8/24/2023 0 Comments 4 d chessFor instance, we commonly talk of "steep learning curves," which technically correspond to easier learning (since you learn more of the subject matter in a shorter time). Often, when a popular understanding conflicts with an expert understanding, (and it's not obviously due to pure ignorance or a superstitious belief system), there is some sort of shallow semantic confusion. You have to go in the other direction: fewer levels, fewer steps ahead. In other words, thinking on more levels, more moves out, isn't even theoretically the right thing to do. The bigger problem is that this understanding of higher-dimensional games is at odds with our best theoretical understanding of higher-dimensional thinking, which suggests that higher dimensional games require lower -dimensional strategies. There are bigger problems with this idea of 4d strategy besides the obvious one that Trump doesn't look like he's thinking on more levels or more moves out (in fact, it is fairly obvious he's thinking on fewer levels and fewer moves out if that's acting, he deserves an Oscar). QAnon is the theory that a Master Persuader is executing a Master Plan too subtle for lower-dimensional mortals to comprehend. This is 4d chess in the sense portrayed by Bradley Cooper in the movie Limitless, where he takes an intelligence-enhancing drug and is able to think on more levels, more moves out, in pursuit of more complex intentions, and powered by deeper insights. This understanding of 4d chess - and what constitutes effective play within it - is why the ridiculous QAnon conspiracy theory has unironic adherents. In the popular and intuitive perception, the idea of higher-dimensional games goes along with higher-dimensional strategies. The idea of 4d chess turned into a popular meme with Trump's victory in 2016 (helped along by narratives like the breathless Master Persuader one peddled by Scott Adams). Let's unpack that and learn how to actually play figurative 4d chess.ĭeterministic versus randomized strategies to approximately calculate area For extra credit, you should try to make the opponent go for the explicit win. To prevail in higher-dimensional games, you not only have to keep things simple, you have to switch from playing to win to playing to not lose, ie just continuing the game. So the headline idea is that players with a certain kind of simpler strategy, and an objective of continuing the game rather than winning, have an advantage. To complete the story you need to add another idea: when you add more dimensions, playing to continue the game (infinite game thinking) gets easier than playing to win (finite game thinking). Yes, things get simpler in a certain sense when you add dimensions, but no that's not the whole story. Then I did a double take: wait, did that really take care of the idea? I went "Doh!" because that insight (which I'll explain in a minute) was one of my favorite ideas (and go-to hacks) from grad school, and I had failed to connect the dots. But I didn't really think about why I thought that until someone pointed out in a recent discussion somewhere (can't find it now) that an important insight from theoretical computer science suggests that 4d chess ought to be simpler than 2d. A few months ago I tweeted an offhand thought: 4d chess is boring.
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