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There are different views on this. An upcoming lecture from my Physics Professor is on the same topic. Here is an extract:"We usually need four numbers to describe an event correctly: e.g. we could use the height above sea level, the longitude and latitude as well as another number to tell us when the event takes place. Hence we usually refer to our world as “four-dimensional”. In modern physics, however, there are theories that need more than these four dimensions. One example is string theory which presumes the existence of six more dimensions."

I personally feel this is a philosophical question to some extent. So, I would like to know more about this from you all.

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    Why do you feel this is a philosophical question to any extent not covered by theoretical physics? – user3164 Jul 4 '13 at 18:49
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    Can you say what exactly you want to know? This could go in the direction of constructivism vs. objectivism, four-dimensionalism and more advanced philosophy of physics,... – Ben Jul 4 '13 at 18:51
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    This is not even a question... – jinawee Jul 5 '13 at 22:03
  • The problem with these theories is Occam's razor and lack of testability. – Xaqron Jul 5 '13 at 23:24
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I don't have any nobel prize, which would be the normal requirement to directly answer this question. I can just say that, if they're all curled up as they say, there can be potentially infinite.

However, they don't affect us directly (so far). There's only 4 dimensions that we can 'handle', 3 spatial and 1 temporal. If there was, let's say, a 4th spatial dimension, then the values for gravity and other forces couldn't be as they are right now.

As an example: if you calculate the gravity of a circle when something is at 1 m from it's radius it will differ greatly from the gravity of the same object if it was an sphere of the same size OR mass. If you used the 3D laws of the sphere to calculate the 2D gravity, your calculus would be wrong, not only the value at 1m, but the rate of change with distance to the center.

I just found an interesting article about this.

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Superstring theory doesn't "presume" the existence of six more dimensions. The number of dimensions rather "falls out of" superstring theory. So, it is more like the other way around. See this answer to a question of mine on Physics SE.

So there are several reasons to believe that d=10 within the framework of superstring theory. The [...] explanations are not independent of each other of course. You can simply pick whichever is your favourite and use that as your explanation for d=10.

Also see these questions on Physics SE: 1, 2, 3, and Why String Theory?: a layman's journey to the frontiers of physics and Number of dimensions.

There are also criticism and proposed alternatives (many, presumably, with different numbers of dimensions) to string theory. I cannot judge whether such criticism holds (any or most) water, but it seems at least partially inspired by ideas in philosophy of science/physics.

There seem to be opposing camps, with a lot of mud-throwing between them. To me, it appears that these camps hold different attitudes to what the philosophy of final theories should be. See also Theory of everything (philosophy).

So, in conclusion, there are people picking fights about candidate physical theories, and for a layman like me it is difficult to even judge whether these fights are constructive in some sense, but they are (presumably) not directly about certain ideas about or attitudes towards the number of dimensions, but rather indirectly.

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