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Home > Category Index for Science Quotations > Category Index I > Category: Integration

Integration Quotes (12 quotes)

Common integration is only the memory of differentiation...
Science quotes on:  |  Differentiation (17)  |  Mathematics (587)

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.
Paraphrased from American Mathematics Monthly (1998) 105, 640-50. Quoted in John De Pillis, 777 Mathematical Conversation Starters (2004), 136.

God does not care about our mathematical difficulties. He integrates empirically.
Quoted, without citation, by Lιopold Infeld in Quest (1942, 1980), 279. If you know the primary source, please contact Webmaster.
Science quotes on:  |  God (454)  |  Mathematics (587)

I see with much pleasure that you are working on a large work on the integral Calculus [ ... ] The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics.
Letter to S. F. Lacroix, 1792. Quoted in S. F. Lacroix, Traité du calcul differentiel et du calcul integral (1797), Vol. 1, xxiv, trans. Ivor Grattan-Guinness.
Science quotes on:  |  Calculus (23)  |  Clarification (6)  |  Follow (66)  |  Generalization (26)  |  Instinct (50)  |  Metaphysics (30)  |  Method (154)  |  Pleasure (98)  |  Reconciliation (9)  |  Route (11)  |  Spirit (113)

In essence, science is a perpetual search for an intelligent and integrated comprehension of the world we live in.
In Matthew M. Radmanesh, Cracking the Code of Our Physical Universe (2006), 248.
Science quotes on:  |  Comprehension (51)  |  Essence (42)  |  Intelligence (138)  |  Intelligent (35)  |  Live (186)  |  Perpetual (10)  |  Science (1699)  |  Search (85)  |  World (667)

Nature laughs at the difficulties of integration.
Quoted in I. Gordon and S. Sorkin, The Armchair Science Reader (1959).

Science is intimately integrated with the whole social structure and cultural tradition. They mutually support one other—only in certain types of society can science flourish, and conversely without a continuous and healthy development and application of science such a society cannot function properly.
The Social System (1951, 1977), Chap. 8, 111. As a functionalist, Parsons argued that social practices had to be studied in terms of their function in maintaining society.
Science quotes on:  |  Application (117)  |  Culture (85)  |  Development (228)  |  Flourishing (5)  |  Function (90)  |  Health (136)  |  Mutual (22)  |  Science (1699)  |  Social (93)  |  Society (188)  |  Structure (191)  |  Support (63)  |  Tradition (43)

Science itself is badly in need of integration and unification. The tendency is more and more the other way ... Only the graduate student, poor beast of burden that he is, can be expected to know a little of each. As the number of physicists increases, each specialty becomes more self-sustaining and self-contained. Such Balkanization carries physics, and indeed, every science further away, from natural philosophy, which, intellectually, is the meaning and goal of science.
Science, The Center of Culture (1970), 92. Quoted by Victor F. Weisskopf, 'One Hundred Years of the Physical Review', in H. Henry Stroke, Physical Review: The First Hundred Years: a Selection of Seminal Papers and Commentaries, Vol. 1, 15.
Science quotes on:  |  Beast (32)  |  Expectation (46)  |  Goal (81)  |  Graduate Student (2)  |  Intellect (157)  |  Knowledge (1128)  |  Meaning (87)  |  Natural Philosophy (21)  |  Need (211)  |  Physicist (130)  |  Science (1699)  |  Self-Sustaining (2)  |  Specialty (8)  |  Tendency (40)  |  Unification (9)

Surely the mitochondrion that first entered another cell was not thinking about the future benefits of cooperation and integration; it was merely trying to make its own living in a tough Darwinian world
Wonderful Life: the Burgess Shale and the Nature of History (1990), 310.
Science quotes on:  |  Benefit (54)  |  Cell (125)  |  Cooperation (27)  |  Darwinian (5)  |  Future (229)  |  Living (44)  |  Thinking (222)  |  Tough (8)  |  Try (103)

The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon… when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms.
Thιorie Analytique de la Chaleur (1822), Art. 428, trans. Ivor Grattan-Guinness.
Science quotes on:  |  Equation (69)

The powers which tend to preserve, and those which tend to change the condition of the earth's surface, are never in equilibrio; the latter are, in all cases, the most powerful, and, in respect of the former, are like living in comparison of dead forces. Hence the law of decay is one which suffers no exception: The elements of all bodies were once loose and unconnected, and to the same state nature has appointed that they should all return... TIME performs the office of integrating the infinitesimal parts of which this progression is made up; it collects them into one sum, and produces from them an amount greater than any that can be assigned.
Illustrations of the Huttonian Theory of the Earth (1802), 116-7.
Science quotes on:  |  Amount (20)  |  Appointment (5)  |  Assignment (10)  |  Change (291)  |  Collection (38)  |  Comparison (53)  |  Condition (119)  |  Decay (31)  |  Earth (487)  |  Equilibrium (16)  |  Exception (33)  |  Force (194)  |  Greater (36)  |  Infinitesimal (8)  |  Law (418)  |  Loose (11)  |  Nature (1029)  |  Performance (27)  |  Power (273)  |  Preservation (28)  |  Production (105)  |  Progression (9)  |  Return (35)  |  State (96)  |  Sum (30)  |  Surface (74)  |  Tendency (40)  |  Time (439)  |  Unconnected (3)

This integrative action in virtue of which the nervous system unifies from separate organs an animal possessing solidarity, an individual, is the problem before us.
The Integrative Action of the Nervous System (1906), 2.
Science quotes on:  |  Action (151)  |  Animal (309)  |  Individual (177)  |  Nervous System (11)  |  Organ (60)  |  Possession (37)  |  Problem (362)  |  Separate (46)  |  Unification (9)  |  Virtue (55)


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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- 90 -
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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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