41–50 of 252 posts
The underlying idea 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". https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore... I have a linkdump on this https://github.com/adamnemecek/adjoint I also have a discord https://discord.gg/mr9TAhpyBW
> Gödel's Incompleteness Theorem: any sufficiently rich formal system, together with an interpretation, has strings which are true but unprovable. This is only half of it! Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people p…
Is there a good book that is similar in spirit, but doesn't require the maturity of GEB? I know an 8th grader that would be a great target, but I don't know if they have the mathematical/logical maturity to get through it.
IMO, to read GEB for its content would be missing the point: what I think is the greatest thing about the book is that it's simply, purely, Hofstadter having fun . The linked post says "GEB is really idiosyncratic in a way no one can imitate", but I'd put it as: it's a deeply personal book. The author's personality shines through in a way I had not encountered before in a mathematics text, and so the book was a revel…
The original review post focuses on Gödel, but you cannot truly review GEB without Escher and Bach. Yes, self-referentiality is a key theme of Hofstadter, but also recursion, symmetry and the foreground/background ambiguity in visual arts and music, after all the whole book is essentially a recursive, self-similiar poem (alternating chapters with prose and dialogues, one dialogue has palindrome form).
Despite that I disagree about his fundamental view of AI, namely that AI is an emergent epiphenomenon, it is still the most-read and most-appreciated book ever for me. I read it first in German and then in English, and given the playfulness with form versus function/content, it is also the best-translated work that I have ever encountered. I'm grateful that I bought it when I was sixteen, simply because it was mentioned in a computer magazine and in a completely different context, so I got curious. I know many people that deeply appreciate it, or that went into AI careers because of it.
The underlying idea 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". https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore... I have a linkdump on this https://github.com/adamnemecek/adjoint I also have a discord https://discord.gg/mr9TAhpyBW
Maybe an ELI5 of "fixed points"?
Earlier quoted context omitted.
Thank you so much for saying this, I find this misconception deeply insulting
(upvoted!) can you say more about this sensibility of yours? I'm genuinely intrigued, as I haven't heard a take like that before :) At risk of asking a leading question: is it some idea that deep truth should come from reason rather than the noise and chaos of psychedelics? (I don't do them myself, but hold them in very high regard as a force in the world)
It's true that many people feel a deep connection to and understanding of consciousness during a psychedelics trip. Did they actually gain any knowledge about how their own brains work in the same way that a neuroscientist or ML expert might understand it? I contend that they did not, even if they feel that they did.
In a similar way a drunk might suddenly feel that he has the ability to dance. That's hardly a replacement for salsa classes.
Of course there are exceptions. Many brilliant people take psychedelics and credit them with breakthroughs in their fields, that can't be ignored. But you'll notice that its always _in their field_, ie they were already thinking about a problem and psychedelics offered them a new perspective.
> Gödel's Incompleteness Theorem: any sufficiently rich formal system, together with an interpretation, has strings which are true but unprovable. This is only half of it! Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people p…
Maybe one day I'll try reading it again and actually finish it, but so far I couldn't do it. Everything is fascinating and mind blowing don't get me wrong, but I feel like there is always this weird pretentious atmosphere going on. I don't know how to describe it, but by the end of the first half reading GEB was not fun anymore.
The second half is weird too, because it describes the academic work he does in the future, but is a stab in the dark compared to the documentarian aspect of the first half.
Think of it like forming a hypothesis:
GEB: This is what we can see.
EGB: This is what I think it means.
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That's quite the strawman, I don't know anyone who says that. And if they did I would ask them if they drank coffee or if they were aware that a good chunk of young professionals are on ADHD medication
> commitment to the material in that depth is not the product of drugs You think this is saying drugs sometimes lead to commitment? It sure reads like an absolute statement to me.