[Doctor Stochastic]

It's the kind of thing that happens in vectors. In ordinary (Gibbs) vector analysis, the three spatial coordinates get unit vectors i,j,k attached. Hamilton used 4 coordinates for the quaternions. (There isn't a 3-dimensional division algebra.) with a basis (1,i,j,k). One gets that i^2=j^2=k^2=-1 but ij=k. Using this rule, the product of two quaternions (0,iy,jz,kw)*(0,ib,jc,kd) would have the first term as the negative of the dot product and the last three terms as the cross product as if the (y,z,w) and (b,c,d) were ordinary 3-vectors. It's kind of weird. If one trys to expand the complex numbers to 3-space analogously to expanding the reals to complex, then one finds that 4-coordinates are needed. (Algebra is full of surprises.)

I'm just speculating here. If one has two time-like dimensions, it seems that one then really needs three such.

[Physicist]

I'm just speculating here. If one has two time-like dimensions, it seems that one then really needs three such.

Speculate no more, you are entirely correct. Well done.

[VadeRetro]

(Algebra is full of surprises.)

I get the basic idea, thanks! My vector skills are pretty rudimentary. I think they're going to have to stay that way.

[longshadow]

If one has two time-like dimensions, it seems that one then really needs three such.

This idea of two or three time dimensions is appealing to me; I'd very much like to do my "aging" at this stage of life in a time coordinate that is orthogonal to the one we normally (no pun intended) experience.

Or did "Dorian Gray" beat me to it?