Samuel Gompers was the founder and first president of the American Federation of Labor. He established in America the tradition of practical bargaining between labor and management which led to an era of growth and prosperity for labor unions. Now, seventy years after Gomper's death, the unions have dwindled, while his dreams-more books and fewer guns, more leisure and less greed, more schoolhouses and fewer jails-have been tacitly abandoned. In a society without social justice and with a free-market ideology, guns, greed, and jails are bound to win.

The poorer half of humanity needs cheap housing, cheap health care, and cheap education, accessible to everybody, with high quality and high aesthetic standards. The fundamental problem for human society in the next century is the mismatch between the three new waves of technology and the three basic needs of poor people. The gap between technology and needs is wide and growing wider. If technology continues along its present course, ignoring the needs of the poor and showering benefits upon the rich, the poor will sooner or later rebel against the tyranny of technology and turn to irrational and violent remedies. In the future, as in the past, the revolt of the poor is likely to impoverish rich and poor together.

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.

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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.

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.

Human beings are so constituted that we take for granted the fact that a direct awareness of our past selves is preserved... We take for granted the durability of the individual self. ...But ...the preservation of memories ...is as great an exercise in magic as the transfer of memories from the dead to the living. ...How the magic works ...is still a dark mystery. ...When once the technology exists to read and write memories from one mind to another, the age of mental exploration will begin in earnest. ...[W]e will look at nature directly through the eyes of the elephant, the eagle and the whale. We will... feel in our own minds the pride of the peacock and the wrath of the lion. That magic is no greater than the magic that enables me to see the rocking horse through the eyes of the child who rode it sixty years ago.

Science and religion are two windows that people look through, trying to understand the big universe outside, trying to understand why we are here. The two windows give different views, but they look out at the same universe. Both views are one-sided, neither is complete. Both leave out essential features of the real world. And both are worthy of respect.

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Duas vozes falam pelo futuro, a voz da ciência e a voz da religião. A ciência e a religião são dois grandes empreendimentos humanos, que perduram ao longo dos séculos e nos ligam a nossos descendentes. Sou um cientista e, ao tentar neste livro olhar para o futuro, falo com a voz da ciência. Descrevo o passado e o futuro conforme o ponto de vista científico que me é familiar. Mas não afirmo que a voz da ciência fale com uma autoridade singular e única. A religião tem, no mínimo, autoridade igual na definição do destino humano. A religião fica mais próxima do coração da natureza humana, e tem mais penetração do que a ciência. Como a natureza humana, a qual reflete. a religião é muitas vezes cruel e pervertida. Nas ocasiões em que a ciência atingiu poder igual ao poder da religião, também ela tornou-se cruel e pervertida.

Unfortunately a large number of people in many countries are strongly opposed to green technology, for reasons having little to do with the real dangers. It is important to treat the opponents with respect, to pay attention to their fears, to go gently into the new world of green technology so that neither human dignity nor religious conviction is violated. If we can go gently, we have a good chance of achieving within a hundred years the goals of ecological sustainability and social justice that green technology brings within our reach.

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.

The essence of Hilbert's program was to find a decision process that would operate on symbols in a purely mechanical fashion, without requiring any understanding of their meaning. Since mathematics was reduced to a collection of marks on paper, the decision process should concern itself only with the marks and not with the fallible human intuitions out of which the marks were reduced. In spite of the prolonged efforts of Hilbert and his disciples, the Entscheidungsproblem was never solved. Success was achieved only in highly restricted domains of mathematics, excluding all the deeper and more interesting concepts. Hilbert never gave up hope, but as the years went by his program became an exercise in formal logic having little connection with real mathematics. Finally, when Hilbert was seventy years old, Kurt Godel proved by a brilliant analysis that the Entscheindungsproblem as Hilbert formulated it cannot be solved.

Godel proved that in any formulation of mathematics, including the rules of ordinary arithmetic, a formal process for separating statements into true and false cannot exist. He proved the stronger result which is now known as Godel's theorem, that in any formalization of mathematics including the rules of ordinary arithmetic there are meaningful arithmetical statements that cannot be proved true or false. Godel'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.