wendy wrote:You don't have any perception of external curvature in hyperspace. This includes three dimensions seen from two dimensions.
wendy wrote:All space is curved. It isn't folded, nor is it curved in some higher space. Something that strikes space from hyperspace will simply not be seen, because it has no refelection.
wendy wrote:Alternately, one must consider that something like light does not follow "straight lines", but always "divides curvature" (which sets the shortest distance).
So if light (which is essentially set in the space it travels), comes to a "crumple", it would follow the space over the crumple (rather like a crumpled picture is still as if it were uncrumpled).
wendy wrote:One notes, that the surface of the earth is S2, carried in E3. Yet we measure distances in the S2 surface, and not the underlying E3 space (ie through the centre).
In the hyperbolic geometry H4, there is a horosphere, whose surface is E3, the distance between points are measured in normal manner on the surface, although the true seperation is something like R.asinh(d/R), which for large d/R, becomes ln(d/R). So at the scale where R=4000 miles, something like 1E80 miles becomes something like 700,000 miles. This is less than the diameter of the sun!
In any case, there is nothing intrinsic in space (including things like topological genus, curvature etc), which implies a specific structure in hyperspace (eg crumpled, surface of some solid, etc), to things that exist in space.
Your arguments are based on using 3d light in crumpled flatland, which would not be seen in two dimensions, simply because it does not reflect, and leaves no path to the eye of the hedrobour.
ParadoxJuice wrote:Also, the Flatlanders would not use light to see. They would not be able to see the sides of other 2D objects, and therefore they would need another way to detect eachother. But, that discussion should be started somewhere else.
Keiji wrote:Inside 2D, light would naturally be 2D, so there'd be no problem with seeing stuff. Same for other dimensions.
And no the forums are not dead, I just haven't felt like posting for a while. Discussion isn't anywhere near as interesting as it used to be - everything's pretty much been figured out now, and the only thing the forums seem to be used for now is teaching newbies.
Tearz wrote:Ok, if you drew a flatworld, then crumpled the paper, (Actually, we'll just say we folded the flatland to make things simpler) than if a flatlander walked over the crease, would he have some perception of space? If so, what kind of things would he feel or noticed? But then, what if someone folded space? What kind of things would we feel as we walked over the crease and would we have any revelation of Tetraspace? Just my thoughts. Any ideas?
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