“History is full of people who thought they were right -- absolutely right, completely right, without a shadow of a doubt. And because history never seems like history when you are living through it, it is tempting for us to think the same.”
“There are only certain intervals of time when life of any sort is possible in an expanding universe and we can practise astronomy only during that habitable time interval in cosmic history.”
“Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don't like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russel pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russel replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse.”
“The sciences paint an impersonal and objective account of the world, deliberately devoid of "meaning", telling us about origins and mechanics of life, by revealing nothing of the joys and sorrows of living.”
“He that loves a book will never want a faithful friend, a wholesome counselor, a cheerful companion, and effectual comforter. By study, by reading, by thinking, one may innocently divert and pleasently entertain himself, as in all weathers, as in all fortunes." - Barrow”
“Next to doing the right thing, the most important thing is to let people know you are doing the right thing.”
“The colonists usually say that it was they who brought us into history: today we show that this is not so. They made us leave history, our history, to follow them, right at the back, to follow the progress of their history.”