JonnyMcA Wrote:
-------------------------------------------------------
...

> Physically it is hard to
> picture, but mathematically movement through extra
> spatial dimensions is treated just the same as
> moving through 3D space. So imagine walking around
> a rectangular garden (i.e. a 2D space). If you go
> 30 feet along x, and 40 feet along y, then it is
> the same as going 50 feet along direction R from
> one corner of the garden to the opposite corner.
> This is simply Pythagoras where R = square root of
> the sum of the squares of x and y. This can be
> expanded to 3D space (x, y, z), where R will be
> equal to the square root of the sum of the squares
> of distance moved along the x, y and z
> dimensions. For a 4D space, R would be the square
> root of the sum of the squares of all the
> distances moved.. and so on for N-dimensional
> space.

...

(Sadly, my knowledge of maths, quantum mechanics, etc., is just about zero. However ... )

"For a 4D space, R would be the square root of the sum of the squares of all the distances moved"

So, despite there being a fourth dimension, R would still be the SQUARE root of the sum of the squares of all the distances moved: it wouldn't be the QUADRUPLE root ... ? And the same for N-dimensional space?

Hermione
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