Don't let someone's proof that some problem is impossible to solve prevent you from solving the problem well
enough to get your work done! (smartest thing said so far in this whole discussion.)

Well, again, "the sphere packing problem" is different
than that. In fact, there have been some neat breakthru's
in the field. We have 9600 baud and up modems thanks to
a trellis-code based on packing spheres efficiently in
8 dimensions. Turns out a single sphere can be touched
by 1024 spheres in a tightly-packed regular array. =)
That result is basically cool in anyone's book.

The original problem was that given a bunch of spheres
that are the same size, how many can you get to touch a
single sphere at the same time. In 2d, the answer is clearly
6. (try it with pennies.) In 3d, 12 is the answer but if you
look at the spherical cone of impact that each outer sphere
makes, it would seem that 13 COULD be possible. The deal is
that no one has found a function that provably states for
each dimension what the number is. Only a special case exists
for multiples of 8. High-weirdness, plain and simple.