On Mon, Jun 2, 2008 at 8:37 PM, Richard Loosemore <[EMAIL PROTECTED]> wrote: > > This misses the point I think. > > It all has to do with the mistake of *imposing* simplicity on something by > making a black-box model of it. > > For example, the Ptolemy model of planetary motion imposed a 'simple' model > of the solar system in which everything could be explained by a set of > nested epicycles. There would have been no need to use any other model > because in principle those epicycles could have been augmented to infinite > depth, to yield as good a fit to the data as you wanted. > > That is a black-box model of the solar system because it stuffs all the real > complexity inside a black box and then models the black box with a > simplistic formalism. If all you care about is getting a precise model of > planetary movement across the sky, this would be (and was!) the simplest > model anyone could ask for. > > But it was wrong. It was wrong because it obscured the real situation. The > real situation could not be understood without inventing a whole new type of > mathematics (calculus) and discovering a new law of nature (universal > gravitation). By any measure, that combination of calculus and gravitation > was a more "complicated" explanation. > > Anyone at the time who knew that Isaac Newton was trying to do could have > dismissed his efforts and said "Idiot! Planetary motion is simple. Ptolemy > explained it in a simple way. I use simplicity-preferring prior, so > epicycles are good enough for me." > > And if that same person insisted that there SHOULD be a simple model of > planetary motion (where "simple" meant 'as simple as epicycles") would have > been insisting that an explanation as complicated as calculus and > gravitation was in some sense bad or unparsimonious. > > In the long run, of course, gravity plus calculus was perceived as being > 'simple' and elegant in the extreme. But that is not the point, because > before it was discovered it could have been criticised as being far, far > more complicated than the epicycle explanation. >
I could argue that your example is a strawman, but it's not a very relevant issue. My point is that you have to have some prior, and prior that prefers simplicity is as good as any (or better, by exploiting implicit statistics-gathering during notation-building). If you do have some additional information that says that this particular distribution is not good enough, it should be updated. Probability expresses incompleteness of knowledge. To believe that you need something more complex, you need evidence. -- Vladimir Nesov [EMAIL PROTECTED] ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=103754539-40ed26 Powered by Listbox: http://www.listbox.com
