“My point in getting into this description of imaginary numbers is that it seems possible to me that, like i, “infinite velocity” is also a purely “imaginary” term”
Indeed, if there are more than 4 dimensions, then traveling in the direction of a higher dimensional axis could lead to instantaneous motion across distances in the lower dimensions, looking like infinite velocity. Yet, we wouldn’t have to accelerate; just make a turn in a direction that to an observer, would be “imaginary”.
Great insight, Boogieman! Indeed, I suspect there are more than four dimensions.