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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.
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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.)
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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.