>Brian writes (in part):
>
>"I think what is really needed is an objective measure of
>complexity that isn't associated with such things as functionality,
>value, meaning, purpose etc. The term I like is organized complexity.
>This certainly carries with it an implication of functionality and
>purpose."
>
>Good post -- food for thought. I'll toss in my 2c worth.
>
>We all will agree (I think) that a "fish" is less complex
>than a "Gish." (reference to my friend Dr. Gish's book).
>
Ah, but which one is more organized? ;-)
Burgie:===================
>But what MEASURE is applied to say this?
>
>Kelvin writes:"When you can measure what you are speaking about,
>and express it in numbers, you know something about it; but when
>you cannot measure it, when you cannot express it in numbers,
>your knowledge is of a meager and unsatisfactory kind; it may be
>the beginning of knowledge, but you have scarcely, in your thoughts,
>advanced to the stage of science."
>
>So I want to know a measure.
>
as an experimentalist, I couldn't agree more. But my views on this tend to
get me in trouble. Discussing "facts" and the "fact of evolution" on
talk.origins, I finally had to reconcile myself to the fact that the
orbital period of Pluto is not a fact. ;-)
Burgy:===============
>Assume Dr. Gish weighs 150 pounds. Consider five objects:
>
>1. Dr. Gish
>2. A dolphin
>3. A motorcycle
>4. A mass of protozoa
>5. A tub of seawater
>
my ranking is, in order of increasing complexity, i.e simplest first:
5 3 4 2 1
It might surprise you to know that Charles Bennett's complexity
measure, "logical depth" would rank them this way, again in order
of increasing complexity:
4 2 1 5 3
Actually, 1 5 and 3 would have a nearly equivalent measure.
Now, I'll leave you in suspense as to how to rationalize such a
seemingly outrageous conclusion ;-).
Burgy:===========
>Assume all five objects weigh the same. They all have the same
>number of elemental particles making them up -- about 10^30 or so.
>
>Now we can SPECIFY EXACTLY each of the five objects ONLY by
>specifying exactle each of the positions and velocities of each of
>the 10^30 elemental particles. Six measurements for each, relative to
>an XYZ grid. 6 x 10^30 measurements in all -- for each one.
>
>But it takes exactly the same number of measurements to specify
>each one! Are they therefore all of the same "specified complexity?"
>I think not. But I do have a measure which suggests that!
>
Very good! This type of example is repeated many times as an example
of how seemingly obvious definitions of complexity don't work. In fact,
the first paper I know of using the term "organized complexity" was
written by Warren Weaver in 1948 and I believe he used something just
like your example to illustrate the difference between "disorganized"
and "organized" complexity. A beaker full of water or a cylinder full
of gas would be complex but disorganized.
Here we run into one of the biggest problems in the complexity
literature, i.e. a disagreemnet about what words such as order,
organized, complex, random, chaotic etc. mean. I've switched terminology
on you above by talking about organized complexity instead of just
plain complexity. A long time ago Bill Hamilton asked me to define
organization. I've now put together a list of "conceptual" definitions
of both complexity and organization which I'll post separately. By
"conceptual definitions" I mean a list of criteria that any
successful objective measure must satisfy. In the complexity literature,
the terms "organized" and "irreducible" are usually redundant, i.e.
most people people have in mind organized irreducible complexity although
they just say "complexity". In the paper mentioned above, Weaver
defines "problems of organized complexity" as:
"problems which involve dealing simultaneously with a sizable
number of factors which are interrelated into an organic whole."
This seems to be a common denominator for many of the intuitive notions
of complexity today.
>If I knew an anser to all this, I'd certainly tell somebody.
>But the answer -- for me -- must be quantitative. It must
>specify a procedure for measure. I've never seen one.
>
There have been a few precise objective definitions of complexity that
have appeared:
Measure Originator
Shannon Entropy Claude Shannon
Kolmogorov Complexity Solomonoff, Kolmogorov, Chaitin
Thermodynamic Depth Pagels
Logical Depth Bennett
Stochastic Complexity Crutchfield
However, they are all surrounded by controversy and there is no general
consensus on which is best. Kolmogorov probably has the best reputation
historically and is my own preference. Actually, I ran across
Crutchfield's stochastic complexity just recently so I should reserve
judgement on it being as I don't know what it is :). Thermodynamic and
Logical Depth are big boo boos, IMHO.
WRT living organisms or biological evolution many have in mind a
so-called "morphological complexity". There is an excellent review
on this:
McShea, Daniel W., "Complexity and Evolution: What
Everybody Knows", <Biology and Philosophy>, vol. 6,
pp. 303-324, 1991.
ABSTRACT: The consensus among evolutionists seems to
be (and has been for at least a century) that the
morphological complexity of organisms increases in
evolution, although almost no empirical evidence for
such a trend exists. Most studies of complexity have
been theoretical, and the few empirical studies have
not, with the exception of certain recent ones, been
especially rigorous: reviews are presented of both the
theoretical and empirical literature. The paucity of
evidence raises the question of what sustains the
consensus, and a number of suggestions are offered,
including the possibility that certain cultural and/or
perceptual biases are at work. In addition, a shift in
emphasis from theoretical to empirical inquiry is
recommended for the study of complexity, and guidelines
for future empirical studies are proposed.
The conclusion is that the question is still open. There is
not enough evidence to say that morphological complexity
increases during evolution nor is there enough evidence to
say unequivocally that it doesn't.
More interesting, to me anyway, would be to see if one could
rank organisms according to the Kolmogorov complexity of
their genomes. This should be possible in theory, although
the practical difficulties may be insurmountable at present.
========================
Brian Harper |
Associate Professor | "It is not certain that all is uncertain,
Applied Mechanics | to the glory of skepticism" -- Pascal
Ohio State University |
========================