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.
If you are happy to focus on the intuitive without worrying about too much maths, the classic work on multiple time dimensions in physics must surely be J W Dunne's The Serial Universe - the second edition, published in 1942, is shorter and (comparatively) more readable. It was the sequel to his bestseller An Experiment with Time and elaborated on the role of the observer in modern physics. His regress of multiple time dimensions was inhabited by a similar regress of observers, thus (in retrospect) proffering a solution to the Schroedinger's Cat + Wigner's Friend regress of discrete real observers.