Gödel, Escher, Bach An Eternal Golden Braid by Douglas R. Hofstadter

CHAPTER X

Levels of Description,

and Computer Systems

Levels of Description

GODEL'S STRING G, and a Bach fugue: they both have the property that

they can be understood on different levels. We are all familiar with this

kind of thing; and yet in some cases it confuses us, while in others we

handle it without any difficulty at all. For example, we all know that we

human beings are composed of an enormous number of cells (around

twenty-five trillion), and therefore that everything we do could in principle

be described in terms of cells. Or it could even be described on the level of

molecules. Most of us accept this in a rather matter-of-fact way; we go to

the doctor, who looks at us on lower levels than we think of ourselves. We

read about DNA and "genetic engineering" and sip our coffee. We seem to

have reconciled these two inconceivably different pictures of ourselves

simply by disconnecting them from each other. We have almost no way to

relate a microscopic description of ourselves to that which we feel ourselves

to be, and hence it is possible to store separate representations of ourselves

in quite separate "compartments" of our minds. Seldom do we have to flip

back and forth between these two concepts of ourselves, wondering "How

can these two totally different things be the same me?"

Or take a sequence of images on a television screen which shows

Shirley MacLaine laughing. When we watch that sequence, we know that

we are actually looking not at a woman, but at sets of flickering dots on a flat

surface. We know it, but it is the furthest thing from our mind. We have

these two wildly opposing representations of what is on the screen, but that

does not confuse us. We can just shut one out, and pay attention to the

other-which is what all of us do. Which one is "more real"? It depends on

whether you're a human, a dog, a computer, or a television set.

Chunking and Chess Skill

One of the major problems of Artificial Intelligence research is to figure

out how to bridge the gap between these two descriptions; how to construct

a system which can accept one level of description, and produce the other.

One way in which this gap enters Artificial Intelligence is well illustrated by

the progress in knowledge about how to program a computer to play good

chess. It used to be thought-in the 1950's and on into the 1960's-that the

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