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[L]attice packing... has the properties that 0 is a center and... if there are spheres with centers <math>u</math> and <math>v</math> then there are … - John Horton Conway
" "[L]attice packing... has the properties that 0 is a center and... if there are spheres with centers <math>u</math> and <math>v</math> then there are spheres with centers <math>u + v</math> and <math>u - v</math>... [i.e.,] the sets of centers forms an . In crystallography these... are... called s... We can find... in general <math>n</math> centers <math>v_1,v_2, ...,v_n</math> for an n-dimensional lattice... such that the set of all centers consists of the sums <math>\sum k_i v_i</math> where <math>k_i</math> are s.
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About John Horton Conway
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.
Also Known As
Alternative Names:
John H. Conway
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JHC
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John Conway
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Conway
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Additional quotes by John Horton Conway
Laplace... wrote Mécanique céleste discussing the motion of the planets. ...[O]ne ...reason why ...determinacy got its ...impetus from the development of science, was that Newton's theory of gravitation ...was entirely deterministic. It left no room for freedom. ...Laplace, who did a lot of work on Newtonian ...theory says ...An intellect ...[or] intelligence, which knew ...where all the particles were at some moment and how fast they were moving, and so on, that every single thing could be known to that intelligence, provided a ...good calculator. ...It could reason out exactly what was going to happen in the future. ...It's the strongest ...assertion of determinism in the scientific literature. I don't believe it for one moment..!
[S]uppose I had a twin brother... [M]y sisters would have had a much better chance... [T]hey could... interrogate us separately... Then we can't change the object. ...Without transmitting information ...we couldn't win... [T]hat's what manages to happen in the particle case. ...[T]his ...Simon also thought of a long time ago.... but he didn't... deduce the .
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