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variety. There are other programs which have randomizing devices that will give some

variety but not out of any deep desire. Such programs could be reset with the internal

random number generator as it was the first time, and once again, the same game would

ensue. Then there are other programs which do learn from their mistakes, and change

their strategy depending on the outcome of a game. Such programs would not play the

same game twice in a row. Of course, you could also turn the clock back by wiping out

all the changes in the memory which represent learning, just as you could reset the

random number generator, but that hardly seems like a friendly thing to do. Besides, is

there any reason to suspect that you would be able to change any of your own past

decisions if every last detail-and that includes your brain, of course-were reset to the way

it was the first time around?

But let us return to the question of whether "choice" is an applicable term here. If

programs are just "fancy marbles rolling down fancy hills", do they make choices, or not?

Of course the answer must be a subjective one, but I would say that pretty much the same

considerations apply here as to the marble. However, I would have to add that the appeal

of using the word "choice", even if it is only a convenient and evocative shorthand,

becomes quite strong. The fact that a chess program looks ahead down the various

possible bifurcating paths, quite unlike a rolling marble, makes it seem much more like

an animate being than a square-root-of-2 program. However, there is still no deep self-

awareness here-and no sense of free will.

Now let us go on to imagine a robot which has a repertoire of symbols. This robot

is placed in a T-maze. However, instead of going for the reward, it is preprogrammed to

go left whenever the next digit of the square root: of 2 is even, and to go right whenever it

is odd. Now this robot is capable of modeling the situation in its symbols, so it can watch

itself making choices. Each time the T is approached, if you were to address to the robot

the question, "Do you know which way you're going to turn this time?" it would have to

answer, "No". Then in order to progress, it would activate its "decider" subroutine, which

calculates the next digit of the square root of 2, and the decision is taken. However, the

internal mechanism of the decider is unknown to the robot-it is represented in the robot's

symbols merely as a black box which puts out "left"'s and "right'"s by some mysterious

and seemingly random rule. Unless the robot's symbols are capable of picking up the

hidden heartbeat of the square root of 2, beating in the L's and R's, it will stay baffled by

the "choices" which it is making. Now does this robot make choices? Put yourself in that

position. If you were trapped inside a marble rolling down a hill and were powerless to

affect its path, yet could observe it with all your human intellect, would you feel that the

marble's path involved choices? Of course not. Unless your mind is affecting the

outcome, it makes no difference that the symbols are present.

So now we make a modification in our robot: we allow its symbols-including its self-

symbol-to affect the decision that is taken. Now here is an example of a program running

fully under physical law, which seems to get much more deeply at the essence of choice

than the previous examples did. When the robot's own chunked concept of itself enters

the scene, we begin to identify with the robot, for it sounds like the kind of thing we do. It

is no longer like the calculation of the square root of 2, where no symbols seem to be

monitoring the decisions taken. To be sure, if we were to look at the robot's program on a

very local level, it would look quite like the square-root program. Step after step is

executed, and in the end "left" or "right" is the output. But on a high level we can see the

fact that symbols are being used to model the situation and to affect the decision. That

radically affects our way of thinking about the program. At this stage, meaning has

entered this picture-the same kind of meaning as we manipulate with our own minds.

A Godel Vortex Where All Levels Cross

Now if some outside agent suggests 'L' as the next choice to the robot, the suggestion

will be picked up and channeled into the swirling mass of interacting symbols. There, it

will be sucked inexorably into interaction with the self-symbol, like a rowboat being

pulled into a whirlpool. That is the vortex of the system, where all levels cross. Here, the

'L' encounters a Tangled Hierarchy of symbols and is passed up and down the levels. The

self-symbol is incapable of monitoring all its internal processes, and so when the actual

decision emerges-'L' or 'R' or something outside the system-the system will not be able to

say where it came from. Unlike a standard chess program, which does not monitor itself

and consequently has no ideas about where its moves come from, this program does

monitor itself and does have ideas about its ideas-but it cannot monitor its own processes

in complete detail, and therefore has a sort of intuitive sense of its workings, without full

understanding. From this balance between self-knowledge and self-ignorance comes the

feeling of free will.

Think, for instance, of a writer who is trying to convey certain ideas which to him

are contained in mental images. He isn't quite sure how those images fit together in his

mind, and he experiments around, expressing things first one way and then another, and

finally settles on some version. But does he know where it all came from? Only in a

vague sense. Much of the source, like an iceberg, is deep underwater, unseen-and he

knows that. Or think of a music composition program, something we discussed earlier,

asking when we would feel comfortable in calling it the composer rather than the tool of

a human composer. Probably we would feel comfortable when self-knowledge in terms

of symbols exists inside the program, and when the program has this delicate balance

between self-knowledge and self-ignorance. It is irrelevant whether the system is running

deterministically; what makes us call it a "choice maker" is whether we can identify with

a high-level description of the process which takes place when the

program runs. On a low (machine language) level, the program looks like any other

program; on a high (chunked) level, qualities such as "will", "intuition", "creativity", and

"consciousness" can emerge.

The important idea is that this "vortex" of self is responsible for the tangledness,

for the Godelian-ness, of the mental processes. People have said to me on occasion, "This

stuff with self-reference and so on is very amusing and enjoyable, but do you really think

there is anything serious to it?" I certainly do. I think it will eventually turn out to be at

the core of AI, and the focus of all attempts to understand how human minds work. And

that is why Godel is so deeply woven into the fabric of my book.

An Escher Vortex Where All Levels Cross

A strikingly beautiful, and yet at the same time disturbingly grotesque, illustration of the

cyclonic "eye" of a Tangled Hierarchy is given to us by Escher in his Print Gallery (Fig.

142) . What we see is a picture gallery where a young man is standing, looking at a

picture of a ship in the harbor of a small town, perhaps a Maltese town, to guess from the

architecture, with its little turrets, occasional cupolas, and flat stone roofs, upon one of