It’s easy, relatively speaking, to develop an intuition for higher spatial dimensions, usually by induction on familiar lower-dimensional spaces. But I’m having difficulty envisioning a universe with multiple dimensions of time. Even if such a thing may not be real or possible, it seems like a good intellectual exercise. Can anyone offer an illustrative example?
Several authors (in particular Itzhak Bars) have written papers about two-time-physics that should help build intuition for the topic.
Infinitely many 'times' appear in integrable systems.
Theories can be formulated in any number of space-time dimensions. Examples of multidimensional theories:
F-theory, 12d theory with two times.
S-theory, 13d theory with three times.
Kalitzin's relativity with r-times or even infinite-dimensional times (the latter much less developed) was studied.
Indeed, I think to remember some people tried to understand quantum mechanics in a multitemporal set-up.
In philosophy, some people studied three-dimensional time theories. These times are called time, hyparxis and eternity.