolutionary cap for the sake of the argument and neither am I sure just how far he might support evolution as a process that has been “front loaded” with the requisite fitness landscape information in order for it to work (See also this blog post of mine where I comment on another video in which Dembksi says something very similar). But I’m gratified that Dembski has implied that his work does not necessarily support those “God of the gaps” ID arguments which  very much hang on discontinuities in natural history. Dembski may or may not support evolution but what he has done is that he has made clear just how mathematically “front loaded” the cosmos must be for evolution to work.

By way of conclusion  (at 49:20 and 50:18) Dembski says this:

Darwinian search works because its carefully fine-tuned to work …… Darwinism is the teleological search for teleological  systems.

My comments, reservations and trial conclusions
Dembski’s theorems have their origins in a fact that is agreeably intuitive; namely, that self-maintaining, self-replicating structures as a class form a negligibly minute proportion of the huge space of possibility. When these kinds of proportions are expressed in terms of ratios (e.g. such as the size of the class of organic configurations to the total mathematically possible configurations or the organic class to the physically constrained possibilities) then this will give us probabilities. In fact Dembski’s Conservation of Information (CoI), a theorem that he introduces in his video in probabilistic terms, can be illustrated with a poor man’s mathematically impressionistic proof as follows (But see Dembski for the McCoy version):

Let T be the total conceivable possibilities available to configuration space and L be the number of organic life forms in that space. Thus, assuming equal-a-priori probabilities then the probability of life given T is,

p = Prob (Life | T) =  L/T

Now let us assume that a physical constraint is applied to the space of possibility which reduces the physical possibilities down to C and that we know living structures are a subset in C.  The probability of finding life given this constraint then becomes

q = Prob (Life | Constraint) = L/C

Let us make the not unreasonable assumption that the probability of finding the constraint class is proportional to its size C given T. It follows then:

Prob (Constraint | T) = C/T  = L/T  x C/L   = p/q

That is, the probability of finding the constraint class is equal to the ratio of p/q. This is not a rigorous proof**  by any means but it conveys the idea of CoI in broad brush terms: To increase the probability of finding life to the value q ( > p) we first need to find the constraint. But the above equation tells us that the probability of finding this constraint is proportional to the extremely small value of p. Therefore if we want a large value of q then the probability of finding the constraint is going to be very small; in short the low probability of finding what we want (i.e. life) cannot be removed. According to Dembski the major computational problem of finding life must be effectively solved before we do any “evolving”.

Of course, in the real world the laws of physics provide the kind of constraint which reduces the search space, but it is not at all clear whether or not these laws imply a sufficiently connected and low linkage set of self-sustaining structures to give standard evolution a realistic chance of finding life. If the known laws of physics do facilitate standard evolution then the cosmos has been effectively “front loaded” with information in the form of the right physical regime. At one time I favored this possibility but now I have my doubts – my reasons are to do with the nature of quantum mechanics; it is both a constraint and potentially a way of making huge numbers of computational steps; if this potential is used then there is no need to front load the search with q (See my Melencoli I series). 

Under quantum circumstances information, in the way Dembski has presented it, is not necessarily conserved. Conservation of Information only applies to small space, short time algorithmics where we envisage computation very much limited by Dembski’s computational upper bound. Keeping within that bound we find that either the result sought for is highly improbable or the search used to find it successfully is improbable; improbability ( = information) swaps from one to the other and we can’t get rid of it; it almost seems to have a conserved property, hence Dembski's CoI. But if that upper bound is taken away it’s a bit like saying that the Cosmos has unlimited energy available: If the processing potential of Quantum Mechanics is accessible, then the upper bound is removed: Without that upper bound huge computational resources turn improbabilities into high probabilities and information seems to just come out of the “vacuum” so to speak. (My pro tem conclusion is that the cosmos is immanent intelligence in action, an intelligence we see only at the low level, much like looking at the neurons of the human brain.)

In the next part of this series I will look at Joe Felsenstein’s reaction to Dembski. I’m not giving away much in saying that his basic argument is that the laws of physics do provide sufficient front loading to make the search for life a realistic option. In my view he is both right and wrong; right because, yes, the laws of physics flow out of quantum mechanics and it is quantum mechanics that does the trick. But he is wrong in that physics hasn't been front loaded in the way Dembski’s work suggests. Rather, if quantum mechanics is the search engine it has such huge processing potential that a smooth fitness landscape would not needed to be front loaded into the cosmos. However, I’m not pushing this as a likely idea, but rather as an avenue to be explored; and yes it could be a dead end.

* Complicating this concept of the fitness landscape is the fact that an organic regime becomes a very important part of that landscape itself and therefore a feedback occurs which will mean that evolution is non-linear.

** This proof is based on the assumption that the cases in favour of life are a subset of the search cases. However, in general the two could simply intersect in which case we find:

                                               Prob (Constraint | T)  < p/q

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