Source: Mathematical Thought from Ancient to Modern Times (1972), p. 177
Context: Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. Euclid assumes in Postulate 2 that a straight-line segment can be extended as far as necessary; he uses this fact, but only to find a larger finite length—for example in Book I, Propositions 11, 16, and 20. For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.
Source: Crystallizing Public Opinion (1923), p. 168
Source: Time, Structure and Fluctuations (1977), p. 1; Introduction.
“The quantum theory of parallel universes is not the problem, it is the solution.”
Source: The Fabric of Reality (1997), Ch. 2
Context: The quantum theory of parallel universes is not the problem, it is the solution. It is not some troublesome, optional interpretation emerging from arcane theoretical considerations. It is the explanation—the only one that is tenable—of a remarkable and counter-intuitive reality.
"Intelligent Machinery." This passage was one of the epigraphs to Cryptonomicon, the influential novel by Neal Stephenson, in which Turing was a fictionalized character. It shared a page with a quote from Imelda Marcos.
“Space offers no problems of sovereignty”
1963, UN speech
Context: Finally, in a field where the United States and the Soviet Union have a special capacity — in the field of space — there is room for new cooperation, for further joint efforts in the regulation and exploration of space. I include among these possibilities a joint expedition to the moon. Space offers no problems of sovereignty; by resolution of this Assembly, the members of the United Nations have foresworn any claim to territorial rights in outer space or on celestial bodies, and declared that international law and the United Nations Charter will apply. Why, therefore, should man's first flight to the moon be a matter of national competition? Why should the United States and the Soviet Union, in preparing for such expeditions, become involved in immense duplications of research, construction, and expenditure? Surely we should explore whether the scientists and astronauts of our two countries — indeed of all the world — cannot work together in the conquest of space, sending someday in this decade to the moon not the representatives of a single nation, but the representatives of all of our countries.
From 1980s onwards, Only Integrity is Going to Count (1983)
“If you cannot solve the proposed problem, try to solve first a simpler related problem.”
Mathematical Methods in Science (1977), p.164
“There are no physical problems—only mental ones.”
Loving What Is: Four Questions That Can Change Your Life (2002)
“When you know that every problem is only a false problem, you are dangerously close to salvation.”
The New Gods (1969)
“Time is never a problem on the God level. Or space.”
Job: A Comedy of Justice (1984)
Context: Time is never a problem on the God level. Or space. Whatever needed to deceive you was provided. But no more than that. That is the conservative principle in art at the God level. While I can't do it, not being at that level, I have seen a lot of it done. A skillful Artist in shapes and appearances does no more than necessary to create His effect.
