Rubik's Tesseract

[0111narwhalz]

28 minutes ago, Camacha said:

I have always felt these 4D representations are a hoax.

If you could view the object in 3D (holograms or stereoscopes), it would model the image projected onto a 4D organism's solid retina. Bringing it to your planar retina is now as simple as projecting a 3D shape to a 2D one. Thus, you're looking at a 2D projection of a 3D projection of a 4D object. It's analogous to looking at a cube through a slit. You're not wrong in saying that it's not accurate, but until we develop some kind of 3D receptor, it's the best we have.

[Camacha]

1 minute ago, 0111narwhalz said:

If you could view the object in 3D (holograms or stereoscopes), it would model the image projected onto a 4D organism's solid retina. Bringing it to your planar retina is now as simple as projecting a 3D shape to a 2D one. Thus, you're looking at a 2D projection of a 3D projection of a 4D object. It's analogous to looking at a cube through a slit. You're not wrong in saying that it's not accurate, but until we develop some kind of 3D receptor, it's the best we have.

A tesseract is a fictional construct, so any representation is both accurate and inaccurate.

[0111narwhalz]

Only as fictional as a plane or cube.

[Camacha]

4 minutes ago, 0111narwhalz said:

Only as fictional as a plane or cube.

You could argue about a plane, but certainly not a cube. It starts going awry from the start with the assumption there is a fourth dimension (other than time) and that we can decently model it. Then we go on, like you said, to project this 4D assumption in a 3D world into a 2D screen or eye. There is so many ifs and buts in there that it is bound to be nonsense. Or fictional, if you so please.

Edit: I am disregarding the discussion that our perception of reality and the universe is just that.

Edited February 16, 2017 by Camacha

[cubinator]

8 minutes ago, Camacha said:

You could argue about a plane, but certainly not a cube. It starts going awry from the start with the assumption there is a fourth dimension (other than time) and that we can decently model it. Then we go on, like you said, to project this 4D assumption in a 3D world into a 2D screen or eye. There is so many ifs and buts in there that it is bound to be nonsense. Or fictional, if you so please.

Edit: I am disregarding the discussion that our perception of reality and the universe is just that.

Even if we can't prove the physical existence of a fourth dimension to actually observe, we can theorize the properties of hypothetical four-dimensional objects just as we can theorize the properties of two and three dimensional objects, and create models of them. It doesn't have to be something you can touch to be interesting to mathematicians, and these warping wireframes are as close to being able to perceive it as we can get at this point. A cube drawn on a computer isn't real either, but it can have all the properties of a real cube, so one should be able to have a tesseract in a simulated space with four axes. 

[Camacha]

Just now, cubinator said:

we can theorize the properties of hypothetical four-dimensional objects [...] It doesn't have to be something you can touch to be interesting to mathematicians [...] simulated [...]

My point exactly. It is a construct.

Just now, cubinator said:

A cube drawn on a computer isn't real either, but it can have all the properties of a real cube, so one should be able to have a tesseract

Comparing a tesseract with a real cube is the issue. We know how a real cube behaves. A tesseract is just something we imagined. It makes a fine plaything, but calling it 4D as if that is how the fourth dimension is pushing it.

[cubinator]

16 minutes ago, Camacha said:

My point exactly. It is a construct.

Comparing a tesseract with a real cube is the issue. We know how a real cube behaves. A tesseract is just something we imagined. It makes a fine plaything, but calling it 4D as if that is how the fourth dimension is pushing it.

Worrying about how a tesseract "really" behaves is also irrelevant precisely because it isn't something we can observe. If you want to try to construct a different model for a fourth dimension, you are free to do so although what mathematicians have come up with over the last two hundred years is pretty consistent. It does make for some pretty great thought experiments, though!

[Camacha]

Just now, cubinator said:

because it isn't something we can observe.

Because we made it up, not because we cannot observe it.

[Dres]

On 2/16/2017 at 3:01 PM, Camacha said:

Comparing a tesseract with a real cube is the issue. We know how a real cube behaves. A tesseract is just something we imagined. It makes a fine plaything, but calling it 4D as if that is how the fourth dimension is pushing it.

Yes, we know how a real cube behaves. We also know how an idealized mathematical cube behaves. And how a perfect square behaves, and how a perfect segment behaves, etc. We also happen to know how an idealized tesseract behaves.

These idealized versions of these objects, yes, aren't real, but mathematics is pretty damn good at describing the world. In fact, maths is pretty damn good at defining the world, because we made it that way. A real cube behaves exactly like a mathematical cube, excluding the problems of living in an imperfect physical world. If your real cube didn't react like the mathematical cube, then what you have is not a cube. An object in three dimensional space, in our world, reacts like a mathematical object in imagined three dimensional space, because that is how we defined three dimensional space. 

It's the same with this tesseract: This is how it would react, otherwise it wouldn't be a tesseract. This is what the projection of a tesseract looks like, otherwise what you're looking at is not a tesseract. This is how the forth dimension behaves, otherwise what you have is not the fourth dimension. Mathematics does not lie.

You can say that this is just what we think the fourth dimension is, after all, one can't observe the fourth dimension, if a fourth spatial dimension even exists. But if we had a real, physical, tesseract, it would act, for almost every intent and purpose, like this.

Edited February 18, 2017 by Dres

[Camacha]

9 hours ago, Dres said:

It's the same with this tesseract: This is how it would react, otherwise it wouldn't be a tesseract. This is what the projection of a tesseract looks like, otherwise what you're looking at is not a tesseract.

Yes.

Quote

This is how the forth dimension behaves, otherwise what you have is not the fourth dimension.

No.

This is where things go down the drain every time in this thread. Only if you define the fourth dimension exactly the way it suits you, this would be true. If you define time as the fourth dimension, like some people do, this tesseract is total bupkis. It is a construct, based on another construct (that being a specific version of the fourth dimension). In that regard, it is critically different than a three dimensional cube.

Theories like we live in a simulation aside, a three dimensional cube is factual thing. A four dimensional cube is not. A two dimensional plane is an interesting discussion

[c4ooo]

On 3/14/2016 at 3:06 PM, Veeltch said:

Just looking at it gives me a headache. No wonder I never completed a single wall of the 3D Rubik's cube.

I remember seeing a 4D platformer. I think it was on xkcd? Does anyone know what the title of the game was?

EDIT: was it this one?: http://miegakure.com/

I think Computerphile did an interview with the creator of the game

[Dres]

1 hour ago, Camacha said:

Yes.

No.

This is where things go down the drain every time in this thread. Only if you define the fourth dimension exactly the way it suits you, this would be true. If you define time as the fourth dimension, like some people do, this tesseract is total bupkis. It is a construct, based on another construct (that being a specific version of the fourth dimension). In that regard, it is critically different than a three dimensional cube.

Theories like we live in a simulation aside, a three dimensional cube is factual thing. A four dimensional cube is not. A two dimensional plane is an interesting discussion

Which is why I later specified, fourth spatial dimension, should it exist 

I agree, with the fourth dimension as time, this makes no sense. But nothing is claiming to represent the fourth dimension as time. 

 

Anyway, I digress, let's get back on track to twisty puzzles:

I hear there's a 120-cell version of this, the dodecahedron analogue. I'd love to see someone solve that xD

[Camacha]

Just now, Dres said:

Which is why I later specified, fourth spatial dimension, should it exist 

This specific version of a spatial fourth dimension. Remember, it is a construct, and as such, can be constructed pretty much in any way. In the case of a tesseract, it is specifically Euclidean space that is extrapolated to create an extra dimension. Euclidean space in itself is a construct or model that differs from our current understanding of the real world and extrapolating an extra dimension that does not differ from the other three dimensions is an additional choice within that construct. In Minkowski space, the fourth dimension does differ from the other three, and is closest to what we perceive to be reality. Considering we still do not have a unified theory, both will probably turn out to be woefully inaccurate.

The tesseract reminds me a bit of that joke about physicists and spherical cows

[kerbiloid]

The next step after the Tesserubik can be to build a ship in a Klein Bottle.

Edited February 19, 2017 by kerbiloid

[WinkAllKerb'']

On 12/03/2016 at 3:03 AM, cubinator said:

For those that don't know about this already, this thread is about 4-dimensional analogues to Rubik's Cube and other twisty puzzles. I am (obviously) a speedcuber, but I have yet to successfully solve a 4-dimensional twisty puzzle. I tried the Magic Cube 4D phone app several months ago, and got pretty far along in solving it, but I got lost at the part in the instructions regarding 4-color pieces. At that point I drifted away from such puzzles. Today I decided to try the computer version of the app, and I discovered that it allows one to select from a plethora of hyperdimensional twisty puzzles, not just the 3x3x3x3 simulated by the phone version. I decided to try my hand at the 2x2x2x2, as it should be much simpler. I managed to get 5 pieces aligned, but now I'm stuck. Unfortunately, even though it only has one type of piece, it happens to be the one piece I least understand . This is a cool brainteaser for anyone who wants to have their mind bent (or should I say 'extruded'?).

^^ out of you know, well ... you know ^^ so you ll get a quote instead ^^