“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 Russell pointed this out in a lecture… — John D. Barrow Copy Share Image
“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… — John D. Barrow Copy Share Image
“One of Nature's deep secrets is the fact that the outcomes of the laws of Nature do not have to possess the same symmetries… — John D. Barrow Copy Share Image
“The effect of the 'time becomes space' proposal is that there is no definite moment or point of creation. In more conventional quantum mechanical… — John D. Barrow Copy Share Image
“Humans are distinguished further by the highly effective way in which they have pooled the individual intelligence of single individuals to produce a collective… — John D. Barrow Copy Share Image
We can predict the present without having to know everything about the past. — John D. Barrow Copy Share Image
All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we… — John D. Barrow Copy Share Image
“If the deep logic of what determines the value of the fine-structure constant also played a significant role in our understanding of all the… — John D. Barrow Copy Share Image
“Each of us is a complicated assymetrical outcome of the laws of electromagnetism and gravity.” — John D. Barrow Copy Share Image
“Impressed by the success of high-level mathematics in the formulation of the general theory of relativity in 1915, we find that Einstein's life-long quest… — John D. Barrow Copy Share Image
“Jewish philosopher Martin Buber, who died in 1965, wrote of how the mere thought of the infinite led him to contemplate suicide: “A necessity… — John D. Barrow Copy Share Image
“As we look way back into the first instants of the Big Bang, we find the quantum world that we described in Chapter 3.… — John D. Barrow Copy Share Image
“The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to… — John D. Barrow Copy Share Image
