Merely knowing that a different, better way is possible, causes the breakthrough to manifest into existence. Our beliefs determine our outcomes.
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One of my favorite Kaggle facts: after a long leaderboard stagnation period for a competition, seeing one team make a sudden breakthrough will often cause multiple independent teams to quickly reproduce the same breakthrough -- with no knowledge of how the first team did it.
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To discover something, you must first expect to find it.
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This reminds me of the story of the first person to run a 4 minute mile, Roger Bannister. As soon as it was publicized that he had achieved that record through meticulous training, other athletes started to as well- even though they hadn’t changed anything about their training.
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Yeah that's a good one! It's pretty remarkable how motivating it is to have conviction that something is attainable...
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Akin to chess puzzles: much easier than a real game as you know there exists a best move and search for it until you find it.
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Good analogy. Although there are a lot of times at least in blitz where I know my position is better either due to "feel" or my evaluation of the position (confirmed true after by engine) and end up not playing a good continuation.
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Interesting. I've observed this too in math and programming competitions. This kinda makes sense if we think of knowledge as a graph of ideas and the competitors as random-walk agents on that graph. Eventually, a bunch of them would end up at the same place at the same time
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This is interesting. It makes sense through the lens of optimization theory— merely knowing that you’re stuck in a sub-optimal local minimum would compel you to climb out in search of a better solution.
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