"Imagining the Tenth Dimension" by Rob Bryanton

[loyalguard]

I searched extensively and did not find a previous thread so I thought I would start this one.

Early in July I came across the website: http://www.tenthdimension.com. This purpose of this site is to promote the aforementioned book in which the author explores the following topic:

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In string theory, physicists tell us that the subatomic particles that make up our universe are created within ten spatial dimensions (plus an eleventh dimension of "time") by the vibrations of exquisitely small "superstrings". The average person has barely gotten used to the idea of there being four dimensions: how can we possibly imagine the tenth?

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The site has a beautifully designed flash animation that IMO does an excellent job of explaining in layman's terms the concepts of each of the ten dimensions.

I have not read the book because even though I understand the concepts in the animation and on the site I wanted to seek out the opinions of those more scientifically inclined than myself on the validity of the author's conclusions.

This topic fascinates me but I find my brain is often too feeble to properly grasp concepts such as these and I often get swept up by with the idea of complex scientific principles wrapped up in a pretty little package with a bow.

I would love to know your opinions of this topic. The flash animation takes about 10-12 minutes if you care to check it out. Based on the animation and other introductory topics does this book seem worthy of a read?

[surftheiop]

I loved that, i have no idea of its accuracy but it really made this stuff make more sense to me

[pzhon]

Nice animations, but it is about 65% crap. I don't recommend getting the book if this is a fair representation of the content.

"Folding" was not well-described, and it doesn't add a dimension. If you fold a piece of paper into a cylinder or Mobius band, it remains intrinsically flat and 2D, so you haven't learned anything about the third dimension. In fact, some surfaces can't be fit into R^3, e.g., the Klein bottle must intersect itself. That gets much worse in higher dimensions. You need about twice the dimension to embed a folded up space. So, what did the video communicate by talking about folding?

There are intuitive higher dimensional spaces. Imagine you toss a hammer into the air. How much information do you need to describe what it is doing at any time? You can describe its center of mass, a 3D point, but the hammer can be turned. The handle can point to any direction on the celestial sphere, which is 2D, but for any direction of the handle, you can spin the hammer about the handle's axis, which is another 1D. So far, we've counted 6 dimensions needed to describe the position of the hammer. However, the hammer is also moving. To describe how the center of mass is moving, you need a 3D velocity. To describe how the hammer is spinning, you need a 3D angular velocity. It may not be obvious that the angular velocities form a 3D space; it is not mysterious but it is worth thinking about why the space of velocities has the same dimension as the space of positions.

So, when you toss a hammer through the air, it actually can be thought of as describing a trajectory in a 12 dimensional space, each of whose points describes a possible position and velocity combination. The dimensions are not identical, and there is a natural geometry on the space. For the trajectory to make sense, the progression of the 6 positional dimensions must agree with the 6 velocity dimensions. This is similar to the some of the geometric structure on the proposed 6 extra dimensions of space-time.

There are other simple, intuitive higher dimensional spaces, such as points endowed with colors, or families of such points (such as what you see with your left eye and right eye).

Just thinking about the motions of a rigid object leads us to a natural 12D space, without pretending that this gives us insights into quantum mechanics, going back in time, or universes with alternate physical laws like the video suggests happens en route to 10D.

[loyalguard]

pzhon-

Thanks, that is a very in-depth analysis.

Specifically:

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...without pretending that this gives us insights into quantum mechanics, going back in time, or universes with alternate physical laws like the video suggests happens en route to 10D.

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This is in sync with other criticisms I have read of this book. There seems to be quite a bit of debate of how he defines dimensions 4-10 and their pertinence to string theory.

I too find "folding" somewhat incomplete and have a hard time envisioning it as a dimension. The only way I could interpret it was that the fold passing through two dimensions is in fact a dimension in of itself but it seems a little contrived.

Thanks for the food for thought...

[Galwegian]

Just to add to pzhon's commentary. One of my favourite examples of a naturally occuring high dimensional space is the space of configurations of the human arm. Your shoulder joint each has 3 degrees of freedom and you elbow and wrist each have 2. So already we have a 7 dimensional space before we even get to the fingers. If you want example of 10,12 or 100 dinensional spaces, the everyday world is filled with them. There is no need to delve into advanced physics to fnd examples (not that there is anything wrong with advanced physics). How many dimensions has the space of configurations of your own skeleton? Probably 100s.

By the way, the next time you pick up a cup of coffee/open a door/do anything with your, consider that your brain is somehow managing to navigate efficiently through the 7-dimensional space that I mentioned. So don't tell me that the human brain can't deal with more than 3 dimensions [img]/images/graemlins/smile.gif[/img]

[Prodigy54321]

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Just to add to pzhon's commentary. One of my favourite examples of a naturally occuring high dimensional space is the space of configurations of the human arm. Your shoulder joint each has 3 degrees of freedom and you elbow and wrist each have 2. So already we have a 7 dimensional space before we even get to the fingers. If you want example of 10,12 or 100 dinensional spaces, the everyday world is filled with them. There is no need to delve into advanced physics to fnd examples (not that there is anything wrong with advanced physics). How many dimensions has the space of configurations of your own skeleton? Probably 100s.

By the way, the next time you pick up a cup of coffee/open a door/do anything with your, consider that your brain is somehow managing to navigate efficiently through the 7-dimensional space that I mentioned. So don't tell me that the human brain can't deal with more than 3 dimensions [img]/images/graemlins/smile.gif[/img]

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You just confused the hell out of me..

aren't those all within the three 3 common dimensions [img]/images/graemlins/confused.gif[/img] (excluding time)

[Galwegian]

How many "coordinates" does it take to take to specify the position of the human arm? At least the 7 that I (roughly) described. Thus the space of all possible configurations of the arm has 7 dimensions. The fact that the arm itself is a 3d object is not the point at all.

[Prodigy54321]

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How many "coordinates" does it take to take to specify the position of the human arm? At least the 7 that I (roughly) described. Thus the space of all possible configurations of the arm has 7 dimensions. The fact that the arm itself is a 3d object is not the point at all.

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oh I see, thank you gent

[4Kings]

Your example and pzhon's example are illustrations of states in a state-space and not dimensions in a geometrical space. In reality there are an infinte number of states to describe the motion of any object, but a lot of the time it's only necessary (at least in engineering applications) to use the mass, velocity, and acceleration of the major degrees of freedom. Imagining higher geometrical dimensions takes a little more effort.

[pzhon]

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Your example and pzhon's example are illustrations of states in a state-space and not dimensions in a geometrical space.

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I'm not sure what point you are trying to make. The examples we gave are indeed higher dimensional spaces (manifolds) in the sense used by, for example, texts on mechanics such as Mathematical Methods of Classical Mechanics by Arnold, et al, not to mention less technical definitions of dimension. The example I gave is a standard example of a manifold carrying a symplectic geometry.

Perhaps you want to introduce a distinction between purely spacial geometries and other, more abstract higher dimensional geometric spaces. In that case, you should vehemently object to the material in the title, which used esoteric and sometimes undefined methods to come up with a 10D context. Our point remains that you do not need esoteric tools to describe higher dimensional objects. Living in the real world gives you some experience dealing with higher dimensional spaces.