[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 .
English mathematician (1937–2020)
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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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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There has been a great deal of nonsense written... about the mysterious fourth dimension. ...4-dimensional space just consists of points with four coordinates instead of three (...similarly for any number of dimensions). ...[I]magine a telegraph ...over which numbers are ...sent in sets of four. Each set... is a point in 4-d... space.
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[T]he best packings in up to eight dimensions belong to families <math>A_n, D_n </math> and <math>E_n</math>, and the corresponding s turn up in apparently unrelated areas... [I]n 24 dimensions the <math>\Lambda_{24}</math> has... connections with , s, and the Monster simple group... [O]ne day someone will write an article on "The Ubiquity of the Leech lattice." ...There are applications of... packings to number theory... [e.g.,] solving s, and to "the "... There are... applications of sphere packings... in digital communications... a typical question from... spread-spectrum communications for mobile radio... how many spheres of radius 0.25 can be packed in a sphere of radius 1 in 100-dimensional space? ...Two and three-d... packings... circles in a two-d... packing may represent s... in... a cable. Three-d... packings have applications in chemistry and physics... biology... antenna design... choosing directions for X-ray tomography... and... statistical analysis on spheres... n-dimensional packings may be used in... numerical evaluation of integrals... on the surface of a sphere in <math>\R^n</math> or in its interior. ...A related application ...n-dimensional search or approximation problems ...[I]n physics... dual theory and superstring theory... have involved the <math>E_8</math> and <math>\Lambda_{24}</math> lattices and the related Lorentzian lattices in dimensions 10 and 26...
I have a very simple way of explaining relativity theory... and if you follow that you'll understand how... it's impossible to... transmit information faster than the speed of light. The reason is, if you could, then seen from another person's point of view, you'd transmit information backward in time... [W]e would know the result of somebody's experiment before they performed it, and if they have free will... you'd know the result of their choice before they've made it, and they're free to make another one.
Lucretius... was an atomist, a follower of Epicurus. The original people who invented the atomic theory were and Democritus. ...Lucretius is discussing ...atoms ...he says, "at quite indeterminate times and places they swerve" ...because it allows for human free will... and "if the atoms never swerve... what is the source of the free will possessed by living things throughout the earth?" He says, "Although many men are driven by an external source, and often constrained involuntarily to advance or rush headlong, yet there is in the human breast something that can fight against it and resist it... So also in the atoms you must recognize the same possibility. Besides weight and impact, there must be a third cause of movement, the source of this inborn power... due to the slight swerve of the atoms... since nothing can come out of nothing." And then he goes on to say, "the fact that the mind itself has no internal necessity to determine its every act, this is due to the slight swerve of the atoms at no determinate time and place."
In many respects, this is not in any way an unorthodox opinion. ...Physicists have lived with these paradoxes ...for 80 years now. They have been accustomed to the fact that quantum mechanics is not a totally predictive theory, and they've proved long ago that no extension of quantum mechanics can be. This is not a defect... It's not a temporary defect, anyway. No extension of quantum mechanics can recover... total predictivity. From our point of view that's... obvious. ...[N]o correct theory can predict what the particle is going to do before it's made its decision... while it's still free to do something else. ...[I]t's not to be seen as a defect in quantum mechanics that it doesn't predict. It's a merit. ...You shouldn't expect to be able to predict things.
Physicists... have seen lots of instances of people... without... qualifications in physics, and presenting some... loony theory... and they don't read it. ...[W]e had this thing in mathematics once. People... thought they'd proved Fermat's Last Theorem... Eventually somebody did, but he was a... distinguished... high-powered mathematician. I'm... prepared for the fact... that physicists, especially ones that don't read our paper, don't believe it. They think it's just another... of those strange things. However, it's... better than that. ...I hope that the physicists stay and... learn something...