# Science Problem Solving

Still, it’s sorta fun to imagine what a real world problem Insight.In the shower, thinking about nothing much, it springs on us, unbidden and sudden.

Still, it’s sorta fun to imagine what a real world problem Insight.In the shower, thinking about nothing much, it springs on us, unbidden and sudden.

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George Pólya in his writes (paraphrased), “You know something like this. ” The history of science, too, is filled with instances of reasoning by analogy. This is not really what an atom looks like, though, but it has stuck with us by way of Rutherford.

Indeed, we can often gain cheap insights into something by borrowing the machinery from another discipline and thinking about it in those terms.

The number of possible moves in a chess match — itself a simplification when compared to, you know, — is \( 10^ \), while the number of atoms in the observable universe is a mere \( 10^ \).

It’s a near certainty, then, that the human mind doesn’t consider an entire graph when solving a problem, but somehow approximates a graph search.

In this case, the insight is changing the representation of pliers as tool-to-hold-objects-together to pliers as weight.

More support for this view comes from another famous insight problem.

The key insight in this problem is that the box that the tacks are contained in is not just for holding tacks, but can be used as a mount, too — again, a change in the representation.

In fact, the rate at which people solve this problem depends on how it’s presented.

You are given the objects shown: a candle, a book of matches, and a box of tacks.

Your task is to find a way to attach the candle to the wall of the room, at eye level, so that it will burn properly and illuminate the room.

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