I remember reading in Scientific American several years back that one of the Grand Unified Field Theories (it may have been one of the Supergravity theories) postulated a universe with 11 space-time dimensions. In this model, things that are apparently “points” in 3 dimensions, like electrons and quarks, are actually infinitely long lines (or even planes!) extending across these “upper” dimensions.

On listening to my book-on-tape version of Stephen Hawking’s Universe, the author mentions that the N=8 Supergravity theory requires something like 26 space-time dimensions.

The link to the original Mailbag item is here: http://www.straightdope.com/mailbag/mdimensions.html …please be sure you’ve read the article before commenting. You can read the article by clicking on that underlined url.

I think the term “dimensions” gets used loosely. Let’s not confuse them with degrees of freedom.

From a mathematical perspective, the calculus and geometry and topology and so forth of n-dimensional space is fairly well known. So they’re really models, that’s all, to do whatever you want to do; there’s no inherent reality, says me. (Karen disagrees.)

BTW, I always found it interesting that there are many theorems that are true in n-dimensional (mathematical) space, when n > 4, that are not true for n = 1, 2, or 3. Three dimensions has too little flexibility.
[Note: This message has been edited by CKDextHavn]

Well, sure, if theorists want to cram a whole lot of dimensions into space-time, there may as well be infinitely long electrons. I mean, if theorists said, Hey there are 324 dimensions and pink elephants fly on fairy wings, would any of us be able to dispute it?

It makes me wonder if there is some sort of theorist contest to see who can invent the most outrageous thing that people believe in.

We might be able to dispute the 324 dimension theory if it makes any predictions that can be tested with existing equipment. Maybe we can paint an elephant pink and drop it off a cliff to see if it flies.

Then again, the most popular theory to explain everything nowadays is no longer Supergravity, but the Superstring Theory, which has the distinct aesthetic advantage of not requiring more than three (3) space dimensions and one (1) time dimension.

Yeah, I know this is hard to swallow at first take, but the math supporting an 11 dimensional spatial universe is quite cogent.

We already know that our 3D+Time universe is bent in ‘other’ dimensions.

We have observe 3D electrons turn into 2D electrons in intense magnetic fields.

So, we have physical evidence that the pure 3D universe is, ummm, flexible.

The equations that describe the fundamental forces of nature work very well together in 26D space. When the equations are worked in, 15 dimensions cancel each other out, leaving 11D. The ‘other’ dimensions are sub-subatomically small, so, no human sized person notices this extra ‘thickness’ to their being. But the sub-atomic particles notice it.

Just like macro-atomic structures affect the geometry of space-time through their gravity, so too, the subatomic particles create a 11D structure that can be likened to strings. The theory is intuitively sound. The math to completely back it up is about two decades away. Who knows when we’ll be able to manipulate subsubatomic particles in a way to physically demonstrate these other dimensions.

Geez, guys, you missed a chance to really confuse the poor kid who asked the original question.

Ya shoulda mentioned infinite-dimensional spaces, (Admittedly, I don’t use 'em myself – nor do I even remember what they’re good for – but I have seen references to them.)

Vep, once you’ve got the mathematics for n-dimensional vector spaces, where n is any integer, it’s not hard to develop a mathematics for infinite-dimensional vector spaces. As far as I am aware, they’re not useful for any practical application, but only an interesting math-theoretic construct.