1. I mostly don’t play chess anymore — it’s too addictive, and tends to take over your brain in a way I don’t like — but one habit I’ve retained is solving puzzles. It’s a mental warm-up, a way of occupying my brain when I don’t want to mindlessly scroll.
Really helpful analysis about decision making. Loved the chess ratio of falsifying vs. moving based on skill level.
Fits very well with and reinforces Daniel Kahneman's rubric of a "pre-mortem." i.e., before we go ahead with "whatever," let's discuss all the ways "whatever" could be a disaster.
This is lovely: “Newton made the mysterious banal.” It occurs to me it would work as a chiasmus. Newton made the mysterious banal and the banal mysterious. There’s so much more wonder in ordinary life when you know a little science as there must have been for those who knew some bible and theology.
Greatly enjoyed this. On the topic of Magnus and chess, here's another good video of Kramnik explaining what makes Carlsen so good (worth watching in full): https://youtu.be/KjRaDPhlyBQ.
Great article! While 'working memory' may be innate and fixed, I've observed that practice/repetition allow us to compress information more effectively (often subconsciously), and thus free up more of that space.
Very interesting read! As a fan of chess (but admittedly not that good of a player), I have often thought about the applicability of chess strategy to other spheres of life.
Chess, as a complex but finite game encourages calculating all the possible outcomes which is why computers easily beat grandmasters.
However, in infinite games, this way of evaluating a move can not only be suboptimal, but also completely opposite to what one would need in real life: experimenting and tinkering. Great post!
The number maximation problem just says "numbers," not integers. By the nature of the problem, we can probably assume *n* is an integer, but there's no reason to assume the same of a[1]...a[n].
My intuition was that the numbers a[n] should be close to e, and that proves to be correct:
Small but confusing typos in the sum = 1000 puzzle in the footnotes: you mean to say 3*333+1 instead of 3^333+1 etc. then for the product it is of course 3^333*1 but not 3^333+1 either.
fascinating piece, excited to check out those books. I'm really curious whether there's been a systematic study of how much "general problem-solving skills" improve with practice problems like chess puzzles and the larson book. I'm imagining two kinds of benefits to this kind of practice: (1) emotional/habit-formation, e.g. building patience & persistence, getting over the negative emotions around "being stuck", etc.; and (2) cognitive improvements, i.e. literally increasing the problem-solving capacity of your mind in some way. but #2 seems less obvious to me. I sometimes have a "what's the point" reaction to programming/math puzzles, and have wondered whether practice on them actually leads to being better at tackling real-life technical/research projects. (they can be enjoyed for their own sake, ofc.) curious what you think.
What a fun read. Something I’ve realized is that I don’t know how the world actually works (obviously). I’ve made hypothesis about people, projects, and other things and I’m proven wrong very very often. It’s not that I didn’t think they would work, it’s more like I knew they might not work but I did it regardless to see whether it would work.
And as expected, sometimes I’m wrong but when I’m right, it’s usually in a big way as obviously other people thought it was not possible or did not believe it the same way I did.
Lots of words to say that I’m very idealistic I prefer to be this way because through projects / my work I can reach that vision. But there are times/projects/ideas that require more nuanced thinking.
Two questions:
1. Have you come across any examples about great context-switching about being idealistic and super persistent and believing fully versus the person who falsifies every move?
2. Do you think it really doesn’t matter and it’s simply about picking something, believing with full certainty that you’ll do it, and being persistent?
Really helpful analysis about decision making. Loved the chess ratio of falsifying vs. moving based on skill level.
Fits very well with and reinforces Daniel Kahneman's rubric of a "pre-mortem." i.e., before we go ahead with "whatever," let's discuss all the ways "whatever" could be a disaster.
Amazing nuggets of wisdom. Reminded me of Peter Thiel's "You Are Not a Lottery Ticket" speech.
Really nice read. Made me want to get back into chess puzzles
> 8, 8, 8 -> 6, 4, 6, 4, 6, 4 -> 2, 4, 2, 4, 2, 4 -> 8, 8, 8...
That should read
8, 8, 8 -> 6, 4, 6, 4 -> 2, 4, 2, 4, 2, 4 -> 8, 8, 8...
This is lovely: “Newton made the mysterious banal.” It occurs to me it would work as a chiasmus. Newton made the mysterious banal and the banal mysterious. There’s so much more wonder in ordinary life when you know a little science as there must have been for those who knew some bible and theology.
Greatly enjoyed this. On the topic of Magnus and chess, here's another good video of Kramnik explaining what makes Carlsen so good (worth watching in full): https://youtu.be/KjRaDPhlyBQ.
Great article! While 'working memory' may be innate and fixed, I've observed that practice/repetition allow us to compress information more effectively (often subconsciously), and thus free up more of that space.
Very interesting read! As a fan of chess (but admittedly not that good of a player), I have often thought about the applicability of chess strategy to other spheres of life.
Chess, as a complex but finite game encourages calculating all the possible outcomes which is why computers easily beat grandmasters.
However, in infinite games, this way of evaluating a move can not only be suboptimal, but also completely opposite to what one would need in real life: experimenting and tinkering. Great post!
The number maximation problem just says "numbers," not integers. By the nature of the problem, we can probably assume *n* is an integer, but there's no reason to assume the same of a[1]...a[n].
My intuition was that the numbers a[n] should be close to e, and that proves to be correct:
(1000/369)^369 = 5.851e+159
(1000/368)^368 = 5.861e+159
(1000/367)^367 = 5.855e+159
1000/368 =~ 2.71739, which is indeed close to e.
In comparison, 3^332*2^2 is only 1.0146e+159.
Small but confusing typos in the sum = 1000 puzzle in the footnotes: you mean to say 3*333+1 instead of 3^333+1 etc. then for the product it is of course 3^333*1 but not 3^333+1 either.
fascinating piece, excited to check out those books. I'm really curious whether there's been a systematic study of how much "general problem-solving skills" improve with practice problems like chess puzzles and the larson book. I'm imagining two kinds of benefits to this kind of practice: (1) emotional/habit-formation, e.g. building patience & persistence, getting over the negative emotions around "being stuck", etc.; and (2) cognitive improvements, i.e. literally increasing the problem-solving capacity of your mind in some way. but #2 seems less obvious to me. I sometimes have a "what's the point" reaction to programming/math puzzles, and have wondered whether practice on them actually leads to being better at tackling real-life technical/research projects. (they can be enjoyed for their own sake, ofc.) curious what you think.
What a fun read. Something I’ve realized is that I don’t know how the world actually works (obviously). I’ve made hypothesis about people, projects, and other things and I’m proven wrong very very often. It’s not that I didn’t think they would work, it’s more like I knew they might not work but I did it regardless to see whether it would work.
And as expected, sometimes I’m wrong but when I’m right, it’s usually in a big way as obviously other people thought it was not possible or did not believe it the same way I did.
Lots of words to say that I’m very idealistic I prefer to be this way because through projects / my work I can reach that vision. But there are times/projects/ideas that require more nuanced thinking.
Two questions:
1. Have you come across any examples about great context-switching about being idealistic and super persistent and believing fully versus the person who falsifies every move?
2. Do you think it really doesn’t matter and it’s simply about picking something, believing with full certainty that you’ll do it, and being persistent?
Thanks, Nabeel.