I'm not sure whether this belongs here or in the Physics SE - please let me know if I'm mistaken!
After reading Wigner's article on "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", I'm not sure what it means for the physical laws in our universe to be amenable or subject to mathematical effectiveness. Can we imagine a universe which isn't such?
Here's my attempt: imagine a physical world where some object replicates itself between 0 (disappears) and 9 times (produces 9 copies of itself) every millisecond according to the digits of some irrational number chosen by the creator, say $\pi$.
Presumably humans living in this world would never be able to predict the next number in the sequence and therefore how many copies of the object will be present in the next moment. But even this is amenable to mathematical analysis and humans could effectively conclude after sufficiently long observation that the replication process is almost surely unpredictable and behaves like a ten-sided dice, in the same way that the measurement of position or spin on the quantum scale is probabilistic.
So my attempt failed. Can anyone imagine a world which isn't amenable to mathematical inquiry, or is Wigner's point that the formulae obtained for a wide range of physical processes in our world are surprisingly simple in that they don't require 100 terms to write down?