The horizontal axis represents the size of a
configuration. The vertical axis is the logarithm of the total number of logically conceivable configurations
consistent with a configuration size of value S. For a given size S, each
possible configuration is counted by mapping it to a point on the Log Z-S plane.
In order to organize this count of points the area under L0 has been
divided up into wedge shaped bands using lines L1 to Ln. If we take a given size
S, then the vertical distance across a band is the Log measure of the number of
configurations that have a particular disorder value, where disorder increases from bands 1 to n respectively.
Arranging configurations of a particular value of disorder
and size into a 1 dimensional line doesn't do justice to the multidimensional
nature of configuration space, a fact I alluded to in the first part of this
series. Mapping configurations of a particular disorder and size onto a single
vertical line in one of the wedges above will have the effect of forcing a
separation on otherwise natural near neighbors in configuration space. In fact
this is similar to the effect that occurs when one maps a multidimensional
space onto linear computer memory; neighbouring points get separated.
In spite of the limitations of my graphical representation
we can nevertheless use it to help talk about the conditions needed for
evolution to occur.
In the first part I defined living structures as
configurations with powers of self-perpetuation - a process that includes
self-repair and reproduction. Therefore the sort of self-perpetuation I'm thinking of is very proactive in that it is not simply down to atomic bonding
stability (as it is for strong crystalline structures), but instead a form of
maintenance that depends on a blend of proactive repair and reproduction; in
fact in terms of molecular bonds living materials are by and large very
fragile.
One of the fairly obvious requirements of evolution as
conventionally understood is that of “reducible
complexity” (I have talked about this point many times in this blog). Given axioms 3 and 4 (Seen part 1), conventional
evolution requires that living configurations, when mapped to configuration
space, give rise a set of points in this space that are close enough to
one-another to form a completely connected region; very likely this region would be the
multidimensional equivalent of a “spongy structure” made up of extremely thin membrane walls. This connectedness will mean that the random agitations
of evolutionary gradualism can set up a diffusional migration across configuration
space without resort to highly improbable saltational leaps. It is this connected
structure that defines what “reducible
complexity” means. It also explains why so many in the de-facto “Intelligent Design”
community are quite sure that living structures are “Irreducibly Complex” rather than “reducibly complex”. A class of structures
is irreducibly complex if they form a
scattered set in configuration space - that is, they do not form a connected set
but are by and large individually isolated. If self-perpetuating structures are arranged
as an irreducibly complex set in configuration space then this means these
structures can only be reached by saltational leaps. The de-facto ID community then contend,
(with some plausibility), that if this is the case then the only agent we know
capable of literally engineering these leaps is intelligence.
To be fair to the ID community, the notion that organic
structures form a reducibly complex set is moot on at least three counts
ONE) If a reducibly complex set of self-perpetuating structures
exists then it is likely to be highly sensitive to the selected physical
regime. I suspect, although I have no proof, that the physical regimes implying
reducible complexity is a very small class indeed; I guess that any old
selected physical regime won’t do. But even if physical regimes that favour
reducible complexity have at least a mathematical existence we are still left
with the question of whether our particular physical regime is one of them!
TWO) Axiom 2 tells us that the set of living structures
is tiny compared to the set of all possible non-self-perpetuating structures.
This fact is an outcome of axiom 1 and the nature of disorder: If living
structures occupy the mid regions between high order and high disorder then the
logarithmic nature of the vertical axis on the LogZ-S graph will imply that
disordered configurations are overwhelmingly more numerous. This raises the
question of whether there are simply too few self-perpetuating structures to populate
configuration space even with a very thin spongy structure; in fact the spongy structure may be so thin that although mathematically speaking we will have an in-principle reducible complexity, in terms of practical probabilities the structure is so tenuous that it may as well not exist!
THREE) My definition of life in terms of self-repair
and reproduction would seem to imply a threshold of sophistication of
configuration that is relatively high. Even if this set of structures form a
completely connected set in configuration space how did the first structures
come about? Their sophistication would seem to demand a size that is too large to have come about spontaneously (see Axioms 2 and 3). Therefore if evolution is to work our
reducibly complex set of structures must be continuously connected to and blend
with a set of small stable structures toward the lower size end of our graph
where small configuration sizes mean that the probability of spontaneous appearance
is relatively high. (An implication of axiom 2). This is the subject of the
Origins of Life (OOL) which as far as I’m aware doesn't have any substantive scenarios
on the table.
I must express (again) my feeling that solutions to the
above questions are not likely to be succinctly analytical, because I suspect
that attempts to solve them analytically will hit Wolfram’s computational irreducibility
barrier. That is, that the only way of probing these questions is to do a full
simulation, because there may be no other
shorter way of computing the result than working, event by event, through the
full natural history of the world. But perhaps I'm being too pessimistic!
***
The de-facto “ID” community, in my opinion, are not getting
the respect and hearing they deserve. After all, the big issues I've outlined
above don’t have obvious answers. Nevertheless, as I have expressed many times
before, I continue to feel uneasy about the de-facto “ID” community’s ulterior philosophy
and underlying motivation. This uneasiness stems from: a) Their failure to register that even bog-standard evolutionary theory presupposes highly computational complex pre-condition;, that is high information conditions (Which is essentially the lesson from their very own William Dembski. b) That many de-facto IDists still see the subject through the fallacious God did it vs. Naturalism did it dichotomy.
This dichotomy is seductive to both
theists and atheists. The polarized and acrimonious state of the debate in
North America, where it is cast in the mould of a “Masculine God vs. Mother Nature” paradigm, has
probably help keep this dichotomy alive. In this context the natural history question is framed entirely in terms of whether it is guided or unguided - guided by a driving masculine homunculus or left unguided by a scatty mother nature. So, in my next part I will look into the
subject of whether evolution, as it is
conventionally conceived, has direction.
North American Paradigm: Mother Nature or Guiding Homunculus?
Finally I must add this caveat: Although I eschew the
North American paradigm that swings so much on the question of whether natural
history is "guided or unguided”, this is not to say that the established picture
of evolution is correct. As I have said before the game of chess is considerably
constrained by its rules, but if you try moving chess pieces about at random
even under the constraint of those rules you are unlikely to end up with a
sensible game. Physics, as we currently understand it, may not be strong enough
constraint to imply a computation that follows the established evolutionary
paradigm. In later parts of this series I may probe whether there are ways
round the problems outlined above.
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