there is up to 3-D but
is 4-D possible ?
Do you mean physically? There was already some hints against it from renormalization theory, and now recently I have noticed additional restrictions could come from quantum mechanics and from gravity.
There are mathematical spaces beyond 3d of course, but the point is if dinamical interacting theories can be consistently built.
In what sense? "dimension", in its most general definition, just means how many numbers you need to identify something of interest. If I'm draw a graph in the plane, I need two numbers to identify each point- that's two dimensional. If I am drawing graphs in space I need 3 numbers- three dimensional. Physicist work, most fundamentally, with "events": things that happen at a particular point at a particular time. That requires 4 numbers- 3 numbers to identify the point and one number to identify the time: 4 dimensions (and the "fourth dimension" is time).
If, instead of individual points, I were doing a problem envolving a stick moving through the air, I might use 3 numbers to identify the position of one end, one number for the time, and two more numbers to identify angles the stick makes with the coordinate axes (so that I can identify the position of any point on the stick at any time): that's 6 dimensional!
Even more complex is dealing with a plasma: I might have thousands of ions (call it n) all at different positions moving at different velocities. Two determine that exactly, I would need to identify the position of each ion (3 numbers each) as well as the velocity of each ion (another 3 numbers each) at time t (one number). That's a total of 6n+ 1 dimensions for some extremely large n!
And that's talking about physics. If you get in abstract mathematics, anything goes! The theory of "fractals" deals with fractional dimensions. In particular, the "Cantor ternary set" has dimension log(3)/log(2).
3-d 4-d 11-d
The fourth dimension is time
But now with the production of superstring theory it requires there to be a minimum of 11 dimensions (that some describe twisted) When Superstring theory first came out it called for over 100 dimenions but now its down to 11 minimum. (you see it is very easy to add a dimension mathmatically although hard if not impossible to visually be able to have a concept of them for example volume of box is side A * side B * side C = volume Therefore a volume of a 5 dimensional object would be side1*side2*side3*side4*side5=volume.
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