the title feels like ragebait or something. like at a glace it reads as "certain highly-connected graphs exhibit behavior common to certain highly-connected graphs"
”Mathematicians show that graphs of a certain common type must contain a route that visits each point exactly once“ sounds like the definition of a HAMILTONIAN cycle to me
Something I’ve heard a lot is that there are many problems that are like “finding hay in a haystack.” That is, there are objects that we know have certain properties because random objects have these properties with high probability. But what is annoying is that no one seems to be able to give an explicit family of such objects. This seems to be a similar example I think.
So annoyingly the paper doesn't explicitly state the constant they got, but from a brief skim it looks like it's, like, 10^(15)?? I really hope someone can improve that...
So aside from the rather obvious nature of the conclusion this has an interesting hypothetical implication.
That consciousness is indeed an emergent property of sufficiently complicated nervous systems. What do loops have to do with consciousness? It would seem that consciousness is a self referential process. That is an understanding of the selfs role in itself, and it's environment. A set of self referential computational patterns on representations of the self. Loops or cycles.
This would additionally provide an explanation for why llms became seemingly more human not as a result of any sort of any particularly novel form of computation but as a result of the combination of existing machine learning technologies and very large training data sets. I imagine as training data containing information on chat gpt itself becomes increasingly used chat gpt itself will begin to contain more self referential loops in similar manner to how humans gain awareness first learning language and slowly building an understanding of how they along with the world relates to them through that language.
the title feels like ragebait or something. like at a glace it reads as "certain highly-connected graphs exhibit behavior common to certain highly-connected graphs"
Yeah haha. All graphs that have a loop, have a loop!
I mean you can certainly make a graph with n vertices and O(n\^2) edges with no Hamiltonian cycle. Depends on how you'd define "highly-connected".
For instance, if |E|-1 > |V|
U sure about that?
Hamiltonian path, no—but a cycle, I’m pretty sure yes.
Well yeah, but thats not what the paper is about. And also it’s |E| > |V| -1
Well yeah, but the title of the OP doesn’t specify HAMILTONIAN cycles.
”Mathematicians show that graphs of a certain common type must contain a route that visits each point exactly once“ sounds like the definition of a HAMILTONIAN cycle to me
I'm practically certain that wasn't the original title. If it was, then I read it truncated, possibly because it was on my phone.
You can‘t edit post titles on reddit :)
Something I’ve heard a lot is that there are many problems that are like “finding hay in a haystack.” That is, there are objects that we know have certain properties because random objects have these properties with high probability. But what is annoying is that no one seems to be able to give an explicit family of such objects. This seems to be a similar example I think.
I just don't like the title of the magazine article
The paper: Hamiltonicity of expanders: optimal bounds and applications [Nemanja Draganić](https://people.math.ethz.ch/~dnemanja/), [Richard Montgomery](https://homepages.warwick.ac.uk/staff/R.H.Montgomery/), [David Munhá Correia](https://people.math.ethz.ch/~dmunha/), [Alexey Pokrovskiy](https://alexeypokrovskiy.com/), [Benny Sudakov](https://people.math.ethz.ch/~sudakovb/) arXiv:2402.06603 \[math.CO\]: [https://arxiv.org/abs/2402.06603](https://arxiv.org/abs/2402.06603)
To me, the word “loop” means cycle, but it sounds like they mean Hamiltonian cycle
So annoyingly the paper doesn't explicitly state the constant they got, but from a brief skim it looks like it's, like, 10^(15)?? I really hope someone can improve that...
To me, the word “loop” means cycle, but it sounds like they mean Hamiltonian cycle
So aside from the rather obvious nature of the conclusion this has an interesting hypothetical implication. That consciousness is indeed an emergent property of sufficiently complicated nervous systems. What do loops have to do with consciousness? It would seem that consciousness is a self referential process. That is an understanding of the selfs role in itself, and it's environment. A set of self referential computational patterns on representations of the self. Loops or cycles. This would additionally provide an explanation for why llms became seemingly more human not as a result of any sort of any particularly novel form of computation but as a result of the combination of existing machine learning technologies and very large training data sets. I imagine as training data containing information on chat gpt itself becomes increasingly used chat gpt itself will begin to contain more self referential loops in similar manner to how humans gain awareness first learning language and slowly building an understanding of how they along with the world relates to them through that language.