Re: Characterizing complexity

From: dkomo (dkomo871_at_comcast.net)
Date: 07/29/04 

Date: Thu, 29 Jul 2004 15:50:42 +0000 (UTC)

Perplexed in Peoria wrote:

> "dkomo" <dkomoNoSpam@cris.com> wrote in message news:ce36sv$13iu$1@darwin.ediacara.org...
>
>>Richard Dawkins mentioned an idea to characterize complexity in his
>>recent book _A Devil's Chaplain_. Dawkins has way of coming up with
>>simple ideas which are often quite powerful. Here's what he wrote:
>>
>>"We have an intuitive sense that a lobster, say, is more complex (more
>>'advanced', some might even say more 'highly evolved') than another
>>animal, perhaps a millipede. Can we measure something in order to
>>confirm or deny our intuition? Without literally turning it into
>>bits, we can make an approximate estimation of the information
>>contents of the two bodies as follows. Imagine writing a book
>>describing the lobster. Now write another book describing the
>>millipede down to the same level of detail. Divide the word-count in
>>one book by the word-count in the other, and you have an approximate
>>estimate of the relative information content of lobster and
>>millipede. It is important to specify that both books describe their
>>respective animals 'down to the same level of detail'. Obviously, if
>>we describe the millipede down to cellular detail, but stick to gross
>>anatomical features in the case of the lobster, the millipede would
>>come out ahead."
>>
>> --Richard Dawkins, _A Devil's Chaplain_, p. 100
>>
>>He then presents a plausibility argument as to why the lobster's book
>>would be longer. The millipede's segments are all the same. So its
>>book would have one chapter describing the segment, followed by the
>>phrase 'repeat N times.' The lobster's segments, on the other hand,
>>are all different, so it needs separate chapters for all its segments.
>>
>>Note that Dawkins is equating information content with complexity
>>here, and supplying a workable, but partially qualitative definition
>>of both.
>
>
> I think that Dawkins is talking about Kolmogorov complexity here. To
> my mind, the key point about Kolmogorov complexity is that it insists
> that the language used to describe the object must be rich enough to
> say things like "repeat N times" and more complicated variations of that
> phrase. It doesn't limit us to a fixed set of phrases. (But, in thus
> unleashing descriptive power, it makes itself somewhat ambiguous and
> very non-operational as a metric.)
>

I just had a series of exchanges with John Wilkins about this very same
thing on talk.origins. I claim that Dawkins is using the term
"description" in a different way than it is used in Algorithmic
Information Theory. Dawkins intends his written descriptions to be
*meaningful* and easily understood. No such restriction is put on
descriptions in AIT. And Dawkins doesn't care if his descriptions are
of minimal length or optimal in some other sense. He just wants to use
a consistent set of descriptions of different organisms to gauge the
relative complexities of those organisms.

Frankly, I wish people would stop even mentioning Kolmogorov complexity
as some kind of a metric to consider. Whatever utility this idea has
for AIT, the sad fact is that there is no known method for even
computing the length of the minimal program that will output a given
string, nor to tell if a particular such program is of minimal length.
As a general metric for complexity, Kolmogorov complexity is useless.

Dawkins' proposal, on the other hand, is practical and could be put to
immediate use. It doesn't differ that much from the kind of verbal,
mathematical and pictorial descriptions biologists and naturalists have
been writing for hundreds of years now.

>
>>I make the following observations. Mammals would come out more
>>complex than "lower" forms of life because describing their
>>neurologies, intelligence and social behaviors would fill volumes.
>>Describing human psychology and culture in detail would fill entire
>>sets of encyclopedias.
>>
>>I'm undecided about how to handle social insects like bees, termites
>>and ants. Individually these creatures are no more complex than other
>>insects. But their interactions produce incredibly complicated group
>>behavior and structure -- an example of the phenomenon of emergence.
>>There's very little neurology involved. It's just large numbers of
>>simple agents following simple rules producing very complex emergent
>>behavior. Do you put just the rules of the individual insect
>>interactions into their "book" or do you describe in full how the
>>entire colony functions? The size of the two books will differ
>>considerably.
>
>
> There are three different kinds of complexity being confused here.
> Or perhaps I should say that you are using your complexity metric to
> measure the complexity of three different kinds of objects.
> These three are:
> * Organism complexity as specified by genetics.
> * Organism complexity after development and learning.
> * Societal complexity - ie. complexity of multi-organism composites.
>
> It should be obvious that societal complexity is the complexity of
> a different kind of thing from organism complexity - hence those
> encyclopedia volumes about human culture just don't count in
> assessing whether a man is more complex than a mouse. They count
> only when assessing whether human culture is more complex than mouse
> culture.
>

Yes, it is good to make these distinctions. However, the overall
complexity of a class of organisms should be the sum total of the three
complexities you mentioned. And you left one out. I don't know what to
call it now since you already used the word "societal". So I'll just
call it Group complexity -- complexity of complete organisms in
interaction. Cultural complexity would be another term for it.

So, IMO, if mice don't form complex societies and human beings do, that
should very much count against the mouse in any descriptive comparison.

> To understand the difference between my first two kinds of objects,
> make the assumption that the essential genetic difference between man
> and mouse is that in the genetic specification of the pre-frontal cortex
> the mouse specification says "repeat N times" whereas the man
> specification says "repeat 2N times". That is not much difference
> between man and mouse in complexity at the genetic level. Also assume
> that the genetics does not preprogram the connectivity of those pre-frontal
> neurons - that the connectivity gets established in the course of
> development by learning. Writing a description of what that interconnect
> ends up being is going to take a lot of information, for either man or
> mouse. But it will take at least twice as much for the man, because there
> are twice as many learned connections to describe. Perhaps some of those
> additional connections serve to encode language. The mouse just doesn't
> have room for language. Hence, the Dawkins/Kolmogoroff iterator "repeat
> N times" doesn't necessarily add much complexity at the genetic level,
> but it enables considerable complexity at the developmental/learning level.
>
>

But connectivity goes up as N^2. That's why even though our brains may
only have three times the volume of a chimp's brain, our thinking
abilities may be nine times greater, at least.

[There are N(N-1) ways to totally interconnect N neurons, while there
are (2N)(2N-1) ways to do so with 2N neurons. That's a factor of 4 to 1.]

I don't think such interconnectivity information belongs in the
description anyway. That'd be a case of description overload. The
differences in neural interconnectivity would come out in descriptions
of behavior and function of the respective organisms.

     --dkomo@cris.com

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