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Elegant six-page proof reveals the emergence of random structure

quantamagazine.org

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Re: Elegant six-page proof reveals the emergence of random structure

#11

Post by dmix »

greggsy wrote: post #8
thetwentyone wrote: post #5

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.

I feel like there’s a market for a publishing service that could partner with popular blogs and websites. They could either allow articles to be selected by the user or the partner site, which could then be auto-paginated and printed being being posted to the subscriber. Hell, sell a service where you will curate articles based on used interests. Add some relevant Twitter threads for letters to the editor. Partner si…

This is a great idea. You could draw in a casual nerdy audience willing to pay a reasonable price for access to high quality OpenAI style explainer pages with access to the raw data and papers.

Re: Elegant six-page proof reveals the emergence of random structure

#12

Post by layer8 »

thomasahle wrote: post #7
tsunamifury wrote: post #2

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…

Surely not _any_ property? From the article I understood that it’s only those that are monotonic under adding edges?

Re: Elegant six-page proof reveals the emergence of random structure

#13

Post by swatcoder »

greggsy wrote: post #8
thetwentyone wrote: post #5

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.

I feel like there’s a market for a publishing service that could partner with popular blogs and websites. They could either allow articles to be selected by the user or the partner site, which could then be auto-paginated and printed being being posted to the subscriber. Hell, sell a service where you will curate articles based on used interests. Add some relevant Twitter threads for letters to the editor. Partner si…

It’s a fine idea, but ignores the importance of typesetting and design for print.

I’m sure plenty of people would want something like this regardless, but the product would usually look much less polished than people expect to see in printed and bound materials and that would reflect on the authors/editors.

Authors and editors who take pride in the presentation of their work might be a hard sell.

Re: Elegant six-page proof reveals the emergence of random structure

#14

Post by noduerme »

thetwentyone wrote: post #5

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.

Agreed! Just for a fun read, you might enjoy this collection they put out a few years ago...

https://mitpress.mit.edu/books/prime-number-conspiracy

Re: Elegant six-page proof reveals the emergence of random structure

#15

Post by nawgz »

layer8 wrote: post #12
thomasahle wrote: post #7

Earlier quoted context omitted.

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…

Surely not _any_ property? From the article I understood that it’s only those that are monotonic under adding edges?

It seems to me most graph problems that people care about are monotonic under adding edges. Actually, I can't think of a single problem in graph theory I've done where that wouldn't hold.

Re: Elegant six-page proof reveals the emergence of random structure

#16

Post by darig »

layer8 wrote: post #12
thomasahle wrote: post #7

Earlier quoted context omitted.

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…

Surely not _any_ property? From the article I understood that it’s only those that are monotonic under adding edges?

No post body was provided.

Re: Elegant six-page proof reveals the emergence of random structure

#18

Post by cevi »

nawgz wrote: post #15
layer8 wrote: post #12

Earlier quoted context omitted.

Surely not _any_ property? From the article I understood that it’s only those that are monotonic under adding edges?

It seems to me most graph problems that people care about are monotonic under adding edges. Actually, I can't think of a single problem in graph theory I've done where that wouldn't hold.

Being a https://en.wikipedia.org/wiki/Perfect_graph is not monotonic under adding edges, and it's certainly an interesting property for a graph to have! (But yes, most interesting properties are monotonic under adding edges)

Re: Elegant six-page proof reveals the emergence of random structure

#19

Post by Rodeoclash »

swatcoder wrote: post #13
greggsy wrote: post #8

Earlier quoted context omitted.

I feel like there’s a market for a publishing service that could partner with popular blogs and websites. They could either allow articles to be selected by the user or the partner site, which could then be auto-paginated and printed being being posted to the subscriber. Hell, sell a service where you will curate articles based on used interests. Add some relevant Twitter threads for letters to the editor. Partner si…

It’s a fine idea, but ignores the importance of typesetting and design for print. I’m sure plenty of people would want something like this regardless, but the product would usually look much less polished than people expect to see in printed and bound materials and that would reflect on the authors/editors. Authors and editors who take pride in the presentation of their work might be a hard sell.

Slightly tongue in cheek, but perhaps you could use ML to automatically typeset it. I've seen some ML that would convert a design to HTML and I'd imagine this isn't too far removed from that.

Re: Elegant six-page proof reveals the emergence of random structure

#20

Post by [deleted] »

cevi wrote: post #18
nawgz wrote: post #15

Earlier quoted context omitted.

It seems to me most graph problems that people care about are monotonic under adding edges. Actually, I can't think of a single problem in graph theory I've done where that wouldn't hold.

Being a https://en.wikipedia.org/wiki/Perfect_graph is not monotonic under adding edges, and it's certainly an interesting property for a graph to have! (But yes, most interesting properties are monotonic under adding edges)

[deleted]
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