Mathematicians have found a new way to impose order on chaos in the form of an answer to a challenge which has puzzled them for nearly a century – a so-called Ramsey problem known as r(4,t).
TLDR if you invite over 25 people to a party, you can know that people can cluster in small groups where everyone in the small group knows each other, or everyone is meeting for the first time.
Even the result with 6 people is super neat. Sent me down a rabbit hole of things like Ramsey theorem and the pigeonhole principle. On a side note, the guy Ramsey was a fucking genius.
As with many articles in science and math, the discovery isn’t that “this weird thing happens”, but that “hey, we can model this weird thing using this equation/model (that sometimes comes from a totally unrelated field).” Maybe in 10, 20, 50 years this discovery will become the key to understanding yet another weird thing, and so on.
“Everyone understands” that if you drop an object it falls to the ground. Yet we still don’t fully understand how gravitation works.
I mean socially, do you want to go to a party and be the only person who doesn’t know anyone? If you had to pick, I’d imagine you’d either want to catch up with a couple people you do know OR meet new people. The trouble gets when the crowd is a mix of old and new and people feel alienated.
I don’t understand how this discovery would prevent that though. You could still get invited to a party with over 25 people where you are the only person who doesn’t know anyone.
If everyone is already familiar with the others and talking about a niche topic and their inside jokes? No. That’s not ideal.
At a party I’d rather either catch up with some mutual friends OR meet some new faces. I don’t want to be stuck between my friend taking about niche topic and a couple other people I don’t know who don’t want to be in that conversation
That’s a good way to think about the actual practical question this result can be used for.
For me, it was just fascinating to learn about Ramsey theorem in the first place, not even this new development. I’ve never heard of it. I couldn’t find any specific practical applications for these type of results, but it is just so elegant.
These types of abstract problems often get applied to physics or various optimization problems where efficient solutions can save a ton of work or enable new techniques
That’s just a simple way to phrase the problem in concrete terms. The immediate applications are usually not of interest, unlike the novel techniques with which hard problems are solved.
there’s a lot of things that feel like they should be obvious, but are almost impossible to prove mathematically. it’s the difference between seeing something happens, and understanding why it happens and proving that it will always happen (or not, and why)
Probably these two paragraphs sum up the background for the problem nicely
A common analogy for Ramsey theory requires us to consider how many people to invite to a party so that at least three people will either already be acquainted with each other or at least three people will be total strangers to each other.
Here, the Ramsey number, r, is the minimum number of people needed at the party so that either s people know each other or t people don’t know each other. This can be written as r(s,t), and we know the answer to r(3,3) = 6.
I was more interested in finding out about Ramsey theorem, though, rather than this new result.
TLDR if you invite over 25 people to a party, you can know that people can cluster in small groups where everyone in the small group knows each other, or everyone is meeting for the first time.
Even the result with 6 people is super neat. Sent me down a rabbit hole of things like Ramsey theorem and the pigeonhole principle. On a side note, the guy Ramsey was a fucking genius.
I’ve read the whole thing and I feel like there’s something that’s just assumed that everyone understands.
What exactly is the problem? Why do we care how many people know each other or don’t? I’m so confused.
As with many articles in science and math, the discovery isn’t that “this weird thing happens”, but that “hey, we can model this weird thing using this equation/model (that sometimes comes from a totally unrelated field).” Maybe in 10, 20, 50 years this discovery will become the key to understanding yet another weird thing, and so on.
“Everyone understands” that if you drop an object it falls to the ground. Yet we still don’t fully understand how gravitation works.
I understood that. I’m asking about the problem with parties that this helps people fix.
no, the story in the article about Ramsey numbers is just meant to make you the life of your next party. try it, I’m sure people will love the debate.
I mean socially, do you want to go to a party and be the only person who doesn’t know anyone? If you had to pick, I’d imagine you’d either want to catch up with a couple people you do know OR meet new people. The trouble gets when the crowd is a mix of old and new and people feel alienated.
I don’t understand how this discovery would prevent that though. You could still get invited to a party with over 25 people where you are the only person who doesn’t know anyone.
That would be the ideal for meeting new people, would it not?
If everyone is already familiar with the others and talking about a niche topic and their inside jokes? No. That’s not ideal.
At a party I’d rather either catch up with some mutual friends OR meet some new faces. I don’t want to be stuck between my friend taking about niche topic and a couple other people I don’t know who don’t want to be in that conversation
That’s a good way to think about the actual practical question this result can be used for.
For me, it was just fascinating to learn about Ramsey theorem in the first place, not even this new development. I’ve never heard of it. I couldn’t find any specific practical applications for these type of results, but it is just so elegant.
These types of abstract problems often get applied to physics or various optimization problems where efficient solutions can save a ton of work or enable new techniques
But this seems to claim it solves some practical problem with parties. I don’t know what that problems.
It’s about what combinations of “nodes” with specific relations to others are possible in a group of different sizes
That’s just a simple way to phrase the problem in concrete terms. The immediate applications are usually not of interest, unlike the novel techniques with which hard problems are solved.
there’s a lot of things that feel like they should be obvious, but are almost impossible to prove mathematically. it’s the difference between seeing something happens, and understanding why it happens and proving that it will always happen (or not, and why)
TL;GU (too long, gave up) 😂
But yeah, the first two or three paragraphs are the important parts.
Probably these two paragraphs sum up the background for the problem nicely
I was more interested in finding out about Ramsey theorem, though, rather than this new result.