Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Elegant six-page proof reveals the emergence of random structure

quantamagazine.org

Post reply on HN
Print view View original

81–90 of 178 posts

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

#81

Post by greggsy »

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.

My other half is an editor and graphic designer and constantly points out bad design. Many CMS platforms do this out if the box to allow cross platform compatibility (at various degrees of success), but you could just define some core defaults to ensure compatibility.

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

#83

Post by gspr »

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?

> Because this seems absurdly obvious to any layman.

That something seems obvious does not suffice for mathematics. It needs to be proven.

> Why is this a complex proof?

Because no one has come up with a simpler proof. (Although this proof is in fact not very complex, as far as modern mathematical proofs go).

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

#84

Post by ccbccccbbcccbb »

fjfaase wrote: post #74

A nice 'visual' illustration of the threshold is found in Percolation theory https://en.wikipedia.org/wiki/Percolation_theory where if you have an infinite grid of square rooms with either a wall or a door between each pair of rooms, that there is shift about what is connected when the percentage of door gets just over 50% as is visualized in this animation: https://en.wikipedia.org/wiki/Percolation_theory#/media/Fil…

I recommend everyone interested in percolation theory to also check https://meltingasphalt.com/interactive/going-critical/ and play with critical thresholds interactively!

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

#85

Post by Keyframe »

Pakaran wrote: post #59
ineptech wrote: post #40

I'm trying to visualize this. I go to Wolfram Alpha and type "chance of getting 504 heads in 1000 coin flips" and see the answer is about 1/40, and when I change 504 to 505 I see the odds are about 1/41 - only slightly worse. Then I check the differences between 524 and 525 and I see that the odds are decreasing much more sharply (1/400, 1/459). The little graph they helpfully provided shows what's happening: I've mo…

The effect you're seeing on the coin flip is best understood by seeing that each coin flip is independent, and in no way connected to the past. So, the odds are based on a fair 50/50 per flip, which leaves you with a simple 2^n sample space of one of each binary combination for n flips. The math for that works out easily, and can be plotted. The emergence of random structure in graphs, however, is different. The chan…

Coins example would work here if he asked what are the odds of getting n of a/b in a row or how many n-length rows for few different ns in a number of flips.

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

#86

Post by feral »

fjfaase wrote: post #74

A nice 'visual' illustration of the threshold is found in Percolation theory https://en.wikipedia.org/wiki/Percolation_theory where if you have an infinite grid of square rooms with either a wall or a door between each pair of rooms, that there is shift about what is connected when the percentage of door gets just over 50% as is visualized in this animation: https://en.wikipedia.org/wiki/Percolation_theory#/media/Fil…

And, to give an example we've probably all become familiar with, this this is equivalent to how a disease becomes an epidemic as the R value crosses 1.

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

#87

Post by Keyframe »

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?

It's not about _can produce_ as much as will it and when which is now an open path for further discovery.

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

#88

Post by jessriedel »

plaguepilled wrote: post #44
yshklarov wrote: post #41

Earlier quoted context omitted.

Actually, the "fluff" in this case is outstanding. The paper itself doesn't provide much context, but the Quanta piece does a great job at explaining why the result is important.

I agree its a pleasant read, but like other Quanta articles, it spends too long on the journey and not enough time on the precise details for my liking. There are few symbolic expressions to be found. Others agree, which is why I shared the link. Plus, calling it 'fluff' is surely the mildest of sassy descriptions, no?

The direct link to the actual paper is certainly very useful and much appreciated. I think yshklarov's point is just (1) it won't be accessible or interesting to the vast majority of HN readers (including me) without significant background info and (2) Quanta does a shockingly good job at this background (but is not intended to replace the paper itself).

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

#90

Post by jiggawatts »

anuvrat1 wrote: post #89

Off Topic: Can I get some more resources like quanta, which explains new research on mainstream or obscure subjects to a layman?

Scientific American, or American Scientist are my go-to favourites.

https://www.scientificamerican.com/

https://www.americanscientist.org/

Post reply on HN