All Quotes

"Some of the later Greeks, such as Archimedes, had just views on the elementary phenomena of and optics. Indeed, Archimedes, who combined a genius for mathematics with physical insight, must rank with Newton, who lived nearly two thousand years later, as one of the founders of mathematical physics."

"There's only one person in the United States we ever wanted to meet … not that he wanted us. And we met him last night. We can't tell you how we felt. We just idolised him so much. … You can't imagine what a thrill that was last night. Nothing really affected me until I heard Elvis. If there hadn't been an Elvis, there wouldn't have been the Beatles."

""One cave she wolf go too farther, and I wolf leaf her" he said to his fave rave horse. Of course the horse didn't answer, because as you know they cannot speak, least of all to a garlic eating, stinking, little yellow greasy fascist bastard catholic Spaniard. They soon made it up howevans and Jesus and wee Spastic were once morphia unitely in a love that knew no Suzie. The only thing that puzzled Jesus was why his sugarboot got so annoyed when he called her his little Spastic in public."

"Christianity will go.. It will vanish and shrink. I needn't argue with that; I'm right and I will be proved right. We're more popular than Jesus now; I don't know which will go first — rock and roll or Christianity. Jesus was all right, but his disciples were thick and ordinary. It's them twisting it that ruins it for me."

"In these days an infinite number of chemical tests would be available. But then Archimedes had to think... afresh. The solution flashed upon him as he lay in his bath. He jumped up and ran through the streets to the palace, shouting Eureka! Eureka! (I have found it! ...) This day... ought to be celebrated as the birthday of mathematical physics; the science came of age when Newton sat in his orchard. Archimedes... had made a great discovery. He saw that a body when immersed in water is pressed upwards by the surrounding water with a resultant force equal to the weight of the water it displaces. ...Hence if W lb. be the [known] weight of the crown, as weighed in air, and w lb. be the [unknown] weight of the water which it displaces when completely immersed, W - w [from which (knowing W) the weight w of the equal volume of water can be derived,] would be the extra upward force necessary to sustain the crown as it hung in the water. [Alternatively, the weight of water, equaling the volume of the crown, and overflowing a tub, could be weighed directly.] Now, this upward force can easily be obtained by weighing the body as it hangs in the water [Fig. 3]...But \frac{w}{W} ...is the same for any lump of metal of the same material: it is now called the ... Archimedes had only to take a lump of indisputably pure gold and find its specific gravity by the same process. ...[N]ot only is it the first precise example of the application of mathematical ideas to physics, but also... a perfect and simple example of what must be the method and spirit of the science for all time. The discovery of the theory of specific gravity marks a genius of the first rank."

"The treatises are, without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader."

"There is here, as in all great Greek mathematical masterpieces, no hint as to the kind of analysis by which the results were first arrived at; for it is clear that they were not discovered by the steps which led up to them in the finished treatise. If the geometrical treatises had stood alone, Archimedes might seem, as Wallis said, "as it were of set purpose to have covered up the traces of his investigations, as if he has grudged posterity the secret of his method of inquiry, while he wished to extort from them assent to his results.""

"Modern mathematics was born with Archimedes and died with him for all of two thousand years. It came to life again with Descartes and Newton."

"To conceive of a parabolic segment or of a triangle as the sum of infinitely many line segments, is closely akin to the idea of Leibniz, who thought of the integral \int y~dx as the sum of infinitely many terms y~dx. But, in contrast to Leibniz, Archimedes is fully aware that this conception is... incorrect and that the derivation should be supplemented by a rigorous proof."

"The estimations, which occur in the summing of infinite series and in limiting operations, the "epsilontics", as the calculation with an arbitrarily small ε is sometimes called, were for Archimedes an open book. In this respect, his thinking is entirely modern."

"In Euclidean geometry the infinitely small was rejected and in the classical treatises of Archimedes we have the finest example of mathematical rigour in antiquity. Notwithstanding, in the discovery method we find him manipulating line and surface indivisibles skilfully, imaginatively and non-rigorously"

"Almost all modern translations of Archimedes’ works stem from a single Greek manuscript that was copied from an earlier original at Constantinople in the ninth or tenth century, was translated into Latin in the thirteenth century, and eventually disappeared without a trace in the sixteenth century."

"Using his masterful understanding of mechanics, equilibrium, and the principles of the lever, he weighed in his mind solids or figures whose volumes or areas he was attempting to find against ones he already knew. After determining in this way the answer...he found it much easier to prove geometrically... Consequently The Method starts with a number of statements on centers of gravity and only then proceeds to the geometrical propositions and their proofs. ...[He] essentially introduced the concept of a thought experiment into rigorous research. ...[He] freed mathematics from the somewhat artificial chains that Euclid and Plato had put on it. ...He did not hesitate to explore and exploit the connections between the abstract mathematical objects (the Platonic forms) and physical reality (actual solids and flat objects) to advance his mathematics."

"Archimedes was the earliest thinker to develop the apparatus of an infinite series with a finite limit ...starting on the conceptual path toward calculus. Of the giants on whose shoulders Isaac Newton would eventually perch, Archimedes was the first."

"Archimedes was a brilliant inventor and a mathematician. He says to the people around him, "Don't just live in the lap of the gods. Don't be dominated by Mother Nature. You, as a man, can take control of your own destiny.""

"According to legend, nothing could get between him [Archimedes] and his work, and sometimes he would even forget to eat. Ideas would come to him at any moment, and he would scribble them on any available surface. Famously, he was in the bath when he discovered the laws of buoyancy, leading him to run naked through the streets shouting "Eureka!" … Eureka means "I have found it," and it could be argued that Archimedes found out more than anyone else before or since."

"Tragically for all of us, he [Archimedes] was cut down by a Roman soldier because he refused to stop working. … If Archimedes hadn't been killed before his time, what could have he achieved? The industrial revolution could have happened two thousand years earlier. He might have kick-started the modern age."

"For our last number, I'd like to ask your help. Would the people in the cheaper seats clap your hands. And the rest of you, if you'll just rattle your jewelry."

"No — we need money first."

"I suppose if I had said television was more popular than Jesus, I would have gotten away with it. I'm sorry I opened my mouth. I'm not anti-God, anti-Christ, or anti-religion. I wasn't knocking it or putting it down. I was just saying it as a fact and it's true more for England than here. I'm not saying that we're better or greater, or comparing us with Jesus Christ as a person or God as a thing or whatever it is. I just said what I said and it was wrong. Or it was taken wrong. And now it's all this."

"Very rich."

"I am he as you are he as you are me And we are all together"

"We thought being offered the M.B.E. [Member of the Order of the British Empire] was as funny as everybody else thought it was. Why? What for? We didn't believe it. It was a part we didn't want. We all met and agreed it was daft."

"I think our society is run by insane people for insane objectives... I think we're being run by maniacs for maniacal ends, you know... I'd be very pleased to know what they think they're doing. I think they're all insane. But I am liable to be put away as insane for expressing that, you know. That's what is insane about it."

"Lots of people who complained about us receiving the MBE received theirs for heroism in the war—for killing people. We received ours for entertaining other people. I'd say we deserve ours more."

"It was just a gradual development over the years. Last year was "All You Need Is Love." This year it's "Give Peace a Chance." Remember love. The only hope for any of us is peace. Violence begets violence. If you want to get peace, you can get it as soon as you like if we all pull together. You're all geniuses and you're all beautiful. You don't need anybody to tell you who you are or what you are. You are what you are. Get out there and get peace. Think peace, live peace, and breathe peace and you'll get it as soon as you like. Okay?"

"That's part of our policy, is not to be taken seriously, because I think our opposition, whoever they may be, in all their manifest forms, don't know how to handle humor. You know, and we are humorous, we are, what are they, Laurel and Hardy. That's John and Yoko, and we stand a better chance under that guise, because all the serious people, like Martin Luther King, and Kennedy, and Gandhi, got shot."

"What's Bagism? It's like... a tag for what we all do, we're all in a bag ya know, and we realised that we came from two bags, I was in this pop bag going round and round in my little clique, and she was in her little avant-garde clique going round and round, and you're in your little tele clique and they're in their...ya know? and we all sort of come out and look at each other every now and then, but we don't communicate. And we all intellectualise about how there is no barrier between art, music, poetry... but we're still all "I'm a rock and roller, he's a poet" … so we just came up with the word so you would ask us what bagism is, and we'd say "WE'RE ALL IN A BAG BABY!""

"We're trying to sell peace, like a product, you know, and sell it like people sell soap or soft drinks. And it's the only way to get people aware that peace is possible, and it isn't just inevitable to have violence. Not just war — all forms of violence. People just accept it and think 'Oh, they did it, or Harold Wilson did it, or Nixon did it,' they're always scapegoating people. And it isn't Nixon's fault. We're all responsible for everything that goes on, you know, we're all responsible for Biafra and Hitler and everything. So we're just saying "SELL PEACE" — anybody interested in peace just stick it in the window. It's simple but it lets somebody else know that you want peace too, because you feel alone if you're the only one thinking 'wouldn't it be nice if there was peace and nobody was getting killed.' So advertise yourself that you're for peace if you believe in it."

"I'd like to say "thank you" on behalf of the group and ourselves and I hope we passed the audition."

"When I was about twelve, I used to think I must be a genius, but nobody's noticed. Either I'm a genius or I'm mad, which is it? "No," I said, "I can't be mad because nobody's put me away; therefore I'm a genius." Genius is a form of madness and we're all that way. But I used to be coy about it, like me guitar playing. But if there's such a thing as genius — I am one. And if there isn't, I don't care."

"If people take any notice of what we say, we say we've been through the drug scene, man, and there's nothing like being straight."

"All that business was awful, it was a fuckin' humiliation. One has to completely humiliate oneself to be what the Beatles were, and that's what I resent. I didn't know, I didn't foresee. It happened bit by bit, gradually, until this complete craziness is surrounding you, and you're doing exactly what you don't want to do with people you can't stand — the people you hated when you were ten."

"It's just natural, it's not a great disaster. People keep talking about it like it's The End of The Earth. It's only a rock group that split up, it's nothing important. You know, you have all the old records there if you want to reminisce."

"If you tried to give rock and roll another name, you might call it Chuck Berry."

"We announce the birth of a conceptual country, NUTOPIA. Citizenship of the country can be obtained by declaration of your awareness of NUTOPIA. NUTOPIA has no land, no boundaries, no passports, only people. NUTOPIA has no laws other than cosmic. All people of NUTOPIA are ambassadors of the country. As two ambassadors of NUTOPIA, we ask for diplomatic immunity and recognition in the United Nations of our country and our people."

"' It makes rock concerts look like tea parties."

"The thing the sixties did was to show us the possibilities and the responsibility that we all had. It wasn't the answer. It just gave us a glimpse of the possibility."

"I've sold my soul to the devil."

"Our society is run by insane people for insane objectives. … I think we're being run by maniacs for maniacal ends and I think I'm liable to be put away as insane for expressing that. That's what's insane about it."

"Reality leaves a lot to the imagination."

"Well, I just want him to grow up happy. That's the main thing."

"If everyone demanded peace instead of another television set, then there'd be peace."

"You have to be! (Laughs) You might get shot!"

"When we say "War is over if you want it," we mean that if everyone demanded peace instead of another TV set, we'd have peace."

"I am returning this MBE in protest against Britain's involvement in the Nigeria-Biafra thing, against our support of America in Vietnam and against "Cold Turkey" slipping down the charts."

"When it gets down to having to use violence, then you are playing the system’s game. The establishment will irritate you – pull your beard, flick your face – to make you fight. Because once they’ve got you violent, then they know how to handle you. The only thing they don’t know how to handle is non-violence and humor."

"It can never be again! Everyone always talks about a good thing coming to an end, as if life was over. But I'll be 40 when this interview comes out. Paul is 38. Elton John, Bob Dylan — we're all relatively young people. The game isn't over yet. Everyone talks in terms of the last record or the last Beatle concert — but, God willing, there are another 40 years of productivity to go. I'm not judging whether "I Am The Walrus" is better or worse than "Imagine." It is for others to judge. I am doing it. I do. I don't stand back and judge — I do."

"I don't have any romanticism about any part of my past. I think of it only inasmuch as it gave me pleasure or helped me grow psychologically. That is the only thing that interests me about yesterday. I don't believe in yesterday, by the way. You know I don't believe in yesterday. I am only interested in what I am doing now."

"Where do people get off saying the Beatles should give $200,000,000 to South America? You know, America has poured billions into places like that. It doesn't mean a damn thing. After they've eaten that meal, then what? It lasts for only a day. After the $200,000,000 is gone, then what? It goes round and round in circles. You can pour money in forever. After Peru, then Harlem, then Britain. There is no one concert. We would have to dedicate the rest of our lives to one world concert tour, and I'm not ready for it. Not in this lifetime, anyway."