Question

Is there a limit in dimension?

Answer 1

The physicists in thermodynamics, describe a 'phase space' for a gas as having six dimensions for each particle of gas.  Now, put that into prospective, 22.4 litres would have at STP, a phase-space of something like 3.6E24 dimensions.  You know, 3,600,000,000,000,000,000,000,000 dimensions.  So there is not a real limit.

Answer 2

Then there is no limit, the oy possible limit is when you run out of ways to define the properties and characteristics of something. In quantum mechanics states of particle described as wave function in an Infinite Dimensional Hilbert space. So the answer is NO, you can have Infinite dimensions