Saturday, February 24, 2007

Very human complications

I think the solution to the three circles having intersecting vertices lying on a straight line problem being solved by adding complexity (ie. another dimension) is a brilliant example of the difficulties that humanity faces.

My reasoning behind that statement is something like this: we are limited by how we experience the universe - which is through our senses. By extending the circle problem to 3D we immediately intuit that the answer is a straight line, because when two planes itersect you find a straight line at their intersection. Imagine a flat chunk of wood intersecting at some angle with another flat chunk of wood.

So we complicate things (unnecessarily?) to fit problems into our world view, once there we can "understand" the problem because it lends itself to our equipment (our senses).

I think this human limitation is connected with the reason we have clocks in our computers, where work is done per clock tick. If you recall that Adrian Thomspon experiment, it showed that there are far more efficient designs for a circuit. But we don't "understand" those more efficient designs, so we don't use them.

Question:

What is meant by the word "understanding"?

I am wondering what "human understanding" is and how it relates to say "computer understanding" of a problem. I see this with human chess grandmasters, they dismiss computers saying "ah, the computer does not understand the position, whereas I do". What does this mean? Isn't "understanding" just a result of some calculation?

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