Although algorithmic complexity often goes by the name Kolmogorov
complexity (after the great Russian mathematician), Gregory Chaitin
has done more than anyone else in developing the theory. He also
proposed the first definition roughly simultaneously with and indepently
of Kolmogorov (and also another fellow, Solomonoff) when he was still
in high school! He has a great web page
http://www.research.ibm.com/people/c/chaitin/
where he has collected electronic versions of almost all of his
papers. Some are "high brow" but others are very understandable
for laymen (like me!). Look for his papers in SciAm, New Scientist etc.
some other related web pages:
http://www.math.washington.edu/~hillman/personal.html
http://www.math.washington.edu/~hillman/entropy.html
[very good]
http://cs-www.bu.edu/faculty/gacs/Home.html
http://www.fmb.mmu.ac.uk:80/~bruce/combib/
[a bibliography of complexity measures]
http://www-personal.engin.umich.edu/~streak/bib/
[another bibliography]
http://www.cc.duth.gr/~mboudour/nonlin.html
[many links to various chaos/complexity pgs]
http://sprott.physics.wisc.edu/pickover/home.htm
Also, some time ago I posted a rather lengthy intro to algorithmic
complexity to the reflector. Look in the archives under Jan-Feb 1996.
Then organize by author. The articles of interest will be
algorithmic complexity [1/2] (23 jan 96)
algorithmic complexity [2/2] (23 jan 96) (split into 3 parts)
complexity definitions (24 jan 96)
I've put a lot of thought into these types of things over the last
year or so. I feel this type of definition of "design" may be
resisted at first by many IDers. The reason is probably obvious
from what I wrote previously. This type of definition gives an
intrinsic measure, i.e. one depending only upon the "structure"
of the object in question. It provides no measure of meaning,
purpose, or intelligent causation or even function for that matter.
For this reason it may be inapproriate to label any measure of
this type as design. But this doesn't mean all is lost necessarily.
For example, do we get up tight at all measuring the complexity
of a protein with a measure such as described here? Do we get
tricked into believing that since complexity does not measure
functionality that proteins are not functional if we can measure
their complexity? No, because we know that proteins are functional.
The point is that this knowledge does not come from the complexity
measure itself. Returning to design, we might imagine some measure
that relates in some way to design, but it won't be the whole story,
i.e. one would need to combine this measure with some additional
information before concluding design.
As I mentioned above, I don't think its really appropriate to talk
about complexity measures in terms of design, but I do see a real
possibility of using them to get an objective measure of irreducible
complexity. Algorithmic complexity is a measure of the degree of
compressibility of an objects description. Compressibility and
irreducibility seem to me to go hand and hand. The real problem
for me is that of tying irreducible complexity to design. For
example, a monkey typing randomly at a keyboard will produce a
document that is irreducibly complex. Clearly we don't want to
call this design ;-). Chaitin has introduced recently some new
complexity measures that, if I remember correctly, are somewhat
analogous to what is called mutual information in information
theory. In any event, these seem to provide a measure of the
inter-relatedness or connectedness between parts of a system
and thus seems to tie in better with what Behe means by
irreducibly complex systems.
But still :), even if we can get an objective measure whereby
we can precisely define irreducible complexity and even if
we can then show that biological systems are in fact irreducibly
complex ... How does one tie this to design? That's the big
question (problem), for me anyway.
Well, these are just a few random (i.e. irreducibly complex :)
thoughts .... Back to work ...
Brian Harper | "If you don't understand
Associate Professor | something and want to
Applied Mechanics | sound profound, use the
The Ohio State University | word 'entropy'"
| -- Morrowitz
Bastion for the naturalistic |
rulers of science |