Space has been represented with a three-dimensional geometry since ancient times. Descartes added coordinates, which make these dimensions more explicit. We call this Euclidean space R^{3} = R × R × R, that is, three dimensions of real-number coordinates.

Newton added time but kept it separate since he considered time absolute and space relative. Call this R^{3} & R. Minkowski integrated time as part of a four-dimensional pseudo-Euclidean geometry, like R^{4} with signature (+ ‒ ‒ ‒) or (‒ + + +).

What do space and time look like with three time dimensions? I see three possibilities:

(1) Six-dimensional spacetime with signature (+ + + ‒ ‒ ‒) or (‒ ‒ ‒ + + +);

(2) C^{3} spacetime, with three dimensions of complex numbers;

(3) R^{3} & R^{3}, with space and time in their own versions of R^{3}.

Since space, time, and spacetime are conventions, which of these representations are chosen will depend on their purpose and use.