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Divide Quotes (77 quotes)

“Divide et impera” is as true in algebra as in statecraft; but no less true and even more fertile is the maxim “auge et impera”.The more to do or to prove, the easier the doing or the proof.
In 'Proof of the Fundamental Theorem of Invariants', Philosophic Magazine (1878), 186. In Collected Mathematical Papers, 3, 126. [The Latin phrases, “Divide/auge et impera” translate as “Divide/increase and rule”.
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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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Copernicus, who rightly did condemn
This eldest systeme, form’d a wiser scheme;
In which he leaves the Sun at Rest, and rolls
The Orb Terrestial on its proper Poles;
Which makes the Night and Day by this Career,
And by its slow and crooked Course the Year.
The famous Dane, who oft the Modern guides,
To Earth and Sun their Provinces divides:
The Earth’s Rotation makes the Night and Day,
The Sun revolving through th’ Eccliptic Way
Effects the various seasons of the Year,
Which in their Turn for happy Ends appear.
This Scheme or that, which pleases best, embrace,
Still we the Fountain of their Motion trace.
Kepler asserts these Wonders may be done
By the Magnetic Vertue of the Sun,
Which he, to gain his End, thinks fit to place
Full in the Center of that mighty Space,
Which does the Spheres, where Planets roll, include,
And leaves him with Attractive Force endu’d.
The Sun, thus seated, by Mechanic Laws,
The Earth, and every distant Planet draws;
By which Attraction all the Planets found
Within his reach, are turn'd in Ether round.
In Creation: A Philosophical Poem in Seven Books (1712), book 2, l. 430-53, p.78-9.
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Prospero: Hast thou, spirit,
Performed, to point, the tempest that I bade thee?
Ariel: To every article.
I boarded the king’s ship. Now on the beak,
Now in the waist, the deck, in every cabin,
I flamed amazement.
Sometime I’d divide
And burn in many places; on the topmast,
The yards, and bowsprit would I flame distinctly,
Then meet and join. Jove’s lightnings, the precursors
O’ th’ dreadful thunderclaps, more momentary
And sight-outrunning were not. The fire and cracks
Of sulphurous roaring the most mighty Neptune
Seem to besiege, and make his bold waves tremble;
Yea, his dread trident shake.
In The Tempest (1611), Act 1, Scene 2, line 193-206.
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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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A New Arithmetic: “I am not much of a mathematician,” said the cigarette, “but I can add nervous troubles to a boy, I can subtract from his physical energy, I can multiply his aches and pains, I can divide his mental powers, I can take interest from his work and discount his chances for success.”
Anonymous
In Henry Ford, The Case Against the Little White Slaver (1914), Vol. 3, 40.
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A sound Physics of the Earth should include all the primary considerations of the earth's atmosphere, of the characteristics and continual changes of the earth's external crust, and finally of the origin and development of living organisms. These considerations naturally divide the physics of the earth into three essential parts, the first being a theory of the atmosphere, or Meteorology, the second, a theory of the earth's external crust, or Hydrogeology, and the third, a theory of living organisms, or Biology.
Hydrogéologie (1802), trans. A. V. Carozzi (1964), 18.
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A student who wishes now-a-days to study geometry by dividing it sharply from analysis, without taking account of the progress which the latter has made and is making, that student no matter how great his genius, will never be a whole geometer. He will not possess those powerful instruments of research which modern analysis puts into the hands of modern geometry. He will remain ignorant of many geometrical results which are to be found, perhaps implicitly, in the writings of the analyst. And not only will he be unable to use them in his own researches, but he will probably toil to discover them himself, and, as happens very often, he will publish them as new, when really he has only rediscovered them.
From 'On Some Recent Tendencies in Geometrical Investigations', Rivista di Matematica (1891), 43. In Bulletin American Mathematical Society (1904), 443.
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All sorts of dung and compost contain some matter which, when mixed with the soil, ferments therein; and by such ferment dissolves, crumbles, and divides the earth very much. This is the chief and almost only use of dung. … This proves, that its (manure) use is not to nourish, but to dissolve, i.e., divide the terrestrial matter, which affords nourishment to the Mouths of vegetable roots.
His underestimate of the value of manure. In The Horse-Hoeing Husbandry (1733), 18.
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All that comes above that surface [of the globe] lies within the province of Geography. All that comes below that surface lies inside the realm of Geology. The surface of the earth is that which, so to speak, divides them and at the same time “binds them together in indissoluble union.” We may, perhaps, put the case metaphorically. The relationships of the two are rather like that of man and wife. Geography, like a prudent woman, has followed the sage advice of Shakespeare and taken unto her “an elder than herself;” but she does not trespass on the domain of her consort, nor could she possibly maintain the respect of her children were she to flaunt before the world the assertion that she is “a woman with a past.”
From Anniversary Address to Geological Society of London (20 Feb 1903), 'The Relations of Geology', published in Quarterly Journal of the Geological Society of London (22 May 1903), 59, Part 2, lxxviii. As reprinted in Annual Report of the Board of Regents of the Smithsonian Institution (1904), 373.
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Amoeba has her picture in the book,
Proud Protozoon!—Yet beware of pride,
All she can do is fatten and divide;
She cannot even read, or sew, or cook…
The Worm can crawl
But has no eyes to look.
The Jelly-fish can swim
But lacks a bride.
Essay read at the Heretics Club, Cambridge (May 1922), 'Philosophic Ants', collected in Essays of a Biologist (1923), 176.
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As we push ever more deeply into the universe, probing its secrets, discovering its way, we must also constantly try to learn to cooperate across the frontiers that really divide earth’s surface.
In 'The President’s News Conference at the LBJ Ranch' (29 Aug 1965). Collected in Public Papers of the Presidents of the United States: Lyndon B. Johnson: 1965 (1966), 945.
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Between animal and human medicine, there is no dividing line—nor should there be.
On the occasion of the centenary of the Veterinary College in Berlin (1856). Translation of original German, “Zwischen Tier und Menschenmedizin gibt es keine Trennlinie, noch sollte eine bestehen.” English translation quoted (without citation), as opening remark in J.V. Klauder, 'Interrelations of human and veterinary medicine', New England Journal of Medicine (23 Jan 1958), 258, No. 4, 170.
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But as no two (theoreticians) agree on this (skin friction) or any other subject, some not agreeing today with what they wrote a year ago, I think we might put down all their results, add them together, and then divide by the number of mathematicians, and thus find the average coefficient of error. (1908)
In Artificial and Natural Flight (1908), 3. Quoted in John David Anderson, Jr., Hypersonic and High Temperature Gas Dynamics (2000), 335.
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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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Consider the eighth category, which deals with stones. Wilkins divides them into the following classifications: ordinary (flint, gravel, slate); intermediate (marble, amber, coral); precious (pearl, opal); transparent (amethyst, sapphire); and insoluble (coal, clay, and arsenic). The ninth category is almost as alarming as the eighth. It reveals that metals can be imperfect (vermilion, quicksilver); artificial (bronze, brass); recremental (filings, rust); and natural (gold, tin, copper). The whale appears in the sixteenth category: it is a viviparous, oblong fish. These ambiguities, redundances, and deficiencies recall those attributed by Dr. Franz Kuhn to a certain Chinese encyclopedia entitled Celestial Emporium of Benevolent Knowledge. On those remote pages it is written that animals are divided into (a) those that belong to the Emperor, (b) embalmed ones, (c) those that are trained, (d) suckling pigs, (e) mermaids, (f) fabulous ones, (g) stray dogs, (h) those that are included in this classification, (i) those that tremble as if they were mad, (j) innumerable ones, (k) those drawn with a very fine camel's hair brush, (l) others, (m) those that have just broken a flower vase, (n) those that resemble flies from a distance.
Other Inquisitions 1937-1952 (1964), trans. Ruth L. C. Simms, 103.
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Events in the past may be roughly divided into those which probably never happened and those which do not matter. This is what makes the trade of historian so attractive.
Dean Inge
In 'Prognostications', Assessments and Anticipations (1929), 149.
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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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For those who have seen the Earth from space, and for the hundreds and perhaps thousands more who will, the experience most certainly changes your perspective. The things that we share in our world are far more valuable than those which divide us.
As quoted, without citation, in Jeffrey O. Bennett, The Cosmic Perspective (1999), 24.
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For what is thought to be a ‘system’ is after all, just conventional, and I do not see how one is supposed to divide up the world objectively so that one can make statements about parts.
…...
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Great knowledge embraces the whole: small knowledge, a part only. [Great knowledge encompasses everything. The little one divides everything.]
As translated from the Chinese original by Herbert A. Giles in Chuang Tzŭ: Mystic, Moralist, and Social Reformer (1889), 13. The brackets contain a translation from a version written in Spanish on the website frasesypensamientos.com.ar
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Have the changes which lead us from one geologic state to another been, on a long average uniform in their intensity, or have they consisted of epochs of paroxysmal and catastrophic action, interposed between periods of comparative tranquillity? These two opinions will probably for some time divide the geological world into two sects, which may perhaps be designated as the Uniformitarians and the Catastrophists.
In 'Review of Charles Lyell's Principles of Geology', Quarterly Review (1832), 47, 126.
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He who can properly define and divide is to be considered a god.
Plato
Quoted by Francis Bacon, in Novum Organum. As translated by Joseph Devey in The Physical and Metaphysical Works of Lord Bacon Including the Advancement of Learning and Novum Organum (1808), 491.
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How twins are born my discourse will explain thus. The cause is chiefly the nature of the womb in woman. For if it has grown equally on either side of its mouth, and if it opens equally, and also dries equally after menstruation, it can give nourishment, if it conceive the secretion of the man so that it immediately divides into both parts of the womb equally. Now if the seed secreted from both parents be abundant and strong, it can grow in both places, as it masters the nourishment that reaches it. In all other cases twins are not formed. Now when the secretion from both parents is male, of necessity boys are begotten in both places; but when from both it is female, girls are begotten. But when one secretion is female and the other male, whichever masters the other gives the embryo its sex. Twins are like one another for the following reasons. First, the places are alike in which they grow; then they were secreted together; then they grow by the same nourishment, and at birth they reach together the light of day.
Regimen, in Hippocrates, trans. W. H. S. Jones (1931), Vol. 4, 273.
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I contend that the continued racial classification of Homo sapiens represents an outmoded approach to the general problem of differentiation within a species. In other words, I reject a racial classification of humans for the same reasons that I prefer not to divide into subspecies the prodigiously variable West Indian land snails that form the subject of my own research.
…...
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If it were always necessary to reduce everything to intuitive knowledge, demonstration would often be insufferably prolix. This is why mathematicians have had the cleverness to divide the difficulties and to demonstrate separately the intervening propositions. And there is art also in this; for as the mediate truths (which are called lemmas, since they appear to be a digression) may be assigned in many ways, it is well, in order to aid the understanding and memory, to choose of them those which greatly shorten the process, and appear memorable and worthy in themselves of being demonstrated. But there is another obstacle, viz.: that it is not easy to demonstrate all the axioms, and to reduce demonstrations wholly to intuitive knowledge. And if we had chosen to wait for that, perhaps we should not yet have the science of geometry.
In Gottfried Wilhelm Leibnitz and Alfred Gideon Langley (trans.), New Essays Concerning Human Understanding (1896), 413-414.
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If the world has begun with a single quantum, the notions of space and would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time. I think that such a beginning of the world is far enough from the present order of Nature to be not at all repugnant. It may be difficult to follow up the idea in detail as we are not yet able to count the quantum packets in every case. For example, it may be that an atomic nucleus must be counted as a unique quantum, the atomic number acting as a kind of quantum number. If the future development of quantum theory happens to turn in that direction, we could conceive the beginning of the universe in the form of a unique atom, the atomic weight of which is the total mass of the universe. This highly unstable atom would divide in smaller and smaller atoms by a kind of super-radioactive process.
In a seminal short letter (457 words), 'The Beginning of the World from the Point of View of Quantum Theory', Nature (9 May 1931), 127, 706.
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If we view mathematical speculations with reference to their use, it appears that they should be divided into two classes. To the first belong those which furnish some marked advantage either to common life or to some art, and the value of such is usually determined by the magnitude of this advantage. The other class embraces those speculations which, though offering no direct advantage, are nevertheless valuable in that they extend the boundaries of analysis and increase our resources and skill. Now since many investigations, from which great advantage may be expected, must be abandoned solely because of the imperfection of analysis, no small value should be assigned to those speculations which promise to enlarge the field of anaylsis.
In Novi Comm. Petr., Vol. 4, Preface.
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If you want to build a ship, don’t recruit the men to gather the wood, divide the work and give orders. Instead, teach them to yearn for vast and endless sea.
Not found as such in a work by Saint-Exupéry. Probably an anonymous paraphrase of a related passage in Citadelle (1948), section 75, 687. See the quote beginning, “One will weave the canvas…” on the Antoine de Saint-Exupéry Quotes page of this website.
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In Aristotle the mind, regarded as the principle of life, divides into nutrition, sensation, and faculty of thought, corresponding to the inner most important stages in the succession of vital phenomena.
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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 the beginning God created the heaven and earth. And the earth was waste and void; and darkness was upon the face of the deep: and the spirit of God moved upon the face of the waters. … God said, “Let there be a vault in the waters to divide the waters in two.” And so it was. God made the vault, and it divided the waters above the vault from the waters under the vault. God called the vault “heaven.”
Bible
Genesis 1:1 in The Holy Bible Containing the Old and New Testaments Translated Out of the Original Tongues. Printed for the Universities of Oxford and Cambridge (1895), 1.
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In the discussion of the. energies involved in the deformation of nuclei, the concept of surface tension of nuclear matter has been used and its value had been estimated from simple considerations regarding nuclear forces. It must be remembered, however, that the surface tension of a charged droplet is diminished by its charge, and a rough estimate shows that the surface tension of nuclei, decreasing with increasing nuclear charge, may become zero for atomic numbers of the order of 100. It seems therefore possible that the uranium nucleus has only small stability of form, and may, after neutron capture, divide itself into two nuclei of roughly equal size (the precise ratio of sizes depending on liner structural features and perhaps partly on chance). These two nuclei will repel each other and should gain a total kinetic energy of c. 200 Mev., as calculated from nuclear radius and charge. This amount of energy may actually be expected to be available from the difference in packing fraction between uranium and the elements in the middle of the periodic system. The whole 'fission' process can thus be described in an essentially classical way, without having to consider quantum-mechanical 'tunnel effects', which would actually be extremely small, on account of the large masses involved.
[Co-author with Otto Robert Frisch]
Lise Meitner and O. R. Frisch, 'Disintegration of Uranium by Neutrons: a New Type of Nuclear Reaction', Nature (1939), 143, 239.
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It is customary to connect Medicine with Botany, yet scientific treatment demands that we should consider each separately. For the fact is that in every art, theory must be disconnected and separated from practice, and the two must be dealt with singly and individually in their proper order before they are united. And for that reason, in order that Botany, which is, as it were, a special branch of Natural Philosophy [Physica], may form a unit by itself before it can be brought into connection with other sciences, it must be divided and unyoked from Medicine.
Methodi herbariae libri tres (1592), translated in Agnes Arber, Herbals: Their Origin and Evolution, 2nd edition (1938), 144.
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It is distinctly proved, by this series of observations, that the reflex function exists in the medulla independently of the brain; in the medulla oblongata independently of the medulla spinalis; and in the spinal marrow of the anterior extremities, of the posterior extremities, and of the tail, independently of that of each other of these parts, respectively. There is still a more interesting and satisfactory mode of performing the experiment: it is to divide the spinal marrow between the nerves of the superior and inferior extremities. We have then two modes of animal life : the first being the assemblage of the voluntary and respiratory powers with those of the reflex function and irritability; the second, the two latter powers only: the first are those which obtain in the perfect animal, the second those which animate the foetus. The phenomena are precisely what might have been anticipated. If the spinal marrow be now destroyed, the irritability alone remains,—all the other phenomena having ceased.
'On the Reflex Function of the Medulla Oblongata and Medulla Spinalis,' Philosophical Transactions of the Royal Society, 1833, 123, 650.
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It is not strictly demonstrated that atoms are indivisible; but it appears that they are not divided by the laws of nature.
In A Philosophical Dictionary (1824), Vol. 1, 339.
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It seems probable to me that God, in the beginning, formed matter in solid, massy, hard, impenetrable, moveable particles, of such sizes and figures, and with such other properties, and in such proportions to space, as most conduced to the end for which He formed them; and that these primitive particles, being solids, are incomparably harder than any porous bodies compounded of them, even so very hard as never to wear or break in pieces; no ordinary power being able to divide what God had made one in the first creation.
From Opticks (1704, 2nd ed., 1718), 375-376.
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Know, Nature’s children all divide her care, The fur that warms a monarch warmed a bear.
In 'Essay On Man', The Works of Alexander Pope (1871), Vol. 2, 403.
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Literature has her quacks no less than medicine, and they are divided into two classes; those who have erudition without genius, and those who have volubility, without depth; we shall get second-hand sense from the one, and original nonsense from the other.
Reflection 552, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 232.
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Looking back over the last thousand years, one can divide the development of the machine and the machine civilization into three successive but over-lapping and interpenetrating phases: eotechnic, paleotechnic, neotechnic … Speaking in terms of power and characteristic materials, the eotechnic phase is a water-and-wood complex: the paleotechnic phase is a coal-and-wood complex… The dawn-age of our modern technics stretches roughly from the year 1000 to 1750. It did not, of course, come suddenly to an end in the middle of the eighteenth century. A new movement appeared in industrial society which had been gathering headway almost unnoticed from the fifteenth century on: after 1750 industry passed into a new phase, with a different source of power, different materials, different objectives.
Technics and Civilisation (1934), 109.
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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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Medicine is the science by which we learn the various states of the human body in health and when not in health, and the means by which health is likely to be lost and, when lost, is likely to be restored back to health. In other words, it is the art whereby health is conserved and the art whereby it is restored after being lost. While some divide medicine into a theoretical and a practical [applied] science, others may assume that it is only theoretical because they see it as a pure science. But, in truth, every science has both a theoretical and a practical side.
Avicenna
'The Definition of Medicine', in The Canon of Medicine, adapted by L. Bakhtiar (1999), 9.
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Newton was probably responsible for the concept that there are seven primary colours in the spectrum—he had a strong interest in musical harmonies and, since there are seven distinct notes in the musical scale, he divided up the spectrum into spectral bands with widths corresponding to the ratios of the small whole numbers found in the just scale.
In 'Light and Colour', Trevor Lamb and Janine Bourriau, Colour: Art & Science (1995), 72.
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Nonmathematical people sometimes ask me, “You know math, huh? Tell me something I’ve always wondered, What is infinity divided by infinity?” I can only reply, “The words you just uttered do not make sense. That was not a mathematical sentence. You spoke of ‘infinity’ as if it were a number. It’s not. You may as well ask, 'What is truth divided by beauty?’ I have no clue. I only know how to divide numbers. ‘Infinity,’ ‘truth,’ ‘beauty’—those are not numbers.”
From Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003), 16.
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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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One of the most immediate consequences of the electrochemical theory is the necessity of regarding all chemical compounds as binary substances. It is necessary to discover in each of them the positive and negative constituents... No view was ever more fitted to retard the progress of organic chemistry. Where the theory of substitution and the theory of types assume similar molecules, in which some of the elements can be replaced by others without the edifice becoming modified either in form or outward behaviour, the electrochemical theory divides these same molecules, simply and solely, it may be said, in order to find in them two opposite groups, which it then supposes to be combined with each other in virtue of their mutual electrical activity... I have tried to show that in organic chemistry there exist types which are capable, without destruction, of undergoing the most singular transformations according to the nature of the elements.
Traité de Chemie Appliquée aux Arts, Vol. I (1828), 53. Trans. J. R. Partington, A History of Chemistry, Vol. 4, 366.
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Petr Beckmann has divided the men who made history into two classes, the thinkers and the thugs. The Greeks were the thinkers and the Romans were the thugs. The general law seems to be that the thugs always win, but the thinkers always outlive them.
In Mathematical Circles Squared (1972), 153. Petr Beckman wrote: “150 years saw the confrontation of Athens and Sparta, the thinkers against the thugs. The thugs always win, but the thinkers always outlast them”, in A History of Pi (1970), 34.
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Returning now to the Malay Archipelago, we find that all the wide expanse of sea which divides Java, Sumatra, and Borneo from each other, and from Malacca and Siam, is so shallow that ships can anchor in any part of it, since it rarely exceeds forty fathoms in depth; and if we go as far as the line of a hundred fathoms, we shall include the Philippine Islands and Bali, east of Java. If, therefore, these islands have been separated from each other and the continent by subsidence of the intervening tracts of land, we should conclude that the separation has been comparatively recent, since the depth to which the land has subsided is so small. It is also to be remarked that the great chain of active volcanoes in Sumatra and Java furnishes us with a sufficient cause for such subsidence, since the enormous masses of matter they have thrown out would take away the foundations of the surrounding district; and this may be the true explanation of the often-noticed fact that volcanoes and volcanic chains are always near the sea. The subsidence they produce around them will, in time, make a sea, if one does not already exist.
Malay Archipelago
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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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Suppose [an] imaginary physicist, the student of Niels Bohr, is shown an experiment in which a virus particle enters a bacterial cell and 20 minutes later the bacterial cell is lysed and 100 virus particles are liberated. He will say: “How come, one particle has become 100 particles of the same kind in 20 minutes? That is very interesting. Let us find out how it happens! How does the particle get in to the bacterium? How does it multiply? Does it multiply like a bacterium, growing and dividing, or does it multiply by an entirely different mechanism ? Does it have to be inside the bacterium to do this multiplying, or can we squash the bacterium and have the multiplication go on as before? Is this multiplying a trick of organic chemistry which the organic chemists have not yet discovered ? Let us find out. This is so simple a phenomenon that the answers cannot be hard to find. In a few months we will know. All we have to do is to study how conditions will influence the multiplication. We will do a few experiments at different temperatures, in different media, with different viruses, and we will know. Perhaps we may have to break into the bacteria at intermediate stages between infection and lysis. Anyhow, the experiments only take a few hours each, so the whole problem can not take long to solve.”
[Eight years later] he has not got anywhere in solving the problem he set out to solve. But [he may say to you] “Well, I made a slight mistake. I could not do it in a few months. Perhaps it will take a few decades, and perhaps it will take the help of a few dozen other people. But listen to what I have found, perhaps you will be interested to join me.”
From 'Experiments with Bacterial Viruses (Bacteriophages)', Harvey Lecture (1946), 41, 161-162. As cited in Robert Olby, The Path of the Double Helix: The Discovery of DNA (1974, 1994), 237.
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Suppose we divide the space into little volume elements. If we have black and white molecules, how many ways could we distribute them among the volume elements so that white is on one side and black is on the other? On the other hand, how many ways could we distribute them with no restriction on which goes where? Clearly, there are many more ways to arrange them in the latter case. We measure “disorder” by the number of ways that the insides can be arranged, so that from the outside it looks the same. The logarithm of that number of ways is the entropy. The number of ways in the separated case is less, so the entropy is less, or the “disorder” is less.
In 'Order And Entropy', The Feynman Lectures on Physics (1964), 46-7.
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That the master manufacturer, by dividing the work to be executed into different processes, each requiring different degrees of skill or of force, can purchase precisely the precise quantity of both which is necessary for each process; whereas, if the whole work were executed by one workman, that person must possess sufficient skill to perform the most difficult, and sufficient strength to execute the most laborious, of the operations into which the art is divided.
In 'On the Division of Labour', Economy of Machinery and Manufactures (1st ed., 1832), chap. 18, 127.
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The absolute extent of land in the Archipelago is not greater than that contained by Western Europe from Hungary to Spain; but, owing to the manner in which the land is broken up and divided, the variety of its productions is rather in proportion to the immense surface over which the islands are spread, than to the quantity of land which they contain.
Malay Archipelago
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The fact that, with respect to size, the viruses overlapped with the organisms of the biologist at one extreme and with the molecules of the chemist at the other extreme only served to heighten the mystery regarding the nature of viruses. Then too, it became obvious that a sharp line dividing living from non-living things could not be drawn and this fact served to add fuel for discussion of the age-old question of “What is life?”
Nobel Lecture (12 Dec 1946), 'The Isolation and Properties of Crystalline Tobacco Mosaic Virus', collected in Nobel Lectures in Chemistry (1999), 140.
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The general public has long been divided into two parts those who think science can do anything, and those who are afraid it will.
From interview with Graham Chedd, 'The Lady Gets Her Way', New Scientist (5 Jul 1973), 59, No. 853, 15-16.
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The invention of the differential calculus marks a crisis in the history of mathematics. The progress of science is divided between periods characterized by a slow accumulation of ideas and periods, when, owing to the new material for thought thus patiently collected, some genius by the invention of a new method or a new point of view, suddenly transforms the whole subject on to a higher level.
In An Introduction to Mathematics (1911), 217. Whitehead continued by quoting the poet, Percy Shelley, who compared the slow accumulation of thoughts leading to an avalanche following the laying down of a great truth. See the poetic quote beginning, “The sun-awakened avalanche…” on the Percy Shelley Quotations page.
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The moment one has offered an original explanation for a phenomenon which seems satisfactory, that moment affection for his intellectual child springs into existence, and as the explanation grows into a definite theory his parental affections cluster about his offspring and it grows more and more dear to him. ... There springs up also unwittingly a pressing of the theory to make it fit the facts and a pressing of the facts to make them fit the theory... To avoid this grave danger, the method of multiple working hypotheses is urged. It differs from the simple working hypothesis in that it distributes the effort and divides the affections... In developing the multiple hypotheses, the effort is to bring up into view every rational exploration of the phenomenon in hand and to develop every tenable hypothesis relative to its nature, cause or origin, and to give to all of these as impartially as possible a working form and a due place in the investigation. The investigator thus becomes the parent of a family of hypotheses; and by his parental relations to all is morally forbidden to fasten his affections unduly upon anyone. ... Each hypothesis suggests its own criteria, its own method of proof, its own method of developing the truth, and if a group of hypotheses encompass the subject on all sides, the total outcome of means and of methods is full and rich.
'Studies for Students. The Method of Multiple Working Hypotheses', Journal of Geology (1897), 5, 840-6.
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The most wonderful mystery of life may well be the means by which it created so much diversity from so little physical matter. The biosphere, all organisms combined, makes up only about one part in ten billion of the earth’s mass. … Yet life has divided into millions of species, the fundamental units, each playing a unique role in relation to the whole.
In 'The Most Fundamental Unit', The Diversity of Life (1992), 35.
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The next difficulty is in the economical production of small lights by electricity. This is what is commonly meant by the phrase, ‘dividing the electric light.’ Up to the present time, and including Mr. Edison’s latest experiments, it appears that this involves an immense loss of efficiency. Next comes the difficulty of distributing on any large scale the immense electric currents which would be needed.
In 'A Scientific View of It: Prof. Henry Morton Not Sanguine About Edison’s Success', New York Times (28 Dec 1879), 1.
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The Telescope, in fact, was comparatively little used until astronomy annexed that important branch of physics to its aid which gave us a Clock—a means of dividing time in the most accurate manner.
In Stargazing: Past and Present (1878), 2.
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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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The word atom signifies without parts—not to be divided. You divide it in thought; for, if you were to divide it in reality, it would no longer be an atom.
In A Philosophical Dictionary (1824), Vol. 1, 338.
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These facts shaw that mitosis is due to the co-ordinate play of an extremely complex system of forces which are as yet scarcely comprehended. Its purpose is, however, as obvious as its physiological explanation is difficult. It is the end of mitosis to divide every part of the chromatin of the mother-cell equally between the daughter-nuclei. All the other operations are tributary to this. We may therefore regard the mitotic figure as essentially an apparatus for the distribution of the hereditary substance, and in this sense as the especial instrument of inheritance.
The Cell in Development and Inheritance (1896), 86.
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This frustration of reading the tabloid press… it would easy to become convinced that the human race is on a mission to divide things into two clean columns… Good or evil, healthy or deadly or natural or chemical… everything organic and natural is good, ignoring the fact that organic natural substances include arsenic… Everything chemical is bad, ignoring that fact the everything is chemicals. Everything is chemicals! The day they discover yoga mats are carcinogenic will be the happiest day of my life.
Introducing his song, 'The Fence', on DVD, Live at the Royal Albert Hall (2011).
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To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.
His handwritten note in the margin, beside the eighth proposition, in his copy of Diophantus' Arithmetica, Book 2. It is known as Fermat’s Last Theorem. (A proof remained elusive until 1994.) In Précis des Oeuvres Mathématiques de P. Fermat et de l'Arithmetique de Diophante (1853), 53-54. As translated by Vera Sandford in David Eugene Smith, A Source Book in Mathematics (1929), 212.
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We [Frisch and Lise Meitner] walked up and down in the snow, I on skis and she on foot (she said and proved that she could get along just as fast that way), and gradually the idea took shape that this was no chipping or cracking of the nucleus but rather a process to be explained by Bohr’s idea that the nucleus was like a liquid drop; such a drop might elongate and divide itself.
Otto Frisch and John A. Wheeler, 'The Discovery of Fission', Physics Today, Nov 1967, 20, 47.
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We all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.
In The Ambidextrous Universe by Martin Gardner (1964).
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We divide the world to stop us feeling frightened,
Into wrong and into right and
Into black and into white…
Yeah we want the world binary, binary - 01001000!
From song, 'The Fence' (2010).
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We divide the world…
Into chemical and natural,
Into fictional and factual.
Into science and supernatural
. But it’s actually naturally not that white and black.
From song, 'The Fence' (2010).
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We divide the world…
Into things that give you cancer and the things that cure cancer
And the things that don't cause cancer, but there's a chance they will cause cancer in the future.
From song, 'The Fence' (2010).
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What politicians do not understand is that [Ian] Wilmut discovered not so much a technical trick as a new law of nature. We now know that an adult mammalian cell can fire up all the dormant genetic instructions that shut down as it divides and specializes and ages, and thus can become a source of new life. You can outlaw technique; you cannot repeal biology.
Writing after Wilmut's successful cloning of the sheep, Dolly, that research on the cloning of human beings cannot be suppressed.
'A Special Report on Cloning'. Charles Krauthammer in Time (10 Mar 1997).
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When I heard the learn’d astronomer,
When the proofs, the figures, were ranged in columns before me,
When I was shown the charts and diagrams, to add, divide, and measure them,
When I sitting heard the astronomer where he lectured with much applause in the lecture-room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander’d by myself,
In the mystical moist night-air, and from time to time,
Look’d up in perfect silence at the stars.
In Leaves of Grass (1881, 1882), 214.
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Words divide, pictures unite.
In Otto Neurath, Empiricism and Sociology (1973), 217.
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Yes, we have to divide up our time like that, between our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.
…...
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You have only to take in what you please and leave out what you please; to select your own conditions of time and place; to multiply and divide at discretion; and you can pay the National Debt in half an hour. Calculation is nothing but cookery.
(1849). Epigraph, without citation, in M.J. Moroney, Facts From Figures (1951), 334.
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You may not divide the seamless coat of learning. What education has to impart is an intimate sense for the power of ideas, for the beauty of ideas, and for the structure of ideas, together with a particular body of knowledge which has peculiar reference to the life of the being possessing it.
In 'The Aims of Education', The Aims of Education and Other Essays (1929), 23.
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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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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 -
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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
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Rene Descartes
Francis Crick
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Francis Bacon
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- 10 -
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John Watson
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Michio Kaku
Isaac Asimov
Charles Darwin
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Florence Nightingale
Isaac Newton


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