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?
gchamonlive · 2h 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?
NoMoreNicksLeft · 8m ago
Most people generally think that it means that there is a higher-level reality, and that there are beings within that higher-level reality engaged in creating our simulation. "Gods" for lack of a better word.
I prefer Greg Egan's interpretation in Permutation City, where simulations can become self-bootstrapping and that simulations need no "simulator" at all. No one's loaded universe.exe in some higher-lever reality, it runs itself.
That still won't stop me from attempting rowhammer attacks.
CGMthrowaway · 1h 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
rnhmjoj · 2h 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.
anentropic · 1m ago
Didn't this same article state that: "They placed two thin layers of graphene in a magnetic field, then measured the energy levels of the graphene’s electrons. The quantum fractal emerged in all its glory."
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 · 2h 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?
I prefer Greg Egan's interpretation in Permutation City, where simulations can become self-bootstrapping and that simulations need no "simulator" at all. No one's loaded universe.exe in some higher-lever reality, it runs itself.
That still won't stop me from attempting rowhammer attacks.
So they actually realised it.
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...
This is exactly the point I was making, so I agree. :)