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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Expand Quotes (23 quotes)

As our circle of knowledge expands, so does the circumference of darkness surrounding it.
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But among all these many departments of research, these many branches of industry, new and old, which are being rapidly expanded, there is one dominating all others in importance—one which is of the greatest significance for the comfort and welfare, not t
http://web.archive.org/web/20070109161311/http://www.knowprose.com/node/12961
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But does Man have any “right” to spread through the universe? Man is what he is, a wild animal with the will to survive, and (so far) the ability, against all competition. Unless one accepts that, anything one says about morals, war, politics, you name it, is nonsense. Correct morals arise from knowing what man is, not what do-gooders and well-meaning old Aunt Nellies would like him to be. The Universe will let us know—later—whether or not Man has any “right” to expand through it.
In Starship Troopers (1959), 186.
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Gödel proved that the world of pure mathematics is inexhaustible; no finite set of axioms and rules of inference can ever encompass the whole of mathematics; given any finite set of axioms, we can find meaningful mathematical questions which the axioms leave unanswered. I hope that an analogous Situation exists in the physical world. If my view of the future is correct, it means that the world of physics and astronomy is also inexhaustible; no matter how far we go into the future, there will always be new things happening, new information coming in, new worlds to explore, a constantly expanding domain of life, consciousness, and memory.
From Lecture 1, 'Philosophy', in a series of four James Arthur Lectures, 'Lectures on Time and its Mysteries' at New York University (Autumn 1978). Printed in 'Time Without End: Physics and Biology in an Open Universe', Reviews of Modern Physics (Jul 1979), 51, 449.
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I despair of persuading people to drop the familiar and comforting tactic of dichotomy. Perhaps, instead, we might expand the framework of debates by seeking other dichotomies more appropriate than, or simply different from, the conventional divisions. All dichotomies are simplifications, but the rendition of a conflict along differing axes of several orthogonal dichotomies might provide an amplitude of proper intellectual space without forcing us to forgo our most comforting tool of thought.
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I had no idea of the worldwide influence of it [the world’s first kidney transplant]. It expanded to other organs, multiple organs.
As quoted by Alvin Powell in 'A Transplant Makes History', Harvard Gazette (22 Sep 2011).
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If the universe is everything, and scientists say that the universe is expanding, what is it expanding into?
Anonymous
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It is not failure but success that is forcing man off this earth. It is not sickness but the triumph of health... Our capacity to survive has expanded beyond the capacity of Earth to support us. The pains we are feeling are growing pains. We can solve growth problems in direct proportion to our capacity to find new worlds... If man stays on Earth, his extinction is sure even if he lasts till the sun expands and destroys him... It is no longer reasonable to assume that the meaning of life lies on this earth alone. If Earth is all there is for man, we are reaching the foreseeable end of man.
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Louise: ‘How did you get here?’ Johnny: ‘Well, basically, there was this little dot, right? And the dot went bang and the bang expanded. Energy formed into matter, matter cooled, matter lived, the amoeba to fish, to fish to fowl, to fowl to frog, to frog to mammal, the mammal to monkey, to monkey to man, amo amas amat, quid pro quo, memento mori, ad infinitum, sprinkle on a little bit of grated cheese and leave under the grill till Doomsday.’
Movie
From the movie Naked
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Man, the cutting edge of terrestrial life, has no rational alternative but to expand the environmental and resource base beyond earth.
On the 'extraterrestrial imperative,' recalled on his death 11 Dec 84
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Many people are shrinking from the future and from participation in the movement toward a new, expanded reality. And, like homesick travelers abroad, they are focusing their anxieties on home. The reasons are not far to seek. We are at a turning point in human history... We could turn our attention to the problems that going to the moon certainly will not solve ... But I think this would be fatal to our future... A society that no longer moves forward does not merely stagnate; it begins to die.
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Mathematics is a science continually expanding; and its growth, unlike some political and industrial events, is attended by universal acclamation.
From remarks made while opening the proceedings for the Mathematics Section (20 Sep 1904), Congress of Arts and Sciences (1905), Vol. 1, 455.
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Once you can accept the universe as matter expanding into nothing that is something, wearing stripes with plaid comes easy.
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One of the most curious and interesting reptiles which I met with in Borneo was a large tree-frog, which was brought me by one of the Chinese workmen. He assured me that he had seen it come down in a slanting direction from a high tree, as if it flew. On examining it, I found the toes very long and fully webbed to their very extremity, so that when expanded they offered a surface much larger than the body. The forelegs were also bordered by a membrane, and the body was capable of considerable inflation. The back and limbs were of a very deep shining green colour, the undersurface and the inner toes yellow, while the webs were black, rayed with yellow. The body was about four inches long, while the webs of each hind foot, when fully expanded, covered a surface of four square inches, and the webs of all the feet together about twelve square inches. As the extremities of the toes have dilated discs for adhesion, showing the creature to be a true tree frog, it is difficult to imagine that this immense membrane of the toes can be for the purpose of swimming only, and the account of the Chinaman, that it flew down from the tree, becomes more credible. This is, I believe, the first instance known of a “flying frog,” and it is very interesting to Darwinians as showing that the variability of the toes which have been already modified for purposes of swimming and adhesive climbing, have been taken advantage of to enable an allied species to pass through the air like the flying lizard. It would appear to be a new species of the genus Rhacophorus, which consists of several frogs of a much smaller size than this, and having the webs of the toes less developed.
Malay Archipelago
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The earth itself assures us it is a living entity. Deep below surface one can hear its slow pulse, feel its vibrant rhythm. The great breathing mountains expand and contract. The vast sage desert undulates with almost imperceptible tides like the oceans. From the very beginning, throughout all its cataclysmic upthrusts and deep sea submergences, the planet Earth seems to have maintained an ordered rhythm.
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The increase of disorder or entropy with time is one example of what is called an arrow of time something that gives a direction to time and distinguishes the past from the future. There are at least three different directions of time. First, there is the thermodynamic arrow of time—the direction of time in which disorder or entropy increases. Second, there is the psychological arrow of time. This is the direction in which we feel time passes—the direction of time in which we remember the past, but not the future. Third, there is the cosmological arrow of time. This is the direction of time in which the universe is expanding rather than contracting.
In 'The Direction of Time', New Scientist (9 Jul 1987), 46.
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The opinion of Bacon on this subject [geometry] was diametrically opposed to that of the ancient philosophers. He valued geometry chiefly, if not solely, on account of those uses, which to Plato appeared so base. And it is remarkable that the longer Bacon lived the stronger this feeling became. When in 1605 he wrote the two books on the Advancement of Learning, he dwelt on the advantages which mankind derived from mixed mathematics; but he at the same time admitted that the beneficial effect produced by mathematical study on the intellect, though a collateral advantage, was “no less worthy than that which was principal and intended.” But it is evident that his views underwent a change. When near twenty years later, he published the De Augmentis, which is the Treatise on the Advancement of Learning, greatly expanded and carefully corrected, he made important alterations in the part which related to mathematics. He condemned with severity the pretensions of the mathematicians, “delidas et faslum mathematicorum.” Assuming the well-being of the human race to be the end of knowledge, he pronounced that mathematical science could claim no higher rank than that of an appendage or an auxiliary to other sciences. Mathematical science, he says, is the handmaid of natural philosophy; she ought to demean herself as such; and he declares that he cannot conceive by what ill chance it has happened that she presumes to claim precedence over her mistress.
In 'Lord Bacon', Edinburgh Review (Jul 1837). Collected in Critical and Miscellaneous Essays: Contributed to the Edinburgh Review (1857), Vol. 1, 395.
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The study of abstract science … offers unbounded fields of pleasurable, healthful, and ennobling exercise to the restless intellect of man, expanding his powers and enlarging his conceptions of the wisdom, the energy, and the beneficence of the Great Ruler of the universe
In 'Report of the Secretary', Annual Report of the Board of Regents of the Smithsonian Institution for 1859 (1860), 17.
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The term ecology comes from the Greek word oikos, and means ‘the household.’ Ecological responsibility, then, begins at home and expands to fill the entire planet.
The Green Lifestyle Handbook
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The Universe knows itself and expands itself through me.
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What is art
But life upon the larger scale, the higher,
When, graduating up in a spiral line
Of still expanding and ascending gyres,
It pushed toward the intense significance
Of all things, hungry for the Infinite?
From poem, 'Aurora Leigh' (1856), Book 4. In Elizabeth Barrett Browning and Harriet Waters Preston (ed.), The Complete Poetical Works of Mrs. Browning (1900), 323.
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When I admire the wonders of a sunset or the beauty of the moon, my soul expands in the worship of the creator.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 165
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Yet I also appreciate that we cannot win this battle to save species and environments without forging an emotional bond between ourselves and nature as well–for we will not fight to save what we do not love (but only appreciate in some abstract sense). So let them all continue–the films, the books, the television programs, the zoos, the little half acre of ecological preserve in any community, the primary school lessons, the museum demonstrations, even ... the 6:00 A.M. bird walks. Let them continue and expand because we must have visceral contact in order to love. We really must make room for nature in our hearts.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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