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Who said: “The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it... That is how we will preserve our planet, commanded to our care by God. That’s what will lend meaning to the creed our fathers once declared.”
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Home > Category Index for Science Quotations > Category Index D > Category: Division

Division Quotes (65 quotes)

“The Universe repeats itself, with the possible exception of history.” Of all earthly studies history is the only one that does not repeat itself. ... Astronomy repeats itself; botany repeats itself; trigonometry repeats itself; mechanics repeats itself; compound long division repeats itself. Every sum if worked out in the same way at any time will bring out the same answer. ... A great many moderns say that history is a science; if so it occupies a solitary and splendid elevation among the sciences; it is the only science the conclusions of which are always wrong.
In 'A Much Repeated Repetition', Daily News (26 Mar 1904). Collected in G. K. Chesterton and Dale Ahlquist (ed.), In Defense of Sanity: The Best Essays of G.K. Chesterton (2011), 82.
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Ode to The Amoeba
Recall from Time's abysmal chasm
That piece of primal protoplasm
The First Amoeba, strangely splendid,
From whom we're all of us descended.
That First Amoeba, weirdly clever,
Exists today and shall forever,
Because he reproduced by fission;
He split himself, and each division
And subdivision deemed it fitting
To keep on splitting, splitting, splitting;
So, whatsoe'er their billions be,
All, all amoebas still are he.
Zoologists discern his features
In every sort of breathing creatures,
Since all of every living species,
No matter how their breed increases
Or how their ranks have been recruited,
From him alone were evoluted.
King Solomon, the Queen of Sheba
And Hoover sprang from that amoeba;
Columbus, Shakespeare, Darwin, Shelley
Derived from that same bit of jelly.
So famed is he and well-connected,
His statue ought to be erected,
For you and I and William Beebe
Are undeniably amoebae!
(1922). Collected in Gaily the Troubadour (1936), 18.
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Dass die bis jetzt unzerlegten chemischen Elemente absolut unzerlegbare Stoffe seien, ist gegenwärtig mindestens sehr unwahrscheinlich. Vielmehr scheint es, dass die Atome der Elemente nicht die letzten, sondern nur die näheren Bestandtheile der Molekeln sowohl der Elemente wie der Verbindungen bilden, die Molekeln oder Molecule als Massentheile erster, die Atome als solche zweiter Ordnung anzusehen sind, die ihrerseits wiederum aus Massentheilchen einer dritten höheren Ordnung bestehen werden.
That the as yet undivided chemical elements are absolutely irreducible substances, is currently at least very unlikely. Rather it seems, that the atoms of elements are not the final, but only the immediate constituents of the molecules of both the elements and the compounds—the Molekeln or molecule as foremost division of matter, the atoms being considered as second order, in turn consisting of matter particles of a third higher order.
[Speculating in 1870, on the existence of subatomic particles, in opening remark of the paper by which he became established as co-discoverer of the Periodic Law.]
'Die Natur der chemischen Elemente als Function ihrer Atomgewichte' ('The Nature of the Chemical Elements as a Function of their Atomic Weight'), Annalen der Chemie (1870), supp. b, 354. Original German paper reprinted in Lothar Meyer and Dmitry Ivanovich Mendeleyev, Das natürliche System der chemischen Elemente: Abhandlungen (1895), 9. Translation by Webmaster, with punctuation faithful to the original, except a comma was changed to a dash to improve readability.
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L’astronomie … est l’arbitre de la division civile du temps, l'ame de la chronologie et de la géographie, et l’unique guide des navigateurs.
Astronomy is the governor of the civil division of time, the soul of chronology and geography, and the only guide of the navigator.
Original French in Leçons Élémentaires d’Astronomie Géométrique et Physique (1764), iii. English as quoted in Preface to Hannah Mary Bouvier Peterson, Bouvier’s Familiar Astronomy; Or, An Introduction to the Study of the Heavens (1855), Preface, 5.
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A casual glance at crystals may lead to the idea that they were pure sports of nature, but this is simply an elegant way of declaring one's ignorance. With a thoughtful examination of them, we discover laws of arrangement. With the help of these, calculation portrays and links up the observed results. How variable and at the same time how precise and regular are these laws! How simple they are ordinarily, without losing anything of their significance! The theory which has served to develop these laws is based entirely on a fact, whose existence has hitherto been vaguely discerned rather than demonstrated. This fact is that in all minerals which belong to the same species, these little solids, which are the crystal elements and which I call their integrant molecules, have an invariable form, in which the faces lie in the direction of the natural fracture surfaces corresponding to the mechanical division of the crystals. Their angles and dimensions are derived from calculations combined with observation.
Traité de mineralogie ... Publié par le conseil des mines (1801), Vol. 1, xiii-iv, trans. Albert V. and Marguerite Carozzi.
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A cell has a history; its structure is inherited, it grows, divides, and, as in the embryo of higher animals, the products of division differentiate on complex lines. Living cells, moreover, transmit all that is involved in their complex heredity. I am far from maintaining that these fundamental properties may not depend upon organisation at levels above any chemical level; to understand them may even call for different methods of thought; I do not pretend to know. But if there be a hierarchy of levels we must recognise each one, and the physical and chemical level which, I would again say, may be the level of self-maintenance, must always have a place in any ultimate complete description.
'Some Aspects of Biochemistry', The Irish Journal of Medical Science (1932), 79, 346.
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As in the domains of practical life so likewise in science there has come about a division of labor. The individual can no longer control the whole field of mathematics: it is only possible for him to master separate parts of it in such a manner as to enable him to extend the boundaries of knowledge by creative research.
In Die reine Mathematik in den Jahren 1884-99, 10. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 94.
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As the Director of the Theoretical Division of Los Alamos, I participated at the most senior level in the World War II Manhattan Project that produced the first atomic weapons.
Now, at age 88, I am one of the few remaining such senior persons alive. Looking back at the half century since that time, I feel the most intense relief that these weapons have not been used since World War II, mixed with the horror that tens of thousands of such weapons have been built since that time—one hundred times more than any of us at Los Alamos could ever have imagined.
Today we are rightly in an era of disarmament and dismantlement of nuclear weapons. But in some countries nuclear weapons development still continues. Whether and when the various Nations of the World can agree to stop this is uncertain. But individual scientists can still influence this process by withholding their skills.
Accordingly, I call on all scientists in all countries to cease and desist from work creating, developing, improving and manufacturing further nuclear weapons - and, for that matter, other weapons of potential mass destruction such as chemical and biological weapons.
[On the occasion of the 50th Anniversary of Hiroshima.]
Letter, Bulletin of the Atomic Scientists (Nov 1995), 51:6, 3.
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At fertilization, these two 'haploid' nuclei are added together to make a 'diploid' nucleus that now contains 2a, 2b and so on; and, by the splitting of each chromosome and the regulated karyokinetic separation of the daughter chromosomes, this double series is inherited by both of the primary blastomeres. In the resulting resting nuclei the individual chromosomes are apparently destroyed. But we have the strongest of indications that, in the stroma of the resting nucleus, every one of the chromosomes that enters the nucleus survives as a well-defined region; and as the cell prepares for its next division this region again gives rise to the same chromosome (Theory of the Individuality of the Chromosomes). In this way the two sets of chromosomes brought together at fertilization are inherited by all the cells of the new individual. It is only in the germinal cells that the so called reduction division converts the double series into a single one. Out of the diploid state, the haploid is once again generated.
Arch. Zellforsch, 1909, 3, 181, trans. Henry Harris, The Birth of the Cell (1999), 171-2.
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Before an experiment can be performed, it must be planned—the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted—nature's answer must be understood properly. These two tasks are those of the theorist, who finds himself always more and more dependent on the tools of abstract mathematics. Of course, this does not mean that the experimenter does not also engage in theoretical deliberations. The foremost classical example of a major achievement produced by such a division of labor is the creation of spectrum analysis by the joint efforts of Robert Bunsen, the experimenter, and Gustav Kirchoff, the theorist. Since then, spectrum analysis has been continually developing and bearing ever richer fruit.
'The Meaning and Limits of Exact Science', Science (30 Sep 1949), 110, No. 2857, 325. Advance reprinting of chapter from book Max Planck, Scientific Autobiography (1949), 110.
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Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably nothing in the modern world could have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility. … Our modern power of easy reckoning with decimal fractions is the most miraculous result of a perfect notation.
In Introduction to Mathematics (1911), 59.
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Biology is the only science in which multiplication means the same thing as division.
Anonymous
[Note: which is what cells do.]
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But, as we consider the totality of similarly broad and fundamental aspects of life, we cannot defend division by two as a natural principle of objective order. Indeed, the ‘stuff’ of the universe often strikes our senses as complex and shaded continua, admittedly with faster and slower moments, and bigger and smaller steps, along the way. Nature does not dictate dualities, trinities, quarterings, or any ‘objective’ basis for human taxonomies; most of our chosen schemes, and our designated numbers of categories, record human choices from a cornucopia of possibilities offered by natural variation from place to place, and permitted by the flexibility of our mental capacities. How many seasons (if we wish to divide by seasons at all) does a year contain? How many stages shall we recognize in a human life?
…...
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Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
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Every creature has its own food, and an appropriate alchemist with the task of dividing it ... The alchemist takes the food and changes it into a tincture which he sends through the body to become blood and flesh. This alchemist dwells in the stomach where he cooks and works. The man eats a piece of meat, in which is both bad and good. When the meat reaches the stomach, there is the alchemist who divides it. What does not belong to health he casts away to a special place, and sends the good wherever it is needed. That is the Creator's decree... That is the virtue and power of the alchemist in man.
Volumen Medicinae Paramirum (c. 1520), in Paracelsus: Essential Readings, edited by Nicholas Goodrick-Clarke (1990), 50-1.
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Every utterance from government - from justifying 90-day detention to invading other countries [and] to curtailing civil liberties - is about the dangers of religious division and fundamentalism. Yet New Labour is approving new faith schools hand over fist. We have had the grotesque spectacle of a British prime minister, on the floor of the House of Commons, defending - like some medieval crusader - the teaching of creationism in the science curriculum at a sponsor-run school whose running costs are wholly met from the public purse.
In The Guardian (10 Apr 2006).
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Fertilization of mammalian eggs is followed by successive cell divisions and progressive differentiation, first into the early embryo and subsequently into all of the cell types that make up the adult animal. Transfer of a single nucleus at a specific stage of development, to an enucleated unfertilized egg, provided an opportunity to investigate whether cellular differentiation to that stage involved irreversible genetic modification. The first offspring to develop from a differentiated cell were born after nuclear transfer from an embryo-derived cell line that had been induced to became quiescent. Using the same procedure, we now report the birth of live lambs from three new cell populations established from adult mammary gland, fetus and embryo. The fact that a lamb was derived from an adult cell confirms that differentiation of that cell did not involve the irreversible modification of genetic material required far development to term. The birth of lambs from differentiated fetal and adult cells also reinforces previous speculation that by inducing donor cells to became quiescent it will be possible to obtain normal development from a wide variety of differentiated cells.
[Co-author of paper announcing the cloned sheep, ‘Dolly’.]
In I. Wilmut, A. E. Schnieke, J. McWhir, et al., 'Viable Offspring Derived from Petal and Adult Mammalian Cells', Nature (1997), 385, 810.
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From the infinitely great down to the infinitely small, all things are subject to [the laws of nature]. The sun and the planets follow the laws discovered by Newton and Laplace, just as the atoms in their combinations follow the laws of chemistry, as living creatures follow the laws of biology. It is only the imperfections of the human mind which multiply the divisions of the sciences, separating astronomy from physics or chemistry, the natural sciences from the social sciences. In essence, science is one. It is none other than the truth.
In Cours d’Economie Politique (1896-97).
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Further study of the division phenomena requires a brief discussion of the material which thus far I have called the stainable substance of the nucleus. Since the term nuclear substance could easily result in misinterpretation..., I shall coin the term chromatin for the time being. This does not indicate that this substance must be a chemical compound of a definite composition, remaining the same in all nuclei. Although this may be the case, we simply do not know enough about the nuclear substances to make such an assumption. Therefore, we will designate as chromatin that substance, in the nucleus, which upon treatment with dyes known as nuclear stains does absorb the dye. From my description of the results of staining resting and dividing cells... it follows that the chromatin is distributed throughout the whole resting nucleus, mostly in the nucleoli, the network, and the membrane, but also in the ground-substance. In nuclear division it accumulates exclusively in the thread figures. The term achromatin suggests itself automatically for the unstainable substance of the nucleus. The terms chromatic and achromatic which will be used henceforth are thus explained.
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However much we may enlarge our ideas of the time which has elapsed since the Niagara first began to drain the waters of the upper lakes, we have seen that this period was one only of a series, all belonging to the present zoological epoch; or that in which the living testaceous fauna, whether freshwater or marine, had already come into being. If such events can take place while the zoology of the earth remains almost stationary and unaltered, what ages may not be comprehended in those successive tertiary periods during which the Flora and Fauna of the globe have been almost entirely changed. Yet how subordinate a place in the long calendar of geological chronology do the successive tertiary periods themselves occupy! How much more enormous a duration must we assign to many antecedent revolutions of the earth and its inhabitants! No analogy can be found in the natural world to the immense scale of these divisions of past time, unless we contemplate the celestial spaces which have been measured by the astronomer.
Travels in North America (1845), Vol. 1, 51-2.
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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 do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics.
to Henry Roscoe, Professor of Chemistry at Owens College (2 Jun 1870), B.C.S Archive Quoted in R.H. Kargon, Science in Victorian Manchester (1977), 215.
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I may finally call attention to the probability that the association of paternal and maternal chromosomes in pairs and their subsequent separation during the reducing division as indicated above may constitute the physical basis of the Mendelian law of heredity.
'On the Morphology of the Chromosome Group in Brachystola Magna', Biological Bulletin (1902), 4, 39.
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I thought that the wisdom of our City had certainly designed the laudable practice of taking and distributing these accompts [parish records of christenings and deaths] for other and greater uses than [merely casual comments], or, at least, that some other uses might be made of them; and thereupon I ... could, and (to be short) to furnish myself with as much matter of that kind ... the which when I had reduced into tables ... so as to have a view of the whole together, in order to the more ready comparing of one Year, Season, Parish, or other Division of the City, with another, in respect of all Burials and Christnings, and of all the Diseases and Casualties happening in each of them respectively...
Moreover, finding some Truths and not-commonly-believed opinions to arise from my meditations upon these neglected Papers, I proceeded further to consider what benefit the knowledge of the same would bring to the world, ... with some real fruit from those ayrie blossoms.
From Natural and Political Observations Mentioned in a Following Index and Made upon Bills of Mortality (1662), Preface. Reproduced in Cornelius Walford, The Insurance Cyclopaedia (1871), Vol. 1, 286-287.
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I took this view of the subject. The medulla spinalis has a central division, and also a distinction into anterior and posterior fasciculi, corresponding with the anterior and posterior portions of the brain. Further we can trace down the crura of the cerebrum into the anterior fasciculus of the spinal marrow, and the crura of the cerebellum into the posterior fasciculus. I thought that here I might have an opportunity of touching the cerebellum, as it were, through the posterior portion of the spinal marrow, and the cerebrum by the anterior portion. To this end I made experiments which, though they were not conclusive, encouraged me in the view I had taken. I found that injury done to the anterior portion of the spinal marrow, convulsed the animal more certainly than injury done to the posterior portion; but I found it difficult to make the experiment without injuring both portions.
Idea of a New Anatomy of the Brain (1811), 21-22.
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In early times, when the knowledge of nature was small, little attempt was made to divide science into parts, and men of science did not specialize. Aristotle was a master of all science known in his day, and wrote indifferently treatises on physics or animals. As increasing knowledge made it impossible for any one man to grasp all scientific subjects, lines of division were drawn for convenience of study and of teaching. Besides the broad distinction into physical and biological science, minute subdivisions arose, and, at a certain stage of development, much attention was, given to methods of classification, and much emphasis laid on the results, which were thought to have a significance beyond that of the mere convenience of mankind.
But we have reached the stage when the different streams of knowledge, followed by the different sciences, are coalescing, and the artificial barriers raised by calling those sciences by different names are breaking down. Geology uses the methods and data of physics, chemistry and biology; no one can say whether the science of radioactivity is to be classed as chemistry or physics, or whether sociology is properly grouped with biology or economics. Indeed, it is often just where this coalescence of two subjects occurs, when some connecting channel between them is opened suddenly, that the most striking advances in knowledge take place. The accumulated experience of one department of science, and the special methods which have been developed to deal with its problems, become suddenly available in the domain of another department, and many questions insoluble before may find answers in the new light cast upon them. Such considerations show us that science is in reality one, though we may agree to look on it now from one side and now from another as we approach it from the standpoint of physics, physiology or psychology.
In article 'Science', Encyclopedia Britannica (1911), 402.
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In general, the more one augments the number of divisions of the productions of nature, the more one approaches the truth, since in nature only individuals exist, while genera, orders, and classes only exist in our imagination.
Histoire Naturelle (1749), trans. by John Lyon, The 'Initial Discourse' to Buffon’s Histoire Naturelle: The First Complete English Translation, Journal of the History of Biology, 9(1), 1976, 164.
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In the year of chan yan..., Jupiter was in [the Zodiacal Division of] Zi, it rose in the morning and went under in the evening together with the Lunar Mansions Xunu, Xu and Wei. It was very large and bright. Apparently, there was a small reddish (chi) star appended (fu) to its side. This is called “an alliance” (tong meng).
Gan De
As given in Chinese Astronomy and Astrophysics (1981), 5, 242.
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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.
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It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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Making out an income tax is a lesson in mathematics: addition, division, multiplication and extraction.
Anonymous
In Evan Esar, 20,000 Quips and Quotes, 419.
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Mathematics—a wonderful science, but it hasn't yet come up with a way to divide one tricycle between three small boys.
In Bob Phillips, Phillips' Treasury of Humorous Quotations (2004), 171.
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Matter, though divisible in an extreme degree, is nevertheless not infinitely divisible. That is, there must be some point beyond which we cannot go in the division of matter. ... I have chosen the word “atom” to signify these ultimate particles.
Dalton's Manuscript Notes, Royal Institution Lecture 18 (30 Jan 1810). In Ida Freund, The Study of Chemical Composition: An Account of its Method and Historical Development (1910), 288.
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Mechanical action may be derived from heat, and heat may be generated by mechanical action, by means of forces either acting between contiguous parts of bodies, or due to electric excitation; but in no other way known, or even conceivable, in the present state of science. Hence thermo-dynamics falls naturally into two divisions, of which the subjects are respectively, the relation of heat to the forces acting between contiguous parts of bodies, and the relation of heat to electrical agency.
In 'On the Dynamical Theory of Heat, with Numerical Results Deduced from Mr Joule's Equivalent of a Thermal Unit, and M. Regnault's Observations on Steam' (1851). Part VI, 'Thermo Electric Currents' (1854). In Mathematical and Physical Papers (1882), Vol. 1, 232.
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Nature progresses by unknown gradations and consequently does not submit to our absolute division when passing by imperceptible nuances, from one species to another and often from one genus to another. Inevitably there are a great number of equivocal species and in-between specimens that one does not know where to place and which throw our general systems into turmoil.
Jean Piveteau (ed.), Oeuvres Philosophiques de Buffon (1965), 10. Trans. in Paul Farber, 'Buffon and the Concept of Species', in Journal of the History of Biology, 1972, 5, 260.
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Not a single visible phenomenon of cell­division gives even a remote suggestion of qualitative division. All the facts, on the contrary, indicate that the division of the chromatin is carried out with the most exact equality.
The Cell in Development and Inheritance (1896), 306.
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Not all living creatures die. An amoeba, for example, need never die; it need not even, like certain generals, fade away. It just divides and becomes two new amoebas.
In talk, 'Origin of Death' (1970).
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One has to divide one’s time between politics and our equations. But our equations are much more important to me, because politics is for the present, while such an equation is for eternity.
Remark to his assistant, Ernst Straus,(late 1940s) while at Princeton University Institute of Advanced Study. As quoted in Albrecht Fösling and Ewald Osers (trans.), Albert Einstein: A Biography (1997), 725. At the time Einstein was one of the Emergency Committee of Atomic Scientists, concerned with informing the public on the atomic bomb and its effects. (He was its Chairman from May 1946.)
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Ordinarily logic is divided into the examination of ideas, judgments, arguments, and methods. The two latter are generally reduced to judgments, that is, arguments are reduced to apodictic judgments that such and such conclusions follow from such and such premises, and method is reduced to judgments that prescribe the procedure that should be followed in the search for truth.
Ampére expresses how arguments have a logical structure which he expected should be applied to relate scientific theories to experimental evidence. In James R. Hofmann, André-Marie Ampère (1996), 158. Cites Académie des Sciences Ampère Archives, École Normale lecture 15 notes, box 261.
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Quantity is that which is operated with according to fixed mutually consistent laws. Both operator and operand must derive their meaning from the laws of operation. In the case of ordinary algebra these are the three laws already indicated [the commutative, associative, and distributive laws], in the algebra of quaternions the same save the law of commutation for multiplication and division, and so on. It may be questioned whether this definition is sufficient, and it may be objected that it is vague; but the reader will do well to reflect that any definition must include the linear algebras of Peirce, the algebra of logic, and others that may be easily imagined, although they have not yet been developed. This general definition of quantity enables us to see how operators may be treated as quantities, and thus to understand the rationale of the so called symbolical methods.
In 'Mathematics', Encyclopedia Britannica (9th ed.).
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Scientists and Drapers. Why should the botanist, geologist or other-ist give himself such airs over the draper’s assistant? Is it because he names his plants or specimens with Latin names and divides them into genera and species, whereas the draper does not formulate his classifications, or at any rate only uses his mother tongue when he does? Yet how like the sub-divisions of textile life are to those of the animal and vegetable kingdoms! A few great families—cotton, linen, hempen, woollen, silk, mohair, alpaca—into what an infinite variety of genera and species do not these great families subdivide themselves? And does it take less labour, with less intelligence, to master all these and to acquire familiarity with their various habits, habitats and prices than it does to master the details of any other great branch of science? I do not know. But when I think of Shoolbred’s on the one hand and, say, the ornithological collections of the British Museum upon the other, I feel as though it would take me less trouble to master the second than the first.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 218.
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Since disease originates in the elementary cell, the organization and microscopic functions of which reproduce the general organization exactly and in all its relationships, nothing is more suited to simplifying the work of classification and of systematic division than to take the elementary cell as the basis of division.
As quoted in article, Marc Klein,'François-Vincent Raspail', in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1975). Vol.11, 300-301.
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So the dividing line between the wave or particle nature of matter and radiation is the moment “Now”. As this moment steadily advances through time, it coagulates a wavy future into a particle past.
In The Development of X-ray analysis (1975) 13.
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The development of the nucleoplasm during ontogeny may be to some extent compared to an army composed of corps, which are made up of divisions, and these of brigades, and so on. The whole army may be taken to represent the nucleoplasm of the germ-cell: the earliest cell-division … may be represented by the separation of the two corps, similarly formed but with different duties: and the following cell­divisions by the successive detachment of divisions, brigades, regiments, battalions, companies, etc.; and as the groups become simpler so does their sphere of action become limited.
In 'The Continuity of the Germ-plasm as the Foundation of a Theory of Heredity' (1885), Essays upon Heredity and Kindred Biological Problems (1891), Vol. 1, 195.
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The distinguishing of the strata, or layers, in the embryonic membrane was a turning-point in the study of the history of evolution, and placed later researches in their proper light. A division of the (disc-shaped) embryo into an animal and a plastic part first takes place. In the lower part (the plastic or vegetative layer) are a serous and a vascular layer, each of peculiar organization. In the upper part also (the animal or serous germ-layer) two layers are clearly distinguishable, a flesh-layer and a skin-layer. (1828)
Quoted in Ernst Heinrich Philipp August Haeckel, The Evolution of Man (1897), Vol 1, 185.
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The division between life and nonlife is perhaps an artificial one.
Speaking at an international meeting on the origins of life, quoted in E. Eckholm, 'Search for the Origins is Widening', International Herald Tribune (7 Jul 1986). As cited in Stuart R. Hameroff, Ultimate Computing: Biomolecular Consciousness and Nanotechnology (1987), 57. https://books.google.com/books?id=VE9RAAAAMAAJ - 1987
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The divisions of science are not like different lines that meet in one angle, but rather like the branches of trees that join in one trunk.
The Works of Francis Bacon (1815), Vol. 6, 68.
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The extracellular genesis of cells in animals seemed to me, ever since the publication of the cell theory [of Schwann], just as unlikely as the spontaneous generation of organisms. These doubts produced my observations on the multiplication of blood cells by division in bird and mammalian embryos and on the division of muscle bundles in frog larvae. Since then I have continued these observations in frog larvae, where it is possible to follow the history of tissues back to segmentation.
'Ueber extracellulare Eutstehung thierischer Zelleu und üüber Vermehrung derselben durch Theilung', Archiv für Anatomie, Physiologie und Wissenschaftliche Medicin (1852), 1, 49-50. Quoted in Erwin H. Ackerknecht, Rudolf Virchow: Doctor Statesman Anthropologist (1953), 83-4.
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The nucleic acids, as constituents of living organisms, are comparable In importance to proteins. There is evidence that they are Involved In the processes of cell division and growth, that they participate In the transmission of hereditary characters, and that they are important constituents of viruses. An understanding of the molecular structure of the nucleic acids should be of value In the effort to understand the fundamental phenomena of life.
[Co-author with American chemist, B. Corey (1897-1971)]
'A Proposed Structure for the Nucleic Acids', Proceedings of the National Academy of Sciences (1953), 39, 84.
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The observer is not he who merely sees the thing which is before his eyes, but he who sees what parts the thing is composed of. To do this well is a rare talent. One person, from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers; another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing into one mass things which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse than if no analysis had been attempted at all.
In A System of Logic Ratiocinative and Inductive (1858), 216.
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The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand and into an electromagnetic field and matter on the other hand. In reality space will probably be of a uniform character and the present theory will be valid only as a limiting case. For large densities of field and of matter, the field equations and even the field variables which enter into them will have no real significance. One may not therefore assume the validity of the equations for very high density of field and matter, and one may not conclude that the 'beginning of the expansion' must mean a singularity in the mathematical sense. All we have to realise is that the equations may not be continued over such regions.
In O. Nathan and H. Norden (eds.), Einstein on Peace (1960), 640.
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The question of a possible physiological significance, in the resemblance between the action of choline esters and the effects of certain divisions of the involuntary nervous system, is one of great interest, but one for the discussion of which little evidence is available. Acetyl-choline is, of all the substances examined, the one whose action is most suggestive in this direction. The fact that its action surpasses even that of adrenaline, both in intensity and evanescence, when considered in conjunction with the fact that each of these two bases reproduces those effects of involuntary nerves which are absent from the action of the other, so that the two actions are in many directions at once complementary and antagonistic, gives plenty of scope for speculation.
In 'The Action of Certain Esters and Ethers of Choline, and Their Relation to Muscarine', The Journal of Pharmacology and Experimental Therapeutics, 1914-15, 6, 188.
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The result of all these experiments has given place to a new division of the parts of the human body, which I shall follow in this short essay, by distinguishing those which are susceptible of Irritability and Sensibility, from those which are not. But the theory, why some parts of the human body are endowed with these properties, while others are not, I shall not at all meddle with. For I am persuaded that the source of both lies concealed beyond the reach of the knife and microscope, beyond which I do not chuse to hazard many conjectures, as I have no desire of teaching what I am ignorant of myself. For the vanity of attempting to guide others in paths where we find ourselves in the dark, shews, in my humble opinion, the last degree of arrogance and ignorance.
'A Treatise on the Sensible and Irritable Parts of Animals' (Read 1752). Trans. 1755 and reprinted in Bulletin of the Institute of the History of Medicine, 1936, 4(2), 657-8.
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The tendency of the sciences has long been an increasing proclivity of separation and dismemberment … The mathematician turns away from the chemist; the chemist from the naturalist; the mathematician, left to himself divides himself into a pure mathematician and a mixed mathematician, who soon part company … And thus science, even mere physical science, loses all traces of unity. A curious illustration of this result may be observed in the want of any name by which we can designate the students of the knowledge of the material world collectively. We are informed that this difficulty was felt very oppressively by the members of the British Association for the Advancement of Science, at their meetings at York, Oxford and Cambridge, in the last three summers. There was no general term by which these gentlemen could describe themselves with reference to their pursuits … some ingenious gentleman [William Whewell] proposed that, by analogy with artist, they might form Scientist, and added that there could be no scruple … when we have words such as sciolist, economist, and atheist—but this was not generally palatable.
In Review of Mrs Somerville, 'On the Connexion of the Physical Sciences', The Quarterly Review (1834), 51, 58-61.
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There are many arts and sciences of which a miner should not be ignorant. First there is Philosophy, that he may discern the origin, cause, and nature of subterranean things; for then he will be able to dig out the veins easily and advantageously, and to obtain more abundant results from his mining. Secondly there is Medicine, that he may be able to look after his diggers and other workman ... Thirdly follows astronomy, that he may know the divisions of the heavens and from them judge the directions of the veins. Fourthly, there is the science of Surveying that he may be able to estimate how deep a shaft should be sunk … Fifthly, his knowledge of Arithmetical Science should be such that he may calculate the cost to be incurred in the machinery and the working of the mine. Sixthly, his learning must comprise Architecture, that he himself may construct the various machines and timber work required underground … Next, he must have knowledge of Drawing, that he can draw plans of his machinery. Lastly, there is the Law, especially that dealing with metals, that he may claim his own rights, that he may undertake the duty of giving others his opinion on legal matters, that he may not take another man’s property and so make trouble for himself, and that he may fulfil his obligations to others according to the law.
In De Re Metallica (1556), trans. H.C. and L.H. Hoover (1950), 3-4.
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There is only one nature—the division into science and engineering is a human imposition, not a natural one. Indeed, the division is a human failure; it reflects our limited capacity to comprehend the whole.
from Recent Development of Physical Science (p. 10)
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This king [Sesostris] divided the land among all Egyptians so as to give each one a quadrangle of equal size and to draw from each his revenues, by imposing a tax to be levied yearly. But everyone from whose part the river tore anything away, had to go to him to notify what had happened; he then sent overseers who had to measure out how much the land had become smaller, in order that the owner might pay on what was left, in proportion to the entire tax imposed. In this way, it appears to me, geometry originated, which passed thence to Hellas.
Heroditus
(II. c. 109) As quoted in Florian Cajori, A History of Elementary Mathematics (1893), 10, footnoted to C.A. Bretschneider, Die Geometrie und die Geometer vor Eukides (1870). Note that the word geometry itself means “land measurement.”
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We sound the future, and learn that after a period, long compared with the divisions of time open to our investigation, the energies of our system will decay, the glory of the sun will be dimmed and the earth, tideless and inert, will no longer tolerate the race which has for a moment disturbed its solitude. Man will go down into the pit, and all his thoughts will perish.
The Foundations of Belief: Being Notes Introductory to the Study of Theology (1895), 30-1.
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William Blake called division the sin of man; Faraday was a great man because he was utterly undivided. His whole, very harmonious, very well balanced, … and used the brain in the limited way in which it is useful…. [H]e built up his few but precious speculations. Their simplicity rivals with their forcefulness.
In 'The Scientific Grammar of Michael Faraday’s Diaries', Part I, 'The Classic of Science', A Classic and a Founder (1937), collected in Rosenstock-Huessy Papers (1981), Vol. 1, 7.
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Within the nucleus [of a cell] is a network of fibers, a sap fills the interstices of the network. The network resolves itself into a definite number of threads at each division of the cell. These threads we call chromosomes. Each species of animals and plants possesses a characteristic number of these threads which have definite size and sometimes a specific shape and even characteristic granules at different levels. Beyond this point our strongest microscopes fail to penetrate.
In A Critique of the Theory of Evolution (1916), 91.
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Words divide, pictures unite.
In Otto Neurath, Empiricism and Sociology (1973), 217.
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You’re aware the boy failed my grade school math class, I take it? And not that many years later he’s teaching college. Now I ask you: Is that the sorriest indictment of the American educational system you ever heard? [pauses to light cigarette.] No aptitude at all for long division, but never mind. It’s him they ask to split the atom. How he talked his way into the Nobel prize is beyond me. But then, I suppose it’s like the man says, it’s not what you know...
Karl Arbeiter (former teacher of Albert Einstein)
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[On Oxygen, Chlorine, Iodine, Fluorine:] The most important division of ponderable substances seems to be that which represents their electrical energies or their respective inherent states. When the poles of a voltaic apparatus are introduced into a mixture of the simple substances, it is found that four of them go to the positive, while the rest evince their state by passing to the negative pole. As this division coincides with one resulting from a consideration of their most important properties, it is that which I shall adopt as the first.
From 5th Lecture in 1816, in Bence Jones, The Life and Letters of Faraday (1870), Vol. 1, 217-218.
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[Simplicio] is much puzzled and perplexed. I think I hear him say, 'To whom then should we repair for the decision of our controversies if Aristotle were removed from the choir? What other author should we follow in the schools, academies, and studies? What philosopher has written all the divisions of Natural Philosophy, and so methodically, without omitting as much as a single conclusion? Shall we then overthrow the building under which so many voyagers find shelter? Shall we destroy that sanctuary, that Prytaneum, where so many students find commodious harbour; where without exposing himself to the injuries of the air, with only the turning over of a few leaves, one may learn all the secrets of Nature.'
Dialogue on the Great World Systems (1632). Revised and Annotated by Giorgio De Santillana (1953), 66.
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“She can’t do Subtraction.” said the White Queen. “Can you do Division? Divide a loaf by a knife—what's the answer to that?”
“I suppose-” Alice was beginning, but the Red Queen answered for her.
“Bread-and-butter, of course.”
Through the Looking Glass and What Alice Found There (1871, 1897), 189-190.
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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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