system
Given the following post, respond as if you're commenting on Reddit:
human
Can someone please explain the theory of multiple dimensions?

Recently in my Astronomy class my professor talked about having more than 3 dimensions. I personally find this inconceivable, so could someone be kind enough to explain having more than three dimensions. My professor talked about there being 9, although there could maybe be a seemingly infinite number?
gpt
It's been well known since Einstein published his papers on special relativity in 1905 that there are at least 4 dimensions, with time being the fourth (in addition to the standard 3 spatial dimensions).  All this means is that time needs to be treated on equal footing with the spatial components rather than as it's own thing, and that, in the laws of physics, time needs to be inseparable from the spatial dimensions.  The big repercussion of this of this is that you can move, rotate, and boost objects between the spatial dimensions and time as naturally as you can move, rotate, and boost things in the 3 familiar dimensions.

Theories such as string theory and M-theory contain more than 4 dimensions (9 and 10, respectively) in an attempt to make the mathematics work probably.  The simple picture is this - 

When trying to do calculations in quantum field theory (which explains electromagnetism, the strong nuclear and weak nuclear forces), you often times end up with infinities in your answer.  These are non-physical, so physicists have to use a mathematical trick called *renormalization*, which turns the infinities in sensible answers. This generally works fine.  However, when trying to incorporate general relativity into quantum field theories to create a quantum theory of gravity, physicists have to do these same calculations on a curved manifold - and it turns out that it's impossible to renormalize to get rid of infinities in the standard 4-dimensions.  However, it turns out it *may* be possible to do this if treated as a 9- or 10-dimensional space, and then using a process called "compactification" to reduce back to the 4-dimensions we're used to.