7 ms·
Simple Set Game Proof Stuns Mathematicians
- pnut 10y agoI did really well in school, and am a professional developer now, and my wife utterly destroys me at this game. She can find sets in real time as the cards are being dealt, while singing along with music, it's maddening.
- exacube 10y agothere are many forms of intelligence!
- treehau5 10y agoReminds me of Sir Ken Robinson's TED talk
- hinkley 10y agoOur friend is so jarringly good at Set and Scrabble that nobody will play with her anymore. She has to play people on the internet and they frequently disconnect mid-match.
- knodi123 10y ago> and they frequently disconnect mid-match. Speaking solely of scrabble, this happens pretty often regardless of skill level. ;-) I try to keep 3 games going at a time, but my last 5 have quit in the first three turns! And I'm using a matchmaking algorithm, so they're players of my approximate skill level too!
- Nadya 10y agoIf you want to lose friends and be disowned from your family - learn to play Monopoly by the actual rules and follow this strategy: http://imgur.com/a/vX3zm http://imgur.com/a/vX3zm I can confirm that it works and nobody wants to play Monopoly anymore. Instead we play more fun board games
- rconti 10y agoThat's awesome, thanks. Also introduced me to Georgism which I naturally relate to Piketty. Now I've got a lot of reading to do.
- tamana 10y agoThis strategy works when one person plays by the complicated rules and everyone else plays for fun. When you go pull out some BGG game, you'll have the same problem: the board game geek rules lawyer playing strategy and trouncing players who play for fun.
- chongli 10y agoThis is why it's better to go to a YouTube channel like Rahdo Runs Through [0] than BGG's ranking page. Rahdo plays with his wife and they prefer games with a lower interaction level than the typical BGG forum power user. This means strategies based on blocking the other players' access to the resources they need are not included or emphasized in the games they play. Though you will find exceptions, of course. The current number one game on BGG is Pandemic Legacy [1], a purely cooperative game. [0] https://youtube.com/user/rahdo https://youtube.com/user/rahdo [1] https://boardgamegeek.com/boardgame/161936/pandemic-legacy-season-1 https://boardgamegeek.com/boardgame/161936/pandemic-legacy-s...
- lmm 10y agoIn any competitive game the majority of players will be losing. So a good game is one that's fun even when you're losing.
- Nadya 10y agoTo be fair - Monopoly is a partially luck-based strategy game. And while having fun is certainly a big part of board games - so is winning and winning is pretty fun for most people. I see it as a split between "casuals" and "competitive" players. Competitive players find fun in attempting to win or giving it their best shot while casual players see winning as a bonus and just want to have fun. Which may or may not involve playing with the best strategies or giving it their best. I also agree entirely with lmm. The best games are games that are fun even when losing. If you can't have fun while losing (eg: Monopoly) then I don't consider it a good game.
- dhekir 10y agoCould it be somehow related to better peripheral vision? I met a woman once who could gather four-leaf clovers nearly instantly, at the same spot where me and my male friends had spent minutes searching. I've seen written in some places (but could not find a worthy source) that women might have better peripheral vision due to food gathering in prehistoric times, but this might just be some old sexist construct (if anyone knows a good source to confirm or refute this, please tell me).
- lettergram 10y agoI don't know if that's a male/female trait. I literally find four leaf clovers so often/fast that I don't even consciousnessly know how I do it. I'll just reach down and grab them. I'm a male btw
- tgb 10y agoAs a kid I would find them all the time. These days if I end up standing around a clover patch with nothing to do, I always look for them but never find them. I can't imagine I had the patience to look for them as a kid for very long, so I feel that my ability must have gone down hill OR that the patches I'm by now just don't have as many of them. I was always convinced that the ones at the house I grew up at had an abundance of four (or higher) leafed clovers and that patches at school, for example, were relatively poor. Perhaps that ability decline is just my current reluctance to get down on my hands and knees and leaf through them by hand.
- imglorp 10y agoI bet it's closer to the pattern matching part of the brain that counts objects at a glance. This is a different skill than counting with words.
- theoh 10y agoFrom https://en.m.wikipedia.org/wiki/Subitizing https://en.m.wikipedia.org/wiki/Subitizing "Subitizing is the rapid, accurate, and confident judgement of numbers performed for small numbers of items. [...] The accuracy, speed, and confidence with which observers make judgments of the number of items are critically dependent on the number of elements to be enumerated. Judgments made for displays composed of around one to four items are rapid, accurate and confident."
- matwood 10y agoSounds like she would be an amazing NFL QB if she can also throw a football :)
- cwmoo740 10y agoMy family is ultra-competitive and this used to be one of our go to games until my sister mastered it. My brother-in-law wrote an android game to help her practice and after about a month she was down to sub 1 minute clears. We had to give up the game after that.
- jackhack 10y agoSynesthesia? Perhaps her brain sees those sets and identifies them in such a way that it takes no conscious effort? A group might appear in a different color, or "taste" or feeling, for example... https://en.wikipedia.org/wiki/Synesthesia https://en.wikipedia.org/wiki/Synesthesia
- deleted 10y ago[deleted]
- pmichaud 10y agoMy wife also is amazing at this game and destroys me every time :)
- Agentlien 10y agoI'm also a professional software engineer who did very well in high school and at the university and, similarly, my wife consistently beats me at this type of games. Granted, my wife is well-educated and I believe she is smarter than I am, but it's like she immediately sees the solution while I see the input and have to work out the solution. I usually attribute this to my deficient color vision, since that's the property that usually trips me up. Alternatively, I've wondered if I'm focusing too hard and if the best approach might be reacting on instinct and relying on my subconscious to solve the problem before I'm consciously aware of having parsed the input.
- Xcelerate 10y ago> The paper soon set off a cascade of what Ellenberg called “math at Internet speed.” Within 10 days, Ellenberg and Dion Gijswijt, a mathematician at Delft University of Technology in the Netherlands, had each independently posted papers showing how to modify the argument to polish off the original cap set problem in just three pages. This is a very interesting trend I've noticed. I wanted to cite a few papers on arXiv in one of my own research papers recently, but my advisor commented that none of the articles had been peer reviewed (since arXiv is a preprint server). I told him that in the last year alone, six papers on arXiv follow a "research trail" (i.e. a paper is put on arXiv in May that builds on results from a February paper that builds on results from December, etc.), and that the most recent peer-reviewed article in a published journal is so far behind the state-of-the-art that completing my paper without any mention to the arXiv works would put me significantly behind the rest of the field. Of course, these papers all relate to math and computer science — whether a new algorithm or proof works is (usually) immediately evident upon implementation, and the papers on arXiv include the complete algorithm and often link to the author's code. Peer-reviewing their work yourself often takes no longer than a half hour or so (unlike, say, a research article in materials science, where a complete replication study could take over a year).
- Ankaios 10y agoThat has been common in physics for a long time, too. For hot new topics, the conversations are often happening through preprints rather than peer-reviewed articles. (The papers are usually eventually published in peer-reviewed journals, though.)
- MichaelBurge 10y agoBuilding on research seems like it's a form of peer review, especially in math where you'd need to understand the entire proof before making incremental improvements to it.
- abritinthebay 10y agoWhile this can be true it's also common to have "assuming X is true" where X is some very complicated hypothesis. We saw this with Fermat's Last Theorem and it was with a great sigh of relief that it was finally proven in the 90s. If the inverse was true then entire fields of Mathematics would have collapsed.
- jerf 10y agoFor those who check the comments first: Not clickbait. Title is literally accurate.
- Smaug123 10y agoI wouldn't say it literally stunned anyone, but it's certainly a very (figuratively) impressive result.
- shasta 10y agoAccording to Google, the average human male foot is 26.3 cm, or 0.86 feet. So I suppose I am literally 7 feet fall.
- joe_the_user 10y agoOh come on, The title and the article seem to be essentially accurate but are written in a breathless "we'll make this math stuff exciting, darn it" tone that some might like but which, as a math person, I find somewhat grating. I think science/math writing of twenty or forty years ago was still reasonably effective and with that, we could get-by with a headline such as "A impressive result in the combinatorics field that uses the 'polynomial method'" Edit: I appreciate that quantamagazine.org is doing a bunch of math articles. But we gotta admit it's injecting about every bit of "this is simply amaaaazing" rhetoric it can muster, which detracts somewhat from at least my enjoyment of it and actually it a harder to figure what's happening (from MA-level perspective).
- tgb 10y agoAs a grad student in math I read a lot of lifeless papers. Seeing the exact opposite is fun. I thought it was a good article. Why does math need to avoid breathlessness if we seem to embrace it with, say, a million breathless articles about Stephen Curry's latest game? It only seems bad because there's not a culture of excitement over math like there is for basketball, so it stands out. But if we want there to be such a culture, maybe we need to start by taking every bit of excitement we have and stretching it to the fullest.
- bdamm 10y agoWonderful piece; what I like is that I remember this game being taught to me by the mathematics professors at my school, and I enjoyed the game but didn't ask any deeper questions about the game, such as its mathematical properties. Now here I see this way of looking at the game, perhaps even the reason for its existence, and it's like rediscovering an old friend.
- ctdonath 10y agoiOS app of the referenced game: https://appsto.re/us/EXmoU.i https://appsto.re/us/EXmoU.i Physical version of the game is available, I suggest adding it to your collection.
- MontagFTB 10y agoVariants exist on the web as well, e.g., http://thebreretons.com/trifecta/ http://thebreretons.com/trifecta/
- henrik_w 10y agoNice to read about mathematics that involves Set! I found out about Set here on Hacker News several years ago, when I read Peter Norvig's blog post on the odds of not finding a set in the 12 cards [1]. I had never heard about the game before, but tried it and really liked it. The simplicity of the rules, the mathematical nature of it, and the fact that adults and kinds can play together makes it such a great game. I continued with the analysis of finding the odds of not set in each round of play, and had fun doing so. It seems very difficult to find an analytical solution (and quite beyond me), but simulation was a nice project that gave some good insights into how the odds vary over the rounds played [2]. [1] http://norvig.com/SET.html http://norvig.com/SET.html [2] https://henrikwarne.com/2011/09/30/set-probabilities-revisited/ https://henrikwarne.com/2011/09/30/set-probabilities-revisit...
- zem 10y agothe similar but easier game "spot it!" works better for playing with kids, i find. (i prefer it as an adult too - i thought i'd love set, but playing it feels more like work than fun to me.)
- dkurth 10y agoThere's some interesting analysis of the math behind Spot It! on stackoverflow [1]. That post mentions the Fano Plane, which, incidentally, I first read about in the book How Not to Be Wrong by Jordan Ellenberg, a mathematician quoted in the article about Set that started this thread. In the book, he uses the Fano Plane to explain how to pick numbers for a specific kind of lottery. [1] http://stackoverflow.com/questions/6240113/what-are-the-mathematical-computational-principles-behind-this-game http://stackoverflow.com/questions/6240113/what-are-the-math...
- zem 10y agothanks, that was a beautiful thread! also a really good diagram explaining the projective plane.
- tokenadult 10y agoA lot of the history of mathematics is summed up in the last paragraph of this very interesting article. "The fact that the cap set problem finally yielded to such a simple technique is humbling, Ellenberg said. 'It makes you wonder what else is actually easy.'" Mathematical progress comes about by some mathematician noticing a pattern that makes solving a formerly difficult problem more easy than solving it used to be. (For this purpose, innovations like place-value decimal numeral notation fit the preceding statement.) Of course the hard thing is being the first human being to figure out the easy way to solve the problem, and then to embed that understanding in a technique that other problem-solvers can learn. But the increasingly rapid collaboration among mathematicians these days (mentioned in a comment posted earlier) speeds the uptake of new techniques and makes more likely that new understanding will rapidly spread among mathematical problem-solvers.
- graycat 10y agoIIRC "Elegance in mathematics is directly proportional to what you can see in it and inversely proportional to the effort required to see it" -- S. Eilenberg
- OJFord 10y ago> a different design with four attributes — color (which can be red, purple or green), Was this game invented to annoy the colour-blind?
- schoen 10y agoIt was invented based on the file-marking symbols used by a geneticist for genetics research: http://www.setgame.com/founder-inventor http://www.setgame.com/founder-inventor https://web.archive.org/web/20130313190253/http://www.setgame.com/set/history.htm https://web.archive.org/web/20130313190253/http://www.setgam... You can play a variant of Set in a single color (which the rules suggest is easier -- but it's also more feasible for color-blind players).
- twic 10y agoAgain with the Ramsey theory! Every day, i'm reading about some amazing new result in Ramsey theory! It's like the microservices of discrete mathematics! Enough already!
- andrewflnr 10y agoI've been bumping into it a lot, too. I think it started with the ZFC-independent turing machines a while back.
- furyofantares 10y agoI don't understand the Alice imagery (nor the witch, not sure if that is also Alice imagery somehow) -- any ideas?
- MaysonL 10y agoThe witch appears to be the Red Queen. (Rotate her head about 135 degrees ccw and you get what is close to the symbol for a chess queen).
- dmd 10y agoFor your entertainment... http://3e.org/set http://3e.org/set
- delhanty 10y agoAnother good link concerned with this problem is from OEIS: https://oeis.org/A090245 https://oeis.org/A090245 "Maximum numbers of cards that would have no SET in an n-attribute version of the SET card game" The OEIS links appear to have been updated to reflect the recent breakthrough of Ellenberg and Gijswijt, including their unified paper arXiv:1605.09223 from May 30.
- aaron695 10y agoMaximal size of cap sets for games with up to six attributes - 2 4 9 20 45 112 https://oeis.org/A090245 https://oeis.org/A090245
- esturk 10y agoTo me the most exciting part is that this may lead to a faster fast matrix multiplication algorithm which will be huge. The current bound is O(n^~2.372). They could very feasibly hit the theoretical limit of O(n^2+e).
- syastrov 10y agoCan anyone explain how these polynomials are generated? Are the constants or exponents based on the card characteristics? And if it is not understood why they work, then how can we use them in a proof?
- deleted 10y ago[deleted]