The idea of “a dimension” in the way you express it doesn’t realluy have meaning in physics and maths. When a phsyicist talks about “a dimension” in that way, you can pretty much gurantee it’s lazy shorthand for a coordinate. For example in relatvity if a phsyicist were to talk about “the time dimension” what they actually talking about 99% of the time is a timelike cooridinate in particular cooridnates syetm or set of coordinate systems.
Okay, I think you and Topologist are right. I had the idea for some reason that Lebesgue dimension was only defined if the space was hausdorff, but the definition doesn’t seem to require it. Looks like it would have uncountable dimension.
And Mapcase, from what I’ve seen, people will define dimension however the hell they want to.
That’s not even pseudoscience, my learned imaginary mathematician. That’s brain damage.
I did not know that!
I’m thinking poor Jake wishes he hadn’t asked 
. IMO the best way to describe this is:
1D: essentially a point, like a period on a piece of paper (to keep it simple)
2D: drawing a line to another point on said paper(I know, the math nuts think this expanation is too simple)
3D: now, imagine being able to take the line off the paper, drawing it straight towards you (math nuts are now ready to crucify me 
)
4D: this is really just a theory, no proof it exists, not really, but it has to do with vector points and other such stuff that’s theory (math nuts now are considering second death sentence by hanging or burning )
5D: they had already filled the spot for the 4th, so once time started to become a concept they just put it here instead of saying ‘hey, lets make time the fourth, and put the 4th in the fifth, cause we know time exists’ (I’m in for it, math nuts now think I’m frankenstien’s monster 
)
Time: It’s actually rather relative, depends on where you are in the universe, it’s said that outside of the earth’s gravitational field it moves slower, while we continue to move normal speed. So someone returning from a 20 year trip returns and has only aged five ten or fifteen years (give or take), while everyone else is just 20 years older. Which is why using lightspeed to measure the age of the universe is a load of horse crap, and if time was speeding up on the planet, we wouldn’t know. (okay, math nuts are now considering crucifixion, burning, hanging and drowning all at once :eek: )
All other dimensions are even more theoretical than the fourth, in other words they don’t really exist, even though people actually get degrees in these fields :rolleyes: . I’m sure I’ve stirred up a real beehive and I’m gonna’ get PM’d to death, but you asked for the Straight Dope on this, and I’ve given it, sorry nerds, but you guys know it’s the truth, stop cunfusing the guy with your weird ideas about the spacetime continuum, let’s open up your brains and see if you’ve got any, cause those are theoretical too until we see proof . (no offense)
The fifth dimension is unconditional love! 
Bosstrain, was that post meant to make sense, or was it supposed to be just sort of surrealist humor? Because if the latter, I’m not sure it was entirely successful.
@Chronos…Both! 
BTW, I’ve spotted you, nerd…Bwahaha
It took you this long to realize that I’m a nerd? You might want to sit down for this one, but while we’re at it, the sun rises in the East, the Pope’s Catholic, and the sky is blue.
Is he? Dammit, I thought he was jewish! 
Oh. That’s disappointing. I felt like I’d found that video quite enlightening. I liked the explanation that an ant crawling across a flat newspaper represents a two-dimensional plane, but if you fold the newspaper together it allows the ant to “jump” between two unconnected 2D points, even though it’ll feel to the ant like he’s crawling in a straight 2D line. And I know the same thing can apply to humans with regard to time: even though time can slow down and speed up (for instance approaching a black hole), it’ll always feel to us like we’re just travelling through it normally in a “straight line”. So I thought the video had enlightened me as to how the higher dimensions work in the same sort of way with alternate timelines, alternate universes, etc.
But if that’s actually complete nonsense, and if the video doesn’t explain what the higher dimensions are at all, then, er… what are they?
The same thing as the lower dimensions, just more of them.
Okay, just to get our resident math experts off some more … what about fractal dimensions?
A bit more about The Sierpinski Triangle referenced in that link.
Doesn’t help the op though …
As to the op, the reference has already been made to the book Flatland which imagined a world populated by 2-D creatures and how they’d view each other and a sphere intersecting their space. The fantasy imaginings of extra dimensions come from this: imagine a flatland world that existed in a plane and another plane immediately above or below it (in the direction they cannot know exists), completely parallel to it also populated by flatland creatures. They’d have no know way to ever be aware of each other’s existences, other than say by way of some force that spreads between all dimensions (say like gravity). How many such parallel worlds could exist within one micron of “width”? Now just imagine that we are the lower dimension space and the stacked “planes” are 3D spatial spaces stacked in a 4D spatial space. Hence the fantasies begin.
Less fantastic is to imagine that some class of “stuff” orients more into a different portion of a curled up extradimensional space than normal matter does. Call it notmatter. We’d see only little bits of it that intersect with the portions of the curled up dimension that the matter we are made of orients in. We’d say very little of it exists and that even though theoretically notmatter should be a mirror image of matter, it is not. And we’d mostly experience the forces from it that would spread through all dimensions, such as gravity. Hmmmm.
Thanks, again, for all your responses!
Jake
That’s already a point where the video has veered off from a decent explanation, believe it or not. It is absolutely allowable mathematically for the ant to disappear from one side of the newspaper and reappear on the opposite side without a 3rd spatial dimension at all.
This is an important, but easily missed point from the perspective of a common person. And actually, anyone who grew up in the early 1980s has experienced this before. For example, mazes in Pac-Man can be thought of as actually sitting in a universe with the same properties as the outside of a cylinder. When Pac-Man disappears through a tunnel on one side of the maze and reappears at the other side, he’s doing exactly what the ant was described as doing, with no need to evoke a 3rd spatial dimension. Even more interestingly, the universe of the arcade game Asteroids has exactly the same properties as a torus (i.e., the surface of a donut). This is a little harder to visualize at first, but an explanation is given here. The general point being that although an additional dimension can be invoked as explanation, it need not actually exist, since we can see that the screens are (essentially) flat in both cases.
To actually visualize a 4th spatial dimension is very tough to do. The Flatland explanation in the movie is actually somewhat decent in this regard, although I can’t recommend the movie either. I’d suggest reading Flatland itself. It’s a short book and 125 years old, meaning it’s out of copyright and its easy to find legal digital copies on the web.
This reminds me of a good video about a two-dimensional space with interesting properties - the story of Mr. ug and Wind http://vihart.com/blog/mobius-story/
For fractals (this would be easier with diagrams, but I’ll give it a try): Let’s say that you have an image of some sort. Put a grid over the image, and count how many grid cells a part of the image is in. Then do it again with a finer and finer grid.
Let’s say our original image was a single point. If I start with a 1x1 grid, 1 grid cell has part of the image in it. If I move to a 2x2 grid, it’s still only 1 grid cell that contains part of the image. Likewise for a 3x3, or 4x4, or 1000x1000 grid, or an n by n grid. The number of filled grid cells, in the limit of n very large, is proportional to n^0.
Or, if the original image is 2 points, the number of filled grid cells will start off as 1, but eventually get to 2 once the grid is fine enough to separate them. But it’ll never be bigger than 2. The number of filled grid cells for large n is still proportional to n^0, just with a different constant of proportionality.
Well, now what if the original image consists of a line drawn across the paper. Now, as I go to a finer and finer grid, more and more grid cells will have a part of the image in them. The number of cells containing part of the image will be proportional to n^1. The constant of proportionality will depend on the total length of the line, and if the line’s a little wiggly, it may take a while to settle down to that pattern, but eventually, it will.
Or suppose instead of a line, I had as my image some shape that was filled in. Now, the number of cells containing part of the image will be proportional to n^2, with the constant of proportionality being the area of the shape.
We could go further, with the “image” being a solid, and so on (provided we’re using a higher-dimensional grid). But this probably is enough to convey the point.
OK, so, we have a mathematical operation now that, when we apply it to a single point, or to a finite set of points, gives us the number 0. And when we apply it to a line, it gives us 1. And when we apply it to a filled-in shape, it gives us 2. And if we applied it to a solid, it would give us 3. What name should we use to refer to this number? Well, for all of these examples, it sure seems to be the dimensionality of the image: A point is zero-dimensional, a line is one-dimensional, a filled shape is two-dimensional, and so on.
But now, suppose we had a shape where, if we applied this operation, it gave us some other number? If our original image were the Snowflake Curve, for instance, we would find that the number of filled cells in an n by n grid is proportional to n^1.2619 . But if we’re going to call that exponent the “dimension”, then that means that the snowflake curve is 1.2619-dimensional.
Can somebody provide a video or a website with visuals that explains the supposed eleven dimensions, like the false one given, except, you know, right? I can’t visualize this stuff without a diagram or something, and I’d never be sure if anything I found was right or not.
I didn’t want to say anything, but since you mention it… yeah that was pretty awful.
The easiest way to understand 11 dimensions is to understand n dimensions in general, and then set n equal to 11.
Yes, I know you said “visualize”, not “understand”, but that’s about the best you’re going to get. I would not completely rule out the possibility of some savant somewhere being able to visualize in 11 dimensions, but it’s not something ordinary humans can do, nor is it necessary for actually doing work with 11 dimensions.