[HN Gopher] A Man Who Thought Too Fast (2020)
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       A Man Who Thought Too Fast (2020)
        
       Author : Anon84
       Score  : 48 points
       Date   : 2024-07-22 18:38 UTC (4 hours ago)
        
 (HTM) web link (www.newyorker.com)
 (TXT) w3m dump (www.newyorker.com)
        
       | woleium wrote:
       | needs (2020)
        
       | woleium wrote:
       | https://archive.is/zimBx
        
       | fallinditch wrote:
       | > Ramsey theory tells us, for instance, that among any six users
       | of Facebook there will always be either a trio of mutual friends
       | or a trio in which none are friends.
       | 
       | AKA Ramsey's Theory of the Bleedin' Obvious.
        
         | Animats wrote:
         | Also see Ramsey Pricing.[1] "Ramsey pricing (for a monopolist)
         | says to mark up most the goods with the least elastic (that is,
         | least price-sensitive) demand or supply." That's kind of
         | obvious.
         | 
         | [1] https://en.wikipedia.org/wiki/Ramsey_problem
        
         | valicord wrote:
         | Why is that obvious?
        
           | lcnPylGDnU4H9OF wrote:
           | If you try, you'll find that you can't think of a
           | configuration for which neither is true.
           | 
           | (Maybe it's not "obvious" but it's easy to arrive at that
           | conclusion after some thought.)
           | 
           | This comment from the other linked discussion describes what
           | was actually proved; the narrow case of facebook friends is
           | just a given example.
           | https://news.ycombinator.com/item?id=23028299
        
             | 01HNNWZ0MV43FF wrote:
             | Correct my math if I'm wrong
             | 
             | 6 people have 6 * (6 - 1) / 2 = 15 possible connections. If
             | you toggle those off and on you have about 2 ^ 15 = 32,768
             | combinations.
             | 
             | Some of those are surely redundant but I don't know stats
             | well enough to de-dupe them.
             | 
             | Either way I feel like it's higher than I can count in my
             | head while also doing anything else mathematical
        
               | bongodongobob wrote:
               | All that is completely irrelevant, you're
               | overcomplicating it. Each person has 1 of 2 states,
               | connected or not. If 4 are connected, 2 aren't, if 4
               | aren't 2 are, etc.
        
           | bongodongobob wrote:
           | Think about it and try to come up with a counterexample.
        
             | valicord wrote:
             | Just because you can't come up with a counterexample easily
             | doesn't make it obvious or even true. Of course in this
             | case it is indeed true, but I'm asking what makes it
             | obvious
        
               | bongodongobob wrote:
               | Because it's saying "you have 6 blocks, they can be
               | either green or blue. No matter what colors they are,
               | you'll always have either 3 blue or 3 green."
        
               | yongjik wrote:
               | You misunderstood the problem. That's not what it's
               | saying at all.
        
         | omnicognate wrote:
         | The proof of that particular case goes like this:
         | 
         | Pick one of the six users. Split the other 5 users into friends
         | and non-friends of the chosen user. There will either be at
         | least 3 friends or at least 3 non-friends of the chosen user.
         | If you can pick 3 friends of the chosen user then if any two of
         | them are friends they plus the original user form a trio of
         | mutual friends. If none of the 3 are friends then you have a
         | trio in which none are friends. Similarly, if you can pick 3
         | non-friends of the original user then either two of them are
         | non friends and you have a trio of non friends or all three are
         | friends, forming a trio of mutual friends.
         | 
         | It's easy to prove but I don't think I'd quite call it
         | "bleedin' obvious". Ramsey's theorem [1], of course, is more
         | general than that and isn't at all obvious (although it's still
         | not very hard to prove).
         | 
         | [1] https://en.m.wikipedia.org/wiki/Ramsey%27s_theorem
        
       | ChrisArchitect wrote:
       | (2020)
       | 
       | Discussion then: https://news.ycombinator.com/item?id=23011233
        
       | TMWNN wrote:
       | The headline reminds me of why Isaac Asimov was bad at chess
       | (start at "In 1994, Isaac Asimov's last autobiography"):
       | <http://billwall.phpwebhosting.com/articles/Asimov_chess.htm>
        
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