This raises the question of which concepts are contingent and might be
different in a different reality, and which are fixed. Does it really
make sense to create a VR where 1+1=3? What would that mean? Would it
be enough for the VR, whenever two identical objects came close together,
to create a third identical object? Or what about two different objects?
It creates a third of some kind? Does this really suffice?
> What a concept. I'm reminded of the time that, teaching the Pythagorean
> theorem to someone, they asked: "What if c equalled a times b instead
> the square root of a squared plus b squared?"
Similarly, how would this be done in a VR? I don't see how you could
even display a geometry where this worked. The units aren't right,
hypoteneuses would scale differently than sides. It seems incoherent.
Making one where c = a+b might be more plausible, but even then I'm not
sure you could derive a consistent geometry and display it.
A more interesting idea would be to have a 4D VR. Of course the visual
field would still be 2D, but it could be a projection of 4D objects.
Maybe everything would have some degree of transparency, but that might
not be necessary. Somehow the person in the VR would have to be able to
move his limbs four dimensionally. I recall reading about a 19th century
mathemetician who spent a lot of time building models of four dimensional
objects out of blocks, and who later claimed to be able to visualize them
directly in four dimensions. This could be a short cut way to achive this
skill.
Hal