Academics From The United States

"Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid. This is what one means when one says that a point is a mathematical abstraction. The question, What is a point? has no satisfactory answer. Euclid's definition certainly does not answer it. The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry? ...It cannot be answered by a definition."

"Scientifically speaking, a butterfly is at least as mysterious as a superstring. When something ceases to be mysterious it ceases to be of absorbing interest to scientists. Almost all things scientists think and dream about are mysterious."

"There is no easy solution to the conflict between fundamentalist Christian dogma and the facts of biological evolution. I am not saying that the conflict could have been altogether avoided. I am saying only that the conflict was made more bitter and more damaging, both to religion and to science, by the dogmatic and self-righteousness of scientists. What was needed was a little more human charity, a little more willingness to listen rather than to lay down the law, a little more humility. Scientists stand in need of these Christian virtues just as much as preachers do."

"Science is not a monolithic body of doctrine. Science is a culture, constantly growing and changing. The science of today has broken out of the molds of classical nineteenth-century science, just as the paintings of Pablo Picasso and Jackson Pollock broke out of the molds of nineteenth century art. Science has as many competing styles as painting or poetry. The diversity of science also finds a parallel in the diversity of religion."

"An awareness of our smallness may help to redeem us from the arrogance which is the besetting sin of the scientists."

"Science and religion are two human enterprises sharing many features. They share these features also with other enterprises such as art, literature and music. The most salient features of all these enterprises are discipline and diversity. Discipline to submerge the individual fantasy in a greater whole. Diversity to give scope to the infinite variety of human souls and temperaments. Without discipline there can be no greatness. Without diversity there can be no freedom. Greatness for the enterprise, freedom for the individual — these are the two themes, contrasting but not incompatible, that make up the history of science and the history of religion."

"A good scientist is a person with original ideas. A good engineer is a person who makes a design that works with as few original ideas as possible. There are no prima donnas in engineering."

"A good cause can become bad if we fight for it with means that are indiscriminately murderous. A bad cause can become good if enough people fight for it in a spirit of comradeship and self-sacrifice. In the end it is how you fight, as much as why you fight, that makes your cause good or bad."

"It is characteristic of all deep human problems that they are not to be approached without some humor and some bewilderment."

"If we had a reliable way to label our toys good and bad, it would be easy to regulate technology wisely. But we can rarely see far enough ahead to know which road leads to damnation. Whoever concerns himself with big technology, either to push it forward or to stop it, is gambling in human lives."

"There is a great satisfaction in building good tools for other people to use."

"... the most important questions and insights and goals are unpredictable."

"There is an enormous variety of things that we never dreamed of, like... black holes, s, quasars, all these unbelievably active goings-on in the universe... [I]n Aristotle's time the universe... was supposed to be quiescent, it was supposed to be perfect and peaceful, and nothing ever happened in the ; and that remained true... throughout all of the revolutions... It remained the general view of astronomers... through Copernicus, and Galileo, and Newton, and everybody else... until just the last 30 years, and now we know it's not like that at all. In fact the universe is full of violent events, and fantastic strong gravitational fields, and collapsed objects, and huge outpourings of energy. ...The things we understand least are the quasars... the most violent and... energetic objects in the universe, and they're totally... mysterious... and... they're rather frequent; and nobody ever dreamed that they existed... [E]ven after they were found it took a long time before people took them seriously. Nature's imagination is always richer than ours."

"There’s very good news from the asteroids. It appears that a large fraction of them, including the big ones, are actually very rich in H2O. Nobody imagined that. They thought they were just big rocks … It’s easier to get to an asteroid than to Mars, because the gravity is lower and landing is easier. Certainly the asteroids are much more practical, right now. If we start space colonies in, say, the next 20 years, I would put my money on the asteroids."

"All the books that I have seen about the science and the economics of global warming, including the two books under review, miss the main point. The main point is religious rather than scientific. There is a worldwide secular religion which we may call environmentalism, holding that we are stewards of the earth, that despoiling the planet with waste products of our luxurious living is a sin, and that the path of righteousness is to live as frugally as possible. … Environmentalism has replaced socialism as the leading secular religion."

"I believe global warming is grossly exaggerated as a problem. It's a real problem, but it's nothing like as serious as people are led to believe. The idea that global warming is the most important problem facing the world is total nonsense and is doing a lot of harm. It distracts people's attention from much more serious problems."

"My first heresy says that all the fuss about global warming is grossly exaggerated. Here I am opposing the holy brotherhood of climate model experts and the crowd of deluded citizens who believe the numbers predicted by the computer models. Of course, they say, I have no degree in meteorology and I am therefore not qualified to speak. But I have studied the climate models and I know what they can do. The models solve the equations of fluid dynamics, and they do a very good job of describing the fluid motions of the atmosphere and the oceans. They do a very poor job of describing the clouds, the dust, the chemistry and the biology of fields and farms and forests. They do not begin to describe the real world that we live in. The real world is muddy and messy and full of things that we do not yet understand. It is much easier for a scientist to sit in an air-conditioned building and run computer models, than to put on winter clothes and measure what is really happening outside in the swamps and the clouds. That is why the climate model experts end up believing their own models."

"The biggest breakthrough in the next 50 years will be the discovery of extraterrestrial life. We have been searching for it for 50 years and found nothing. That proves life is rarer than we hoped, but does not prove that the universe is lifeless. We are only now developing the tools to make our searches efficient and far-reaching, as optical and radio detection and data processing move forward."

"In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, "How many arbitrary parameters did you use for your calculations?" I thought for a moment about our cut-off procedures and said, "Four." He said, "I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk." With that, the conversation was over."

"The laws of nature are constructed in such a way as to make the universe as interesting as possible."

"Anyone who compares the bibliography with the reprinted papers will notice that mathematics and physics have not been given equal treatment. There is a strong bias in favor of mathematics. The bias arises from the fact that mathematical papers, provided that are correct and not trivial, have permanent value, whereas most papers in physics journals are ephemeral. For this reason, it is customary to publish complete collected works of mathematicians but only selected works of physicists."

"The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design."

"Man occupies a special place in the Cartesian scheme. He alone is endowed with mind. Descartes believed that animals did not possess one, that they were simply extremely complicated automatons. Other thinkers have rejected this point of view and proposed to endow all matter in the universe — living or inanimate — with consciousness. This "panpsychism" has been promoted by, among others, Teilhard de Chardin and, more recently by the British-American physicist Freeman Dyson, who holds that mind is present in every particle of matter."

"Freeman’s gift? … It’s cosmic. He is able to see more interconnections between more things than almost anybody. He sees the interrelationships, whether it’s in some microscopic physical process or in a big complicated machine like Orion. He has been, from the time he was in his teens, capable of understanding essentially anything that he’s interested in. He’s the most intelligent person I know."

"You'll have received an application from Mr Freeman Dyson to come to work with you as a graduate student. I hope that you will accept him. Although he is only 23 he is in my view the best mathematician in England."

"Many people know of the mathematician but not the engineer. Some had read of Dyson the physicist but not Dyson the diplomat. They had read Disturbing the Universe but not '. They might have known about Orion and but not about Socinus. ...Dyson had not won the... Nobel for... explaining way the infinities... when you get closer and closer to the electron... relying on an artful redefinition of the mass and charge... But he had won ...[the Templeton prize] for explaining the disparities that arise when you use science to explain the whole universe, physical and moral. Dyson's attempt at smoothing over potential conflicts between science and religion had swept the apparent incompatibility not under the carpet but out beyond the edge of the universe."

"Freeman Dyson’s winning the took many people by surprise, including Dyson... the Templeton Foundation gave its... prize for "progress in religion"... In receiving a million dollars, Dyson may have lost his amateur status as a theologian. ...In Dyson's acceptance speech he sounded the themes... that good works... are better than volumes of theology; that both science and religion... grapple with mysteries; that God and mind... are one and actively present simultaneously at the microscopic level of atoms, at the macroscopic level of human beings, and at the cosmic level of the universe... that green technology... is reexerting its primacy over gray technology... machines and fossil fuels; that the marketing of high-tech and the capitalist system... must be tempered by ethics; that this attention to social justice will... help alleviate human misery and enlarge the global economy; and that we must utilize both... science and religion... Dyson should probably be placed somewhere between a pantheist and a deist whose God is a kind of meta-scientific, ."

"When Freeman Dyson, the physicist, greeted John Forbes Nash, Jr. at the Institute for Advanced Study one day in the early 1990s, he hardly expected a response. A mathematics legend in his twenties, Nash had suffered for decades from a devastating mental illness. A mute, ghost-like figure who scrawled mysterious messages on blackboards and occupied himself with numerological calculations, he was known around Princeton only as “the Phantom.” To Dyson’s astonishment, Nash replied. He’d seen Dyson’s daughter, an authority on computers, on the news, he said. “It was beautiful,” recalled Dyson. “Slowly, he just somehow woke up.”"

"Mr Dyson is absolutely unusual in his ability and accomplishments. I can say without reservation that he is the best I have ever had or observed."

"Greene takes it for granted, and here the great majority of physicists agree with him, that the division of physics into separate theories for large and small objects is unacceptable. ... Greene believes that there is an urgent need to find a theory of quantum gravity that applies to large and small objects alike. ... As a conservative, I do not agree that a division of physics into separate theories for large and small is unacceptable. ... The essence of any theory of quantum gravity is that there exists a particle called the graviton ... I looked at various possible ways of detecting gravitons and did not find a single one that worked. Because of the extreme weakness of the gravitational interaction, any putative detector of gravitons has to be extremely massive. If the detector has normal density, most of it is too far from the source of gravitons to be effective, and if it is compressed to a high density around the source it collapses into a black hole. There seems to be a conspiracy of nature to prevent the detector from working."

"I had the good luck a few years ago to visit the archeological site of Zippori in Israel ... I could see here displayed the Greek culture that Jesus decisively rejected, the same Greek culture that infiltrated the Christian religion soon after his death and has dominated Christianity ever since."

"The common root of modern science and Christian theology was Greek philosophy. The historical accident that caused the Christian religion to become heavily theological was the fact that Jesus was born in the Eastern part of the Roman Empire at the time when the prevailing culture was profoundly Greek."

"It is more difficult for a modern scientist to be a serious Christian, like Polkinghorne, than to be a serious Muslim, like the Nobel Prize-winning physicisit Abdus Salam. Salam happily proclaimed his Muslim faith but did not feel any need to write books about it. For Salam, the idea of a conflict between his faith and his science was ludicrous. Muslim faith has nothing to do with science. But Polkinghorne writes books to prove to himself and to us that his theology and his science can live together harmoniously.."

"It is probably not an accident that modern science grew explosively in Christian Europe and left the rest of the world behind. A thousand years of theological disputes nurtured the habit of analytical thinking that could also be applied to the analysis of natural phenomena. On the other hand, the close historical relations between theology and science have caused conflicts between science and Christianity that does not exist between science and other religions."

"It is a curious accident of history that the Christian religion became heavily involved with theology. No other religion finds it necessary to formulate elaborately precise statements about the abstract qualities and relationships of gods and humans. ... The idea that God may be approached and understood through intellectual analysis is uniquely Christian."

"When all is said and done, science is about things and theology is about words. Things behave in the same way everywhere, but words do not. ... Theology works in one culture alone. If you have not grown up in Polkinghorne's culture, where words such as "incarnation" and "trinity" have a profound meaning, you cannot share his vision."

"Nobody knows what dark matter is. It is another deep mystery waiting to be explored. We know only that it is there, and that it weighs more than the stuff that we can see."

"Astronomers have so far escaped the extreme specialization that has overtaken physicists. Telescopes are big, but they are not as complicated as accelerators. Observations with a big telescope can be carried out in hours rather than years."

"Rutherford did not pretend to understand quantum mechanics, but he understood that the Gamow formula would give his accelerator a crucial advantage. Even particles accelerated at much lower energies ... would be able to penetrate into nuclei. Rutherford invited Gamow to Cambridge in January 1929 ... [They] became firm friends and Gamow's insight gave Rutherford the impetus to go full steam ahead with the building of his accelerator."

"Rutherford's discovery was the beginning of the science that came to be called nuclear physics. ... The projectiles that he used to explore the nucleus were particles produced in the disintegration of radium ... discovered by Marie Curie in 1898. The particles are helium nuclei that are emitted at high speed when radium atoms decay ... The twenty years between 1909 and 1929 were the era of tabletop nuclear physics. ... Small and simple experiments were sufficient to establish the basic laws of nuclear physics."

"Black holes are not rare, and they are not an accidental embellishment of our Universe. They are a fundamental driving force of its evolution. They are a dominant source of energy. For every ounce of matter consumed, they yield more than ten times as much energy as the nuclear reactions of fusion and fission that cause our sun to shine and our hydrogen bombs to explode."

"The two great conceptual revolutions of twentieth-century science, the overturning of classical physics by Werner Heisenberg and the overturning of the foundations of mathematics by Kurt Gödel, occurred within six years of each other within the narrow boundaries of German-speaking Europe. ... A study of the historical background of German intellectual life in the 1920s reveals strong links between them. Physicists and mathematicians were exposed simultaneously to external influences that pushed them along parallel paths. ... Two people who came early and strongly under the influence of Spengler's philosophy were the mathematician Hermann Weyl and the physicist Erwin Schrödinger. ... Weyl and Schrödinger agreed with Spengler that the coming revolution would sweep away the principle of physical causality. The erstwhile revolutionaries David Hilbert and Albert Einstein found themselves in the unaccustomed role of defenders of the status quo, Hilbert defending the primacy of formal logic in the foundations of mathematics, Einstein defending the primacy of causality in physics. In the short run, Hilbert and Einstein were defeated and the Spenglerian ideology of revolution triumphed, both in physics and in mathematics. Heisenberg discovered the true limits of causality in atomic processes, and Gödel discovered the limits of formal deduction and proof in mathematics. And, as often happens in the history of intellectual revolutions, the achievement of revolutionary goals destroyed the revolutionary ideology that gave them birth. The visions of Spengler, having served their purpose, rapidly became irrelevant."

"Starting from Einstein's theory of general relativity, Oppenheimer and Snyder found solutions... that described what happens to a massive star when it has exhausted its supplies of nuclear energy. The star collapses gravitationally and disappears from the visible universe, leaving behind only an intense gravitational field to mark its presence. The star remains in a state of permanent free fall, collapsing endlessly inward into the gravitational pit without ever reaching the bottom. ... In my opinion, the black hole is incomparably the most exciting and the most important consequence of general relativity. But Einstein ... was actively hostile to the idea of black holes. ... Oddly enough, Oppenheimer too in later life was uninterested in black holes, although... they were his most important contribution to science. ... Oppenheimer in his later years believed that the only problem worthy of attention of a serious theoretical physicist was the discovery of fundamental equations of physics. Einstein certainly felt the same way."

"It is a curious paradox that several of the greatest and most creative spirits in science, after achieving important discoveries by following their unfettered imaginations, were in their later years obsessed with reductionist philosophy and as a result became sterile. Hilbert was a prime example of this paradox. Einstein was another."

"Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas."

"Science as subversion has a long history. ... Davis and Sakharov belong to an old tradition in science that goes all the way back to the rebels Benjamin Franklin and Joseph Priestley in the eighteenth century, to Galileo and Giordano Bruno in the seventeenth and sixteenth. If science ceases to be a rebellion against authority, then it does not deserve the talents of our brightest children. ... We should try to introduce our children to science today as a rebellion against poverty and ugliness and militarism and economic injustice."

"Progress in science is often built on wrong theories that are later corrected. It is better to be wrong than to be vague."

"Over periods of 10,000 years the distinctions between Western and Eastern and African cultures lose all meaning. Over a time span of 100,000 years we are all Africans. And over a time span of 300 million years we are all amphibians, waddling uncertainly out of dried-up ponds onto the alien and hostile land."

"I have to clear away a few popular misconceptions about space as a habitat … It is generally considered that planets are important. Except for Earth, they are not. Mars is waterless, and the others are, for various reasons, basically inhospitable to man. It is generally considered that beyond the sun’s family of planets there is absolute emptiness extending for light-years until you come to another star. In fact, it is likely that the space around the solar system is populated by huge numbers of comets, small worlds a few miles in diameter, rich in water and the other chemicals essential to life."

"The progress of science requires the growth of understanding in both directions, downward from the whole to the parts and upward from the parts to the whole. A reductionist philosophy, arbitrarily proclaiming that the growth of understanding must go only in one direction, makes no scientific sense. Indeed, dogmatic philosophical beliefs of any kind have no place in science."