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The most important idea in math (and philosophy of math) is the idea of fixed points (aka spectra, diagonalizations, embedding, invariants, braids). By fixed po

The most important idea in math (and philosophy of math) is the idea of fixed points (aka spectra, diagonalizations, embedding, invariants, braids). By fixed point I mean something like the "Lawvere's fixed point theorem". Fixed points give rise to “meaning” (it’s really that general). https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theorem https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore... I have a linkdump on this https://github.com/adamnemecek/adjoint https://github.com/adamnemecek/adjoint I also have a discord https://discord.gg/mr9TAhpyBW https://discord.gg/mr9TAhpyBW

openfuture 4y ago
Consider matrix bridge for those of us who will never use discord?
Koshkin 4y ago
There goes my evening...
morelisp 4y ago
Smells like ⸣ to me.
- adamnemecek 4y ago
  Which part?
  - morelisp 4y ago
    The part where you take a basic mathematical concept and claim it solves all "meaning".
    - adamnemecek 4y ago
      It’s not a basic concept. If you think it is you legit don’t understand it.
raphlinus 4y ago
I vouched this. I have no idea whether it's true, but I think it's worth discussing and relevant to the topic. My first real introduction to fixed points was in Dijkstra's weakest precondition semantics of imperative programs, where supplies the semantics of a while loop (via the Knaster-Tarski theorem). I wouldn't be surprised if there were indeed something deeper and more general there.
practal 4y ago
I would say the most important idea in math is logic. Of course, fix points do play an important role in logic as well. For example, Cantor's theorem means that it really makes no sense when studying a mathematical universe, to try to include all operators on that mathematical universe in the mathematical universe as well. Which is what all type theories are trying to do. Of course, it is impossible, so all that type theories are doing is cutting the mathematical universe into disjoint pieces.

openfuture 4y ago

Consider matrix bridge for those of us who will never use discord?

Koshkin 4y ago

There goes my evening...

morelisp 4y ago

Smells like ⸣ to me.

adamnemecek 4y ago
Which part?
- morelisp 4y ago
  The part where you take a basic mathematical concept and claim it solves all "meaning".
  - adamnemecek 4y ago
    It’s not a basic concept. If you think it is you legit don’t understand it.

raphlinus 4y ago

I vouched this. I have no idea whether it's true, but I think it's worth discussing and relevant to the topic. My first real introduction to fixed points was in Dijkstra's weakest precondition semantics of imperative programs, where supplies the semantics of a while loop (via the Knaster-Tarski theorem). I wouldn't be surprised if there were indeed something deeper and more general there.

practal 4y ago

I would say the most important idea in math is logic. Of course, fix points do play an important role in logic as well. For example, Cantor's theorem means that it really makes no sense when studying a mathematical universe, to try to include all operators on that mathematical universe in the mathematical universe as well. Which is what all type theories are trying to do. Of course, it is impossible, so all that type theories are doing is cutting the mathematical universe into disjoint pieces.