The cantor set exists in a real phenomenon? Any real phenomenon? That makes me feel like we live in a simulation perhaps more than anything else I’ve heard. This story is a nice description of the people, but I want more on implications. What is going on here?
CGMthrowaway · 9m ago
I THINK they are saying that when the parameter alpha (magnetic flux) is an irrational number, the allowed energy levels of the electron form a structure that resembles a Cantor set. The gaps in the energy levels (forbidden energies) correspond to the “missing middle thirds” in the Cantor set
gchamonlive · 50m ago
> That makes me feel like we live in a simulation perhaps more than anything else I’ve heard
I'm never quite sure what this is meant to mean. Is it comparing to other simulations like computer games or physical simulations where you could change a seed or a data structure and have it manifest in reality? What is expected from a simulation to differ from reality? What does it even mean to make this distinction when we are observing inside the process we are trying to distinguish between real and simulated?
rnhmjoj · 48m ago
Well, if you consider that the setting of the problem is non-interacting, two-dimensional electrons in an infinite lattice, there's not much real about it. These patterns will likely disappear in a more realistic situation.
Also: Church encodings for integers and bootstrapping number systems from the empty set.
https://en.m.wikipedia.org/wiki/Church_encoding
And Lisp, of course; where the book Gödel, Escher, Bach shows's up how to build a number system from empty lists:
An approximation, I’d imagine. I wouldn’t expect it to manifest in any real physical sense, any more than I’d expect an actual physical “unit circle” object to have a circumference of exactly two Pi.
gsf_emergency_2 · 1h ago
It's as much an approx as any physical measurement is. As for "real world" implications, Hinton probably deserves the physics Nobel more than (the) Hofstadter who predicted this phenom (as a grad student)
I'm never quite sure what this is meant to mean. Is it comparing to other simulations like computer games or physical simulations where you could change a seed or a data structure and have it manifest in reality? What is expected from a simulation to differ from reality? What does it even mean to make this distinction when we are observing inside the process we are trying to distinguish between real and simulated?
Also: Church encodings for integers and bootstrapping number systems from the empty set. https://en.m.wikipedia.org/wiki/Church_encoding And Lisp, of course; where the book Gödel, Escher, Bach shows's up how to build a number system from empty lists:
https://wiki.xxiivv.com/site/church_encoding.html
https://en.wikipedia.org/wiki/Hofstadter%27s_butterfly#:~:te...