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Topic: Cool Math Lessons
Replies: 42   Last Post: Mar 9, 2012 2:08 PM

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 Robert Hansen Posts: 11,328 From: Florida Registered: 6/22/09
Re: Cool Math Lessons
Posted: Mar 1, 2012 2:52 PM
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I am fine with gestalt, it is certainly more catchy than trivial, though its dictionary definition isn't what I meant. I was using trivial to mean that the problem is solvable (by a human) in very short (constant or less) time even though algorithmically (using current algorithm technology) the problem requires polynomial or exponential time. It is difficult to compare neural nets to turing machines but I am pretty sure that if you insist on making the comparison you have to accept that the brain is somewhere between massively and infinitely parallel, probably closer towards infinitely.

Humans are horrible at direct algorithmic computation which is essentially the state of the art of current algorithm technology. Humans utilize instinct and strategy and I am fine with saying they "process information" but I am not fine with calling that process algorithmic. The main reason is that we don't have anything yet or even in the works like this. And even if we came up with just one example, say chess, where a computer used instinct and strategy (ran the Kasparov algorithm) I would still be doubtful that we are truly there unless that algorithm was applicable to any general problem having trivial solutions (i.e. any problem solvable by humans).

I think factoring, finding LCDs, simplifying fractions etc are different than comparing two whole numbers or addition with carry. I think the former require instincts and strategy because they involve search paths, while the later do not. I am not saying these are hugely instinctive, but plenty enough to realize that there is a difference in mental process. I think these types of activities are the nascent precursors and trainers of the stronger and more generally applicable instincts we see later, like those employed in solving much more general or ingenious problems.

Bob Hansen

On Mar 1, 2012, at 1:17 PM, Joe Niederberger wrote:

> Don't know what you mean by "trivial" -- that the particular instance has features producing a
> a Gestalt that leads to rapid solution by humans?