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Imagining ten dimensions

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The stage at which I do not accept this argument is when they "build" the 7th dimension. Basically they treat the 6th dimension (all possible outcomes over time from our universe) as a point of infinity and add another point of infinity that represents all possible outcomes of a different universe (one with a different set of initial conditions).

First, this presupposes "initial" conditions for which we have no evidence (i.e. it is impossible to state as a fact right now that our universe had a beginning). Second it presupposes other universes -- what evidence do we have for other universes? Why is this taken as a given?

I need to do some homework, but the way he summarized it at the end makes me think that the math of string theory requires 10 dimensions and consequently this argument attempts to rationalize an existence of 10 dimensions. I suspect that if the math of string theory required only 6 or 7 dimensions the argument would have ended there... (just as it ended at 10 dimensions).

Comments? What does everyone else think?

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The stage at which I do not accept this argument is when they "build" the 7th dimension.
Judging the article by the link, those descriptions are not a proof of anything. They are simply metaphores to describe what would it mean to have so many dimensions.

... and consequently this argument attempts to rationalize an existence of 10 dimensions.
Can you quote which parts lead you to think that? I didn't see such attitude in the text.
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I saw this and it got me thinking about how much akin it is to all the other "positing of other realities" irrational metaphysics. Noumenal worlds, heavan, nirvana, and now "dimensions 5-10".

Ten Dimensions

That link is great! I always wanted to know what physicists mean by all these different dimensions. These little videos made it very clear. Thanks for posting this! Dimensions 5-10 are mere speculation as far as I can see, but it's a nice game to play and a good model to incorporate everything that could possibly be (and not just everything that is), even though I have no idea how such a model could be even tested.

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  • 6 months later...

I don't think that video was supposed to be an endorsement of string theory. There was even a disclaimer at the end saying that it is not accepted as an explanation of string theory.

I think it does a good job of extrapolating to 10 dimensions though, by using the same principles that connect the 3 dimensions we live in. If you take those connections and project them forward, it does indeed seem that there would be 10 dimensions.

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In its current state, string theory cannot be tested empirically. It is not falsifiable and is therefore not a good scientific theory.

I don't know much about string theory, but I do know that the hypothetical strings are so small that it will probably never be testable on an empirical level. As such, they can only use math to try and prove why it might be correct. I'm no physicist or mathematician, but if the math can be elegant enough, I see no reason why string theory should not be considered a legitimate theory.

I know that people will say it is highly rationalistic, but the video describing those dimensions made me think of something. If they can extrapolate out to 10 dimensions, by applying the relationships between the first 3 to higher possible dimensions, why can they not extrapolate out to superstrings, by applying the same relationships and principles here in our own empirical understanding of physics? I hope that makes sense, but I suspect that I didn't put my thoughts into English very well.

Am I off base?

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  • 2 months later...

I think the theory in this link becomes more and more silly as it goes up. A dimension is merely some necessary, measurable aspect of a thing that can vary independently of the other aspects. (See the article referenced in my signature for more on this!)

Mathematics will only tell you the logical results of certain fundamental numerical processes. There is no substitute for actually finding out the nature of the aspects in question and the relations, if any, between them. Time, for example, is not merely an aspect of existence of the same order or type as length etc. There is not necessarily analogous "traffic" between all "dimensions."

Edited by radn
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  • 4 weeks later...
I wouldn't be so dismissive.

The link actually describes the meaning of such high dimensions very well. It looks more logical now.

I would not have used the word "logical". I would have said it looks more -intuitive- now. The only way we can intuitively grasp higher dimensional spaces is by using analogies. here is where we see the advantage of mathematics. Going to higher dimensional manifolds is simply a matter of adding more independent parameters. Why stop with ten dimensions. How about an infinite number of dimensions? Easy Peasy.

See

http://en.wikipedia.org/wiki/Differentiable_manifold

for a jump-off to the subject of differentiable manifolds of many dimensions. The presentation is a bit incomplete but the bibliography is useful.

Bob Kolker

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The stage at which I do not accept this argument is when they "build" the 7th dimension. Basically they treat the 6th dimension (all possible outcomes over time from our universe) as a point of infinity and add another point of infinity that represents all possible outcomes of a different universe (one with a different set of initial conditions).

First, this presupposes "initial" conditions for which we have no evidence (i.e. it is impossible to state as a fact right now that our universe had a beginning). Second it presupposes other universes -- what evidence do we have for other universes? Why is this taken as a given?

I need to do some homework, but the way he summarized it at the end makes me think that the math of string theory requires 10 dimensions and consequently this argument attempts to rationalize an existence of 10 dimensions. I suspect that if the math of string theory required only 6 or 7 dimensions the argument would have ended there... (just as it ended at 10 dimensions).

Comments? What does everyone else think?

If you work at it you can come up with as many dimensions as you please. Mathematically we can formulate spaces with an infinite set of dimensions. For example a function over the real numbers can be thought of as a vector with aleph-1 components. Take the aleph-1 Cartesian product of the real number set with itself and you have the space of all real valued functions.

I suspect ten is the "magic" number because a ten-space is the smallest space that can accommodate both general theory of relativity and quantum field theory. In short a ten space is the smallest big tent into which we can stuff physics. On the other hand there is a theory which requires eleven dimensions. Go figure.

Mathematics can be both a liberating tool and a springboard into absurdity. One must be careful how one formulates and -interprets- the mathematics.

Bob Kolker

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