Wigner wondered about the unreasonable effectiveness of mathematics in describing our universe.
That is, why are our physical laws as described by precise mathematics produce predictions that turn out to be true?
Let’s look at it from three perspectives.
#1 We grasp the graspable bits
By definition, we model aspects of reality that we are capable of modeling. The remaining part may be truly random or complicated. For example, where do quantum measurements come from? Or the incompatibility between general relativity or quantum mechanics.
We hit the limits of our models in those cases, so it’s a bit of survivorship bias when we ask ourselves why our models work so well in cases where do they do.
#2 The Anthropic Argument
Out of all universes that could exist, the universes in which any science is possible upper-bounds their complexity (if universe were any more complex, no science is possible as laws would be too complicated and Winger wouldn’t be asking this question).
The lower bound of complexity is given by the fact that Wigner has to exist and hence laws have to be complex enough for intelligent life to be possible.
Hence the universe we should find ourselves in should have laws and dynamics to produce life, but simple enough to be understood by the very same life.
#3 The Simplicity Prior
The Anthropic argument gives us a range, but it seems like our universe is at the simple end of that range. Given that the standard model fits on a page, the question isn’t why laws are graspable but why are they so simple?
If you assume a prior over universes where simpler universes are more probable, then we should find ourselves in the simplest universe that’s capable of supporting life (which might be the case with our universe).
What would motivate simplicity prior? Well, if we assume some kind of “universe generator” that churns through simpler universes first before getting to more complicated ones, we would find ourselves in the simplest universe that’s complex enough for intelligent life to emerge.
So, are there multiverses?
Given, how successful Anthropic argument is for illuminating puzzles like Wigner’s makes me seriously consider the possibility that many, many possible universes exist beyond our own but that we just happen to find ourselves in a particular one that’s suited for us.
Of course, there’s no way to experimentally prove it (yet), but given that the alternative is assuming our precise universe with specific laws and constants exists as a bridge fact, I’d pick multiverses and Anthropic argument as a more likely explanation for what we observe.
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