Lakoff: Math is made up by your brain

Tonight I was on YouTube, and in my 'recommended videos' section there was a selection from the channel Closer to Truth asking physicist Max Tegmark the old granddaddy of questions, "Why is there something rather than nothing?" Tegmark goes on to expound on his view that the universe is fundamentally mathematical and that mathematics are discovered, not invented.

Tegmark's view is an example of a view called mathematical Platonism, a form of mathematical realism which holds that:
  • There are mathematical objects
  • Mathematical objects are abstract
  • Mathematical objects are independent of intelligent agents and their language, thought, and practices.
There are several difficulties that this point of view faces, both conceptually (what, exactly, is an "abstract object" and how does it causally interact with the brain?) and given what we actually observe here in the physical universe. Alexander Vilenkin touched on Tegmark's ideas in his book Many Worlds In One:
The number of mathematical structures increases with increasing complexity, suggesting that “typical” structures should be horrendously large and cumbersome. This seems to be in conflict with the simplicity and beauty of the theories describing our world.
It just so happens that in the 'related videos' sidebar, YouTube recommended this vid from George Lakoff on embodied mathematical cognition — a condensed version of his book Where Mathematics Comes From. It's a scientific alternative to folk theories of mathematics like mathematical Platonism and though it's a relatively nascent field with plenty of challenges ahead, there's growing evidence that it's correct [1, 2, 3]. It's not without controversy, but challenging intelligent people to case aside philosophies entrenched in academia for centuries is inevitably going to meet resistance.

My take is that the conceptual ambiguities intrinsic to mathematical realism put it at a disadvantage to embodied mathematical cognition, which builds on research from the broader field of embodied cognition. Is it true? I don't know. And as a non-mathematician, some of this stuff is over my head. But I think it's fascinating as hell, and the fact that it grounds conceptual abstraction within the purview of scientific inquiry instead of mysterious 'metaphysical realms' is a big reason why I'm such a fan of Lakoff's work.

Anyway... here's the lecture. 


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