> Brouwer’s fixed point theorem. The theorem says that for any continuous function, there is guaranteed to be one point that the function leaves unchanged — a fixed point, as it’s known. This is true in daily life. If you stir a glass of water, the theorem guarantees that there absolutely must be one particle of water that will end up in the same place it started from.
Wait. What if by stirring I shook the glass and at the end set it back down a foot away from its initial location. Is this author claiming that Brouwer’s theorem guarantees a particle floating somewhere where the glass used to be? Unchanged?
I can imagine an unlimited number of scenarios where I can guarantee the water particles are displaced.
This seems like a bad application of the theorem, right?
Wait. What if by stirring I shook the glass and at the end set it back down a foot away from its initial location. Is this author claiming that Brouwer’s theorem guarantees a particle floating somewhere where the glass used to be? Unchanged?
I can imagine an unlimited number of scenarios where I can guarantee the water particles are displaced.
This seems like a bad application of the theorem, right?