Psychology is the study of human thought on an individual level. Sociology: thought on a cultural level. Philosophy: thought on a cosmic level.
The so-called "social sciences" begin and end with the study of human thought, in each situation and of each consideration to which it can be applied.
Sometimes, though, I think we have it wrong, we philosophers, we pretentious liberal-arts majors studying the Fundamental Truths of the Universe According to Dead Racists. Sometimes, I think the best way to examine human thought is with a math problem.
Here's an interesting one, which some of you may have encountered before. It's called the Mutilated Chessboard problem, which makes it both educational and hilarious.
Imagine a chessboard with two squares, each in an opposite corner, removed. Now, take 31 dominoes, each of which covers exactly two squares. Place them on the chessboard such that the dominoes cover all 62 squares, or explain why this is impossible.
Take a moment to try to come up with the answer before I tell it to you. It's an interesting little problem, and actually much harder than it looks.
....until you figure out the trick.
What is the fundamental property of a chessboard? 64 squares, alternating black and white, so that no two adjacent squares are of the same colour. Thus, the two squares removed when the chessboard was mutilated (ideally in some kind of horror-movie sequence involving a psychopathic grand master) must have been the same colour. However, any given domino must cover two differently-coloured squares, which means that the problem is impossible.
But that's not how most people would go about solving that problem, is it? I would guess that the vast majority of people, on being handed a chessboard, a knife, and 31 dominoes, would start by putting dominoes on the board and trying to see if some sort of pattern emerged. Humans are programmed to be experiential, rather than logical - in most cases, we prefer to touch, rather than think, to do, rather than see.
Maybe that's why people so freqently make obviously bad decisions. Sure, if you thought about it the right way, you'd know that the Xtreme stunt/questionable relationship decision/substance abuse isn't really the cleverest of ideas - not the optimal solution to the problem - but sometimes, you just have to spend an hour playing with dominoes before you figure it out.
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5 comments:
You say
"Imagine a chessboard with two squares, each in an opposite corner, removed. Now, take 31 dominoes, each of which covers exactly two squares. Place them on the chessboard such that the dominoes cover all 62 squares, or explain why this is impossible."
and then you say
"However, any given domino must cover two differently-coloured squares, which means that the problem is impossible."
Am I missing something? Where is that specified?
Well, just try putting a domino on a chessboard so that it covers two squares of the same colour.
On a chessboard, no two adjacent squares are the same colour, because the colours alternate. But dominoes are contiguous, so they have to cover two adjacent squares if you put them on the board... thus, no domino can cover two of the same-colour squares. It's not a property of the problem so much as it is a property of dominoes.
Yeah. I totally got it.
I'm a doctor.
Oh, I see, my bad. Thanks.
I got it.
If I remember correctly, I first found the answer in the same math-textbook which helpfully informed me that in the event that you are abducted by aliens, you should ask them the universal gravitational constant to more digits then is currently known. Really.
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