Quantity Quotes - page 11
The careful experiments of Joule, who developed heat in various ways by the application of mechanical force, establish almost to a certainty, not only the possibility of increasing the quantity of heat, but also the fact that the newly-produced heat is proportional to the work expended in its production.
Rudolf Clausius
As for negative numbers... most mathematicians of the sixteenth and seventeenth centuries did not accept them... In the fifteenth century Nicolas Chuquet and, in the sixteenth, Stifel both spoke of negative numbers as absurd numbers. ...Descartes accepted them, in part. ...he had shown that, given an equation, one can obtain another whose roots are larger than the original one by any given quantity. Thus an equation with negative roots could be transformed into one with positive roots. Since we can turn false roots into real roots, Descartes was willing to accept negative numbers. Pascal regarded the subtraction of 4 from zero as utter nonsense.
Morris Kline
Because they [the ancient Greeks] feared infinite processes they missed the limit process. In approximating a circle by a polygon they were content to make the difference smaller than any given quantity, but something positive was always left over. Thus the process remained clear to the intuition; the limit process, on the other hand, would have involved the infinitely small.
Morris Kline
When we examine this suggestion, we see that it is no more than a formal acknowledgement of a problem, the problem of how (by what institutional arrangement, by what organization of affairs) the equilibrium prices are to be discovered. Repeated trial and error, while the market stands in suspense awaiting the outcome, is not a practical resort. The number of distinct trials, even if confined to discrete steps of price and quantity, would be so immense that the necessary 'market day' would extend beyond human life-times... [The] theoretical ideal applies to mutually isolated days or moments, each to be treated as perfectly self-contained and looking to no yesterday and no tomorrow. But the real market is dealing with goods inherited from yesterday, and in means of production whose products will not be ready till tomorrow. Meanwhile the non-economic circumstances are changing and rendering each successive equilibrium obsolete.
G. L. S. Shackle
My friends and relations ... urged ... that the quantity [of food] I took was too little for one so advanced in years; against this, I urged that nature was content with little, and that with this small quantity, I had preserved myself for many years in health and activity, that I believed as a man advanced in years, his stomach grew weaker, and therefore the tendency should be to lessen the amount of food rather than to increase. I further reminded them of the two proverbs, which say; he who has a mind to eat a great deal, must eat but little; eating little makes life long, and, living long, he must eat much; and the other proverb was: that, what we leave after making a hearty meal, does us more good than what we have eaten.
Luigi Cornaro
[W]hen a body has experienced any changes, and when after a certain number of transformations it returns to precisely its original state, that is, to that state considered in respect to density, to temperature, to mode of aggregation-let us suppose, I say, that this body is found to contain the same quantity of heat that it contained at first, or else that the quantities of heat absorbed or set free in these different transformations are exactly compensated. This fact has never been called in question. It was first admitted without reflection, and verified afterwards in many cases by experiments with the calorimeter. To deny it would be to overthrow the whole theory of heat to which it serves as a basis. For the rest, we may say in passing, the main principles on which the theory of heat rests require the most careful examination. Many experimental facts appear almost inexplicable in the present state of this theory.
Nicolas Léonard Sadi Carnot
It turns out that certain picture shapes don't allow you to use different kinds of quantity distributions of color for different expressions. The quantities and configurations of colors are as important as the colors themselves. When I first started painting circles, I went fairly quickly to a 6-foot square module. I think de Kooning said in an interview or artist's discussion that he only wanted to make gestures as big as his arm could reach. It struck me that he was saying this physical size had to do with the expressive size of the pictures he wanted to make. And as far as I know, when I got to the 6-foot square size, it was right in terms of myself and wasn't too much of a field. Or it was a field, yet it was still physical. And that's why I used it for so long.
Kenneth Noland
The steam-engine having furnished us with a means of converting heat into a motive power, and our thoughts being thereby led to regard a certain quantity of work as an equivalent for the amount of heat expended in its production, the idea of establishing theoretically some fixed relation between a quantity of heat and the quantity of work which it can possibly produce, from which relation conclusions regarding the nature of heat itself might be deduced, naturally presents itself. Already, indeed, have many successful efforts been made with this view; I believe, however, that they have not exhausted the subject, but that, on the contrary, it merits the continued attention of physicists... The most important investigation in connexion with this subject is that of S. Carnot.
Rudolf Clausius
Those things, which are experienced to be in their whole nature, or in their most remarkable properties, so contrary to animal life, as in a small quantity to prove destructive to it, are called Poisons: whether they are hurtful by being taken inwardly at the mouth, or communicated to the body externally by a wound.
Richard Mead
We resolved to end our poison-enquiries by tasting the venomous liquor. According, having diluted a quantity of it, with a very little warm water, several of us ventured to put some of it upon the tip of our tongues. We all agreed, that it tasted very sharp and fiery, as if the tongue had been struck through with something scalding or burning. This sensation went off in two or three hours: and one gentleman, who would not be satisfied without trying a large drop undiluted, found his tongue swelled with a little inflammation and the soreness lasted two days. But neither his nor our boldness was attended with any ill consequence.
Richard Mead
[Another significant aspect of the concept of growth is the distinction that Mesarovic and Pestel draw between "undifferentiated" and "organic" growth. The former type of growth, according to these authors, consists of mere replication of cells by cellular division, usually expotentially, with an increase in quantity alone. The latter type of growth] involves a process of differentiation, which means that various groups of cells begin to differ in structure and function... During and after differentiation the number of cells can still increase, and the organs grow in size, but while some organs grow, others might celine.
Mihajlo D. Mesarovic
The historical associations of the word algebra almost substantiate the sordid character of the subject. The word comes from the title of a book written by... Al Khowarizmi. In this title, al-jebr w' almuqabala, the word al-jebr meant transposing a quantity from one side of an equation to another and muqabala meant simplification of the resulting expressions. Figuratively, al-jebr meant restoring the balance of an equation... When the Moors reached Spain... algebrista... came to mean a bonesetter... and signs reading Algebrista y Sangrador (bonesetter and bloodletter) were found over Spanish barber shops. Thus it might be said that there is a good historical basis for the fact that the word algebra stirs up disagreeable thoughts.
Morris Kline
To a person whose experience has never been brought into relation with the object sulphur, the name signifies nothing; to the scientist... his concept involves the ideas of specific gravity, crystalline form, element, atom, and the like, derived from past experiences. His concept is distinguished from the other by involving... number or quantity.
J. R. Partington
Definite portions of a manifoldness, distinguished by a mark or by a boundary, are called Quanta. Their comparison with regard to quantity is accomplished in the case of discrete magnitudes by counting, in the case of continuous magnitudes by measuring. Measure consists in the superposition of the magnitudes to be compared; it therefore requires a means of using one magnitude as the standard for another. In the absence of this, two magnitudes can only be compared when one is a part of the other; in which case also we can only determine the more or less and not the how much. The researches which can in this case be instituted about them form a general division of the science of magnitude in which magnitudes are regarded not as existing independently of position and not as expressible in terms of a unit, but as regions in a manifoldness.
Bernhard Riemann
The method applied by Newton to the grounding of the Infinitesimal Calculus, and which since the beginning of this century has been recognised by the best mathematicians as the only one that furnishes sure results, is the method of limits. The method consists in this, viz., instead of considering a continuous transition from one value of a quantity to another, from one position to another, or, speaking generally, from one determination of a concept to another, one considers in the first place a transition through a finite number of intervals and then allows the number of these intervals to increase so that the distances of two successive points of division all decrease infinitely.
Bernhard Riemann
Measure-relations can only be studied in abstract notions of quantity, and their dependence on one another can only be represented by formulæ. On certain assumptions, however, they are decomposable into relations which, taken separately, are capable of geometric representation; and thus it becomes possible to express geometrically the calculated results. In this way, to come to solid ground, we cannot, it is true, avoid abstract considerations in our formulæ, but at least the results of calculation may subsequently be presented in a geometric form. The foundations of these two parts of the question are established in the celebrated memoir of Gauss, Disqusitiones generales circa superficies curvas.
Bernhard Riemann
The discontinuation of bodily exercises afforded a proportionable quantity of leisure time for the cultivation of the mind; so that the manners of mankind were softened by degrees, and learning, which had been so long neglected, became fashionable, and was esteemed an indispensable mark of a polite education.
Joseph Strutt
