Numbo the Human Computer

Hofstadter's Numbo is not necessarily supposed to deliver fast and accurate results to the number problems, it's tackling, but rather to mimic the way we come about with a solution. So instead of brute-force trail-and-error of combinations which are doomed to be wrong from the beginning (at least from the human perspective) Numbo tries to juggle with the numbers in a probabilistic way to combine previous particles to likely bonds. This way solutions are found in a much smarter way, disregarding the enormous overhead created in the process.

Hofstadter is not really satisfied with "smart", he wants to compare it to human cognition 1:1. Therefore he compared the trace of Numbo runs to the mental protocols of human players (as good as they could remember or introspect). The comparison reveals certain similarities but also yields different results, since Numbo comes up with easy solutions in a way, humans would not think of first. So it does not seem to be as "smart" after all. Or do we just come up with weird and complicated solutions?

We are given a tiny peek under the hood of the mysterious Numbo-machine and discover that the complexity of human thought process was tried to be modeled by mere probabilistic functions in most cases. In my eyes, this is one fundamental flaw which cannot be eluded that easily. Humans have association with every number, context and method they use. The seeming randomness in their actions might be a result of the current environment and situation they are in. A human might use one technique to solve a problem once and another technique the next time, not because of statistic equivalent of the two approaches, but because all prior events taught her/him to use the one most promising one at the time.

The codelets from the coderack, Hofstadter uses, are supposed to stand for the thought processes we use in turns to come to a solution. They are supposed to contain as few prior knowledge as possible. This is what I see as another fundamental flaw in Hofstadter's approach. I have the notion that we literally learn the results of addition, subtraction and multiplication by heart (at least the easy ones). And from there, we draw analogies between problems like 3+2=5 and 30+20=50 or 24+7=31 and 64+7=71. But there is even a more basic level humans operate on. We associate a certain context and knowledge around numbers or operants and therefore pick those which pop up more easily to us.

In my opinion, Hofstadter is quite on the right track, but still misses a lot of essential processes, naturally going on in the human brain.