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can I get an ELI5?
by luxuryballs 6y ago
can I get an ELI5?
- ComodoHacker 6y agoI guess that's already it. :)
- system2 6y agoToday's 5 year olds are all mathematicians anyway.
- visarga 6y agoand an application ... what can I use it for?
- Mountain_Skies 6y agoPerhaps not much now but a use for them might come along and it will be good that this will be there ready to fill the need. It's my understanding that quaternions were mostly a curiosity when first described in the mid 1800s but now are used extensively in computing. From wikipedia "quaternions are used in computer graphics, computer vision, robotics, control theory, signal processing, attitude control, physics, bioinformatics, molecular dynamics, computer simulations, and orbital mechanics." When Sir William Rowan Hamilton first described them, he had no concept of most of the above, much less that quaternions would be important for them. Good for us that he still pushed forward with them.
- 101008 6y agoFirst paragraph of the article says something interesting that can be useful at parties :)
- dpatterbee 6y agoI can't possibly imagine why you would want an application for recently developed mathematics. I would have thought that by now mathematics would have proven its worth enough to not have to justify itself.
- enchiridion 6y agoBecause most people here are engineers, not mathematicians. The newness of mathematics has little to do with its utility, so it is reasonable to ask if there are any relevant applications.
- xmprt 6y agoI'm doubt there's an immediate application for this result but have there been any similar proofs in the past and what have those been applied to?
- visarga 6y agoI assumed an implied AI application on graphs.
- jerf 6y agoRamsey theory in a nutshell is about studying what must be true about graphs as they get large in certain ways, because the very size of the graph makes it impossible for the things to be false any longer. My impression is that it tends to be more useful for putting bounds on how good a practical technique can be rather than directly producing said direct techniques. It's not quite the same as complexity theory in computer science, but it's a pretty close analogy. Complexity theory doesn't necessarily have a lot of direct use, but it's certainly indirectly useful to engineering, and a very useful tool for an engineer to have in their toolbelt for measuring and talking about things that are otherwise too abstract to measure. Even if you aren't inclined to study it directly yourself, don't slag on it, because you benefit from the people who do.
- visarga 6y agoThanks, great answer
- politician 6y agocryptocurrency
- msoad 6y agoThe article is very approachable actually. Don't be intimidated by the title. They explain this very nicely. You don't even have to know what a graph is
- mFixman 6y agoThe Erdős–Hajnal conjecture says that for any graph `H`, then every graph in the set of graphs `F_H` that does not contain `H` as an induced subgraph will either have a polynomial amount of cliques or a polymomial amount of independent sets. The growth rate of the exponent depends on the size of each graph in `F_H` and on some properties `H`. Like with most simple questions in Ramsay theory no proof or contradiction has been found for the general conjecture, but there has been some progress for some `H`. The latest paper proves that the conjecture is true if `H` is a cycle of 5 graphs. Since proving this was so hard and provided so much insight, there's hope that the general conjecture can be proved without a lot more work. ⠀ Here's an actual ELI5: There's a party where some pairs of guests know each other and some don't. A genie told you that there isn't any group of 5 people that only know two people from that group in a way that those relationships form a loop (1 — 2 — 3 — 4 — 5 — 1). Knowing that, you reason that this cannot be a regular party. Instead, it has to be one of these two: ⒈ A class reunion, where there's a large group of people that all know each other. ⒉ A group blind date, where there's a large group of people where nobody knows anyone. Being a smart 5-year-old the genie pushes you to publish a 19-page paper proving this, but you find out in Hacker News that some academics beat you and published it this February.
- Hfjfjdjfjceijfj 6y agoexponential -> polynomial
- mFixman 6y agoThanks, edited. I first understood the conjecture as bounding the exponential function on the size of the graph of an element of `F_H`, but apparently the odd thing is the exponent depends solely on `H`.
- ball_of_lint 6y agoI think I'm misunderstanding or you left out an important condition. For your example where H forms a loop, I imagine an element of F_H which is a larger loop. Then it could be arbitrarily large, have no cliques above size 2, a linear number of cliques of size 2, and have only one independent set.
- Hfjfjdjfjceijfj 6y agoThere's a conjecture about graphs, and the conjecture was proven true for a new specific case. So we still don't know whether the conjecture is true in general. For understanding the conjecture itself, I think the mathematical description is the easier to comprehend than any analogy. See the intro of the Erdős–Hajnal conjecture Wikipedia article[1]. Graphs are pretty intuitive mathematical structures and the description of the conjecture only uses basic graph structures. Although maybe I'm just not clever enough to come up with a suitable analogy. [1]: https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Hajnal_conjecture https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Hajnal_conj...