The number of dimensions are, well infinite
I have a standard prediction of a science breakthrough that comes after having studied the standard model.
In the standard model of physics they combine all natural forces but gravity in one formulation. The basic building block there seems to be fields that have properties that comes from the Yang Mills and Pauli theory. To understand the standard model it is good to think about what Yang Mills and Pauli try to describe. I played around with it a little got an understanding. It feels like these fields describe disturbances in a kind of ray fluid.
Lets move some atoms