Corrected entry: Nash says that he believes the universe is infinite in size because "all the data indicate it". As far back as Newton (1692) there have been problems with the theory that the universe is infinitely big. In 1929 - well before the time in which the film is set - Edwin Hubble discovered the universe is expanding and effectively put an end to the infinite universe theory. It is inconceivable Nash would not know this. (00:53:25)
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Correction: Not necessarily. Nash may well believe that the universe is infinite in size and he may be right. Hubble's Law does state that galaxies move away from each other leading to a picture of an ever expanding universe. The controversy is whether this expansion will continue forever. There are serious proponents of both views, perpetual expansion or eventual contraction. If you believe in perpetual expansion then you enter the realms of a philosophical debate about what "infinite universe" actually means. Since the universe is perpetually expanding we can never have to hand a number that measures the size of the universe. Therefore, it may be appropriate to define an infinitely expanding universe as infinite in size.