Mathematicians have found a new upper limit to the Ramsey number | Hacker News Reader

Mathematicians have found a new upper limit to the Ramsey number

quantamagazine.org

252 pointsgeorgehill42 comments

Heh. I was not prepared for the punchline that this "only" goes from 4^k to 3.993^k. I mean, they're creating a whole new form of proof that will almost certainly allow further decreases, and they generously aren't holding back until they make a bigger dent, but it just intuitively feels like the true value has got to be way, way smaller.

(On a side note, I am so often stunned by the quality of articles on Quanta Magazine. I sorta thought this type of quality writing was dead and gone from the freely accessible web.)

> Quanta Magazine

Their YT videos are also top notch.

are we talking about the same YT channel?

the one I looked at had overly-pretentious zooms and panning, while almost no actual info

I think you are possibly missing the possibility that going from 4^k to 3.993^k might involve learning something new about the problem. Frequently learning something new is more important than the absolute magnitude of the improvement.

> might involve learning something new about the problem

I think that's almost literally what sfink said though:

> > they're creating a whole new form of proof that will almost certainly allow further decreases

> I sorta thought this type of quality writing was dead and gone from the freely accessible web

It is working because its funded by Hedge fund founder billionaire/mathematician and they are not looking for subscription revenues (yet).

That explains it. I also wondered how the ad-supported Buzzfeed style web could make the money math work out. Its good to know that’s not the source.

Oh, I didn't notice it's Jim Simmons's. I saw his opening lecture at 2014's ICM in Seoul, before the Fields Medals. There were lots of questions about how to make money, even when he previously stated that he wouldn't answer any of those.

did it change from a year ago?

for the last 1-1,5 years quality of explanations in quanta's publications had been aaawful - with situation improving to the previous level only a month or so ago

I don't think funding source is the main explanation for quality (tho maybe for _ability_ to have quality)

> Can we improve 3.993 to 3.9? Maybe to 3.4? And what about 3?”

Pi is feeling a little left out. If that turns out to be the true asymptotic behavior of Ramsey numbers, it would make one of the worst ever methods for computing digits of pi...

I thought it was entertainingly specific, and fortunately the abstract at least [0] was slightly less immediately beyond me than I feared, to satisfy my curiosity a bit:

The main proof is an improvement to the 4^k bound (standing since 1935) to (4-eps)^k for some epsilon.

They additionally prove (I guess they have properties that make it slightly easier than other rounder/bigger numbers?) it for eps=2^-10 and eps=2^-7 specifically.

(3.993 then comes from the latter, 4 minus it gives 3.9921 and change, but of course you need to round that up to 3.993 in order to say it's a bound: it's not definitely less than 3.992, since it could lie between the two.)

So yes maybe/it probably can be improved from 3.993, because that's a bit of a tangential claim anyway - the main thing is that it's 'some non-zero amount less than 4'^k.

(But mostly yes it was beyond me, I won't pretend to be able to even attempt to understand the proof really.)

[0]: https://arxiv.org/abs/2303.09521

Do i get this right? This discovery let you calculate the minimun amount of grafana dashboards you need to monitor a kubernetes cluster or the minimun amount of dasboards behind you in a linkedin photo to look cool enough?

Yes, exactly. Care to share an example of what you're talking about? You may have found a new realm for research...

It also how the EKS (Entropy Khaos Service) returns a timestamp representing the end of the universe.

Finally, omega star will get their shit together.

only theoretically, and only if UP=nP, in practice we know that k = 8s (or in smaller abelian deployment rings k = 3s = 0s mod 443)

Contemporaneous thread from the Cambridge edition of the seminar https://nitter.net/wtgowers/status/1636632071069106181#m

(They celebrated with a pint)

Can someone explain to me why changing the top right and bottom right edges to blue in the R(3) = 6 does not work ?

There's still a red clique. And changing any of those 3 to blue crates a blue clique.

Ah, thanks. I see it now.

Im not a mathematician, but does this have potential application in some Neural Networks and such where dangerous connections or isolated information flows could exist?

One of the key aspects of Ramsey theory is that is has basically no potential applications because the objects it talks about have trouble fitting in the observable universe.

I get that this is really interesting and I surely enjoyed the read... But has it really any practical implications? I mean, in a sense, there are so many mathematical riddles... Anyways, I'm fine to ignore this question. Very nice!

Before someone jumps at you for daring to ask this question... yes, there are many many math riddles, and indeed not all are equally important, and we may not always know in advance which ones are.

Some turn out to be more "productive" in the sense of leading to development of techniques, connections to other fields, etc.

Ramsey theory (the riddle discussed in the article) is one of these, here is just a short list of nontrivial applications to CS (admittedly, mostly to theory of CS):

https://www.cs.umd.edu/~gasarch/TOPICS/ramsey/ramsey.html

Interesting, thank you!

Not sure, one can just state that chaos does not exist as with a huge number of items (10^200+) some sort of a rule always emerges.

I submitted this link 1 day ago, but I am not sure why it's on the front page now, as it says I posted it just 1 hour ago

https://news.ycombinator.com/submitted?id=georgehill

Moderators often resubmit submissions with fake time. (I pretty much hate this. I don't like people lying things about me, like I was using HN at a time I wasn't. Be aware of this.)

Why?

It's an invasion of privacy. Imagine that a post appears under your name with a date/time where you are supposed to be working. If you are paid by somebody else, this may get you into trouble, or even fired.

In fairness in such an extreme situation it seems likely there would be a conversation where you'd have the opportunity to explain.

If there weren't, well, probably you're better off?

> If there weren't, well, probably you're better off?

That’s for the person to do something with or not. :) Not something that moderators should intervene in indirectly.

How do you explain if you're not aware of the policy?

There is no privacy invasion here (that isn't even the right argument). If you think that HN misrepresents the data then sure that's a valid concern, but it's not a privacy invasion. But really, the HN date is when it got exposed initially.

It does suggest that an "(updated)" marker would not go amiss.

I won't explain my justification, since I'm supposed to be working right now. ;-)

Fortunately the moderation here isn't a faceless monolith and if you email them they would most likely be happy to cooperate with your concerns about this.

You’ve definitely described an invasion of privacy, just not one perpetrated by HN.

pretty sure it's because HN's position/rank algorithm is heavily weighted towards post age. so if it got upmodded but retained yesterday's timestamp it would not get much hang time.

(speaking as someone with a few previous second-chance submissions)

As dang explains in one of the linked posts, it's because if they don't do it, the discussion usually becomes "how is this on the front page when it's 2 days old?" instead of discussing the topic at hand.

Of course in this case we're now discussing the opposite question and still not discussing the topic at hand.

dang explains the mechanics behind the second-chance pool here: https://news.ycombinator.com/item?id=26998308

Regarding timestamp inconsistencies: https://news.ycombinator.com/item?id=19774614

Wow, this is super cool! Thanks!

I wonder what would happen to Reddit if moderators could order posts manually (other than stickies).

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