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[Chris Whitman]

I'm afraid to say that all of this "This isn't the way the universe works because I wouldn't like it/understand it" talk is a bit suspicious.

If the universe conformed to everything I want, I could stay home all day today playing video games instead of waiting for the bus in the rain to go do math stuff.

[moi]

Playing videogames? I'd be in the games

[Chris Whitman]

Captain N, is that you?

[neon]

Ah, but you forget that the laws of the universe don't immediately conform to the human mind. Being incomprehensible doesn't mean being impossible.

but, according to what we know, it's the most logical option.  yes, empiricism.  do i believe in it?  no.

[andy wolff]

ten dimensions of metaphysics / string theory?

[agj]

Hm, this string theory deal makes more sense to me than the geometric approach to the fourth dimension and beyond...

[Chris Whitman]

Dimensions in math are more general than dimensions as we would consider them on a day to day basis.

The dimension of a space is basically the minimal number of different directions you need to give instructions on how to get to a specific point. So, for example, as every colour on your monitor can be represented by combinations of red, green and blue, the RGB 'colour space' is 'spanned' by the colours red, green and blue and has three dimensions.

If you don't feel you can wrap your head around ten dimensions, it's a lot easier to think of it that way.

[Chris Whitman]

Oh, right. I almost forgot to mention: the 'imagining the ten dimensions' thing is easier because it's also wrong.

[andy wolff]

Oh, right. I almost forgot to mention: the 'imagining the ten dimensions' thing is easier because it's also wrong.

Oh. How so specifically?

[increpare]

(The 'imagining the 10th dimension' site is a lot of bullshit, fwiw (i looked at it a while back.  I have no desire to go back and look at it again, so you'll have to take my insubstantiated (though professional) opinion at face-value)).

[Chris Whitman]

I was going to try to explain what was wrong with it, and then I figured it would be easier to explain what was right with it, which is nothing.

Intuitively speaking, 'dimension' is the minimum number of coordinates required to describe a location in space. That is it. Ten dimensions means you need ten different coordinates to describe a point. You could easily imagine a six dimensional space where objects were defined by position in x,y and z coordinates and colour in r,g and b coordinates, so every position/colour would be defined by six coordinates, like (1,0,0,0.5,1,1). That's really the easiest way to think about higher dimensional spaces. Whether you can 'visualize' them or not is irrelevant, really. No one who works with these things tries to visualize them spatially, and I doubt there'd be much of an advantage if you could.

I mean, the idea of dimension expresses itself in a bunch of different ways, depending on whether you're talking about vector spaces or manifolds or fractals or whatever, but that is pretty much what the idea is based on.

All this stuff about flatlanders and folding things up to go from place to place is just unnecessary and confusing in this context. It sort of sounds like he's trying to come up with an intuitive definition of what's called a 'manifold,' which can be thought of as a topological space which behaves like (for a specific definition of like which I won't go into) Euclidean space over small distances, but can also do other wacky stuff (there are additional stipulations, but I don't want to go into too much detail).

So you can construct mathematical spaces that behave a bit (although not very much) like what he's talking about (at least, for what I watched of the video), but that doesn't really make it a valid theory of physics. You can construct weird spaces and sets that are just all wild and crazy and don't relate to anything in the real world. It's pretty clear he doesn't have even the vaguest notion of what string theory is or how it functions as a mathematical model, so he just kind of puts together some weird notion about what a 'dimension' is and how it does some creeeeeepy stuff.

I mean, I could go on, but like I said, it's hard to critique because there really isn't anything in it to even compare to string theory. It would be a bit like if you asked me to dispute that a half-eaten sandwich is an accurate mathematical model for global warming. It's really more of a non sequitur than anything else.

[increpare]

Intuitively speaking, 'dimension' is the minimum number of coordinates required to describe a location in space. That is it.

That's one way.  There's a really beautiful overview article by Manin on the various notions of dimension in mathematics here.  It should make for pleasant reading for mathematicians and (at least the introduction, and maybe the odd paragraph scattered later on) nonmathematician alike.

[Chris Whitman]

Nice! I have to go meet my family for dinner, but I will definitely check that out when I get back.

I understand that dimension can really mean a lot of things, but I tend to bust out what is really a layman's description of the dimension of vector spaces (i.e., cardinality of the basis) in most cases, because that's typically how we describe spatial dimension, and it is fairly intuitive.

[Chris Whitman]

I mean, if you try to explain topological dimension you end up having to explain a lot more things before you can get to the point.

[andy wolff]

I see what you're saying (a little), you who enjoys Cake, and I agree that what is described there has little to do with actual dimensions, or probably anything else in recent memory.

What I got from the video more than anything else was that the "dimensions" described in it seemed to loop. Below conceiving them as space or time or whathaveyou, the 1 dimensional point is indiscriminate from the 10 dimensional point. (possibly stupidly) excluding all other ideas or factors than this, one could have infinite theoretical dimensions. I know the thing said that its concept of the tenth dimension was "every possible infinity in every possible anything," meaning there could never be any more, but looking at it like you suggested, as cardinal mathematics, you could still have more than 10 by just adding another ,#.
The way I understand it, the only differences between 5 dimensions and 6 are the effects the 6th has on the 5th. However, knowing what we know about 1-3 dimensional space, this kindof contrasts with the idea of unreachable infinity. a 1-dimensional point can't ever reach more than 2 dimensions until you add another dimension. a plane can't be more than a plane without a 3rd dimension.
I guess what i'm saying is, adding more dimensions when you think about things is cheating.

[Chris Whitman]

Well, there are infinite dimensional vector spaces, like the Hilbert spaces l², spaces of square summable sequences, and L², spaces of square integrable functions, and these things have actual uses, so beyond ten dimensions, even having infinite dimensions is really not unusual in math.

I think the real problem with trying to define 'dimension' in the way he does is that his dimensions are not really something which can be counted. That is to say, each dimension doesn't relate to the other ones in any kind of consistent way. You might as well say that the eighth dimension is a dog named Robert and the ninth dimension is the concept of mushroom soup. He doesn't really have an abstract definition of what it means for something to be a dimension, which leaves one to wonder how it is he is supposedly counting these things.

[Chris Whitman]

That's one way.  There's a really beautiful overview article by Manin on the various notions of dimension in mathematics here.  It should make for pleasant reading for mathematicians and (at least the introduction, and maybe the odd paragraph scattered later on) nonmathematician alike.

I've just started reading this, but I already have a few problems with things he is saying. Specifically, he starts off with the notion that objects are given ontically and this should not be interrogated any further (I understand how you'd be reluctant to get into that, but he's sort of saying "this notion of conceptual, mathematical entities and language forms the basis of my paper, but I'd rather not talk about it, so you can just assume it is as such."), and then he starts going off into 'left/right brain styles of thinking,' which are pretty much bunk as far as neurology is concerned. Left/right brain lateralization has nothing to do with your ability as far as 'conceptual' or 'creative' behavior, as both hemispheres are actually strongly involved in all of these as meaningful activities: it is only very specific components (like understanding a word) that are highly lateralized.

[Valter]

ten dimensions of metaphysics / string theory?

Wow. I know I'm getting into this discussion a bit late, but I'm shocked by how much the video is mirroring what I think about the subject.

However, I think it's slightly off with its beliefs about each dimension. I think that every dimension is actually representative of a line. The first dimension is an infinity of points all strewn upon a line. The second dimension is an infinity of lines also arranged on a line, creating a plane. The third dimension is an infinity of planes arranged on another line, creating a new figure. The video tries to insinuate that dimensions follow a pattern of lines, branches, and curves, but I think it follows a more basic pattern only of lines.

My views begin to differ at the seventh dimension, though. If you have permanent, set laws about how the universe would work, wouldn't the result always be the same? Even with quantum physics involved, the laws of physics are basically infallible, which makes "alternate realities" impossible.

[Chris Whitman]

The first dimension is an infinity of points all strewn upon a line. The second dimension is an infinity of lines also arranged on a line, creating a plane. The third dimension is an infinity of planes arranged on another line, creating a new figure

Congratulations, you have just come across a mathematical concept known as a factor group!

[Valter]

i so smrt

Uh, I'm guessing that's sarcasm? I really am clever!

I was mostly just saying that the video dude tries to say that dimensions follow a pattern of point-line-bend, which I think is too complicated. Technically, new dimensions are created by extending the current dimension in a hither-to-unexplored direction, so basically extending it on a line.

Also, the way the narrator was explaining it, you could technically extend any object in a further two dimensions as long as it can be sent along a line, which I think is somewhat suspect. He had already run out of ideas by the 7th dimension, but he tried to extend it into the 8th and 9th dimensions just by "branching" and "curving" the one line he had without any basis on how to do so. I think he was considering his line-branch-curve theory too seriously.

I would expect from his video and my own thoughts that there would only be 6 dimensions total, or possibly 7.

Then again, there's also a chance that denizens of a certain dimension are literally only capable of speculating on the nature of dimensions that are only a few above them. Something that somehow resided in the 7th dimension might be able to imagine another 4 dimensions above itself.

Of course, on that note, there's a chance that things residing in lower dimensions can conceive of even lower dimensions. Perhaps  there are beings that live in the zero dimension, which have imagined a "negative three" dimension.

Naturally, though, following that pattern, it could be that every single organism, no matter what dimension it resides in, regards itself as living in the third dimension, and then labels three dimensions below it and three above. An infinite pattern of dimensions, trailing off into infinity... it does follow mathematic theory fairly well, considering that most things are regarded as being potentially infinite, and I don't see why dimensional theory would be any different.


Then again, I'm beginning to drift into the rampant speculation territory. My other theory is that it's impossible to contemplate dimensions above your own, and doing so mostly just results in a big headache.