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variety. There are other programs which have randomizing devices that will give some
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variety but not out of any deep desire. Such programs could be reset with the internal
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random number generator as it was the first time, and once again, the same game would
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ensue. Then there are other programs which do learn from their mistakes, and change
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their strategy depending on the outcome of a game. Such programs would not play the
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same game twice in a row. Of course, you could also turn the clock back by wiping out
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all the changes in the memory which represent learning, just as you could reset the
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random number generator, but that hardly seems like a friendly thing to do. Besides, is
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there any reason to suspect that you would be able to change any of your own past
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decisions if every last detail-and that includes your brain, of course-were reset to the way
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it was the first time around?
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But let us return to the question of whether "choice" is an applicable term here. If
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programs are just "fancy marbles rolling down fancy hills", do they make choices, or not?
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Of course the answer must be a subjective one, but I would say that pretty much the same
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considerations apply here as to the marble. However, I would have to add that the appeal
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of using the word "choice", even if it is only a convenient and evocative shorthand,
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becomes quite strong. The fact that a chess program looks ahead down the various
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possible bifurcating paths, quite unlike a rolling marble, makes it seem much more like
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an animate being than a square-root-of-2 program. However, there is still no deep self-
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awareness here-and no sense of free will.
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Now let us go on to imagine a robot which has a repertoire of symbols. This robot
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is placed in a T-maze. However, instead of going for the reward, it is preprogrammed to
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go left whenever the next digit of the square root: of 2 is even, and to go right whenever it
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is odd. Now this robot is capable of modeling the situation in its symbols, so it can watch
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itself making choices. Each time the T is approached, if you were to address to the robot
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the question, "Do you know which way you're going to turn this time?" it would have to
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answer, "No". Then in order to progress, it would activate its "decider" subroutine, which
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calculates the next digit of the square root of 2, and the decision is taken. However, the
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internal mechanism of the decider is unknown to the robot-it is represented in the robot's
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symbols merely as a black box which puts out "left"'s and "right'"s by some mysterious
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and seemingly random rule. Unless the robot's symbols are capable of picking up the
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hidden heartbeat of the square root of 2, beating in the L's and R's, it will stay baffled by
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the "choices" which it is making. Now does this robot make choices? Put yourself in that
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position. If you were trapped inside a marble rolling down a hill and were powerless to
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affect its path, yet could observe it with all your human intellect, would you feel that the
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marble's path involved choices? Of course not. Unless your mind is affecting the
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outcome, it makes no difference that the symbols are present.
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So now we make a modification in our robot: we allow its symbols-including its self-
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symbol-to affect the decision that is taken. Now here is an example of a program running
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fully under physical law, which seems to get much more deeply at the essence of choice
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than the previous examples did. When the robot's own chunked concept of itself enters
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the scene, we begin to identify with the robot, for it sounds like the kind of thing we do. It
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is no longer like the calculation of the square root of 2, where no symbols seem to be
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monitoring the decisions taken. To be sure, if we were to look at the robot's program on a
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very local level, it would look quite like the square-root program. Step after step is
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executed, and in the end "left" or "right" is the output. But on a high level we can see the
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fact that symbols are being used to model the situation and to affect the decision. That
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radically affects our way of thinking about the program. At this stage, meaning has
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entered this picture-the same kind of meaning as we manipulate with our own minds.
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A Godel Vortex Where All Levels Cross
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Now if some outside agent suggests 'L' as the next choice to the robot, the suggestion
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will be picked up and channeled into the swirling mass of interacting symbols. There, it
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will be sucked inexorably into interaction with the self-symbol, like a rowboat being
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pulled into a whirlpool. That is the vortex of the system, where all levels cross. Here, the
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'L' encounters a Tangled Hierarchy of symbols and is passed up and down the levels. The
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self-symbol is incapable of monitoring all its internal processes, and so when the actual
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decision emerges-'L' or 'R' or something outside the system-the system will not be able to
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say where it came from. Unlike a standard chess program, which does not monitor itself
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and consequently has no ideas about where its moves come from, this program does
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monitor itself and does have ideas about its ideas-but it cannot monitor its own processes
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in complete detail, and therefore has a sort of intuitive sense of its workings, without full
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understanding. From this balance between self-knowledge and self-ignorance comes the
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feeling of free will.
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Think, for instance, of a writer who is trying to convey certain ideas which to him
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are contained in mental images. He isn't quite sure how those images fit together in his
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mind, and he experiments around, expressing things first one way and then another, and
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finally settles on some version. But does he know where it all came from? Only in a
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vague sense. Much of the source, like an iceberg, is deep underwater, unseen-and he
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knows that. Or think of a music composition program, something we discussed earlier,
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asking when we would feel comfortable in calling it the composer rather than the tool of
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a human composer. Probably we would feel comfortable when self-knowledge in terms
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of symbols exists inside the program, and when the program has this delicate balance
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between self-knowledge and self-ignorance. It is irrelevant whether the system is running
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deterministically; what makes us call it a "choice maker" is whether we can identify with
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a high-level description of the process which takes place when the
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program runs. On a low (machine language) level, the program looks like any other
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program; on a high (chunked) level, qualities such as "will", "intuition", "creativity", and
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"consciousness" can emerge.
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The important idea is that this "vortex" of self is responsible for the tangledness,
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for the Godelian-ness, of the mental processes. People have said to me on occasion, "This
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stuff with self-reference and so on is very amusing and enjoyable, but do you really think
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there is anything serious to it?" I certainly do. I think it will eventually turn out to be at
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the core of AI, and the focus of all attempts to understand how human minds work. And
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that is why Godel is so deeply woven into the fabric of my book.
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An Escher Vortex Where All Levels Cross
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A strikingly beautiful, and yet at the same time disturbingly grotesque, illustration of the
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cyclonic "eye" of a Tangled Hierarchy is given to us by Escher in his Print Gallery (Fig.
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142) . What we see is a picture gallery where a young man is standing, looking at a
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picture of a ship in the harbor of a small town, perhaps a Maltese town, to guess from the
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architecture, with its little turrets, occasional cupolas, and flat stone roofs, upon one of
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