Can YOU imagine the Tenth Dimension? Stupid people need not click here

Don't laugh at me, but in my eyes, visualizing the 10th dimension is simple:

Let q be a 10-tuple such that q = (x1,x2,x3,x4,x5,x6,x7,x8,x9,x10).

Depending on what number system each xi is in, then q can be an element in the reals, rationals, integers, or natural numbers(or doesnt neccessarily have to be exclusive). If there exists a natural number j such 1<=j<=10 and xj = a+bh, where h is an imaginary number, then q is in the complex domain. Simply put, anything that is 10 dimensional is just a vector in the set of all elements in the form of q.

In 1 dimension space, we view these elements as a line.
In 2 dimension space, we can view them on a coordinate axis
In 3 dimension space, we can view then in space as volumes, etc.

There is no geometry for anything greater than four, but the principle is the same. In other words, I don't think physicists can give you a geometric representation of a 4 dimensional string theory function, hehe.

Sorry I just see things from the perspective of a mathematician.

Jam it back in, in the dark.

Originally Posted by Dee

I enjoyed the flash, but at the same time being the nerd I am, I wouldn't mind seeing some mathematical backing to these ideals. I delved a little into multiple dimensions thanks to my vector/multivariable calculus class, and the whole 2D people in the flash reminded me of countour lines.

But my prof lost me when he described 4D as "think about 3D contour lines." Seriously... how? Of course, time is the base of how most people judge the fourth dimension but to visually comprehend it is only through 3D contour plots.

Although it has hard to visually see dimensions larger than 3, I have seen some strange, very strange, plots of up to 27 dimensions, using colors, textures, volumes, shapes, etc. In a sense, each dimension can be visualized by a different variable, such as a through z.

The flash didn't really give anything mathy for my liking, but it's still very intriguing to think of the tenth dimension as the "everything" dimension.

I agree with you as well on the whole "more mathematics" thing. The only probably though is they'll never show us what "other" mathematical concepts they've used to prove certain ideas. This may not sound like a big thing to most, but I think it would give us a firm idea, from the ground up, how certain things were conceived.

There's nowhere I can't reach.

Originally Posted by x86

Yeah, time as a dimension is even less of a dimension than money. :doh:

I've been speculating...since each of the spatial axis (x, y, z) is orthogonal with the other two axis, why don't we take into account the imaginary (sqrt -1) axis associated with their real counterparts, which are orthogonal to them? Euler's equation involved the numbers e, pi, and a imaginary and real axis [ e^(pi*i)+1=0 ]

Extrapolating that idea to each one of the axis...it'd give six dimensions (x, xi, y, yi, z, zi) or, well, three complex dimensions (X, Y, Z or whatever notation could be used)


PD: Oh well, money may be a dimension, since it's a degree of freedom. (Theoretically) it can go up and down infinitely! :dealer:

It is definitely possible to use the imaginary axis argument, especially if the conditions are met, but I would like to point out two things:

1) One of the reasons complex analysis is used in proving certain theories is to avoid dealing with anything sinusoidal. Sinusodial oscillating functions, in the physical sense, may give insight to certain things that may exhibit wave behavior. Often though, they can present difficult mathematical challenges. If this is the case, then complex analysis can be used to make the mathematics a little simpler and to give other insight on additional things. An example of this is applications of the fourier series.

2) The imaginary axis was a good point, and it is possible that is something string theorists are doing in their theoretical work. They're not going to tell us nor are we ever going to know they because we're not researchers, LOL.

One more thing (x,xi,y,yi,z,zi) is incorrect.

To express this in complex domain, it is simply the following:

Assume that x,y,and z are elements in the complex number system. Then anything in {The set of complex numbers}^3 is the ordered triple (x,y,z), where x=a+bi, y=c+di, z= e+fi. So, that six dimensional ordered pair is essentially (a+bi,c+di,e+fi), which is in essence, reduces a six dimensional problem into a 3D one. WHile it is true that the ordered pair of real numbers(g,h) expresses the number g+hi, (g,h) is not an element in the 1d case of the set of complex numbers. g+hi, on the otherhand, is in that set.

How ya doing, buddy?