Division Quotes (34 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.

**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!

*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.]*

*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.

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.

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.

Biology is the only science in which multiplication means the same thing as division.

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?

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.
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.

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.

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.

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.

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.

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.

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.
Mathematics—a wonderful science, but it hasn't yet come up with a way to divide one tricycle between three small boys.

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.

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.

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.

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.

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.

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.

The division between life and nonlife is perhaps an artificial one.

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 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.

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)]*
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.
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.

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.

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.

Words divide, pictures unite.

[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.

“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.”

“I suppose-” Alice was beginning, but the Red Queen answered for her.

“Bread-and-butter, of course.”