**extratricky**17

ExtraTricky - A Rant About AlphaGo Discussions

february 2017 by nhaliday

The most important idea to be able to analyze endgames is the idea of adding two games together. The sum of two games is another game where on your turn you pick one of the two games to play in. So you could imagine a game of "chess plus checkers" where each turn is either a turn on the chess board or a turn on the checkers board. Say your opponent makes a move on the chess board. Now you have a choice: do you want to respond to that move also on the chess board, or is it better to take a turn on the checkers board and accept the potential loss of allowing two consecutive chess moves?

If you were to actually add a game of chess and a game of checkers, you'd have to also determine a way to say who wins. I'm going to conveniently avoid talking about that for general games, because for Go positions the answer is simple: add up the points from each game. So you could imagine a game of "Go plus Go" where you're playing simultaneously on two boards, and on your turn you pick one of the boards to play on. At the end of the game, instead of counting territory from just one board, you count it from both.

As it turns out, when a Go game reaches the final stages, the board is typically partitioned into small areas that don't interact with each other. In these cases, even though these sections exist on the same board, you can think of them being entirely separate games being added together. Once we have that, there's still the question: how do you determine which section to play in?

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If you were to actually add a game of chess and a game of checkers, you'd have to also determine a way to say who wins. I'm going to conveniently avoid talking about that for general games, because for Go positions the answer is simple: add up the points from each game. So you could imagine a game of "Go plus Go" where you're playing simultaneously on two boards, and on your turn you pick one of the boards to play on. At the end of the game, instead of counting territory from just one board, you count it from both.

As it turns out, when a Go game reaches the final stages, the board is typically partitioned into small areas that don't interact with each other. In these cases, even though these sections exist on the same board, you can think of them being entirely separate games being added together. Once we have that, there's still the question: how do you determine which section to play in?

february 2017 by nhaliday

ExtraTricky - On Taking Notes in Math Class

december 2016 by nhaliday

Perhaps this fictional story convinced you, and perhaps it didn't. I'm not going to claim I have proof that notes are detrimental to every student, or even on average. I don't know about any research in that area. But if you want to try out not taking notes for yourself, here are my recommendations for how to do it.

- During lecture, try to find the main new ideas being presented. If something is just algebraic manipulation, trust yourself to be able to do that on the homework if you need to.

- If the course doesn't have written materials available, do write down definitions. Keep these very short. Most definitions are only a single sentence. If you're writing more than that you're probably writing something that's not included in the definition.

- Be ready to struggle with the homework. Being stuck on a problem for hours is extremely common for mathematicians, even though it doesn't always seem that way. On one of my problem sets at MIT I was stuck near the end of a solution for around ten hours before realizing that it could be finished in a reasonably simple manner.

- When you get your homework back, make sure you have a complete and correct solution. If it's the one you turned in, great. If the teacher posts homework solutions, read through and keep that. Those solutions are now your notes.

- When exam time comes, go through those homework problems as study materials. If you end up getting stuck on one of those problems again, chances are it'll be in the same place you got stuck the first time, and your mind will connect the dots.

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- During lecture, try to find the main new ideas being presented. If something is just algebraic manipulation, trust yourself to be able to do that on the homework if you need to.

- If the course doesn't have written materials available, do write down definitions. Keep these very short. Most definitions are only a single sentence. If you're writing more than that you're probably writing something that's not included in the definition.

- Be ready to struggle with the homework. Being stuck on a problem for hours is extremely common for mathematicians, even though it doesn't always seem that way. On one of my problem sets at MIT I was stuck near the end of a solution for around ten hours before realizing that it could be finished in a reasonably simple manner.

- When you get your homework back, make sure you have a complete and correct solution. If it's the one you turned in, great. If the teacher posts homework solutions, read through and keep that. Those solutions are now your notes.

- When exam time comes, go through those homework problems as study materials. If you end up getting stuck on one of those problems again, chances are it'll be in the same place you got stuck the first time, and your mind will connect the dots.

december 2016 by nhaliday

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