Why do I think that Turing's paper "On computable numbers" is so important? Well, in my opinion it's a paper on epistemology, because we only understand something if we can program it, as I will explain in more detail later. And it's a paper on physics, because what we can actually compute depends on the laws of physics in our particular universe and distinguishes it from other possible universes. And it's a paper on ontology, because it shows that some real numbers are uncomputable, which I shall argue calls into question their very existence, their mathematical and physical existence.
Gregory ChaitinRelated topics
compute detail epistemology existence later numbers ontology opinion paper particular physical physics possible program question real something think universe well lawsRelated quotes
The mathematical thermology created by Fourier may tempt us to hope that, as he has estimated the temperature of the space in which we move, me may in time ascertain the mean temperature of the heavenly bodies: but I regard this order of facts as for ever excluded from our recognition. We can never learn their internal constitution, nor, in regard to some of them, how heat is absorbed by their atmosphere. We may therefore define Astronomy as the science by which we discover the laws of the geometrical and mechanical phenomena presented by the heavenly bodies.
Auguste Comte
George Orwell once wrote: "And it's not a matter of whether the war is not real or if it is. Victory is not possible. The war is not meant to be won, it is meant to be continuous. Hierarchical society is only possible on the basis of poverty and ignorance. This new version is the past and no different past can ever have existed. In principle the war effort is always planned to keep society on the brink of starvation. The war is waged by the ruling group against its own subjects and its object is not the victory over either Eurasia or East Asia but to keep the very structure of society intact."
Michael Moore
Fresh beauty opens one's eyes wherever it is really seen, but the very abundance and completeness of the common beauty that besets our steps prevents its being absorbed and appreciated. It is a good thing, therefore, to make short excursions now and then to the bottom of the sea among dulse and coral, or up among the clouds on mountain-tops, or in balloons, or even to creep like worms into dark holes and caverns underground, not only to learn something of what is going on in those out-of-the-way places, but to see better what the sun sees on our return to common every-day beauty.
John Muir
There are things about organized religion which I resent. Christ is revered as the Prince of Peace, but more blood has been shed in His name than any other figure in history. You show me one step forward in the name of religion and I'll show you a hundred retrogressions. Remember, they were men of God who destroyed the educational treasures at Alexandria, who perpetrated the Inquisition in Spain, who burned the witches at Salem. Over 25,000 organized religions flourish on this planet, but the followers of each think all the others are miserably misguided and probably evil as well.
Frank Sinatra
God always was, and always is, and always will be. Or rather, God always Is. For Was and Will be are fragments of our time, and of changeable nature, but He is Eternal Being. And this is the Name that He gives to Himself when giving the Oracle to Moses in the Mount. For in Himself He sums up and contains all Being, having neither beginning in the past nor end in the future; like some great Sea of Being, limitless and unbounded, transcending all conception of time and nature, only adumbrated [intimated] by the mind, and that very dimly and scantily.
Gregory of Nazianzus
