Monday, January 25, 2016

This was my submission for the recent FQXI essay contest on the role of mathematics and physics. It didn't win a prize but I think it makes some important points hence am reposting it here. It connects to a couple of earlier posts in this blog:

There are three basic points in the essay:

  1. The universe must obey mathematical laws since there is no other possible source of structure.
  2. The mathematical laws that we see are plausibly the only ones compatible with life.
  3. Although it must be described by mathematics (point #1), the universe cannot be a mathematical structure since the laws of quantum mechanics cannot be fully axiomatized.
Point #3 means that we can not think of our universe as being just one member of an infinite "mathematical multiverse" consisting of all mathematical structures. Mathematical structures can be axiomatically defined, but aspects of our universe (indeed aspects of quantum mechanics) can not be captured by axioms. Nevertheless point #1 implies that "everything there is to know" about the universe must be specified by mathematics; hence, our universe seems to lie at a sort of boundary of mathematical description. It is fully mathematical but it is not pure mathematics.

If the universe is not a mathematical structure then it can not be viewed in the Tegmarkian way, as part of an eternal "mathematical multiverse". It must therefore be a singular "creation" of some sort. Point #1 implies that any such creation must be based on mathematics, and point #2 implies that, if evolution of life is the "goal", that mathematics may be essentially unique.

Putting it all together suggests that our universe is a "singular, almost-entirely mathematical" creation which exists for the purpose of evolving life. It satisfies the unique mathematical laws which enable this outcome, so in this sense one could say there was "no choice" in its creation.

Of course this begs the question of what entity "created" the universe in the first place. I don't attempt to resolve this problem but am only concerned with the universe that we experience, not a larger "meta-universe" in which it may be contained. If one dislikes the overall hypothesis, the points 1,2, and 3 are still separately worthy of consideration.

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