'ten Martini' Proof Uses Number Theory to Explain Quantum Fractals
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The "Ten Martini" proof has sparked a lively discussion about the intersection of number theory and quantum fractals, with commenters debating the existence of mathematical concepts like the Cantor set in the real world. While some, like hawkjo, are struck by the idea that such abstract sets might exist in reality, others, like taneq, counter that physical manifestations are likely approximations rather than exact representations. The conversation meanders into related topics, such as the nature of simulations and the limits of measuring physical constants like pi, with some, like gchamonlive, questioning the implications of these ideas and others, like NoMoreNicksLeft, offering context on the simulation hypothesis. Amidst the tangents, interesting facts emerge, like Douglas Hofstadter's father Robert winning the physics Nobel, adding to the thread's eclectic charm.
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https://en.wikipedia.org/wiki/Hofstadter%27s_butterfly#:~:te...
This is exactly the point I was making, so I agree. :)
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.
It could even be a very simple system, as long as it produces complex behavior.
As I put it, the older understanding of the universe working in mechanical ways does not imply the universe is actually a machine nor that it was built by someone or for some purpose similar to the way we build machines. Likewise, the newer understanding of the universe working in computational ways does not imply the universe is actually running on some computer nor that its code was written by someone or for some purpose similar to the way we run simulations.
Metaphysically, I'm strongly opinionated on this now after many years of research on this topic. -see this video from a group of philosophers and idealism-minded thinkers - (also it is way more plausible to me than simulation theory)
https://youtu.be/m4DwQDaUANU?si=sL92PP-MSzjd0PiV
So they actually realised it.
https://www.youtube.com/watch?v=tLPL8pM8Xkw
Update: https://www.youtube.com/watch?v=iW1MZWBZbQU
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