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Pacman looks down on the one-dimensional pong game. It consists of a one pixel-width line, a one pixel wide paddle at each end, and a single pixel ball that bounces back and forward along that line. He looks down on it, because the ball is very stupid indeed. The ball's ability to perceive its environment is limited to a single item of information - it knows what is dead ahead.

Perceptual dimensions are equal to the spatial dimensions, minus one. Pacman, living in his two dimensional world, has a one dimensional field of view. He sees the colour of everything that surrounds him, displayed as a single line, each point of which represents a different angle of his peripheral vision. Depth is inferred, but not experienced.

The one-dimensional pong ball, being a far simpler creature, has zero perceptual dimensions. He sees just one thing (because anything raised to the power zero is one), which is the paddle ahead of him. He doesn't know any better.

If Pacman stands perpendicular to the pong game, he can see the entireity of the ball's path. He knows what is ahead, he can see past obstacles that the ball cannot. If there is anything beyond the paddle, Pacman can see that too. He gets rather smug, at times, because he can go around obstacles using his additional dimension. The only barriers to Pacman's perception are the walls, and he can go around those.

Sometimes, though, Pacman dreams of what it might be like to live in three dimensions. By standing perpendicular to his current plane of existence and bouncing three-dimensional photons at said plane, he would have complete cognisance of the entire world he lives in. He would be able to see where the ghosts are at any time, see where the yellow pills are, see the complete layout of everything. He would have a two dimensional field of perception, which could fully perceive his native two dimensional world.

Of course, in the real world, Pacman doesn't actually dream of that. His tiny yellow mind can't possibly conceive of a third dimension at a right angle to his regular two - for him, the necessary direction does not exist!

And so this brings us to us.. Assuming that our physical universe does indeed exist in three dimensions (rather than being a slice of a four+ dimension universe), then were we able to take ourselves into a fourth dimension, we could effectively perceive everything. With four-dimensional photons, we could access any atom in the universe by approaching it from an angle outside of the normal 3D space. Just as Pacman can see every pixel that makes up his world when he becomes 3D, were it possible for us to become 4D theoretically our 3D field of vision would enable us to see everything that exists in our universe.. And just as Pacman can go around objects that a fewer-dimension being cannot, so could we go through/around objects in four dimensions that we could not in three.

It's just a kind of neat thought..

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This is a very interesting concept. It sort of suggests to me that we have the potential to see beyond the three axes of our everyday existence.

That would be quite a curious thing, I think.

Not really, no.. No more so than Pacman jumping off the screen and taking a look at it from outside.. We exist in three dimensions, not four. I see nothing in the universe as it currently stands that implies any potential for that.

That's fair.

Mathematically, all we need are three dimensions anyway. Diagonals are just factors of each axis and whatnot.

I'll pretend you were looking for the 'Exit without saving' button rather than the one marked 'Post'

You're just pissed that you accidentally read it, instead of closing your browser :oP

This kind of thinking (your pacman/pong anology) was turned into a book called "Flatland : A Romance of Many Dimensions" in about 1880, and was one of the first ever pop-maths books and was very popular at the time. Dealt with a two dimensional beings perception of a three dimensional world, extended this to describe what an n-dimensional euclidian space would look like, and managed to throw some observations of victorian society in there as well :p More recently, Ian Stewart released a book called Flatterland: Like Flatland, Only More So", which expands on that theme to explain various non-euclidian geometries (projective plane, fractal geometries) in the same manner. And is a darn good read to boot..

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