A Man Who Thought Too Fast (2020) | Hacker News Reader

A Man Who Thought Too Fast (2020)

newyorker.com

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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>

> The conclusion that I finally came to (right or wrong) was that I was unwilling to study the chessboard and weigh the consequences of each possible move I might make. Even people who couldn't see complex patterns might at least penetrate two or three moves ahead, but not I. I moved entirely on impulse, if not at random, and could not make myself do anything else. That meant I would almost certainly lose.

> And again - why? To me, it seems obvious. I was spoiled by my ability to understand instantly, my ability to recall instantly. I expected to see things at once and I refused to accept a situation in which that was not possible.

Interesting. I was also fairly bad at chess as a kid, and my self-diagnosis was similar. I found "checking" all the possible moves too tedious, so I just did the first one that looked promising, to terrible effect.

I've tried to play a little as an adult, and now I have more patience, but that means I find chess too stressful! I don't want to go until I'm fairly sure I have a good move, but I still can't quite "check" all the possible moves, so I sweat the whole time and don't enjoy playing.

Thanks for sharing, I have the same experience with chess, and have never liked it for the same reasons. There's no mediocre version of chess that you can do instinctively, and I don't really like to do tedious and repetitive mental work when playing games.

I just suck at chess, and have given it up, as it's something that's not for me. I can play some decent poker though (not really great, just better than chess).

I think “puzzle storms” on lichess can be considered a way of fiddling with chess instinctively. I found it also helps with not giving pieces for free when playing full games and also seeing the blunders your opponent makes way faster

In real life, you've always got to go with your gut. But in chess you have perfect prescience: there is a very limited set of parameters, and things can only occur within them. Its good training for real life, since you can have both foresight and risk, and for me at least I always have a multitude of different plans about both my near and far future sitting somewhere in the back of my head, switching between and adjusting them depending on the circumstances that arise.

There's a good arguement that backgammon and bridge are better training for real life because of the mixture of strategy and randomness.

I would argue strongly for poker. No limit hold 'em poker is a fantastic game!

My experience learning the game, alongside my wife, who we learned later in life is an exemplary player! (The story behind that involves a period of high work travel for me, a Playstation, and Doyls Room online poker and a $2K seed bankroll...)

...my experience is this game will, or can if you allow it, change how you think. Maybe the more accurate thing to say would be the game opens up more kinds of thought.

If you're interested in games that teach real-world epistemic skills, Jane Street just publicly released Figgie: https://www.lesswrong.com/posts/PypgeCxFHLzmBENK4/poker-is-a...

Poker has strategy, randomness and asymmetric info.

I also agree chess is tedious. I feel the same way about Sudoku.

While I enjoy coming up with algorithms as part of my living, I take little pleasure in executing them myself (beyond testing and a few thought exercises to find the right solution).

But as a counterpoint, I thoroughly enjoy games where I build something based on resources I myself have aquired. Whether it's voxels or virtual scrap piles, it is gratifying to earn what I build with.

Interesting experience.

I love sudokus, I like speed running sudokus, I try to see how fast and accurately I can recognise certain patterns.

But then, /factorio/... I love the idea of factorio, I love watching factorio gameplay, but whenever I try to play it myself, I get overwhelmed immediately. My perfectionist brain refuses to immediately have a perfect factory and so I just shut down the computer.

> I've tried to play a little as an adult, and now I have more patience, but that means I find chess too stressful! I don't want to go until I'm fairly sure I have a good move, but I still can't quite "check" all the possible moves, so I sweat the whole time and don't enjoy playing.

Do you use a timer? I feel like a moderate per-turn timer should prevent you from reaching the "can't quite check everything" zone, while still encouraging you to evaluate several positions.

I feel the same way. I don't have the patience to see the next move. however I've noticed that I do quite well in Othello by intuitive moves, beating people who strategise and think deeply about their next move. it's frustrating for them when I declare that I just picked the move that felt right! intuition has its place in games, there is certainly some form of intelligence there, but in chess it probably only works when you have a mind like Fischer or Carlsen.

The faculty of re-solution is possibly much invigorated by mathematical study, and especially by that highest branch of it which, unjustly, and merely on account of its retrograde operations, has been called, as if par excellence, analysis. Yet to calculate is not in itself to analyse. A chess-player, for example, does the one without effort at the other. It follows that the game of chess, in its effects upon mental character, is greatly misunderstood. I am not now writing a treatise, but simply prefacing a somewhat peculiar narrative by observations very much at random; I will, therefore, take occasion to assert that the higher powers of the reflective intellect are more decidedly and more usefully tasked by the unostentatious game of draughts than by all the elaborate frivolity of chess. In this latter, where the pieces have different and bizarre motions, with various and variable values, what is only complex is mistaken (a not unusual error) for what is profound. The attention is here called powerfully into play. If it flag for an instant, an oversight is committed, resulting in injury or defeat. The possible moves being not only manifold but involute, the chances of such oversights are multiplied; and in nine cases out of ten it is the more concentrative rather than the more acute player who conquers. In draughts, on the contrary, where the moves are unique and have but little variation, the probabilities of inadvertence are diminished, and the mere attention being left comparatively unemployed, what advantages are obtained by either party are obtained by superior acumen.

-- From "The Murders in the Rue Morgue" by Edgar Allan Poe. Read it at https://poestories.com/read/murders

There are principles that help when playing chess as I learned watching some YouTubers:

- Develop your minor pieces early in the game (bishop/knight)

- Castle

- Connect the rooks

- Put pieces in a way they are protected by other pieces, so you don't blunder.

- Don't put out queen to early or make heroic attacks with 2 pieces at the beginning of the game.

- Don't start pushing pawns like crazy before you've developed. Especially pawns in front of the king while board is still crowded by minor/major pieces. I think I've only lost a single game where opponent pushed pawns like crazy while leaving rest of the army behind.

- Watch out for ways how opponent can check you and do harm.

- See what forcing moves you have. Look for 1. checks and 2. captures.

- You don't always have to defend piece that is being attack - you can be more aggressive and make a thread yourself by advancing some other piece.

- To take is a mistake - you don't always want to take opponents pawn or piece as it can help develop them/put another piece on a more active square. Or it may help open up an open file for a rook, tldr makes opponent pieces more active (active means pieces cover more squares). You may sometimes benefit of enemy capturing your piece first and you recapture by leaving some file closed/blocked by pawn.

- Usually there is little calculation needed in the opening. GM Igor Smirnov also mentions that he doesn't always calculate. And he doesn't calculate what happens when opponent pieces go backwards, usually calculates what is the biggest threat opponent can make. And it can be beneficial to calculate just 2-3 moves ahead.

- Try to see what your opponent wants to do

- You must have some kind of a plan - why do you want to put piece on that square? Not just put it there because you have to move and on the next move that same piece is being threatened with, say, no defenders.

- Jumping in with the knight deep into enemy territory without a way to back out may cost you a knight.

- Putting a piece on a square that opponent can kick you out on next move maybe just looses tempo if the goal is not to reposition your piece or there is another thought to it.

Anyways, knowing all of this I'm only 800 rated. I blunder alot. Or I have a great advantage until I make it to the endgame where I loose. I also come to realization that one must remember / know lot of stuff to be good at chess. I thought my logical thinking is strong, but yeah, I don't enjoy the skillset needed to become good at chess.

When I was studying about memory and learning, the example of chess masters came up when talking of chunking. The idea that bigger problems can be reduced to a number of chunks that can be understood and recalled instantly. So chess master might not be so much about being able to see x move ahead, but being able to look at the current board state and recall what pattern it is fitting into.

You don't play by checking all possible moves on every turn like a machine. It's mostly intuition based, but it takes a while before it develops.

Also there are levels to this game, the range of players that is fun to play against is kind of narrow, outside of that you either obliterate or get obliterated.

This is how I played chess when I was a kid. Scan for all the possible next moves, all replies, do some pruning, repeat etc. I think my max depth was probably around 12 moves into the future or so.

But now, thinking about it as an adult and it terms of AI, why are we using our conscious mind to calculate when we have a whole brain in place to do the work for us? You instead want to train your brain to recognize positions, opportunities and let it empirically calculate for you in the background.

Looking at how chess masters play they seem to employ both these.

Same story but although I have more patience now I still don't have lots for chess.

For this reason I don't excel nor enjoy long games but I found quick games, bullet and blitz, pretty fun. You end up moving on instinct most of the time but calculating lines when things look sketchy.

https://archive.is/zimBx

Question, Do they have to measure a persons brain speed? I wonder what the bell curve is on society, there has to be some very fast outliers.

Such a multidimensional question, I think there's probably little point in being able to boil brain speed down to one number (or even small set of numbers). There's so many parts that all combine: The rate of propagation of activation-potentials along neural dendrites (well known that caffeine speeds this up, until your brain adapts to make it 'normal speed' again by extra myelination!), there's stuff like the frequency of brainwaves, which surely must have some effect.. and then the conscious-perception of the passage of time could kinda feed in too, not to mention memory-speed or speed at tasks that have been very highly practiced. Very interesting to think about though, thanks!

Also, to follow up, the question is speed in what domain?

Speed reading, speed computation, speed memorization, there are many domains of the mind in which the question of speed could be applied.

> caffeine speeds this up, until your brain adapts to make it 'normal speed' again by extra myelination

Any more info or source on this? Thanks.

(2020)

Discussion then: https://news.ycombinator.com/item?id=23011233

needs (2020)

> 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.

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

Why is that obvious?

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

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

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.

No, each edge in the graph has 2 states. There are 15 edges between the 6 people.

But the edge states don't matter, the node states do. They're either connected friends or they aren't. What's the third state?

2 groups of 3 mutual friends is a different graph than 3 pairs of friends

No, the connections are what matters. A may be friends with both B and C, but that doesn't mean that B is necessarily friends with C.

I understand that. That's the encoding of being "connected".

Where did you get "connected" from? We're talking about whether they are "a trio of mutual friends" or not; that requires them all to be friends with each other, not merely "connected".

In this encoding of the problem, the graph is fully connected, the edges indicate the state of a connection (ie. friendship) between 2 users, and the goal is to check that there is either a chain of 2 "connected" edges (A to B and B to C for any A,B,C in the nodes) or 2 "disconnected" edges, which indeed isn't easy to do the tedious way.

The crucial property here is the symmetry between connected and disconnected edges: for any given configuration, if it's difficult to check it on one hand, then it should be easy to do it on the other.

The simple version: Among 6 people, to avoid a trio of friends, no sub-group can be 3 or more. Maximize the size of the sub-groups to minimize the number of non-friends: 2 + 2 + 2. One from each sub-group is a trio of non friends.

So either you have enough sub-groups to create a trio of non-friends, or there's a sub-group large enough to create a trio of friends.

Think about it and try to come up with a counterexample.

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

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."

You misunderstood the problem. That's not what it's saying at all.

How isn't it? There's no way to have 3 connected friends and 4 unconnected friends.

You can have all 6 connected and still be in either category.

For example, 6 friends in a loop can be divided into even and odd trios, where each trio has no direct friend connections within it.

But six people in two separate triangles fall into the other category, with two trios of mutual friends.

Notice how both of these cases give each person 2 friends. It's not nearly as simple as assigning everyone a color at the start.

Another thing to think about: If you have a triangle of 3, and a line of 3, then you can find 3 mutual friends and three mutual non-friends. How would you use colors to differentiate this situation from the two-triangles situation?

No, that's what I'm saying. You're either a member of the 3-group or you're not. It clearly requires 3 members, so...

It's proving the 3 nodes with no direct connections to each other that is the complicated part.

It's not "you have a group of 3 or you don't".

You can have all six people tangled up in lots of different combinations, so how do you prove there's a way to pick three that only connect indirectly?

You could have one green and five blue

Uh, exactly. You've got 3 blue in that 5.

Sorry I was thinking too fast

Just so you know: you've completely misunderstood the statement.

I think it’s more accurate as: at least 3 which are blue or at least 3 which aren’t blue. Which is obvious even if perhaps the statement at the top of the thread is not.

You have not understood the statement.

In that case, would you mind writing a more enlightening comment?

It's probably most clearly stated in the original post, but the point is you would either be able to find three people who are all friends with the other two, or you would be able to find three friends who are not friends with any of the others. The non-obviousness is due to the fact that someone may have only one friend, or someone may have two friends but those two would not be friends with each other, so I wouldn't call it blindingly obvious that there would always be a subset with one of these properties (I think the main intuition that is useful is that if you have a sparsely connected graph of friends, it's easy to find a group that aren't friends at all, and if you have a densely connected graph then you can find a group that are mutual friends. The theorem is then proving that there's no middle ground: it's either dense enough a mutual group must exist or sparse enough a non-friend group must exist.)

In your version, the color of a vertex is independent of other vertices. The real problem is about entirely about connections to other vertices. The latter cannot be reduced to the former.

Does this formulation work?

You have 6 wooden blocks, each can be 1 of 6 colors. There will always be either (A) 3 blocks of the same color, or (B) 3 blocks of different colors.

Iterating through all possibilities:

6 of 1 color - case A

5 of 1 color, 1 of another - case A

4 of 1 color, 2 of another - case A

4 of 1 color, 1 of another, 1 of yet another - case A and B

3 of 1 color, 3 of another - case A

3 of 1 color, 2 of another, 1 of yet another - case A and B

3 of 1 color, 1 of another, 1 of yet another, 1 of another another - case A and B

2 of 1 color, 2 of another, 2 of yet another - case B

2 of 1 color, 2 of another, 1 of yet another, 1 of another another - case B

2 of 1 color, 1 of another, 1 of yet another, 1 of another another, 1 of another another another - case B

all colors different - case B

Your formulation is not equivalent. The actual Ramsey theory formulation is something more like...you need to color, either red or blue, all of the edges of a fully connected graph of 6 elements (there are 15 such edges). No matter which coloring you choose (there are 2^15 of these), there will always be a "triangle" between three nodes where the entire triangle is either fully red, or fully blue. If you were to instead restrict yourself to a graph with 5 elements instead of 6, it's possible[1] to color the edges so there's no triangle where all the elements are the same.

As an exercise, try repeating your same argument for 5 colors/blocks, and note that it still works, when it shouldn't.

[1] - https://commons.wikimedia.org/wiki/File:RamseyTheory_K5_no_m...

Let me see if I can clear up your misunderstanding: it is totally possible to have 5 people without having a group of 3 which are all friends nor a group of 3 none of which are friends. Draw a fully connected pentagon with all the outer edges one color and the inner edges another color. There is no triangle that is all the same color.

But with 6 nodes you must have a triangle that is all the same color. It is the edges that are colored, not the nodes.

Well it’s written down right there, isn’t it? Who’d have written it down if it wasn’t true? Obviously nobody would do such a thing!

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

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