In the last post I talked about a neuron assembly in the brain that when it fires makes you feel you have been in the current situation before, and another neuron assembly that makes you feel that you are dealing with a persistent object with consistent behavior. I want to make it clear that I don’t know precisely how these brain functions are implemented, and I know of no research literature on these topics.

Brain research has shown that many different kinds of behavior, including thinking about different real and unreal things, causes activity in specific parts of the brain. I claim that the idea that there is a déjà-vu site and a persistent-thing-recognizing site is plausible and consistent with what we know about the brain. And they are far more plausible than any explanation of déjà-vu as coming from past lives or any explanation that mathematical objects are real and live in some ideal non-physical realm that we have no evidence for at all.

Another point: If our perception that when we think about and calculate with math objects we are dealing with things that are “out there” comes from the way our brains are organized, then we mathematicians should feel free to think about them and talk about them that way. We are making use of a brain mechanism that presumably evolved to cope with physical reality, as well as a general metaphor-mechanism that everyone makes use of to think about both physical and non-physical situations in a productive and creative way.

This point of view about metaphors has a lot of literature: see the section “about metaphors” here.

Again, it is a reasonable hypothesis that the metaphor-mechanism is implemented in some physical way in the brain that involves neurons and their connections.

To sum up, when we mathematicians think and act like Platonists we are using some of the main mechanisms of our brain for learning and creativity, and we should go ahead and be Platonists in action, without feeling embarrassed about it and without subscribing to any idealistic airy-fairyness.

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