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" "Even today, there persists... a feeling that the creation of the Universe out of nothing must violate some basic conservation law that stops one from getting something for nothing. Nevertheless, there is actually no evidence that the Universe as a whole possesses a non-zero value of any such conserved quantity. The total mass-energy of all the constituents of a finite Universe appears to be always equal in magnitude but opposite in sign to the total gravitational potential energies of those particles. ...Similarly, there is no evidence that the Universe possesses any overall net rotation or electric charge.
John David Barrow, FRS (November 29, 1952 – September 27, 2020) was an English cosmologist, theoretical physicist, mathematician, writer of popular science, and an amateur playwright.
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A less inflexible picture of mathematics is one that focuses on the fact that it is an open-ended human activity. Inventionism is the belief that mathematics is nothing more than what mathematicians do. ...We invent mathematics; we do not discover it. ...The independent discovery of the same mathematical theorems by different mathematicians from totally different economic, cultural, and political backgrounds—often at widely separated times in history—argues against such a simple view. The inventionist could respond by pointing to the universality of human languages. ...One might expect that those aspects of this universal grammar that share features of logic, and hence counting, would also make counting appear instinctive. In fact, although simple counting... is fairly universal in ancient and primitive cultures, virtually none of them went on to carry out mathematical operations more sophisticated than counting. This suggests that these higher mathematical operations are not genetically programmed into the human brain... They are more likely to be by-products of multi-purpose pattern-recognition capabilities.
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