I read that book,. So even though I can't view the flash right now, I have a pretty good idea what's going on

One thing I found intriguing was the seemingly supernatural powers an extradimensional being would have over a being of lower dimensions. If a Flatlander had cancer, for instance, we 3D beings could just pluck the tumor out seemingly by magic, because there's a whole side of him not covered in the third dimension. An extradimensional being traveling through lower dimensions would appear to disappear and then reappear again while he was traveling. For example if you were walking on Flatland, its citizens would only see 2D cross-sections of your feet and then see them disappear as you lift your feet. If beings of higher dimensions were traveling thorugh 3D space, we would see random blobs appear and then disappear as they were traveling.

Also, to the people who reamrked it's hard to envisage things in higher dimensions, it's actually physically impossible. Our brains have evolved only to visualize three dimensional space or lower. That's why higher dimensions can only be explained in terms of analogs between us and lower dimensions. All of you should definitely pick up either Hyperspace or this other guy's book. It's some very cool stuff.

Interesting. It's pretty easy to follow his argument, though I'm a bit disappointed at the treatment of time as another dimension. I was expecting 10 spatial dimension (10 lines perpendicular to each other).

Come on, you don't believe this do you?

I understand what he's saying, but he's already going wrong at number 5. The creatore of this flash confuses the split as, on one hand a concrete other direction, and on the other hand an alternate path. Those two things are not the same, not even metaforically.

The theory of Einstein suggests that the fifth dimension is just a spacial dimension that we can't see and that creates gravity. And for that power another dimension is needed, and for that again another. Therefore, there is an infinite number of dimensions. We experience the fourth dimension as time, but maybe it's also spacial and we might just be traveling through it at a constant speed. We might just experience the rest of them in again another different way, or we might not experience them at all. And then our mind would not be capable of understanding an comprehense those things.
but don't let that bother you, i can't imagine it would make you any happier.

I like these subjects. Even though I don't completely understand them.
By the way, Einstein had a theory on bending time and travel the universe
from one point to another in 0 time. Just like point 3 in the flash.

Good God.
If you use big words, spell them correctly. I'm only saying this so you can save yourself some grief.


Anyway....

As a firm believer in Superstring Theory and practically martyred by my own junior high school (bunch of bible beating louts :eyebrow: :boxing: ), I can safely say that from the flash, one can deduce that the only way that there could be an 11th Dimension would be if there were another way of creation of a similar (or completely different, as the case may be) universe in which time is experienced.

As we'll never be able to reach another dimension alive, I also would say that it's not to be worried about. It is interesting to think about, though.

Okay, so this guy builds up to 10 dimensions through a simple cycle, Point, Line, Split, Fold, and then the fold becomes the point and the cycle starts over, until the point is every possible anything, in which case it is the only point possible.

Now, if dimensions 3, 6 and 9 are folds as well as points, then why can't dimension 0 be a fold as well as a point? Can you have dimensions less than zero? Unless I misunderstood this flash, then one should be able to prove their existence.

Also, what about dimensions that are in between whole numbers? They exist according to chaos theory. All fractals have dimensions with decimal places. I'm pretty sure I once read about a fractal triangle that had a dimension of 2.3, and you could prove it using logarithms. (I'm searching for a link, I promise...)

Well, can you HAVE anything that is less than zero?

No. So chances are that there are no negative dimensions unless you consider the idea of non-existence having it's own universe.
But if that's true, wouldn't that mean that not-existing was in existence? So even then, the diminsions would be positive, not negative.

Nothing will always be nothing. It doesn't exist. If it did exist, it would be something, not nothing.

String Theory, similar to quantum mechanics, is based completely on mathemaical equations and complete physics. Wherein the math might be flawless, without empirical evidence and experimentation, these theories remain theories.

Understandably, the interest in String Theory has rose greatly over the past 2 decades following Bohrs atomic model and the next Quantum Mechanics. But you must realize that the dilema of Schrodinger's Cat best exmplifies all theories and physics reasoning beyond what is physically unobservable with any instrument.

I commend physicists for venturing into Sting Theory because they risk a lot studying something that is so difficult to quantify. Compared to some other literature I have read concerning String Theory, this particular flash does a good job explaining although it conflicts with other observatinos on the subject. With so much disagreement among scientists, how can we hold one theory as more valid above another when there is no evidence?

Oh well, its very confusing. At the very least, String Theory is a intriguing idea which had me interested all of last year.

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.

Science made simple -- I like it!

The concept of other dimensions has always been somewhat interesting to me, but I've never really tried to conceptualize it beyond the fourth (I'm a simple person). I can't say I totally understand the flash (I suspect I'll need to read the book, or at least watch the flash over a few times) but it'll make for some interesting conversation, I guess.

Sorry, I messed up the details ;) - I was just trying to illustrate a "non-dimensional time, Complex 3D space" idea :biggrin:

I have a question about this. The one visual it uses during the description of a 2d man shows the cross-section of a human going by, as if a 2d man will see each layer of a person as if that person is cut in half from head to toe an infinite number of times. My question is why wouldn't the 2d man simply see a human as if I would close one of my eyes to look at it? If you're looking at at a human in 2d, wouldn't the skin still be what is being observed? What causes the 2d eye to look past the outside surface of the object and see it in cross sections?

I'm not a exactly a expert in this area, but I'll try to explain.
The reason the "flatlander" could potentially see a 3D being (the human) as cross-sections is because the flatlander cannot perceive depth in any sense.
In our world, according to the flash. We can see this depth or cross-sections of us as one being. The flatlander can only see the length and width of that being. Even if that is technically peering through the 3D human's insides. You could go as far and say we're passing through 2D worlds all the time =p.
Again this works the same for us when we try to imagine the 4th dimension. We can only see a cross-section of what we're experiencing as err time.

Closing one eye would not render everything in 2D, rather it takes 3D objects and put them into a plane of projection, thus giving it the "flat" appearance.

"Flatlanders" can see projections, but, in the case of 3D objects as they cross through the 2D world, only a slice is visible. However if the 3D object were to stand outside of the 2D world and have a light shine through it, then we have a projection and an effect of 2D on 3D objects, much like how movies appear on screen.

Plain and simple version of the world we live in:

No Dimension: A point. For instance, were you to point out a specific place in the air (not the sky) around you, that would have no dimension. Same thing with a dot on a piece of paper. The dot has dimension, but the point is specifies does not.

1st: Lets take that dot on the piece of paper. You can draw a line from one end of the dot to the other. A line from point A to point B is 1D.

2nd: Say you draw a picture, good or bad. The picture is 2D even if it gives the illusion of being 3D. Van Gogh is not 2D as most of his paint sticks out from the canvas.

3rd: 3D is you and me, living together in perfect harmony (no, that's just a lie) Anything that sticks out is 3D. (no lude comments, please)