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[inverted_man]

http://www.tenthdimension.com/flash2.php

Click "Imagining the 10th Dimension".

*Always thought that a flatlander on a Mobius strip would become a mirror image of herself since she has essentially been lifted through the 3rd dimension and flipped over.

Comments

[inverted_man]

it's like saying the axiom of choice cant be true because it lets you cut up a sphere and reassemble it into 2 spheres of identical size, simply because it's impossible in reality.

Not to nitpick, but it just doesn't seem like that at all to me. In the first case, the objection is that you have equated the description of an object with the object itself (the description is X therefore the reality is X), thereby concluding that imagining 10-dimensional obects has nothing tricky about it because the tools used to describe the object have nothing tricky about them. The person objecting is really saying "the reality is different from the model".

In the second case, via enhanced Argumentum ad logicam, you are describing a situation wherein I would object to a description of an object behaving differently from the reality of the object - that is, comparing my first objection with one that sounds like "the model is different from the reality, therefore it cannot be true". They're actually mutually exclusive positions. I just wanted to clarify that.

I don't object to that whole equi-decomposability thing.

In any case, I like your description.

[inverted_man]

"to answer your objection differently: it's a constructive proof of a sorts. there will never exist a touchable turing machine, since it requires infinite tape. there will also never exist a non-deterministic turing machine since that on top of the infinite tape has to split into infinite dimensions in order to perform it's computations"

Holy crap, never thought about that. Gonna see if I can't find some reading on that.