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g comments on Artificial Addition - Less Wrong

36 Post author: Eliezer_Yudkowsky 20 November 2007 07:58AM

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Comment author: g 22 November 2007 02:51:14AM 0 points [-]

Anonymous (re Planck scales etc.), sure you can truncate your representations of lengths at the Planck length, and likewise for your representations of times, but this doesn't simplify your *number* system unless you have acceptable ways of truncating all the other numbers you need to use. And, at present, we don't. Sure, maybe really the universe is best considered as some sort of discrete network with some funky structure on it, but that doesn't give us any way of simplifying (or making more appropriate) our mathematics until we know just what sort of discrete network with what funky structure. (And I think every sketch-of-a-theory we currently have along those lines still uses continuously varying quantities as quantum "amplitudes", too.)

James (re mathematics and infinite sets and suchlike), it seems unfair to criticize something as being handwavy when you demonstrably don't remember it clearly; how do you know that the vagueness is in the thing itself rather than your recollection? There is a perfectly clear and simple definition of what a sum like 1 + 9/10 + 9/100 + ... means (which, btw, is surely enough to call it "a sensible theoretical concept"), and what that particular one means is 2. If you have a different definition, or a different way of doing mathematics, that you like better, then feel free to adopt it and do mathematics that way; if you end up with a theory at least as coherent, useful and elegant as the usual one then perhaps it'll catch on.

Anonymous (re humility, reductionism, etc.): I think your comment consisted mostly of applause lights. Science is demonstrably pretty good at questioning fundamental assumptions (consider, say, heliocentricity, relativity, quantum mechanics, continental drift); what evidence have you that more effort should go into questioning them than currently does? (Clearly some should, and does. Clearly much effort spent that way is wasted, and produces pseudoscience or merely frustration. The question is how to apportion the effort.)