By D. M. Burley, J. S. Griffith, J. H. E. Cohn and N. J. Hardiman (Auth.)
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Extra resources for Exploring University Mathematics. Lectures Given at Bedford College, London, Volume 2
Why was it such a shameful matter? The Greeks of that time, the sixth century before Christ, believed that all significant quantitative relations in nature could be described in terms of whole numbers (natural numbers). ), on which the different planets moved, were in whole-number ratios to each other, and that so were the lengths of the harp strings which sounded harmonious chords. ) It is worth noting that the Greeks' belief about the radii of planetary orbits was still held at the end of the sixteenth century by Kepler, one of the founders of modern astronomy.
Suppose that an observer O is at rest, as we have considered before, and at time / = 0 on his clock and observer O' passes him with a speed υ. Ο' moves off to a great distance and while he does so O sends signals to him and receives back reflections. At a great distance O' has the good fortune to meet another observer O" who is moving towards O with exactly the same speed as O' is moving away. At the moment when they are coincident these two observers check their time reckonings t = t«+ t t = 0 4 FIG.
There is no paradox (although this is often called the clock paradox) since it is evident that there is no symmetry between the twins. One of them has undergone a large acceleration. We can look at it from an economic point of view: it is immensely more expensive to send a man out to a distant planet than to provide his brother with an armchair in the laboratory. Moreover, the two brothers do not give similar descriptions of events. Let us imagine they are both billiard players. The stay-at-home brother finds that at all times during the experiment he has a most satisfactory game.
Exploring University Mathematics. Lectures Given at Bedford College, London, Volume 2 by D. M. Burley, J. S. Griffith, J. H. E. Cohn and N. J. Hardiman (Auth.)