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Originally Posted by cliche
As mentioned at the start, the whole question is predicated on the idea of time as being exactly equivalent to a spatial dimension so I'm not keen to take your 'it's just a fourth number' argument even though that's what I believe myself...
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Not quite. Time is simply a mathematical degree of freedom. In relativistic cases, energy, momentum, and mass can be distributed among the four degrees of freedom, 3 spatial and 1 time, by taking some tensor transformations. While the temporal spatial degree of freedom is orthogonal to the spatial, you can think of the time basis vector as being imaginary (while the three spatial basis vectors are pure real). To make the units equivilent, you always measure time in units of ct. time and space are not exactly equivilent.
A "cube" is in 4-space is not a physical object. It's not the same thing as thinking about a cube in 3-D. It doesn't suddenly gain special properties because it has "lenght in time".