This is fantastic, Doc- I have been thinking about it for awhile, since the universe is "to scale" if our constants changed locally we would not know about it, because everything else would adjust accordingly.
One of the most intriguing findings is the discovery of below absolute zero temperatures and how they seem to mimic how matter would behave in a tachyonic universe (hint, everything is reversed, add more heat and the temperature goes down.)
It would be sheer irony if we eventually found out that every piece of matter and energy in the universe cancels out to result in a sum of nothing...... ex nihilo nihil fit! (I hope I got that right, I was going from memory.)
No but dividing by zero (except in the special case of 0/0) tends to infinity. The 'singularity' of our number system- haha. On some level maybe numbers loop too and if you go high enough, you reach the lowest possible number (tangential curves with asymptote 'singularities' come to mind- perhaps the different possible layers in the omniverse are arranged in the same way.)
If the numbers loop back to negative, then you haven't gone high enough. To illustrate with y=tan(x), that means you stepped too far in x, and thus missed a bunch of y. In fact you did not just miss a bunch, but an infinite amount of it. Get closer and closer to that singularity, and you move through ever vaster amounts of y for ever smaller amounts of x.