I strongly disagree that anthropics explains the unreasonable effectiveness of mathematics.
You can argue that a world, where people develop a mind and mathematical culture like ours (with its notion of “modular simplicity”) should be a world where mathematics is effective in everyday phenomena like throwing a spear.
This tells us nothing about what happens if we extrapolate to scales that are not relevant to everyday phenomena.
For example, physics appears to have very simple (to our mind) equations and principles, even at scales that were irrelevant during our evolution. The same kind of thought-processes are useful both for throwing spears / shooting cannons and for describing atoms. This is the unreasonable effectiveness of mathematics.
On the other hand, there are many phenomena where mathematics is not unreasonably effectice; take biological systems. There, our brains / culture have evolved heuristics that are useful on a human scale, but are entirely bogus on a micro-scale or macro-scale. Our mathematics is also really bad at describing the small scales; reductionism is just not that useful for understanding, say, how a genome defines an organism, and our brains / culture are not adapted to understanding this.
I think a counterfactual world, where physics outside the scales of human experience were as incomprehensibly complex (to our minds) as biology outside human scales does sound realistic. It does seem like a remarkable and non-trivial observation that the dynamics of a galaxy, or the properties of a semiconductor, are easy to understand for a culture that learned how a cannonball flies; whereas learning how to cultivate wheat or sheep is not that helpful for understanding cancer.
I strongly disagree that anthropics explains the unreasonable effectiveness of mathematics.
You can argue that a world, where people develop a mind and mathematical culture like ours (with its notion of “modular simplicity”) should be a world where mathematics is effective in everyday phenomena like throwing a spear.
This tells us nothing about what happens if we extrapolate to scales that are not relevant to everyday phenomena.
For example, physics appears to have very simple (to our mind) equations and principles, even at scales that were irrelevant during our evolution. The same kind of thought-processes are useful both for throwing spears / shooting cannons and for describing atoms. This is the unreasonable effectiveness of mathematics.
On the other hand, there are many phenomena where mathematics is not unreasonably effectice; take biological systems. There, our brains / culture have evolved heuristics that are useful on a human scale, but are entirely bogus on a micro-scale or macro-scale. Our mathematics is also really bad at describing the small scales; reductionism is just not that useful for understanding, say, how a genome defines an organism, and our brains / culture are not adapted to understanding this.
I think a counterfactual world, where physics outside the scales of human experience were as incomprehensibly complex (to our minds) as biology outside human scales does sound realistic. It does seem like a remarkable and non-trivial observation that the dynamics of a galaxy, or the properties of a semiconductor, are easy to understand for a culture that learned how a cannonball flies; whereas learning how to cultivate wheat or sheep is not that helpful for understanding cancer.
shminux wrote a post about something similar:
Mathematics as a lossy compression algorithm gone wild
possibly the two effects combine?