In terms of physical reality as understood and studied by physical sciences, there are four (4) dimensions - three spatial dimensions and one temporal one. Together, they constitute the 4-dimensional space-time of Relativity Theory, the physical universe, the reality as we know it, so to speak. So, one possible answer to your question is "4".

On the other hand, there are different mathematical models of multi-dimensional structures containing more than four dimensions. In fact, there can in principle be an infinite number of dimensions, as far as mathematics is concerned, and that's the second possible answer.

Some of these higher-dimensional mathematical structures are interesting in terms of physical reality, too, because our theoretical models of the universe depend on them. In particular, various string theories use them in order to describe those famous extra-dimensional patterns which are somewhat of string theories' trademark. In fact, they all propose extra dimensions existing alongside the 4-D space-time that we perceive, although there is some disagreement on the exact number of these extra dimensions. The third possible answer to your question, then depends on which particular string theory do you favour. Ten (10) and eleven (11), the Superstring theory and the M-theory, respectively, are the most popular ones.

A particular mathematical structure on which all these theories relay is an eight-dimensional, 248 point symmetry matrix called E8 - a so-called Lie group, a mathematical means of describing symmetrical objects.

There is another possible Theory Of Everything, proposed by one Garrett Lisi, which uses the same E8 matrix in an attempt to model the universe. Unlike string theories, Lisi's model does not require any extra dimensions in order to successfully explain the world as we know it. And, it unifies, conceptually, gravity with other fundamental forces of nature, which is required of any potential Grand Unified Theory.

By Occam's razor, Lisi's theory, being the simplest successful model of reality, should be considered first. It fills all the slots in the E8 matrix without making any assumptions, such as the existence of extra dimensions, unsupported by evidence.

Therefore, my final answer to you is - it's back to four (4)!

Normally, speaking of coordinate geometry, there are 3 dimensions, viz. length, breadth & height or X, Y & Z.

Einstein's theory of Special Relativity says that "Time" makes the 4th dimension. It also says that "Gravity" is the 5th dimension.

But, to our surprise, scientists believe that there are 10 dimensions in the "Brane" world ("Brane" stands for membrane"). I won't go into much details because I am neither a scientist nor can the explanation be accommodated here. There are volumes of fat books on this theory.

http://www.ccmr.cornell.edu/education/ask/index.html?quid=961
http://www.msnbc.msn.com/id/13070896/
http://www.astronomycafe.net/cosm/dimens.html

Anyway, that makes;

3 dimensions in the world of Classical Mechanics and Coordinate Space.
5 dimensions according to the theory of Special Relativity by Einstein.
10 dimensions in the brane world.

Unimaginable!

Good question.Thanks

I completely agree with the previous answer, but I wanted to add that all dimensions only exist through cognition. Therefore, the Buddha may tell you that there are no dimensions.

If you meet the Buddha on the road, kill him.

Quick, simplified science lesson:

According to superstring theory, each particle is one end of a "string" which vibrates in a certain number of dimensions. These vibrations are related to the properties of the particle, including mass, energy, and the forces it propagates or carries.

There are five basic superstring theories, each conjecturing a different reason for how the superstrings operate. Each requires 10 different dimensions (including the three spatial dimensions and the fourth dimension, time or space-time). However, each of them predicts different properties for the universe.

There is a sixth theory (known as M-Theory) which the five string theories into one, which requires an eleventh dimension. This eleventh dimension essentially allows us to view the five theories from different angles.

So, the direct answer is that, according to current common mathematical models, there are no fewer than 10 dimensions, and there are probably 11.

The more complicated answer? While one type of elementary particle (fermions) vibrates at ten dimensions, another (bosons) seems to vibrate in 26 dimensions. So, there may be many more dimensions. So, as Gary Moring would answer, "As many dimensions as it takes."

For more information, you can check out the link below, which provides the most complete and understandable answer I was able to find on the web.

Lyca and interzone both have wonderful scientific answers to this question.

I hope to simplify, based upon their answers as well as based upon consciousness my answer to the question how many dimensions are there.

If we look at the Universe we consciously perceive, and apply the theories of science and philosophies, of this perceived universe, then the ultimate answer becomes that the number of dimensions within the existing universe as we consciously perceive is; “infinite”. There are an infinite number of dimensions within our perceived universe.

Now to extend this.

If within each of these infinite number of dimensions within the perceived Universe, resides an infinite number of Universes each with their infinite number of dimensions, then we have within this perceived Universe and infinite number of dimensions each with infinite Universes each with infinite numbers of dimensions ...

Going further:

That’s just for the Universe we perceive! In the Chaos theory there is a theory of the Multiverse, (also part of the “Bubble Universe theory”). Multiverse; basically the theory that at the time of the Big Bang, out of “Nothingness” (please note that this is different than Nothing), multiple Universes were formed, in a chaotic inflation of matter/energy...

Physicist Andrei Linde’s Chaotic Inflation Theory or model proposes that our perceived universe is one of many (I suggest an infinite number of) that grew as part of the multiverse that was created. Now when we couple this with the other theories or models that propose multiple dimensions, within each universe then we see that once again the number of dimensions becomes infinite.

Nothingness:

Infinity by definition cannot reside within a finite structure, therefore infinity to exist (i.e. our perceived universe which is one of an infinity of Universes with infinity of dimensions, with infinity of universes etc) must to be perceived reside within a not finite structure or existence. This can therefore only be a “Nothingness”. From nothingness, the Big Bang creates an infinite multiverse which can only reside within Nothingness.

And the Buddha laughs!