Celebrating 18 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “A people without children would face a hopeless future; a country without trees is almost as helpless.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index F > Category: Finite

Finite Quotes (22 quotes)

La théorie des séries infinies en général est justqu’à présent très mal fondée. On applique aux séries infinies toutes les opérations, come si elles aient finies; mais cela est-il bien permis? Je crois que non. Où est-il démonstré qu/on ontient la différentielle dune série infinie en prenant la différentiaella de chaque terme. Rien n’est plus facile que de donner des exemples où cela n’est pas juste.
Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.
Quoted in Reinhold Remmert and Robert B. Burckel, Theory of Complex Functions: Readings in Mathematics (1991), 125.
Science quotes on:  |  Differential (2)  |  Infinite (88)  |  Operation (96)  |  Series (38)  |  Term (87)  |  Theory (582)

Anyone who believes in indefinite growth in anything physical, on a physically finite planet, is either mad—or an economist.
Expressing concern about ecosystems ruined by the arrival of man. As quoted by Philip Maughan, 'Sixty Years of Attenborough Through the Eyes of the New Statesman', New Statesman (21 Dec 2012), 141, No. 5138, 34. The quote came from Attenborough writing in an April 2013 issue of the same periodical.
Science quotes on:  |  Belief (400)  |  Economist (13)  |  Growth (111)  |  Indefinite (7)  |  Mad (15)  |  Physical (94)  |  Planet (199)

For me, the first challenge for computing science is to discover how to maintain order in a finite, but very large, discrete universe that is intricately intertwined. And a second, but not less important challenge is how to mould what you have achieved in solving the first problem, into a teachable discipline: it does not suffice to hone your own intellect (that will join you in your grave), you must teach others how to hone theirs. The more you concentrate on these two challenges, the clearer you will see that they are only two sides of the same coin: teaching yourself is discovering what is teachable.
…...
Science quotes on:  |  Achieve (36)  |  Challenge (37)  |  Clear (52)  |  Coin (9)  |  Compute (10)  |  Concentrate (11)  |  Discipline (38)  |  Discover (115)  |  Discrete (6)  |  First (174)  |  Grave (20)  |  Important (124)  |  Intellect (157)  |  Intertwine (3)  |  Join (15)  |  Large (82)  |  Less (54)  |  Maintain (22)  |  Mold (26)  |  Order (167)  |  Problem (362)  |  Same (92)  |  Science (1699)  |  Second (33)  |  See (197)  |  Side (36)  |  Solve (41)  |  Suffice (3)  |  Teach (102)  |  Theirs (3)  |  Universe (563)

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.
Science quotes on:  |  Astronomy (175)  |  Axiom (26)  |  Consciousness (71)  |  Constantly (19)  |  Domain (21)  |  Expand (14)  |  Exploration (93)  |  Future (229)  |  Kurt Gödel (5)  |  Hope (129)  |  Inexhaustible (10)  |  Inference (26)  |  Information (102)  |  Life (917)  |  Meaningful (14)  |  Memory (81)  |  New (340)  |  Physical (94)  |  Physics (301)  |  Prove (60)  |  Pure Mathematics (27)  |  Question (315)  |  Rule (135)  |  Set (56)  |  Unanswered (3)

I am afraid all we can do is to accept the paradox and try to accommodate ourselves to it, as we have done to so many paradoxes lately in modern physical theories. We shall have to get accustomed to the idea that the change of the quantity R, commonly called the 'radius of the universe', and the evolutionary changes of stars and stellar systems are two different processes, going on side by side without any apparent connection between them. After all the 'universe' is an hypothesis, like the atom, and must be allowed the freedom to have properties and to do things which would be contradictory and impossible for a finite material structure.
Kosmos (1932), 133.
Science quotes on:  |  Acceptance (41)  |  Accommodation (5)  |  Accustom (7)  |  Afraid (15)  |  Apparent (26)  |  Atom (251)  |  Change (291)  |  Connection (86)  |  Contradiction (44)  |  Difference (208)  |  Evolution (482)  |  Freedom (76)  |  Hypothesis (227)  |  Idea (440)  |  Impossibility (50)  |  Material (124)  |  Modern (104)  |  Paradox (35)  |  Physical (94)  |  Process (201)  |  Property (96)  |  Quantity (35)  |  Radius (4)  |  Star (251)  |  Stellar (3)  |  Structure (191)  |  System (141)  |  Theory (582)  |  Universe (563)

Infinite space cannot be conceived by anybody; finite but unbounded space is difficult to conceive but not impossible. … [We] are using a conception of space which must have originated a million years ago and has become rather firmly imbedded in human thought. But the space of Physics ought not to be dominated by this creation of the dawning mind of an enterprising ape."
In The Nature of the Physical World (1929), 80-81.
Science quotes on:  |  Ape (39)  |  Conceive (22)  |  Conception (63)  |  Creation (211)  |  Dawn (10)  |  Difficult (62)  |  Dominate (13)  |  Human (445)  |  Impossible (68)  |  Infinite (88)  |  Million (89)  |  Mind (544)  |  Originate (14)  |  Physics (301)  |  Space (154)  |  Thought (374)  |  Unbounded (2)

Interestingly, according to modern astronomers, space is finite. This is a very comforting thought—particularly for people who can never remember where they have left things.
Side Effects (1981), 36.
Science quotes on:  |  Astronomer (50)  |  Comfort (42)  |  Remember (53)  |  Space (154)  |  Thought (374)

It is going to be necessary that everything that happens in a finite volume of space and time would have to be analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition [that physics is computer-simulatable] is right, physical law is wrong.
International Journal of Theoretical Physics (1982), 21 Nos. 6-7, 468. Quoted in Brian Rotman, Mathematics as Sign (2000), 82.
Science quotes on:  |  Analysis (123)  |  Computer (84)  |  Infinite (88)  |  Infinitesimal (8)  |  Physical Law (3)  |  Physics (301)  |  Proposition (47)  |  Simulation (6)  |  Space (154)  |  Theory (582)  |  Time (439)  |  Wavelength (5)

It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this it follows that the population of the whole Universe is also zero, and that any people you may meet from time to time are merely the products of a deranged imagination.
In The Restaurant at the End of the Universe (1980, 2005), 142-143. Slightly revised from 'Fit the Fifth', The Original Hitchhiker Radio Scripts (1985), 102. The show was recorded for the BBC on 21 Feb 1978.
Science quotes on:  |  Deranged (2)  |  Division (27)  |  Imagination (209)  |  Infinite (88)  |  Inhabitant (19)  |  Meet (16)  |  Number (179)  |  Planet (199)  |  Population (71)  |  Universe (563)  |  World (667)  |  Zero (15)

Our knowledge can only be finite, while our ignorance must necessarily be infinite.
Essy, 'On the Sources of Knowledge and of Ignorance', in Conjectures and Refutations: The Growth of Scientific Knowledge (1962), 28.
Science quotes on:  |  Ignorance (190)  |  Infinite (88)  |  Knowledge (1128)  |  Necessarily (13)

Our mind, by virtue of a certain finite, limited capability, is by no means capable of putting a question to Nature that permits a continuous series of answers. The observations, the individual results of measurements, are the answers of Nature to our discontinuous questioning.
…...
Science quotes on:  |  Answer (201)  |  Capability (35)  |  Capable (26)  |  Certain (84)  |  Continuous (24)  |  Discontinuous (3)  |  Individual (177)  |  Limit (86)  |  Means (109)  |  Measurement (148)  |  Mind (544)  |  Nature (1029)  |  Observation (418)  |  Permit (20)  |  Question (315)  |  Result (250)  |  Series (38)  |  Virtue (55)

Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of the infinitude.
Dialogue 21 (28 Jun 1941). Dialogues of Alfred North Whitehead (1954, 2001) 160.
Science quotes on:  |  Infinite (88)  |  Life (917)  |  Mind (544)

Technology can relieve the symptoms of a problem without affecting the underlying causes. Faith in technology as the ultimate solution to all problems can thus divert our attention from the most fundamental problem—the problem of growth in a finite system
et al., The Limits to Growth (1972).
Science quotes on:  |  Affect (10)  |  Attention (76)  |  Cause (231)  |  Divert (3)  |  Faith (131)  |  Fundamental (122)  |  Growth (111)  |  Problem (362)  |  Relieve (3)  |  Solution (168)  |  Symptom (16)  |  System (141)  |  Technology (199)  |  Ultimate (61)  |  Underlying (14)

The known is finite, the unknown infinite; spiritually we find ourselves on a tiny island in the middle of a boundless ocean of the inexplicable. It is our task, from generation to generation, to drain a small amount of additional land.
As given in Herbert and W. Roesky and Klaud Möckel, translated from the original German by T.N. Mitchell and W.E. Russey, Chemical Curiosities: Spectacular Experiments and Inspired Quotes (1996), 212. It is a restatement of an original quote from concluding remarks to a chapter by Thomas Huxley, 'On the Reception of the ‘Origin of Species’', the last chapter in Charles Darwin and Francis Darwin (ed.), The Life and Letters of Charles Darwin (1887), Vol. 1, 557. Webmaster suggests, the original Huxley quote was translated for the original German text, and when that was translated for the English edition, the quote morphed into into the form above.
Science quotes on:  |  Additional (4)  |  Amount (20)  |  Boundless (11)  |  Drain (6)  |  Generation (111)  |  Inexplicable (5)  |  Infinite (88)  |  Island (17)  |  Known (15)  |  Land (83)  |  Middle (10)  |  Ocean (115)  |  Small (97)  |  Spiritually (3)  |  Task (68)  |  Tiny (25)  |  Unknown (87)

The progress of mathematics can be viewed as progress from the infinite to the finite.
In 'A Mathematician's Gossip', Indiscrete Thoughts, (2008), 214.
Science quotes on:  |  Infinite (88)  |  Mathematics (587)  |  Progress (317)

There is a finite number of species of plants and animals—even of insects—upon the earth. … Moreover, the universality of the genetic code, the common character of proteins in different species, the generality of cellular structure and cellular reproduction, the basic similarity of energy metabolism in all species and of photosynthesis in green plants and bacteria, and the universal evolution of living forms through mutation and natural selection all lead inescapably to a conclusion that, although diversity may be great, the laws of life, based on similarities, are finite in number and comprehensible to us in the main even now.
Presidential Address (28 Dec 1970) to the American Association for the Advancement of Science. 'Science: Endless Horizons or Golden Age?', Science (8 Jan 1971), 171, No. 3866, 24.
Science quotes on:  |  Animal (309)  |  Bacterium (5)  |  Cell (125)  |  Comprehension (51)  |  Conclusion (120)  |  Difference (208)  |  Diversity (46)  |  Earth (487)  |  Energy (185)  |  Evolution (482)  |  General (92)  |  Genetics (98)  |  Great (300)  |  Inescapable (4)  |  Insect (57)  |  Life (917)  |  Life Form (5)  |  Metabolism (11)  |  Mutation (25)  |  Natural Law (26)  |  Natural Selection (79)  |  Number (179)  |  Photosynthesis (15)  |  Plant (173)  |  Protein (43)  |  Reproduction (57)  |  Similar (22)  |  Species (181)  |  Universal (70)

We come no nearer the infinitude of the creative power of God, if we enclose the space of its revelation within a sphere described with the radius of the Milky Way, than if we were to limit it to a ball an inch in diameter. All that is finite, whatever has limits and a definite relation to unity, is equally far removed from the infinite... Eternity is not sufficient to embrace the manifestations of the Supreme Being, if it is not combined with the infinitude of space.
'Universal Natural History and Theory of the Heavens' (1755), part 2, ch.7. In W. Hastie (ed. and trans.), Kant's Cosmogony: As in his Essay on the Retardation of the Rotation of the Earth and his Natural History and Theory of the Heavens (1900), 139-40.
Science quotes on:  |  Creation (211)  |  Eternity (44)  |  God (454)  |  Infinite (88)  |  Milky Way (19)  |  Space (154)  |  Sphere (40)

We know that there is an infinite, and we know not its nature. As we know it to be false that numbers are finite, it is therefore true that there is a numerical infinity. But we know not of what kind; it is untrue that it is even, untrue that it is odd; for the addition of a unit does not change its nature; yet it is a number, and every number is odd or even (this certainly holds of every finite number). Thus we may quite well know that there is a God without knowing what He is.
Pensées (1670), Section 1, aphorism 223. In H. F. Stewart (ed.), Pascal's Pensées (1950), 117.
Science quotes on:  |  Addition (22)  |  Change (291)  |  Even (2)  |  Falsity (12)  |  God (454)  |  Infinity (59)  |  Knowledge (1128)  |  Number (179)  |  Odd (12)  |  Unit (25)

We should like Nature to go no further; we should like it to be finite, like our mind; but this is to ignore the greatness and majesty of the Author of things.
Letter to S. Clarke, 1715. Trans. M. Morris and G. H. R. Parkinson, Leibniz: PhilosophicalWritings (1973), 220.
Science quotes on:  |  God (454)  |  Mind (544)  |  Nature (1029)

What is the shape of space? Is it flat, or is it bent? Is it nicely laid out, or is it warped and shrunken? Is it finite, or is it infinite? Which of the following does space resemble more: (a) a sheet of paper, (b) an endless desert, (c) a soap bubble, (d) a doughnut, (e) an Escher drawing, (f) an ice cream cone, (g) the branches of a tree, or (h) a human body?
The Fourth Dimension: And How to Get There (1985), 91.
Science quotes on:  |  Bent (2)  |  Body (193)  |  Branch (61)  |  Bubble (12)  |  Cone (5)  |  Desert (27)  |  Doughnut (2)  |  Drawing (18)  |  Endless (20)  |  Flat (13)  |  Human (445)  |  Infinite (88)  |  Paper (52)  |  Resemblance (18)  |  Shape (52)  |  Sheet (6)  |  Shrink (10)  |  Soap (11)  |  Space (154)  |  Tree (143)  |  Warp (5)

What remains to be learned may indeed dwarf imagination. Nevertheless, the universe itself is closed and finite. … The uniformity of nature and the general applicability of natural laws set limits to knowledge. If there are just 100, or 105, or 110 ways in which atoms may form, then when one has identified the full range of properties of these, singly and in combination, chemical knowledge will be complete.
Presidential Address (28 Dec 1970) to the American Association for the Advancement of Science. 'Science: Endless Horizons or Golden Age?', Science (8 Jan 1971), 171, No. 3866, 24.
Science quotes on:  |  Atom (251)  |  Chemistry (239)  |  Closed (9)  |  Combination (69)  |  Complete (43)  |  Dwarf (5)  |  Imagination (209)  |  Knowledge (1128)  |  Limit (86)  |  Remain (77)  |  Universe (563)

Whatever answers faith gives.. .such answers always give an infinite meaning to the finite existence of man; a meaning that is not destroyed by suffering, deprivation or death. This means only in faith can we find the meaning and possibility of life.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 19
Science quotes on:  |  Answer (201)  |  Death (270)  |  Deprivation (5)  |  Destroy (63)  |  Existence (254)  |  Faith (131)  |  Find (248)  |  Give (117)  |  Infinite (88)  |  Life (917)  |  Mean (63)  |  Means (109)  |  Possibility (96)  |  Suffer (25)


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
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

- 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



who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.