Wednesday, 25 April 2012

Thinking in Four Dimensions

No, not time.
It seems to be quite often I tell people I'm making a 4D application that they think "Fourth dimension? Just like Doc Brown!"
But no, what I'm talking about is four spatial dimensions, ie Length, Width, Depth and a fourth perpendicular to the afore mentioned three. "But Lachlan" you may ask "that doesn't seem physically possible"
And I say "That's technically a statement"
But you would be right in that statement in that it is not physically possible in our superfluous little 3D world. If you're interested then I recommend watching these two videos :

Still confused? Good then get lost nobody likes you anyway.
If you didn't watch because you're internet's too slow or you haven't grasped the concept of "multimedia" then her's a quick run down:

The number of dimensions of any given space can be determined by how many coordinates are needed to represent a single point in that space.

Starting with a zero dimensional space we have a single point. Don't let this confuse you into thinking it should be one dimensional as if it were 1D, we would NEED 1 coordinate to represent a point. But as we already only have an infinitely small point, we don't ANY coordinates to define a point. Because what other point could it be is my point.

Moving along we hit one dimensional space. 1D can be achieved by placing an infinite number of 0D spaces in a row. Your grade 2 maths teacher might call this new shape a "line", but who am I kidding? You didn't pass grade 2. 

Stretching out our single dimension perpendicular to the way we stretched the zero dimensions we end up with an amazing two dimensional square. If you would like to know what a square looks like, you can't... No I'm serious. Even if you cut a piece of paper perfectly (oh hey, alliteration) you wouldn't have a square, you'd have a prism.

Of course if we stacked this square infinitely on top of itself (perpendicular to previous two stackings) we end up with our glorious three dimensional space. It's good to be home. But wait a minute... There's more?

Why yes indeed there's more, there's many many more. But in order to follow the same pattern from going from one dimension to the next... It gets a bit... Tricky... It can take a while but can sort of visualise, or more so interpret four dimensional space by looking at how lower dimensions would need to interpret ours. A great tutorial on how to interpret 4D can be found here.

To be continued...

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