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Jinyoung Park is literally one of the co-authors of the paper in question.
Can someone explain to my why proving random graphing can produce known shapes is important? Because this seems absurdly obvious to any layman. Why is this a complex proof? I’m guessing it’s more that they proved the thresholds for these shapes being formed more than why?
The interesting thing a out graph properties (like the emergence of connectivity, giant components, Hamiltonian paths etc.) is that they happen as "phase transitions". A classic example is cuckoo hashing: You want to know how many edges the random graph of hashes can have before it contains a cycle, since that's when you need to rehash into a larger table. You might expect that this number is "pretty random" in that…
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If you think something is absurdly obvious you usually need to re-read what you've read.
No. It's not that rare for absurdly obvious things to get published to great fanfare. I'm still bitter about "De Morgan's Laws". There are two of them: 1. If two things are not both true, then one or more of them is false. 2. If neither of two things is true, then both of them are false. Of course this is obvious to everyone. Writing it down did not merit having it named after yourself. I guarantee many other people…
The title of this paper is not misleading at all. They basically just reinvented Riemann sum in 1994.
Can someone explain to my why proving random graphing can produce known shapes is important? Because this seems absurdly obvious to any layman. Why is this a complex proof? I’m guessing it’s more that they proved the thresholds for these shapes being formed more than why?
The interesting thing a out graph properties (like the emergence of connectivity, giant components, Hamiltonian paths etc.) is that they happen as "phase transitions". A classic example is cuckoo hashing: You want to know how many edges the random graph of hashes can have before it contains a cycle, since that's when you need to rehash into a larger table. You might expect that this number is "pretty random" in that…
The puzzle instances are pseudo-random graphs in which edges are defined by the siphash24 hash function, and the solutions are cycles of length L, which have a chance of about 1/L of occurring.
I wish Quanta was a print publication I could subscribe to. Definitely the types of articles I'd like to sit down and read not on a computer.
Here Quanta's editor-in-chief explains his thoughts on a print version [2018]: https://www.publishersweekly.com/pw/by-topic/columns-and-blo...
I wonder if this has implications for evolution of life. Life is about DNA which is about a graph of nucleoids connecting to each other in specific structures. But DNA must have evolved out of random structures and random mutations. So if there's a threshold at which structures become inevitable, then DNA has a chance to be born?
I wish Quanta was a print publication I could subscribe to. Definitely the types of articles I'd like to sit down and read not on a computer.
That said, I've really enjoyed New Scientist. It's not as deep or esoteric as Quanta but still satisfying for a layman like me.
Jinyoung Park's Path to Math video on IAS is a really wonderful 3 minute story of how she came to study threshold behavior in random discrete structures, just like this work. Highly recommended. https://www.ias.edu/ideas/paths-math-jinyoung-park
Jinyoung (after having been a secondary school Math teacher for 7 years):
"... there was a big obstacle in studying mathematics or pursuing my career in mathematics, which was me, myself. Because I just couldn't stop thinking that oh I'm too old and I started too late or I didn't learn enough amount of mathematics in college ..."
and now here she is with some world class work to her name.
I wonder if this has implications for evolution of life. Life is about DNA which is about a graph of nucleoids connecting to each other in specific structures. But DNA must have evolved out of random structures and random mutations. So if there's a threshold at which structures become inevitable, then DNA has a chance to be born?
I read a book on it by Stuart Kauffman from the Santa Fe Institute of Complexity about 20 years ago; things may well have changed since then, but the core idea was amazing.
Also reminds me of rates of reaction from Physical Chemistry, how some concentrations of chemicals can have a huge impact on the overall reaction.
Edit: Updated with the author’s name.