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thomblake comments on Bayes' Theorem Illustrated (My Way) - Less Wrong
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It might help to read the sequences, or just read Jaynes. In particular, one of the central ideas of the LW approach to rationality is that when one encounters new evidence one should update one's belief structure based on this new evidence and your estimates using Bayes' theorem. Roughly speaking, this is in contrast to what is sometimes described as "traditional rationalism" which doesn't emphasize updating on each piece of evidence but rather on updating after one has a lot of clearly relevant evidence.
Edit: Recommendation of Map-Territory sequence seems incorrect. Which sequence is the one to recommend here?
Updating your belief based on different pieces of evidence is useful, but (and its a big but) just believing strange things based on imcomplete evidence is bad. Also, this neglects the fact of time. If you had an infinite amount of time to analyze every possible scenario, you could get away with this, but otherwise you have to just make quick assumptions. Then, instead of testing wether these assumptions are correct, you just go with them wherever it takes you. If only you could "learn how to learn" and use the Bayesian method on different methods of learning; eg, test out different heuristics and see which ones give the best results. In the end, you find humans already do this to some extent and "traditional rationalism" and science is based off of the end result of this method. Is this making any sense? Sure, its useful in some abstract sense and on various math problems, but you can't program a computer this way, nor can you live your life trying to compute statistics like this in your head.
Other than that, I can see different places where this would be useful.
And so it is written, "Even if you cannot do the math, knowing that the math exists tells you that the dance step is precise and has no room in it for your whims."