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Simple Set Game Proof Stuns Mathematicians

quantamagazine.org

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Re: Simple Set Game Proof Stuns Mathematicians

#61

Post by tamana »

Nadya wrote: post #33
hinkley wrote: post #6

Earlier quoted context omitted.

Our 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.

If 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 I can confirm that it works and nobody wants to play Monopoly anymore. Instead we play more fun board games

This 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.

Re: Simple Set Game Proof Stuns Mathematicians

#63

Post by vintermann »

Xcelerate wrote: post #3

> 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 arX…

Yup. An example from machine learning: This paper, "Weighted Residuals for Very Deep Networks"

https://arxiv.org/abs/1605.08831

from May 28, cites this paper, "Wide Residual Networks"

https://arxiv.org/abs/1605.07146

from May 23. Less than a week between them! And it's with good reason too, because they want to compare with state of the art on a certain problem/dataset, and that improved five days ago.

Both of these papers are about very basic advances, in a sense: If you have a residual network implementation lying around (and there are plenty of open source ones), it's trivial to implement the improvements they propose. So it's not as crazy to cite a 5 day old paper as it seems.

Re: Simple Set Game Proof Stuns Mathematicians

#64

Post by chongli »

tamana wrote: post #61
Nadya wrote: post #33

Earlier quoted context omitted.

If 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 I can confirm that it works and nobody wants to play Monopoly anymore. Instead we play more fun board games

This 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.

This 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

[1] https://boardgamegeek.com/boardgame/161936/pandemic-legacy-s...

Re: Simple Set Game Proof Stuns Mathematicians

#66

Post by Natanael_L »

tamana wrote: post #59
btilly wrote: post #47

Earlier quoted context omitted.

The consequence is that a whole body of work winds up coming with an asterisk until people figure out what they can and can't trust. Papers may be looked at for inspiration, but won't be quoted for results. Eventually some of it gets proved properly, and the rest is abandoned. After that the older papers become mere historical curiosities. A reasonably recent example of this is the https://en.wikipedia.org/wiki/Itali…

But when the results are useless anyway, it doesn't really matter if they are right or wrong...they just may be speculative of some alternate universe, or may still contain ideas that are applicable elsewhere.

Prime numbers used to be useless when first researched (edit: during the previous two centuries, when their properties was studied). We don't always know in advance what will turn up useful.

Re: Simple Set Game Proof Stuns Mathematicians

#67

Post by A1kmm »

Xcelerate wrote: post #3

> 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 arX…

The situation could be even better if the proposition and proof could be written in a machine verifiable form using a proof assistant like Coq.

Potentially you could have a section in a maths journal which 'papers' (in the form of computer readable propositions and proofs) are immediately reviewed for correctness by a computer. Post-publication, humans may then assess the impact / significance by voting (perhaps with propositions from significant conjectures potentially configured to instantly go to the top of the significance rankings).

Re: Simple Set Game Proof Stuns Mathematicians

#68

Post by Agentlien »

pnut wrote: post #2

I 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.

I'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.

Re: Simple Set Game Proof Stuns Mathematicians

#69

Post by kragen »

Natanael_L wrote: post #66
tamana wrote: post #59

Earlier quoted context omitted.

But when the results are useless anyway, it doesn't really matter if they are right or wrong...they just may be speculative of some alternate universe, or may still contain ideas that are applicable elsewhere.

Prime numbers used to be useless when first researched (edit: during the previous two centuries, when their properties was studied). We don't always know in advance what will turn up useful.

You say, "Prime numbers used to be useless when first researched," but when the Middle-Kingdom Egyptians were doing their initial research on prime numbers, they needed them for the algorithms they used to calculate with fractions. These were used in the Rhind Papyrus to calculate things like the volumes of granaries. You could hardly have picked a worse example.

Re: Simple Set Game Proof Stuns Mathematicians

#70

Post by kragen »

tamana wrote: post #60
function_seven wrote: post #50

Earlier quoted context omitted.

I like how you introduce a correlating attribute in the beginning of your comment, get me thinking about the relationship between musical ability and set-identifying ability, then clobber whatever hypothesis I was putting together just as fast with the confounding "field trips" variable. Nice work :)

But why is set so popular on band trips, but not football trips?

Band nerds aren't retards.
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