Maze proof establishes a 'backbone' for statistical mechanics
quantamagazine.org
Maze proof establishes a 'backbone' for statistical mechanics
1–10 of 12 posts
Re: Maze proof establishes a 'backbone' for statistical mechanics
#2Curious how typical “kids” mazes are made. They’ve got to be tough to see through to the end and usually cover much of the sheet. Similarly intrigued by the construction of cross word puzzles…
Re: Maze proof establishes a 'backbone' for statistical mechanics
#3Nice work!
I usually like the writing at Quanta, but omg just put "this is percolation theory on a hexagonal grid" in the first paragraph.
Re: Maze proof establishes a 'backbone' for statistical mechanics
#4I always marvel at Quanta’s skill in trying to translate these intricate mathematical and physical ideas for a broad audience. I can’t always wrap my mind around their analogies, but I always admire their effort.
Their visualizations seemed especially helpful here. I am curious, though-they allude to this discovery relating to modeling phenomena like fluid perfusing porous materials. Are precise values of constants like this “backbone exponent” a practical barrier to that sort of modeling, or is this a more basic discovery that’s satisfying just in the sense of the completeness of human knowledge?
Re: Maze proof establishes a 'backbone' for statistical mechanics
#5Curious how typical “kids” mazes are made. They’ve got to be tough to see through to the end and usually cover much of the sheet. Similarly intrigued by the construction of cross word puzzles…
Anecdote: I learned BASIC in 1981, and one of my first programs generated mazes. I tested it a couple times on smaller grids, then submitted a job to fill an entire sheet of green bar paper. Next morning, I asked the operator for my printout, and got chewed out because they killed my job after it had consumed some insane amount of core time.
That was my first lesson in complexity. My program was something like O(N^3) or worse.
But I've read that good crossword puzzles are as much of a literary exercise as a computational one.
Re: Maze proof establishes a 'backbone' for statistical mechanics
#6Nice work! I usually like the writing at Quanta, but omg just put "this is percolation theory on a hexagonal grid" in the first paragraph.
Amen. For those interested, google 'percolation theory in two dimensions' to see general results.
Re: Maze proof establishes a 'backbone' for statistical mechanics
#7I always marvel at Quanta’s skill in trying to translate these intricate mathematical and physical ideas for a broad audience. I can’t always wrap my mind around their analogies, but I always admire their effort. Their visualizations seemed especially helpful here. I am curious, though-they allude to this discovery relating to modeling phenomena like fluid perfusing porous materials. Are precise values of constants l…
I was coming here to say the same, but with less words: I fuckin love Quanta.
I'm broke as heck, but I really hope people with more discretionary income are able to support them financially <3
Re: Maze proof establishes a 'backbone' for statistical mechanics
#8Curious how typical “kids” mazes are made. They’ve got to be tough to see through to the end and usually cover much of the sheet. Similarly intrigued by the construction of cross word puzzles…
You might enjoy this: https://www.jamisbuck.org/mazes/. The section headers link to his (IMO really excellent) articles about maze generation algorithms, plus there’s a more comprehensive book you can buy.
(I doubt kid’s mazes are made using these precise algorithms, but either way they’re interesting!)
Re: Maze proof establishes a 'backbone' for statistical mechanics
#9I always marvel at Quanta’s skill in trying to translate these intricate mathematical and physical ideas for a broad audience. I can’t always wrap my mind around their analogies, but I always admire their effort. Their visualizations seemed especially helpful here. I am curious, though-they allude to this discovery relating to modeling phenomena like fluid perfusing porous materials. Are precise values of constants l…
> I can’t always wrap my mind around their analogies, but I always admire their effort.
I mean as a mathematician I also can't always wrap my head around their analogies, but I don't think that is always an issue on my part. I am somewhat of the belief that there is an inherent amount of complexity that can't really be diminished for a lot of these concepts, and "dumbing it down" too much may not be a good.
Re: Maze proof establishes a 'backbone' for statistical mechanics
#10I always marvel at Quanta’s skill in trying to translate these intricate mathematical and physical ideas for a broad audience. I can’t always wrap my mind around their analogies, but I always admire their effort. Their visualizations seemed especially helpful here. I am curious, though-they allude to this discovery relating to modeling phenomena like fluid perfusing porous materials. Are precise values of constants l…
I was coming here to say the same, but with less words: I fuckin love Quanta. I'm broke as heck, but I really hope people with more discretionary income are able to support them financially <3
> I'm broke as heck, but I really hope people with more discretionary income are able to support them financially
That made me smirk considering who launched and funds Quanta: the Simons Foundation.
James Simons is the founder of hedge fund: https://en.m.wikipedia.org/wiki/Renaissance_Technologies and also reponsible for: https://en.m.wikipedia.org/wiki/Chern%E2%80%93Simons_theory