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?
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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?
4th dimension is time.
In terms of physics there are 12 dimensions.
Yes we can draw them. If you acknowledge the wikipedia then check this out:
http://en.wikipedia.org/wiki/Tesseract
Uhm, how do you know this?Quote:
Originally Posted by ninja9578
http://en.wikipedia.org/wiki/Dimension#In_physicsQuote:
Originally Posted by Grod
I thought there was only 11Quote:
Originally Posted by ninja9578
there was a video about it
I remember it being posted here ages ago....
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.
Yes.Quote:
Originally Posted by A Roxxor
Lolwut.Quote:
Originally Posted by Bonsay
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.
Misconceptions.Quote:
4th dimension is time.
In terms of physics there are 12 dimensions.
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.Quote:
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.
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.
It's a 2D projection onto your monitor...Quote:
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 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.
Fifth dimension is just a product of deduction.Quote:
Originally Posted by Xei
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" :P
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.
Strings are 11 dimensional, they vibrate in the 12th dimension. 12.
There is no point to a hypercube, it's just geometry.
So it's just nifty, but that's it? :P
It's valuable for understanding higher dimensions. We wouldn't understand advanced 3D geometry without first understanding the cube. Same goes for higher dimensions.
Sounds like a royal pain though; only able to work with shadows.
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.
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.Quote:
Originally Posted by ninja9578
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?
Ok...?Quote:
Originally Posted by A Roxxor
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.
Just more spacial dimensions... points have 11 or 12 coordinates instead of 3.Quote:
What is the 11th, and 12th dimension?
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.Quote:
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.
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.
No, no. That isn't a drawing, it's what a square is to a cube.Quote:
Originally Posted by Bonsay
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:
http://www.deimel.org/images/plain_cube.gif
it does not magically turn into this
http://www.bizzybecscardmakingscrapb...20envelope.jpg.
This
http://nodebox.net/code/data/shared/..._tesseract.png
is most definitely a drawing of a tesseract in 2D.
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.
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.
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