Crumpling Flatland, Crumpling Space

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Crumpling Flatland, Crumpling Space

Postby Tearz » Thu Feb 19, 2009 11:52 pm

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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Re: Crumpling Flatland, Crumpling Space

Postby wendy » Fri Feb 20, 2009 6:55 am

You don't have any perception of external curvature in hyperspace. This includes three dimensions seen from two dimensions.
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Re: Crumpling Flatland, Crumpling Space

Postby ParadoxJuice » Sat Feb 21, 2009 12:34 am

wendy wrote:You don't have any perception of external curvature in hyperspace. This includes three dimensions seen from two dimensions.


Hold on-what if the source of light (the lightbulb) was on the bottom of Flatland (imagine Flatland being folded, the bottom part of that shape), wouldn't the light stop hitting the Flatlanders on the top part, making it go dark, and cause the bionions on the bottom to see...something...

Exactly how do you 'fold' Flatland? Is it sitting on a piece of paper? Wouldn't that cause the bionians on the bottom to see the paper? And wouldn't gravity cause the bionians up top to fall? If the paper was transparent, the Flatlanders would see whatever was on the other side of the fold...possibly the jerk who decided to morph the universe.
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Re: Crumpling Flatland, Crumpling Space

Postby wendy » Sun Feb 22, 2009 8:33 am

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.
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Re: Crumpling Flatland, Crumpling Space

Postby ParadoxJuice » Tue Feb 24, 2009 12:24 am

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.


That is irrelevant. A trionian would only be seen by the bionions if the light somehow managed to reach the trionian. Of course, a bionian wouldn't 'see' by our standards, as it would not see much. Also, how would you know that space is curved? Have you gone all four-dimensional and seen for yourself (that thing underneath your name says that :sweatdrop: ). I don't care if the speed of light multiplied by the distance of the universe to the square root of infinity shows something like that. If space was curved, I'd imagine that the light would go flying out of this universe. How can it be curved yet not across a different dimension? In that case, what would happen if we flew to 'the edge', would we just see a large curve that we can or can't get past?
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Re: Crumpling Flatland, Crumpling Space

Postby wendy » Tue Feb 24, 2009 7:23 am

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).
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Re: Crumpling Flatland, Crumpling Space

Postby ParadoxJuice » Tue Feb 24, 2009 11:21 pm

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).


So you're saying that light would curve across the bends? I guess its possible, but I wouldn't think so, unless if there is something that is somehow holding things into this universe. :\

Still, if there wasn't anything holding us in place, it might mean that things would randomly dissapear. I like to think that we simply stay in our dimensions because there is nothing causing the particles to move ana/kata.
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Re: Crumpling Flatland, Crumpling Space

Postby Sideshow » Wed Feb 25, 2009 2:47 am

Why wouldn't it cross the bend? Since we're using paper as our example of Flatland, you need to imagine Flatlanders being a part of the paper. Not on top of it, but as inside the paper itself. To move from point A to point B on the paper, they need to move "inside" of it. Now say that the paper is folded in between point A and point B. They can still move between the points and "across" the fold because they are still inside the paper. The paper still connects to itself even though it's now folded in the third dimension. Since the Flatlanders move inside the paper, they can travel between any connecting points, i.e. across the fold, without any troubles.
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Re: Crumpling Flatland, Crumpling Space

Postby wendy » Wed Feb 25, 2009 7:18 am

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.
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Re: Crumpling Flatland, Crumpling Space

Postby ParadoxJuice » Sat Feb 28, 2009 12:01 am

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.


Assuming that you are reffering to the surface of the Earth being 3D yet we treat it as 2D, I see what you mean. But, now we're getting on to the topic of what Flatland is actually like. I believe that in the book, Flatland, it was described as sitting on top of a pool of water. I'm not sure why there are never any waves, though.

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.

What was the main point of this? Oh yeah, what would a Flatlander detect after moving across a bend in there very universe? Well, assuming they somehow move with the bend, I'd say nothing that wouldn't be shrugged off. They might snap, if the bend was sharp enough, but that might also assume something about there molecular makeup...

It's impossible to talk about this without knowing more about the bionions. How do they percieve the environment? Will they 'snap' if given enough pressure from the third dimension (not sure if they would be built for that...)? Etc.
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Re: Crumpling Flatland, Crumpling Space

Postby Keiji » Thu Mar 05, 2009 10:05 am

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.


2D objects don't have sides (the "side" of it would be like the "inside" of a 3D object to us). So yes, they would use light to see.
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Re: Crumpling Flatland, Crumpling Space

Postby ParadoxJuice » Sat Mar 07, 2009 12:19 am

Keiji? Thought these forums were dead.

I'm talking about what the Flatlanders would call a side, which is infinitely thin, and therefore you wouldn't be able to use light to see it (thought that was basic knoweledge). The exception, of course, would be if there was some kind of strange 2D light, which wendy seems to mention. Of course, that IS possible, but once again, that gets into how the laws of physics of a 2D universe would be, how everything would work (moving inside the paper?). That needs its own thread, maybe even its own section.
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Re: Crumpling Flatland, Crumpling Space

Postby Keiji » Sat Mar 07, 2009 2:02 pm

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.
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Re: Crumpling Flatland, Crumpling Space

Postby ParadoxJuice » Thu Mar 12, 2009 7:58 pm

Keiji wrote:Inside 2D, light would naturally be 2D, so there'd be no problem with seeing stuff. Same for other dimensions.


This assumes that Flatland has light, and not just grapejuice. *DUN DUN DUN*

Once again, this is speculation. Unless if the hath traveled through the universe and discovered a 2D planet (or universe, for that matter) its all just a big guessing game.

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.


Well then, guess its time to rename the forums Pentaspace and move on, eh?
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Re: Crumpling Flatland, Crumpling Space

Postby Halfbaker » Sat Jun 04, 2011 6:25 am

Pentaaspace? Good luck with that. There's really not enough easy comparisons the way there is for tetraspace. (:
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Re: Crumpling Flatland, Crumpling Space

Postby PatrickPowers » Fri Dec 11, 2015 8:05 pm

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?


The whole idea of a Universe is that nothing whatsoever going on outside of it has any influence. So Flatworld beings would have no way of knowing it is crumpled. Indeed, their world could be fractal, which would allow an infinite Flat universe to fit inside of a matchbox.
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