Quote:
Originally Posted by mtaylor
Thanks Steve, but I am still confused.
Granted if one attached an object to the balloon, it would not expand while the balloon did. But if I understand the metaphor, the surface of the balloon is the two-dimensional substitute for the 3 dimensional world in which we live. We are to suppose that we are two dimensional beings living "in" the surface, not "on" it. There is nothing "outside" or "on" the surface of the balloon, unless it is a 4th or 5th dimensional object.
Sorry if this is taking a metaphor to far, but its always bothered me.
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lol... that
is a metaphor too far. You'll need to pretend the coins and the surface of the balloon are in the same dimension, while not forgetting we have 'subtracted' a dimension from our 3d reality (which you obviously have a good handle on from the rest of your post).
You'll probably come across another common analogy that places ants on the 2d surface - same thing applies, the idea is to imagine the ants exist in the same dimension, not the next higher dimension they occupy in reality.
Invasion of the Fifth Dimension Ants!
You don't happen to have Spielbergs number?