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the penalty of projection - madame spectrum lyrics

“astronomers sometimes say that sp-ce is curved or that the universe is finite but unbounded. whatever they’re talking about… and what’s more, has witnessed a greeting coming from his insides. a voice from within. he surely is getting a little worried about his sanity. the three dimensional creature is unhappy about being considered a psychological aberration and so he descends to actually enter flatland, but the three dimensional creature exists in flatland only partially: only a plane, a cross-section through him can be seen. so, when the three dimensional creature first reaches flatland it’s only the points of contact which can be seen. well, represent that set of objects who mysteriously appear from nowhere inside a closed room and change their shape dramatically. his only conclusion could be that he’s gone bonkers. well, the apple might be a little annoyed of this conclusion, so

r: we imagine our universe to be flat in three dimensions but maybe it’s curved into a fourth. we can talk about a fourth dimension but we can’t experience it

l: but maybe more interesting is the other direction in dimensionality. what about the fourth dimension? to touch that let’s consider a cube

now if we look at the shadow of a three dimensional object in two dimensions we see that in this case not all the lines appear equal, not all the angles are right angles. a three dimensional object has not been perfectly represented in its projection in two dimensions but that’s part of the cost of losing a dimension in the projection. now let’s take this three dimensional cube and project it through a fourth physical dimension. not that way… but at right angles to those three directions. i can’t show you what direction that is but imagine that there’s a fourth physical dimension. in that case we would generate a four dimensional hypercube which is also called a tesseract. i cannot show you a tesseract because i and you are trapped in three dimensions but what i can show you is the shadow in three dimensions of a four dimensional hypercube or tesseract. this is it!
and now the real tesseract in four dimensions would have all the lines of equal lenght and all the angles right angles. that’s not what we see here but that’s the penalty of projection.”

- madame spectrum lyrics

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