Monday, November 13, 2006

The non-complexity of the mind

Creationists make an argument against the theory of evolution that goes by the name "irreducible complexity". I refer you to Wikipedia here for a detailed discussion of the argument. The idea is that that if a biological system is useless if any of its components is missing or modified then it could not have evolved - arisen from an accumulation of small changes. An every day example would be a mousetrap - it has no utility if any of its parts is missing, and so could not have evolved.

It turns out that in all cases suggested so far by the Creationists, the argument doesn't work. It doesn't work in the case of the mousetrap, either - somewhere out on the net is an example of how a good mouse-trap could arise from a series of small changes to a primitive mouse-trap. Biological systems have another trick up their sleeves as well. While the system may be useless at its current apparent function if a part is missing or changed, the modified system might very well have another use. Thus, e.g., a bacterial secretion system might evolve into a seemingly irreducibly complex flagellum - a means of locomotion that doesn't work if its parts are missing, but very plausibly works as a secretory mechanism.

As puzzles, the latter type of seemingly irreducible complex systems are the most interesting, their evolutionary pathway is not apparent from simple inspection. During the early part of its evolutionary history, the system was under a selection pressure different from that during the latter part. At some point the system "discovers" a new use, and now selection chooses improvements on the new function. Quite unlike, e.g, the idea of how the giraffe neck evolved. Supposedly, the giraffe neck is an accumulation of small changes, each small additional growth in the neck length giving its possesor an advantage in browsing tree-high foliage.

To come to the purpose of this post - it is that the evolutionary explanations of human intelligence and self-awareness to be more like the story of the giraffe neck than like the story of the bacterial flagellum. So, e.g., how did human mathematical ability arise? The standard story would be that mathematical ability is a manifestation of intelligence and from general primate intelligence to human intelligence there is a simple evolutionary pathway, small increments in intelligence almost always being advantageous selection-wise. So our minds have grown in some way analogous to the giraffe neck. Without something seemingly irreducibly complex intervening, our minds and behavior are explained by the conditions under which our predecessors evolved. This parody is the kind of explanation that bothers me. But maybe, the pathway to mathematical ability is more subtle, e.g., the functions associated with language were being selected for, and at some point those faculties "discovered" the new use of mathematics.

Anyway, enough said, I'm already sufficiently confused.

1 comment:

CapitalistImperialistPig said...

I think you are exactly right. Keith Devlin has written a book called The Math Gene which purports to discuss how mathematical thinking evolved, but it just about as incomplete as one might guess. He traces math to language, but I would guess there is more.

As I get older and stupider I have been noticing some of the kinds of effort I need to make to solve math problems.

One needs to parse a problem into its components, which is perhaps related to language, but also related to all sorts of planning tasks that even our pre-human ancestors needed to perform.

Short-term and longer-term memory are clearly involved. One needs to remember the parts of the problem, and their relationship to each other, as well as the facts, theorems, and ideas necessary for the solution.

Pattern recognition is probably most crucial of all.

Throw in some visual processing, and add the clearly linguistic ability to generate the answer as a symbol string, and you have most of mathematics - at least up to my level.

Back to stupidity - one of my toughest problems is with my short to medium term memory. I tend to lose the thread of detailed calculations, so I need to write more stuff down.