Author: Walter Koroljow
Date: 04:55:59 12/13/99
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On December 13, 1999 at 05:59:39, Masciulli Gianluigi wrote: >On December 12, 1999 at 11:41:54, Enrique Irazoqui wrote: > >>Both strings are concentric, so no pulling up. The distance from string A to >>string B is constant at every point, with A being exactly the equator of Earth, >>40 million meters. So you have two concentric circles, one of 40 million meters >>in length and the other of 40 million and 1 meter. The question was what is the >>distance between A and B. Gianluigi gave the right answer, but he had to >>calculate it. "Intuitively", people say that this distance is near zero. And >>Wittgentein went fishing... :) >> >I'll not calculate but i'll give you more: >to be fair I have to say that I knew a very similar story so for me was easy ;-) > >I already knew that the distance is non made by the lenght but by the differece >of length: the lenght of the first circle symply don't matter. >there is no trick. >basically you can do the same on moon, on sun (or maybe around your head;-) >and the answer will be the same. >wittgentein was right ... this is not intuitive but is right!! > >ciao > >gianluigi But intuition changes. I first came across the concentric circle problem in relation to distances run on a track. After that, the answer _became_ a part of my intuition. This happens all the time in mathematics. As one learns more, the abstract becomes concrete and "intuitive". I have often heard people say, e.g., "...consider a concrete example, such as a complex vector space in N dimensions...". An interesting example of developing intuition was a program which interactively allowed people to manipulate an object in four dimensions (you could see a two dimensional projection of the object on a screen). People became proficient in this very non-intuitive manipulation. I think we would have to say it became intuitive for them. I imagine that chess program issues will also become more intuitive as we learn more. Cheers, Walter
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