# Off-Topic Discussion > The Lounge > Tech Talk >  >  The Fourth Dimension

## Sornaensis

How is this useful in a Three (spacial) dimensional universe?

Basically, we can't draw or show these things, just express them mathematically. How is this useful?

----------


## ninja9578

4th dimension is time.

In terms of physics there are 12 dimensions.

----------


## Bonsay

Yes we can draw them. If you acknowledge the wikipedia then check this out:
http://en.wikipedia.org/wiki/Tesseract

----------


## Grod

> 4th dimension is time.



Uhm, how do you know this?

----------


## Ynot

> Uhm, how do you know this?



http://en.wikipedia.org/wiki/Dimension#In_physics





> In terms of physics there are 12 dimensions.



I thought there was only 11

there was a video about it
I remember it being posted here ages ago....

----------


## Sornaensis

No, no.

I mean spacial dimensions.

I know about the fourth and fifth dimensions.

We move freely along three axses, one direction along a fourth, and stay rooted in a single spot on a fifth, and so on.

What I mean is, what is the purpose of a hypercube? You can't draw it, and you can't make it. So what is it used for?

And yes, I get the basic idea-- A cube made of an infinite amount of cubes stacked together.

----------


## poog

> How is this useful in a Three (spacial) dimensional universe?
> 
> Basically, we can't draw or show these things, just express them mathemeatically. How is this useful?



Yes.

----------


## Sornaensis

> Yes we can draw them. If you acknowledge the wikipedia then check this out:
> http://en.wikipedia.org/wiki/Tesseract



Lolwut.

That's a false 3D projection of something impossible to draw.

That isn't a spacial impossibility, just a projection.

I mean really drawing a hypercube.

----------


## Xei

> 4th dimension is time.
> 
> In terms of physics there are 12 dimensions.



Misconceptions.

There are three spacial dimensions and one temporal dimension; that's four dimensions in total but to say that time is the 'next one up' from space so to speak is wrong. The OP was talking about the fourth spacial dimensions which is a different matter.

Also, virtually all realistic models of physics use 3 space dimensions and a time dimension. String theory has solutions with many more dimensions, but there is no empirical evidence for these, and there are a few different numbers of dimensions possible.




> No, no.
> 
> I mean spacial dimensions.
> 
> I know about the fourth and fifth dimensions.
> 
> We move freely along three axses, one direction along a fourth, and stay rooted in a single spot on a fifth, and so on.
> 
> What I mean is, what is the purpose of a hypercube? You can't draw it, and you can't make it. So what is it used for?
> ...



I don't know what you mean by the fifth dimension.

The hypercube is a bit of pure maths really; just geometry. As with most pure maths it is initially created out of curiousity, but eventually such things almost always find applications in the real world. As ninja said, for example, multiple spacial dimensions may be a route to a theory of everything.

It's not completely impossible to visualise a hypercube, by the way. Here's how I do it;

Imagine a point which is separated into two points with a line between them.

Then imagine this line is then separated into a two lines with two new lines between the end points of the lines; a square.

Imagine this square separating into two squares, with four new lines connecting the corners; a cube.

Finally imagine the cube separating in two, each corner connected to the identical corner of the new cube, just as before.

You've created 8 (connecting) + 12 (new cube) new lines and 8 new corners, so in total your tesseact has 32 edges and 16 corners. Which is correct.




> Lolwut.
> 
> That's a false 3D projection of something impossible to draw.
> 
> That isn't a spacial impossibility, just a projection.
> 
> I mean really drawing a hypercube.



It's a 2D projection onto your monitor...

It is not impossible to draw a 4D object on a 2D surface, you just loose some perspective. Exactly as it is not impossible to draw a 3D object on a 2D surface.

----------


## Sornaensis

> Misconceptions.
> 
> There are three spacial dimensions and one temporal dimension; that's four dimensions in total but to say that time is the 'next one up' from space so to speak is wrong. The OP was talking about the fourth spacial dimensions which is a different matter.
> 
> Also, virtually all realistic models of physics use 3 space dimensions and a time dimension. String theory has solutions with many more dimensions, but there is no empirical evidence for these, and there are a few different numbers of dimensions possible.
> 
> I don't know what you mean by the fifth dimension.
> 
> The hypercube is a bit of pure maths really; just geometry. As with most pure maths it is initially created out of curiousity, but eventually such things almost always find applications in the real world. As ninja said, for example, multiple spacial dimensions may be a route to a theory of everything.
> ...



Fifth dimension is just a product of deduction.

If there is a fifth, then we don;t move along it at all, because we only travel in one direction across the fourth, and in two directions along three spacial dimensions.

What's the theory of everything?

Yes, I know. But you end up with a box inside of a box in three dimensions. 

I know it's a '2d projection', that's why I said "false 3D"  :tongue2: 

Yeah, but with 4 dimensions you lose perspective entirely. Instead of a tesseract, you end up with a box inside of another box-- Something that can be constructed in 3 dimensions.

Technically, if you divided a tesseract into layers, each layer would be a cube.

----------


## ninja9578

Strings are 11 dimensional, they vibrate in the 12th dimension.  12.

There is no point to a hypercube, it's just geometry.

----------


## Sornaensis

So it's just nifty, but that's it?  :tongue2:

----------


## ninja9578

It's valuable for understanding higher dimensions.  We wouldn't understand advanced 3D geometry without first understanding the cube.  Same goes for higher dimensions.

----------


## Sornaensis

Sounds like a royal pain though; only able to work with shadows.

----------


## Xei

I'm sure tesseracts will have quite a few real world applications actually.

Even the most obscure areas of pure maths like number theory have found useful functions. Something as basic as a tesseract is sure to have quite a few uses in physics at least. Probably also computing.

----------


## drewmandan

> There is no point to a hypercube, it's just geometry.



That's not true. Sometimes it's absolutely necessary to go to higher dimensions in math to find truths that are then applicable to the lower dimensions that wouldn't otherwise be knowable.

----------


## slayer

I only saw a video about 10 of them. I heard of an 11th, but did not know of the 12th.

What is the 11th, and 12th dimension?

----------


## Bonsay

> Lolwut.
> 
> That's a false 3D projection of something impossible to draw.
> 
> That isn't a spacial impossibility, just a projection.
> 
> I mean really drawing a hypercube.



Ok...?

I don't understand what you want then. You said we can't draw them and I said we can. From my understanding "drawing something" never meant materializing something in your space. Do you create a 2D object when you "draw" a square? No you don't, and neither do you create a 4D object when you draw a hypercube.

I don't know what you don't understand about that. Maybe you're just troubled because you can't comprehend it (By that I mean all of us since we live in a seemingly 3D world)? That really is a drawn hypercube, some in 2D and some in 3D.

----------


## Xei

> What is the 11th, and 12th dimension?



Just more spacial dimensions... points have 11 or 12 coordinates instead of 3.

I don't think there are string theories which suggest 12 dimensions... but it doesn't really matter, you get the same comprehension of an incomprehendible number either way, I suppose.

----------


## wendylove

> I don't think there are string theories which suggest 12 dimensions... but it doesn't really matter, you get the same comprehension of an incomprehendible number either way, I suppose.



String theory originally had 26 dimensions, then it got reduced to 11, then somebody said add one more, so its no 12 dimensions. Also, there are some models that say there are two time dimensions, which is stupid.

Anyway, string theory has no evidence for it, so it seems that it is just another religion. Saying that I did read a book called "not even wrong", which might have biased me against string theory.

----------


## Sornaensis

> Ok...?
> 
> I don't understand what you want then. You said we can't draw them and I said we can. From my understanding "drawing something" never meant materializing something in your space. Do you create a 2D object when you "draw" a square? No you don't, and neither do you create a 4D object when you draw a hypercube.
> 
> I don't know what you don't understand about that. Maybe you're just troubled because you can't comprehend it (By that I mean all of us since we live in a seemingly 3D world)? That really is a drawn hypercube, some in 2D and some in 3D.



No, no. That isn't a drawing, it's what a square is to a cube.

----------


## Xei

No, it is not what a cube is to a tesseract. When you draw a tesseract, it does not somehow loose a dimension. Just like when you draw this:



it does not magically turn into this

.

This



is most definitely a drawing of a tesseract in 2D.

----------


## Sornaensis

What?

That drawing of a tesseract is a 3D projection. That's not what a tesseract looks like for real. That's just one way of expressing it in 3D space.

That's a shadow, not the actual object. You cannot draw a tesseract.

Basically, if you were in 2D space, and were trying to draw a cube, you would end up with two squares because you can't express depth in 2 dimensions.

----------


## Xei

That's a 2D projection of a tesseract. If it were 3D it would not fit in your monitor.

You can draw a 3D object on a 2D surface. There's one above, in addition to virtually every picture ever being a drawing of a 3D object. You can also draw a 4D object. Obviously you loose the depth and the perspective is incorrect, but again, this happens when you draw a 3D object.

----------


## Kushna Mufeed

Basically, just like you can represent 3 dimensions in 2 dimensional space, you can represent 4 dimensions in 2 dimensional space. Or 5 or however many you want.

Also:
http://news.bbc.co.uk/2/hi/science/nature/6466129.stm

----------


## Sornaensis

It's a 3D projection drawn on a 2D surface.

A 2D tesseract is a Cube drawn on a 2D surface.

You cannot draw a 4D object from any angle. The only thing you can draw is it's 3D projection. 

A drawing of a 3D object can be mimicked in reality-- a 4D object can't.

You can't draw a 4D object. What am I saying that isn't making sense?  ::?:

----------


## Kushna Mufeed

I was drawing a tesseract while the teacher was teaching the rest of the kids how to draw 3D vectors.

So, no.

----------


## Sornaensis

> I was drawing a tesseract while the teacher was teaching the rest of the kids how to draw 3D vectors.
> 
> So, no.



Again, you weren't drawing a tesseract like you might draw a cube-- A mirror to the actual thing.

What you were drawing was basically it's shadow. You can't express four spacial dimensions in three dimensions. I don't care how hard you try. You just end up with a shadow.

----------


## Xei

> What am I saying that isn't making sense?



Pretty much all of it. For a start,





> A 2D tesseract is a Cube drawn on a 2D surface.





≠

----------


## Sornaensis

> Pretty much all of it. For a start,
> 
> 
> 
> 
> ≠



That's a 3D tesseract on a 2D surface  :tongue2:

----------


## Xei

Explain why the drawing of a tesseract is not a drawing whilst the drawing of the cube is a drawing.

----------


## Sornaensis

> Explain why the drawing of a tesseract is not a drawing whilst the drawing of the cube is a drawing.



It is a drawing. It is a 3 dimensional drawing of a four dimensional object.

----------


## Kushna Mufeed

> Again, you weren't drawing a tesseract like you might draw a cube-- A mirror to the actual thing.
> 
> What you were drawing was basically it's shadow. You can't express four spacial dimensions in three dimensions. I don't care how hard you try. You just end up with a shadow.



I wasn't drawing it in 3 dimensions. That's called sculpting.

----------


## Sornaensis

> I wasn't drawing it in 3 dimensions. That's called sculpting.



What?

You can draw in 3 dimensions on a 2 dimensional surface.  ::?:  That's what this discussion is about.

----------


## Kushna Mufeed

If you're drawing it on a 2D surface, you are only drawing in 2 dimensions.

BUT

You can still represent 3 dimensions on a 2D surface.

And 4 and 5 and as many as you see fit.

----------


## Xei

Ew, I think this is becoming a bit convoluted...




> That isn't a drawing







> It is a drawing



Well, at least we agree now.

----------


## Sornaensis

> Ew, I think this is becoming a bit convoluted...
> 
> 
> 
> 
> 
> 			
> 				That isn't a drawing



When I said drawing there I meant a 4D representation of a 4D object on a 2D surface in 3D space.





> If you're drawing it on a 2D surface, you are only drawing in 2 dimensions.
> 
> BUT
> 
> You can still represent 3 dimensions on a 2D surface.
> 
> And 4 and 5 and as many as you see fit.



Yes, but not in 3D space. Which happens to be the kind we live in :-/

----------


## Kushna Mufeed

Lost cause...

----------


## Sornaensis

> Lost cause...



It's a pretty simple concept  ::?:

----------


## Xei

> When I said drawing there I meant a 4D representation of a 4D object on a 2D surface in 3D space.



Uh I'll drop out now.  :tongue2: 

To be honest I don't think we should fight over silly things, it's an interesting topic when you don't get hung up about the details.

----------


## Sornaensis

All I said was you can't draw a tesseract, and this erupts, so...

++Postcount;

----------


## Kushna Mufeed

I know it is.

I'm not saying you CAN draw a 4 dimensional object. I'm saying you can REPRESENT it.

Just like you can't draw a 3D object on a 2D plane. You can only represent it.

----------


## Sornaensis

> I know it is.
> 
> I'm not saying you CAN draw a 4 dimensional object. I'm saying you can REPRESENT it.
> 
> Just like you can't draw a 3D object on a 2D plane. You can only represent it.



Well, not in 2D space, at least. It's all about the space the surface is in.

----------


## Bonsay

But drawing IS representing. So you can draw a 4D object on a 3D or a 2D surface. You can't comprehend the extra dimension, so the object you draw will always seem to be a 2D/3D object. Because of our spacial perception the drawn 4D object (Either in 2D or 3D) will look like a "complex" 3D object. I thought this was obvious. As for an actual 4D object being made, that's not possible.

----------


## Xei

I have a projection of a tesseract in my room now... made out of geomag.  :tongue2: 

It's really quite cool. I did it a bit different to the standard way (i.e. this thing) by giving it sides of equal length, to make it more realistic... it worked actually. You can see very clearly all 8 cells and how they have been warped in exactly the same way that the faces of a cube are warped when you draw it in 2D. I've also discovered that from the right angle it can be made to look like a cube drawn in 2D, which is interesting.

----------


## Sornaensis

> But drawing IS representing. So you can draw a 4D object on a 3D or a 2D surface. You can't comprehend the extra dimension, so the object you draw will always seem to be a 2D/3D object. Because of our spacial perception the drawn 4D object (Either in 2D or 3D) will look like a "complex" 3D object. I thought this was obvious. As for an actual 4D object being made, that's not possible.



No, you CAN'T. How many times do I have to explain? It is IMPOSSIBLE to draw a 4D object in 3D space.

----------


## Bonsay

Are you going to say it's impossible to draw a 3D object in 2D?

----------


## drewmandan

> Are you going to say it's impossible to draw a 3D object in 2D?



That is impossible. But you can project a 3d object in 2d, and you can project a 4d object in 2d as well.

----------


## Xei

Of course you can draw a 3D object...

----------


## Bonsay

> That is impossible. But you can project a 3d object in 2d, and you can project a 4d object in 2d as well.



Is this a drawn or projected object?

----------


## Sornaensis

> Is this a drawn or projected object?



It is a 3D projection of a 4D object onto a 2D surface in 3D space. To be exact.

Drawing a cube in 2D space would look like two squares drawn over each other to a 3D viewer, but they would appear as a strangely convex box rather than a cube, because everything you see in 2D is made up of 1D lines.

That is what this is, only for 4D.

----------


## drewmandan

> Is this a drawn or projected object?



It's a drawn 2D object (we might call it a jumble of quadrilaterals), a projected 3D object (looks like it could be two cubes, one inside the other), *or* a projected hypercube. There is this ambiguity which defines what it is to be a projection.

EDIT: Roxxor doesn't know what the fuck he's talking about. He's just confusing himself and everyone else.

----------


## Kushna Mufeed

Yeah, I figured that a while ago.

----------


## Sornaensis

> It's a drawn 2D object (we might call it a jumble of quadrilaterals), a projected 3D object (looks like it could be two cubes, one inside the other), *or* a projected hypercube. There is this ambiguity which defines what it is to be a projection.
> 
> EDIT: Roxxor doesn't know what the fuck he's talking about. He's just confusing himself and everyone else.



That isn't a post, that's just a random jumble of pixels that one might interpret to be written words and a picture. If they're lucky, they'll see english and might be able to draw meaning from it.

Yea, I thought his question was specific. You know, wanting a specific answer that was meaningful.

----------


## Bonsay

Ah I get it! So Xei's real life hypercube model is a "drawn" 3D object or a projected 4D object. Well in that case you couldn't draw it I guess.

----------


## drewmandan

> Ah I get it! So Xei's real life hypercube model is a "drawn" 3D object or a projected 4D object. Well in that case you couldn't draw it I guess.



Correct. I'm assuming his real life model is actually 3-dimensional. So something like that would be like looking at a hypercube from a certain 'angle' (and projecting), although the angle is now in 4-space and you can't picture it.

----------


## Xei

Hmm... no, actually I just realised you can definitely draw a 4D object in 2D:

----------


## Bonsay

Apparently that's a drawing of a circle. But it can also be a projection of a sphere or some 4D sphere equivalent.

----------


## drewmandan

> Hmm... no, actually I just realised you can definitely draw a 4D object in 2D:



If that's a 4-sphere, it's just a projection, not an actual drawing.

----------


## Sornaensis

> Hmm... no, actually I just realised you can definitely draw a 4D object in 2D:



Yeah, exactly.  :tongue2:

----------


## Xei

> If that's a 4-sphere, it's just a projection, not an actual drawing.



This is really a load of nonsense to be honest. To draw something is to represent something on a surface.

If you were to ask an artist what drawing something is, he would not say, 'oh, but remember it can only be n+1 dimensions or fewer!'. Just why? You lose information when you represent a 3D object in 2D. That object is no longer 3D, it's a 2D representation. Here, the object is no longer 4D, it's another 2D representation too.

Seriously, unless you can find an accepted definition of drawing something to be 'representing something in 2D from no more than n+1 dimensions', I don't see what the argument is.

Incedentally, that's not a 4-sphere. When I drew it I intended it to be a 4D equivalent of a disc or a ball (a 4-ball I suppose it would be called).

Technically a circle is 1D, a sphere is 2D, and so actually the n+1 dimensional equivalent is a 3-sphere.

----------


## drewmandan

> If you were to ask an artist what drawing something is, he would not say, 'oh, but remember it can only be n+1 dimensions or fewer!'. Just why? You lose information when you represent a 3D object in 2D. That object is no longer 3D, it's a 2D representation. Here, the object is no longer 4D, it's another 2D representation too.



Representation is what mathematicians call "projection". 





> Seriously, unless you can find an accepted definition of drawing something to be 'representing something in 2D from no more than n+1 dimensions', I don't see what the argument is.



I don't know where you're getting this "n+1" stuff. Any number of dimensions can be projected to the plane. 





> Incedentally, that's not a 4-sphere. When I drew it I intended it to be a 4D equivalent of a disc or a ball (a 4-ball I suppose it would be called).
> 
> Technically a circle is 1D, a sphere is 2D, and so actually the n+1 dimensional equivalent is a 3-sphere.



Ok, technically the 4D sphere is "called" a 3-sphere. That's just arbitrary notation and it's not logical. But convention is convention. Without checking, I wouldn't have thought a 2D object would be called 1D and a 3D object called 2D, but apparently they are.

----------


## Xei

> Representation is what mathematicians call "projection".



I know. Swap all the instances of the word representation for projection in my post if you want.




> I don't know where you're getting this "n+1" stuff. Any number of dimensions can be projected to the plane.



I'm getting it from you, saying you can't draw an n+2 dimensional object on an n dimensional object, ie a hyperball on a plane.




> Ok, technically the 4D sphere is "called" a 3-sphere. That's just arbitrary notation and it's not logical. But convention is convention. Without checking, I wouldn't have thought a 2D object would be called 1D and a 3D object called 2D, but apparently they are.



It is logical. This is maths we're talking about here, I can assure you it's logical.  :tongue2: 

A circle is a 1D line (formed by the set of points which are of a fixed point from the origin) and a sphere is a 2D plane (formed in the same way). Hence the next dimensional analogue of a sphere is 3D.

A disc however is the 2D area/plane bounded by the line of a circle, and a ball is the 3D volume/space bounded by the plane of a sphere.

----------


## drewmandan

> I'm getting it from you, saying you can't draw an n+2 dimensional object on an n dimensional object, ie a hyperball on a plane.



But...I didn't say that. I have said about a dozen times now: any higher dimensional object can be projected onto a lower dimensional object.

----------


## Xei

But... you did. That's why we're talking.




> not an actual drawing.



Judging by your above post you've now decided that a projection _can_ actually be a drawing, so we don't disagree any more.

----------


## drewmandan

> But... you did. That's why we're talking.
> 
> Judging by your above post you've now decided that a projection _can_ actually be a drawing, so we don't disagree any more.



The word "drawing" was being used in a different way before. People were using it like a "true" representation of the object, and then saying that you can't "draw" a 4D object because you're "drawing" it on a 2D plane. So there was an inconsistency there, and I'm not quite certain everyone understands. So for now on, I suggest we all use the word "projection" when referring to a projection, and "sculpture" when referring to the recreation of the original object.

Hence, a circle on a sheet of paper is a sculpture of a circle and a projection of either a sphere or any higher order of sphere. A sphere in 3D is a sculpture of a sphere and a projection of higher dimensional spheres. And so on.

----------


## Sornaensis

In this case, a drawing is the expression of all the spacial dimensions of an object. So, if you're in 2D then a 3D drawn object is a 2D projection-- Still a drawing, but if you're going to call it 3D then it's a projection of a 3D object, not a "true" drawing of a 3D object, which would express Height, width and depth.

----------


## Kromoh

Any representation of an object in fewer dimensions is actually a representation, and not a real thing. That's how you can draw a cube in 2D, but you lose some aspect of it - see how you can't see the opposite side of the drawn cube. The drawing is an orthogonal projection of the image - just like a shadow, really.

4D can be represented into 2D, but instead of losing only one dimension, it actually loses 2, making it even less accurate a representation. It is a valid representation, nonetheless.

So, yes, that is the drawing of a tesseract.

--

Funny as physics can be, you can actually substitute one of the dimensions in a projection for a dimension of time. That's what allows us to represent a perfect cube in 2D - you make it an animation (making use of the time dimension), and rotate it around. Unfortunately, we still haven't invented hologram monitors, but once we do, it'd be much easier to represent tesseracts.

--

Regarding the original question - what's the use of a fourth physical dimension. Well, You know you can actually work with each dimension separately, including movement even. I don't see any other practical use for it right now, but maybe it can help in explanations for fundamental physics, the origin of the universe, etc. Finally, it could be used in art  ::D:

----------

