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RobinZ comments on Bayes' Theorem Illustrated (My Way) - Less Wrong

126 Post author: komponisto 03 June 2010 04:40AM

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Comment author: RobinZ 07 June 2010 04:03:25PM *  1 point [-]

That said, I started to watch a video series lately [...] and was struck when he said that to roughly figure out the doubling time you simply divide 70 by the percentage growth rate. I went to check it myself if it works and later looked it up. Well, it's NOT obvious why this is the case, at least not for me. Not even now that I have read up on the mathematical strict formula.

Well, it's an approximation, that's all. Pi is approximately equal to 355/113 - yeah, there's good mathematical reasons for choosing that particular fraction as an approximation, but the accuracy justifies itself. [edited sentence:] You only need one real revelation to not worry about how true Td = 70/r is: that the doubling time is a smooth line - there's no jaggedy peaks randomly in the middle. After that, you can just look how good the fit is and say, "yeah, that works for 0.1 < r < 20 for the accuracy I need".