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I might be talking past you here, but: The idea that mathematics is entirely mental is a contentious statement and not one a lot of mathematicians would necessarily agree with.

https://plato.stanford.edu/entries/philosophy-mathematics/

I think your intuition is right but I think it’s more because of the embodiment of humans in the world. The machine wouldn’t invent calculus because it wouldn’t be in a physical world that needed to.



Again nonsensical body-experience argument. Do you need to see 11 dimensional world in order to invent math to deal with string theory? Do physicist see those extra dimensions in their eyes?


Discussion here seems to be about "invention" of mathematics. I am pretty sure math does not happen without human bodies in the physical world as it is. Eg. imagine a life happening on a small gravity object travelling through space at speed approaching speed of light: how does space exploration look like and with what math?

11 dimensional vector calculus is a pretty clear example of recogniting generality between 1, 2 and 3 dimensions we can experience, and extending it to an arbitrary number.

While humans, in their mind, do construct things they did not experience, we develop tools to do that based on what we do (even things like axiom of parallelism: we experience "intersections" or lack of them, so we can ask ourselves "what if two parallel lines do intersect?").

Mathematics has really become abstract in the last 2 centuries, and was pretty tied to physical reality up to that point.


What you mean is just a dataset of records of interaction around gravity as input to a system, and math as the output. There is no necessity for a "boby" to be included in here.

And you are required to see 11 dimension to stand for your body experienceism. You are not allowed to extend linear algebra from 3D to arbitrary dimensions.


I have no idea what you are talking about, sorry — what do you mean with "not allowed"?


No they were trained in 4 dimensions, and had equations that seemed to make more sense in 11 dimensions.




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