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" "[Leibniz] has this ... "that nothing happens without a reason why it should be so..."
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician, and Professor Emeritus of Mathematics at Princeton University in New Jersey. He was active in the theory of s, , number theory, and . He also made contributions to many branches of , most notably the invention of the with . Born and raised in , Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. He died of complications from COVID-19 at age 82.
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[Y]ou've probably heard of the theory of relativity. ...Most of us have heard the assertion that you can't transmit information faster than the speed of light. Most of us... hear it on authority only. We don't really understand why not. ...The reason is ...there's no absolute notion of time. Time depends on which coordinate system you're using... on your frame of reference... As seen from one frame of reference, event A can be before event B and as seen from another frame of reference, event B came first. The world [universe] hasn't got a standard definition of time.
The general... problem... packing... in n-dimensional space. ...[T]here is nothing mysterious about n-dimensional space. A point in real n-dimensional space <math>\R^n</math> is... a string of real numbers<math>x = (x_1,x_2,x_3, ...,x_n)</math>.A sphere in <math>\R^n</math> with center <math>u = (u_1,u_2,u_3, ...,u_n)</math> and radius <math>\rho</math> consists of all points <math>x</math>... satisfying <math>(x_1-u_1)^2 + (x_2-u_2)^2+ ... +(x_n-u_n)^2 = \rho^2</math>. We can describe a sphere packing in <math>\R^n</math>... by specifying the centers <math>u</math> and the radius.
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