I've been using this website to try to envision and understand a hypercube but I can't fully understand it. All it looks like to me is a regular cube with thick cube-like sides.
Can't really wrap my mind around 4 physical dimensions
- Thread starter archcommus
- Start date
silverpig
Lifer
- Jul 29, 2001
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Just go from 2D to 3D.
You have a 2D square, and in order to make a cube you travel along the z axis. Every increment you go up along the z you see a new 2D square.
So for 4D just imagine a 3D cube, and then move along the w-axis. Every time you go up in w you get a new cube.
I think the easiest way to think about it is to use colour. Set w=0 to be red, and w = l (the size of your cube) to be purple. Now as you travel along w the cube goes from red to orange, yellow, green...
You have a 2D square, and in order to make a cube you travel along the z axis. Every increment you go up along the z you see a new 2D square.
So for 4D just imagine a 3D cube, and then move along the w-axis. Every time you go up in w you get a new cube.
I think the easiest way to think about it is to use colour. Set w=0 to be red, and w = l (the size of your cube) to be purple. Now as you travel along w the cube goes from red to orange, yellow, green...
And why should it make sense? You've got a highly evolved brain for working in 3D. You would need a new brain architecture to think in 4D.
zephyrprime
Diamond Member
- Feb 18, 2001
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Keep in mind that a tesseract is not a hypercube; it's merely the shadow of a hypercube in 3d space.
Well that clears up that image of a cube inside a cube then I guess.
I'll try to stop using images on websites since they are all 2D and just think of it in my mind instead.
I understand the concept of replicating squares on the z axis to produce 3D, so you replicate cubes on the w axis to produce 4D. But what DIRECTION does the w axis go in? No matter how I think of it I just think of some diagonal in 3D space, which makes sense since we are living in a 3D world. I think this is something that can be understood as a concept but I don't believe people who say they understand this can actually picture a 4th physical dimension that this w axis goes in.
Carl Sagan had a very cool explanation of the hypercube in one of his Cosmos episodes, but yes, what it boils down to is that the tesseract is the shadow of a 4d cube in 3d space. When you draw a 3d cube on a piece of paper, not all of the lines intersect at 90', like they would if you built it out of matchsticks. The same is true of the hypercube - when viewed in a 3d world it appears to be a cube within a cube, with non-90' sides. In a 4d world, all of the edges of the hypercube intersect at 90' to one another. What we see is a limitation of our 3d universe.
See, yeah, I understand how they explain the concepts of the fourth dimension, and picturing n+1 dimensions by correlating the differences between n and n-1 dimensions, but it's all just a made up concept, just a way to say "this is how we would do it IF there were 4 spatial dimensions." The fact is, there are only 3 spatial dimensions, so to me the whole things sounds entirely made up and just like a big "what if" fantasy.
Analog
Lifer
- Jan 7, 2002
- 12,755
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Thanks, that kicked ass, but it's different. Instead of saying the fourth dimension is spatial, it says the fourth dimension is time, and then each dimension above that is culminating all the previous dimensions into a single point. So in this sense a hypercube wouldn't really be a 4D physical object, instead it'd be an object that represents the 3D world through all of time. Really makes sense though!
Yep the original thread about that link sparked quite a debate, as you have to remember these spatial demention theories all differ and concept and number...but anyway it is one cool flash explanation.
It's entirely possible, even rather simple, to represent 4 spatial dimensions mathematically. But you're right, it is just a fantasy to think about living in a universe with 4 spatial dimensions, or at least 4 easily observable (large) spatial dimensions. There are, as you probably know, many physical theories that posit extra dimensions, anywhere from one to 7 extra dimensions in fact.
I'm not too keen on string theory's 10 or 11 dimensions, for no other reason than the fact that it makes me uncomfortable, but it could well be right. Hopefully we'll have more answers when the data from the Large Hadron Collider starts flooding in later this year or early next year.
The biggest problem here is trying to draw four deminsions onto 2. Thats equivilent to trying to convey a 3 deminsionsal object as a 1 deminsional line. Can you imagine looking at a line and being able to distinghish what you would look like as a line (just a 6 ft tall line) vs a house (a 20ft tall line). Pretty much all the information is lost since you are taking away 2 deminsions. With 2 deminsions you can get an idea of a 3D object, but only a profile of it, still not a very good idea of the whole thing. The only way to get even a decent view is to see a 3D model of a 4-D hypercube. Preferably a set of 3D models that would show disections of the hypercube. I think one of the biggest reason people have trouble is because they are usign a 2D screen which is absolutely 100% impossible to even get the remotest idea.
Fenixgoon
Lifer
- Jun 30, 2003
- 33,385
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Originally posted by: latino666
my head hurts
i actually thought it made a lot of sense.
0 - a point
1 - a line
2 - a flat shape
3 - 3space
4 - time
5 - instantaneous probability
6 - all probability in time
7 - all the probabilities in time for a universe
8 - probabilities for different universes (multiverses/parallel dimensions?)
9 - shifting from one universe to another
10 - all possible combinations of existence; strings
im actually quite tempted to buy the book
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