The first dimension

[brad89]

I was just doing some work out by my pool today. I stared at the sky and looked at the moon. Then for some wierd reason I started thinking about string theory, and I wonder if I could explain the other dimensions. To make this short, I started wondering. Each dimension is an expandature of the last. The first dimension is thought to be the line, while the second dimension is thought to be the plane, and the third the cube. But I began to think. If the first dimension were the line, wouldn't the line have originated from an infinitesimal point? It is confusing to explain. Say this. A point in geometry is imaginary, because a dot has a two dimensional plane. But a real point doesn't, perhaps its marker does, such as a dot. But the point is imaginary, and in itself infinitely small. If this point were to expand, than it would add another point. This would create a line

[greentea]

the transition from a dot to a line is indeed a big problem and a lot of math revolves around it. but it seems to be on the boundary with philosophy. and a big problem for imagination which is tuned to 3d. i personally think that actually people naturally think of the dimensions backwards. a plane is imaginable contained in 3d space, then a line lies on a plane and a dot is a location on that line. then, after this intuitive approach, you formally construct mathematics beginning with the dot.

[insane_alien]

Its something to do with our minds having adapted through evolution to base everything on 3 dimensions so we havea bit of trouble imagining less dimensions but we can actually do it but more its damn near impossible since we cannot basee it in a 3dimensional enviroment

[YT2095]

another "spanner in the works" would be the TIME taken to travel from point A to B in that dimension?

esp if you consider Time to be the forth dimension.

 

real headache material

[DQW]

I was just doing some work out by my pool today. I stared at the sky and looked at the moon. Then for some wierd reason I started thinking about string theory, and I wonder if I could explain the other dimensions.

Explain what about them ? They have already been explained.

 

To make this short, I started wondering. Each dimension is an expandature of the last. The first dimension is thought to be the line, while the second dimension is thought to be the plane, and the third the cube.

"Thought to be" ? By who ? There is no ordinality (first, second, third, etc) among dimensions. And even if there were, then the second spatial dimension, as well as the third, fourth or fifth, would all be single dimensional. The "second dimension" is not a plane (it is the plane which is a two-dimensional object). It is a dimension like the first, but orthogonal to it and the others. In n-dimensional Euclidean space, all these dimensions are identical and orthogonal. The space in which string theories (as well as GR) work, however, is not Euclidean; and the symmetry between dimensions id broken by their curvatures, which can be specified to not be identical. Indeed, in string theories, the curvatures of the spatial dimensions other than the 3 we can relate to are said to be extremely high.

 

But I began to think. If the first dimension were the line, wouldn't the line have originated from an infinitesimal point?

Mathematically speaking, a point is infinitesimal. A line is an infinite set of such points that satisfy certain properties.

 

It is confusing to explain. Say this. A point in geometry is imaginary, because a dot has a two dimensional plane.

A point is certainly not imaginary - it is perfectly well-defined. The spot you make with a marker on a white-board has nothing to do with a point, and must not be confused with it.

 

But a real point doesn't,

What's a real point ? Do you mean the one that is defined mathematically as a 0-dimensional object, which can be specified in n-dimensional space using n coordinates ? And what doesn't a real point ?

 

perhaps its marker does, such as a dot.

Now you are using terminology that you've just cooked up to talk about well-defined mathematical objects. If you are using new terminology, you had better first define what these terms mean. In math, points do not have "markers"; the only thing that can be said about a point is its location with repect to other fixed points, using any of several possible co-ordinate (Cartesian, Spherical, Cylindrical, etc.) systems. A "dot" is not a mathematical object either. So, are you suggesting that a "dot" is a "marker" for a point ? And this "dot/marker" does what ? Have two dimensions like a plane ? And if it does, what does that do ? You do not seem to return to the "dot/marker" after this, so there must be some moral learned from the "dot/marker" having two dimensions. What is the moral and how is it useful ?

 

But the point is imaginary, and in itself infinitely small.

The latter is true, the former is not a mathematical statement.

 

If this point were to expand,

Please define "expand"...or are you doing that in the next part of this sentence ?

 

than it would add another point.

Okay, I'll take this as your definition of expansion, but you have not specified where you add another point (at what location/co-ordinates), so it would seem that this is not a required detail for an expansion.

 

This would create a line

How ? I only see a pair of points. Where is the line ? Are you talking about the line made by including all the points that are "between" these two ? The act of expanding to two or three or four (or any integral number of) points does not create a line by itself. You have to do other things too (making the "expansion" virtually irrelevent to the transition from a point to a line).

 

Or are you suggesting that a pair of points (arranged in some specific manner, not yet specified by you) constitutes a line. If you are, then you're mistaken. A line (segment) is a continuum (or a compact, connected space) of points, and hence contains an infinite number of points.

 

Now how did all of this explain the "other dimensions" ? Maybe I just don't understand...

[bascule]

Explain what about them ? They have already been explained.

 

Explained how, with one of thousands of potential Calabi-Yau spaces?

[DQW]

Explained how, with one of thousands of potential Calabi-Yau spaces?

Guess that hinges on the word 'explain'. If you choose to use a compact Calabi-Yau space to describe some physics (as is done in string theories), then you know the characteristics of this space, and it is well-defined. If the physics that comes out of using "it" is verified (eperimentally), then there is no more "explaining" to be done.

 

By saying "they have been explained" I was merely implying that the space in which the physics "works" is well-defined and its characteristics are well-explained. And the usefulness of using such a space is known too.

[brad89]

Sorry, I fell asleep when I was posting this. I shortened it up a bit and went to sleep to see some replies. Anyway, to answer some questions, I will say a bit about what was stated above. The thing is, a 'real' point is non existant, because even the smallest dot has dimensions. That is why I called it imaginary, just to clear that up. Second, I mentioned nothing about the other dimensions. What I wanted to say was that the curve, the cylinder, the cylindric curve, the spiral, the cylindric spiral, time, and absolute zero, plus the point, are the real 11 dimensions. I thought this because a line is perfectly strait, why would the curve be a bent line? It must be its own dimension. Thing is, I am not even in geometry class yet, I am smart, but I don't know much past what I have been taught, and that is just some basic stuff. Anyway, this is just theory, because I thought the 11 dimensions of string theory haven't been defined so far. They were just considered to be closed up so tighly that we couldn't see them. I didn't know they were already defined.

[DQW]

What I wanted to say was that the curve, the cylinder, the cylindric curve, the spiral, the cylindric spiral, time, and absolute zero, plus the point, are the real 11 dimensions.

And you got this revelation how ?

 

I thought this because a line is perfectly strait, why would the curve be a bent line? It must be its own dimension. Thing is, I am not even in geometry class yet, I am smart, but I don't know much past what I have been taught, and that is just some basic stuff. Anyway, this is just theory, because I thought the 11 dimensions of string theory haven't been defined so far.

I have a suggestion. Take your geometry classes and then go to college, and then grad school, and now you may be ready to give it a reasonable shot. Until that time, let's trust the experts.

 

They were just considered to be closed up so tighly that we couldn't see them. I didn't know they were already defined.

Anyway, I believe this is in the wrong forum.

[brad89]

Well, for one, I didn't get a revelation, I just thought about it for a while. The thing is, why should I have to be in college and geometry to place a thought? The ancient greeks developed math from the ground up, and they had to come up with this stuff originally. I did the same thing with trigonometry. Taught myself. The same with science, I used the base stuff I already knew, and expanded upon that. There is no revelation involved, I just think about this stuff alot.

[DQW]

What I wanted to say was that the curve, the cylinder, the cylindric curve, the spiral, the cylindric spiral, time, and absolute zero, plus the point, are the real 11 dimensions.

It is statements like this that demonstrate where your method fails. You first must understand metric spaces and manifolds before you go about constructing them. You've thrown together a general binary function, a 3-dimensional object, a dimensionless object, a temperature, and several different curves, and called them dimensions in some space.

[Hyd]

Our minds have difficulty visualizing higher dimensions because we just have NO way to see it, or have ever seen it.

 

It has been said that those had higher dimensional sight were killed off by, oh say a tiger. The couldn't avoid the tiger because they were killed in the tigers 3D while they could see 4D and were unable to react or adapt. The idea of Natural selection came into play and these people were killed off. Only a theory.

 

One way to better visualize the 4th Spatial dimension would be to look at a Hypercube. It is like a Cube which is 3D or a Square which is 2D.

 

http://www.cs.brown.edu/people/dla/polytope/gifs/Complete.hypercube.foldout.gif