Monday, March 30, 2009

Darwin Bicentenary 17: Information and Evolution - Some Preliminary Thoughts

Shannon’s concept of information leads, in some cases, to trivially obvious conclusions. Consider for example the illustration of DNA (example 5 in part 15): As we get to sequence DNA it gives up its information, and thus it becomes less information bearing simply because we have less to learn from it. The information has moved from DNA to our heads and books. The reason for this is that Shannon was concerned with the transmission of information, its movement from place to place. Once the information has been successfully received, whatever it means to the recipient, the signal is now redundant (literally) and Shannon’s job is finished. (Shannon was not concerned with the “meaning” of information; the latter is bound up with the epistemological effect of information once it has been received) Trivially, then, DNA loses its information as we learn from it. However, in spite of that, what DNA doesn’t lose is its potential to inform an ignorant recipient, like for example a ribosome. DNA’s potential load of information is never lost and so in this sense DNA, even after its information has passed on to us, remains information rich.

But now consider the examples I related in part 15 of this series; the crystal lattice, the Mandelbrot set and a pattern of 1s and 0s generated by a “random” sequence generator. In each case a simple algorithm is used to generate a pattern, although the resultant patterns have a diversity of form that spans a very large window of the order-disorder spectrum. In spite of their complexity the Mandelbrot set and the output of a random sequence generator are potentially informationless. This is because a pattern that can be described using a relatively simple algorithm has the potential of losing its ability to inform to any recipient coming into possession of the algorithm and who knows how to operate it. But to an observer who doesn’t know the Mandelbrot algorithm or the algorithm of a random sequence generator, the patterns generated by these methods are information rich because this observer is unable to store their information succinctly. And yet relative to another observer who knows the algorithms and can therefore effectively store the patterns in a few bits of information, the Mandelbrot set and the output of a random sequence generator are information sparse. For the ignorant observer the in principle compressibility of the Mandelbrot set, becomes practical incompressibility. These information sparse patterns are only information rich relative to uninitiated observers. This relativity becomes even more apparent from a Divine perspective. God, presumably, knows everything with certainty and thus no pattern holds any surprises for Him. Moreover, His own being, in spite of being the seat of infinite complexity, is presumably based on some kind of logical truism and is thus absent of all information. Information in Shannon terms is a measure for the ignorant, for the fallible, and for the human.

As I pointed out in part 15 of this series, information is an observer relative term and therefore conflating observers really can give the impression of lots of information being created out of next to nothing. I have heard ID theorists say that one can’t create information. To that I would say “yes and no”. “No” because it is conceivable that an information rich pattern in actual fact has its origin in the few bits of information implicit in a simple algorithmic recipe; under these circumstances conflating observers leads us to the conclusion that information laden patterns may have their origins in something containing very little information. “Yes” because an improbable information rich pattern may be derived from the information inherent in prior conditions. That is, if a pattern is strongly conditioned on antecedent patterns, then it must derive its improbability from those antecedent patterns. Human probabilities are always conditional, and as such based on assumed circumstances. Consequently a pattern with a high information content may condition on a succession of preconditions that are themselves the source of improbability and thus of information.


Given the precedents of the foregoing paragraph it is natural to ask: Is it possible that the complex patterns of DNA potentially contain a lot less information than is apparent to the know-nothing reader? This is indeed what evolutionists are effectively claiming about life; that is, that life has a high probability given the relatively simple laws of the cosmic physical regime*. If evolutionists are right in assuming that the cosmic regime elevates the probability of the structures of life, thus depressing their information content (or at least to someone who knows that physical regime and understands its implications), then life’s information content is actually embodied in the relatively elementary algorithmic forms of physical law. Needless to say ID theorists believe that physical law has not achieved this feat of elevating the probabilities of living structures or implicitly containing life’s apparently rich information content.

***

The number of simple algorithms is in limited supply because simple algorithms, by definition, are constructed from a relatively small set of parts. A small set of parts can only be combined in a relatively small number of ways, thus severely limiting the number of possible simple algorithms that can be constructed. Hence, the class of simple algorithms capable of generating complex forms in realistic time runs out before it covers even the tiniest fraction of the class of complex configurations. The same mapping argument applies even if (in line with a more real world scenario) these algorithms are simply required to raise the probability of complex forms rather than generating them with a probability of unity. It therefore seems very unlikely that simple algorithms could be used to generate something as complex as life, or even flag it with an elevated probability.

But I only said “unlikely” because given that simplicity can create complexity (if only a limited class of complexity such as fractals), it remains conceivable that there is some relatively simple algorithmic regime out there capable of raising probabilities on living structures away from the uniform light grey spread implied by absolute randomness. If this is actually the case then the structures of life are potentially a relatively high probability, low information phenomena. If such a regime has a platonic existence, and moreover has been reified in our cosmos, this would mean that trying to get an estimate of the information content of life from the enormous combinatorial space of possibilities using unweighted probabilities, as ID theorists so often do, doesn’t tell the whole story; for it is conceivable that the use of unweighted probabilities is only valid relative to observers who either do not understand and/or do not know the full implications of the physical regime. Under such conditions the probability of evolution is, in fact, a conditional probability conditioned on the probability of the “chosen” physical regime of the cosmos. And yet I would concede that ID theorists are right in delivering an important challenge to evolutionists: OK, so we can find simple algorithms that generate complex fractals and nearly random sequences; but chaotic patterns are one thing; the cybernetic complexity of living structures is something different again.

At this stage in my investigation, however, I feel I cannot absolutely rule out that a relatively simple algorithmic physical regime can weigh probabilities in favour of the evolution of complex living structures. But in the same breadth I would want to acknowledge ID theorists’ robust challenge to this possibility (not to mention the challenges over the interpretation of paleontological evidence). But ironically herein is the rub for ID theorists: once the concept of a quasi-divine designer is invoked as the source reifying the apparently remote probabilities of living configurations by means of a special creative dispensation, there is no telling where such a Designer might employ his creative skills in reifying low probability configurations - for example, perhaps in the selection of a rare elegant algorithmic regime (if such has a mathematical existence) that elevates the probability of life. If a Divine Designer is capable of providing a special creative dispensation directly to living structures He may of take one step back and select a life enhancing algorithmic regime expressed by elementary laws, and this act would be a design feat in its own right.

It is surely an irony that the biggest challenge to haunt ID theory maybe the notion of design itself; once one allows in a designer who offers special Providences the floodgates of possibility are open. Contemporary Design theory with its antievolution ethos may prove to be its own worst enemy. The question I am left with is this: Did intelligence fill in for the very low probability of life by direct action, or does it work through a very elegant but very rare (and therefore low probability) algorithmic regime? Expressed theologically the question is this: Has God provided two special creative dispensations; one for the physical regime and yet another for living matter, or is creation a single dispensation? I am hoping the answers to such deep questions will come to light as I proceed in this investigation.



Footnote
* I disagree with ID theorists that given what ID theorists call “chance and necessity” (What I call “law and disorder”) it is chance that is called to do the “heavy lifting” in aid of evolution. If evolution is to work, the extreme improbabilities of pure chance have no chance of generating life and thus it is down to physical law to elevate negligible chances to realistic probabilities, perhaps via the structure of morphospace.

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