I mean as sugested by the book Flatland. Is this only some kind of theoretical mind game or could such a “place” exist? Could one have an actual tesseract in one’s room–not just the “model”?
BTW, I’m not very mathmatically inclined. If the discussion turns to donuts, I’m outta here.
Sure it could exist. Look at it this way: Suppose we constructed a simulated universe in a huge digital supercomputer. We could set the number of dimensions to be 2, 3, 4, 10, or any number we wanted. We could make part of the simulation 3-dimensional, and part 6-dimensional.
Since there’s no way to know that we aren’t in a simulation, the conclusion is that we can’t rule out the possibility of higher dimensions.
AFAIK, no one is claiming that any material object observable in our universe is merely a 3-D slice of a higher-dimensional object. Some versions of string theory hypothesize that elementary particles have dimensions that are closed on a very small scale, and so not directly observable. And other theories suppose that our entire space-time is part of a larger hyperuniverse (“branes”).
The question is somewhat complicated in that it can be supposed that our 3-D space has an instrinsic curvature without actually being curved in a higher dimension.
I don’t mind higher dimensions as long as there are donuts there.
PBS produced an excellent series on the subject a few years ago based on Brian Greene’s book The Elegant Universe. You can watch it online.
I thought I posted earlier, but it apparently vanished into a higher dimension.
There are some real problems with 4 or more spatial dimensions, which is why all the major string theories have the additional dimensions hidden in some fashion.
For a human point of view, the worst fault is that orbits aren’t stable in four dimensions, so there could be no planets. It’s not clear (to me) whether even electron orbitals would be stable, so atom formation might not happen.
This puts a crimp into most solid objects, although I’ve tasted some donuts too dense for this to matter.
In a higher dimension, you would order a twelve pack of torus.
Tripler
I’ll have a double-double and a side of Tim-torus . . . es.
Seems to me one’s room could merely intersect with a tesseract, not contain it.
In higher dimension, tesseract contain YOU!
There are ways around that. The real fault with four or more spatial dimensions, which leads to people supposing that they’re compactified, is that we only observe three. So any extras have to be hidden in some manner or other.
How do you get around unstable orbits? Serious question.
We can’t rule out the possibility of higher dimensions existing. However, as this thread is already beginning to demonstrate, much of the discussion can be very fairly described as “theoretical mind games.”
The Matrix is everywhere…
I remember seeing or reading once that with the fourth spatial demension, shadows of objects would be three dimensional. (We see the shadows of 3-D objects now in only two demensions.) I wonder if we would be able to see the shadows.
I can’t wrap my head around this concept. I mean, what if a donut is just the 3 dimensional “shadow” of a more complicated, tastier, four dimensional pastry? And how does the “donut hole” fit into this puzzle?
And what about Jelly Donuts?
So every time I eat a donut I’m leaving a big fourth-dimensional chunk of it? Damn, that’s wasteful, not to mention annoying as I paid for the whole donut!
If they weren’t 4-dimensional you couldn’t get the jelly in.
Light is confined to our three dimensions so there’s no way a 4-D being could cause a shadow without entering our “plane”. Even if light could somehow traverse the fourth dimension, the being would be blocking a light source we couldn’t see anyway, so the “shadow” would look a lot more normal than an object illuminated from no visible light source.
Plus just because something is three-dimensional in a four-dimensional universe wouldn’t mean it was entirely confined to our three dimensions. Imagine a square that intersects a plane perpendicular to it. The part of that square that intersects the plane is only a line, and that’s all a two-dimensional being on the plane would see. Likewise, a three-dimensional object that intersects (but isn’t confined to) our three-dimensional plane could look like a two-dimensional object.
I’m partial to jelly-filled Klein bottles, myself.
You mean jelly-covered Klein bottles. Eating those is so messy.