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ETpro's avatar

How do you envision space in more than 3 dimensions, then rotate it to see what happens? (Strange Universe 2011)

Asked by ETpro (34472points) January 7th, 2011

Garrett Lisi, surfer and iconoclastic quantum physicist, gave a fascinating TED Talk. In it, he covered his controversial Theory of Everything. Interesting as that Theory is, that isn’t the focus of this reference. In his talk, he showed a number of views of the 226 known subatomic particles arrayed in 4 or more dimensions. He then rotated the views and showed that some fascinating patterns emerged. Interestingly, these patterns indicate that there must be some particles missing. The Higgs Boson is one of those suspected AWOL particles.

Enough of that. My question is how do you construct 4, 5, 6 or 8 dimensional space within a computer model so you can then rotate the space and see how things align along various axes.

This question is the first of the 2011 Strange Universe Series. The entire 2010 Series of 20 questions can be found from here

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17 Answers

YoBob's avatar

Perhaps something similar to what this guy did with a hypercube visualization would work for you.

iamthemob's avatar

I think that part of it may be that it’s potentially better to consider movement of particles as would be perceivable in our perceivable timespace than to consider how to represent imperceivable dimensions in ours.

I don’t know if this is remotely helpful, but someone was asking about quantum teleportation and how information was transmitted over distances at faster than light speed.

I gave the example of two points on a paper at the far ends of it. If you move along two dimensions between them, that distance is fixed. Something moving in two dimensions can only move in that manner between the two.

If you crumple it into a ball, however, an object moving between three dimensions can get from one point to the other in a much shorter line, and therefore much quicker. From the perspective of the two dimensional traveler, the three dimensional traveler skips instantaneously – if it’s even perceivable – from the points squished between the two points on the paper instantaneously and jerkily. If the points are right next to each other – like, if the paper is folded end to end so the points are pretty much touching in three dimensional space, it would just disappear from one point and reappear at the other.

The three dimensional traveler, however, just steps from one point to the other. From its perspective, the two dimensional traveler is traveling not in a straight line, but moving down and up and sideways and around – perhaps even backwards, to get to a new destination that’s right in front of it.

So, if you focus on the way a particle would travel through three dimensional space if it had access to other dimensional shortcuts, you might be able to construct the three dimensional “tunnels” it’s traveling through or along,

It’s sort of like drawing in the extra three dimensional space between the three dimensional space we see. Think of a drawing of a wormhole. Looking at the top of the wormhole, you see the layers of three dimensional space behind it. Looking at the bottom, you see the reverse. As you turn it to the side, you can either conceptualize it as a tunnel between the two points with the intermittent space deleted, turn it to the side and as you get more and more to a 90 degree view, the space between collapses until it disappears from view.

Wow…a picture really is worth a thousand words.

YoBob's avatar

Ok, so apologies for the original pedestrian answer. I didn’t really read the details and thought you were asking about how to visualize a 4 dimensional construct.

As far as how to model it, my first gut reaction would be to represent the data set in the form of a multi-dimensional array. Most high level languages allow for the specification of arrays that have more than 2 dimensions. The trick, of course, is indexing the points within the multi-dimensional array from the perspective of the 3 dimensional space it is being observed from. I’m sure there are some uber math geeks out there that can point you to some multi-dimensional matrix manipulation formulas (I’m not one of them). Heck, I even wouldn’t be surprised if there isn’t library with the functions you need already implemented.

mathsphysicsnormally's avatar

http://www.dimensions-math.org/Dim_reg_E.htm

First off hasn’t Garrett Lisi model been seen to have big problems in it as it stands? These set of videos in the link given are to give an understanding to view the higher dimensions

ETpro's avatar

@iamthemob “So, if you focus on the way a particle would travel through three dimensional space if it had access to other dimensional shortcuts, you might be able to construct the three dimensional “tunnels” it’s traveling through or along,” That’s a mighty bigh might. But I am so looking forward to finding out.

@YoBob Thanks. Here’s hoping one of those uber math geeks chimes in on this.

@mathsphysicsnormally Very nicely done. Thanks.

mattbrowne's avatar

If you give me a different brain, I’ll try.

ETpro's avatar

@mattbrowne If I had the kind of brain it takes, I’d clone you a copy. :-)

Rarebear's avatar

This is how I used to think about this as a kid:
1) Take a point, and draw a circle around the point. The circle is a one dimensional line in a two dimensional surface.

2) Now take a line stretched to infinity. You can draw a circle around that line with a plane creating a cylinder. The circle is a 2 dimensional surface drawn in a 3 dimensional space.

3) Now this is where it gets hard. Take a plane, and stretch it to infinity. You can actually draw a circle around that plane, but you do it with a space in the 4th dimension.

Mathematically, you can draw a circle around an object with dimension n, with an object in dimension n+1, through the dimension n+2.

ETpro's avatar

@Rarebear Thanks for that. Intellecually, I can understand that perfectly well. But my mind melts as I try to visualize what it really looks like. Of course, with these old eyes, seeing across the street is difficult enough. Beyond infinity is a non-starter.

Rarebear's avatar

Don’t worry. I’ve been thinking about this for almost 35 years and I still can’t wrap my head around it.

iamthemob's avatar

This interactive website shows 12 things that will change everything – one of them being the discovery of extra dimensions. It has a visual animation of the teseract @YoBob links to above – but also, awesomely – a video demonstration of a four dimensional version of tetris which shows how the shapes are manipulated by the gamer across a fourth dimension of space.

What’s interesting is that at times the movement ends up with the shape in two places at the same time! (of course, that’s how we see it in three dimensional space).

Rarebear's avatar

@iamthemob I love the tetris game.

ETpro's avatar

Great link, @iamthemob. Thanks. I see the tesseract, and indeed it is fascinating to view. I’ve seen similar computer simulations of 5 and 6 dimensions, and of 8 and 11. Eleven works well for string theory.

But in none of these higher dimensional simulations do we find the weirdness we observe in this Universe. No matter where you go in our Universe, it appears that the most distant objects in any direction are equally far from your point of view. There is no apparent edge. Not so with the tesseract or any of the higher dimensional computer simulations. Maybe the computer’s mind is just as wigged out as mine.

iamthemob's avatar

@ETpro – Well, the computer itself and any simulation has to have an edge.

And indeed, our minds are limited and created by our ability to assemble various stimuli into a concept of reality. A lot of what we see, for instance, is our mind filling in sensual “gaps” or correcting for small distinctions that are irrelevant.

hiphiphopflipflapflop's avatar

Alicia Boole, the third daughter of George Boole (he being the logician who gave us Boolean logic), may have had the ability to visualize four-dimensional objects.

ETpro's avatar

@hiphiphopflipflapflop Good lord, what kind of a stratospheric IQ must she have possessed?

hiphiphopflipflapflop's avatar

That she made such fundamental contributions to geometry with no formal training and little support until so late in life… it is amazing. And a pity at the same time.

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