Thus Quotes - page 77
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
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
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
Which alternative is worse, I wonder?” she said. "To deny death and thus risk never being wholly alive, or to face oblivion squarely and risk paralysis by dread?”
"Nobody knows,” I said. "It's ambiguous.”
"If I ever get to be God,” she said, unleashing the grin of the person who'd invented Largesse, "my first act will be to make ambiguity illegal.
James K. Morrow
The characteristic method of social invention in general and of the development of negative capability in particular is to seize on deviant, subsidiary, or repressed elements in present or remembered experience and to push them toward a dominant position, all the while changing them in the course of this extension.... [T]he most successful transmutations over the long run-the ones least vulnerable to subversion by practical rivalry, moral indignation or aspiration, and by theoretical insight-are likely to be those that permit or invite further tinkering. Thus, they may be repeatedly corrected rather than entirely replaced.
Roberto Mangabeira Unger
If society is organized to insulate its own arrangements from challenged and change, and thus to give itself the semblance of a natural object or an alien fate, the noncomputable and the nonmodular aspects of the mind will remain no more than a penumbral light around the darkness of computability and modularity. However, as society acquires the features of democratic experimentalism, those aspects become central to the life of the mind. The hold of the innate mental faculty on our experience gets turbinated by a political construction.
Roberto Mangabeira Unger
It is hard to suggest a remedy for this situation, which is one no military man enjoys. One alternative would be to refuse to permit military officers to appear before Congress and leave the defense of military matters to the civilian secretaries. This is the solution followed in Great Britain and many European countries. I doubt that it will ever be accepted in the United States, where the COngress wants to hear the facts from military men who presumably are without political motivation. A second alternative would be to take the position that the advice of the Chiefs of Staff to their civilian superiors is privileged and not to be revealed under Congressional interrogation. Thus far the Executive authority has not seen fit to raise the storm such a stand would create.
Maxwell D. Taylor
In Brazil as in the United States, we find two voices of a New World promise of happinessː a promise to raise up human life to the exuberance of nature itself while breaking down the hierarchies and privileges that keep people distant from one another. A society of originals whose enhanced powers and self-possession enable them to accept one another more fully is the aim of this American and Brazilian dream. Translated into another, more universal vocabulary, this longing represents one form of the effort to reconcile a pagan ambition of greatness with a Christian idea of tenderness, purging the former of its impulse toward masterfulness and the latter of its knack for resentment. Thus, empowerment and solidarity can come more fully together.
Roberto Mangabeira Unger
The earlier political thinkers used the term "organization" in the broadest sense of the term, that is, with reference to the widest aspects of the patterns of political forces in a given state. Thus a political society might be organized as a monarchy, aristocracy, or democracy, as a city-state, feudal state, a national state, imperial state, or a world state. Emphasis was also placed on the organs of organization. These came to be standardized in the course of time under the categories of legislative, executive, and judicial organs, the combination of which in some form of balance was held to be the indispensable basis of sound organization.
Charles Edward Merriam
It has been thought, correctly and nicely, that everyone who is in peril will be helped. Practically this is implemented in the way that everyone who can say the word "asylum" is allowed to enter Europe and Finland, that word creates a subjective right to cross the border. Even for no proper reason, one gets a full investigation that lasts years, and if the preconditions for an asylum are not met, one can avoid coercive measures and thus stay in the country which he entered wrongly.
Sauli Niinisto
There exists also another type of galaxy agglomeration. These have diameters between roughly one and ten times those of large clusters, but have much smaller densitities; they are usually irregular, with patchy density variations and no central concentration. The larger and most conspicuous of these agglomerations may contain several clusters, which explains why they have been given the name "superclusters." In their longer dimensions, crossing times exceed the age of the Universe. They are thus unrelaxed. Unrelaxed apperance, together with large size, might be taken as a definition of superclusters.
Jan Oort
But a sculpture which sets out to achieve the same ends demands an almost unbelievable effort of concentration. Practically none of the episodes or moments of such a legend, [of Prometheus ] really lends itself to sculpture, and the sculptors of the nineteenth century were often quite careless or foolish in the choice of the moment which they set out to represent. Their works could thus become cluttered with all sorts of narrative details which detract from the monumental quality of the whole... That's why, in my 'Prometheus', I represent the fire as an integral part of the presence or appearance of the hero; he stands there before us in all his awe-inspiring grandeur, a human figure that seemed in the eyes of the men who first saw him to be actually consumed by the fire that he was bearing.
Ossip Zadkine
The most successful, hence most prominent amongst these grammarians was Panini. His grammar, surpassing all others in tightness and precision, became the standard and remained so undisputedly until today. Panini was able to joint the original devanagari language into an exact framework of rules, thus preserving it for the posterity. Since his time, this language is called Sanskrit, "joined together, refined.”.
Pāṇini
The author of the oldest extant Sanskrit grammar was Panini, a native of extreme north-west India, ... His work consists of nearly 4000 aphorisms, each of which owing to the extreme conciseness of the style, generally consists of not more than two or three words. Hence, the whole grammar could be printed within the compass of about thirty-five octavo pages. Yet it describes the entire Sanskrit language with a completeness which has never been equalled elsewhere. Thus it is at once the shortest and the fullest grammar in the world.
Pāṇini
I think that every woman who has any margin of time or money to spare should adopt some one public interest, some philanthropic undertaking, or some social agitation of reform, and give to that cause whatever time and work she may be able to afford; thus completing her life by adding to her private duties the noble effort to advance God's Kingdom beyond the bounds of her home.
Frances Power Cobbe
Thus it is with all pictures, there are many layers, and with good reason an analysis nearly always deals with the last [layer]. The last layer in a superficial sense. But how then can one talk of what one cannot see, the overpainted or wiped-off layers, how to go about for example, photographs that are like slates with layers which no longer exist. The answer is that they exists nevertheless, taken up into the visible layer by a rubbing-off, but the problem, on the whole, is how one deals with the visible layer. The angle-sure, viewpoint seeking and in the worse sense 'analytic' intercourse with the picture.
Per Kirkeby
Under the new circumstances discontent is universal; all the workers feel depressed under capitalist superiority; fuel for explosions has accumulated everywhere. It is not for others, it is for themselves if they join the fight. As long as they feel isolated, afraid to lose their job, uncertain what the comrades will do, without firm unity, they shrink from action. Once, however, they take up the fight, they are changed into new personalities; selfish fear recedes to the background and forth spring the forces of community, solidarity and devotion, rousing courage and perseverance. These are contagious; the example of fighting activity rouses in others, who feel in themselves the same forces awakening, the spirit of mutual and of self-confidence. Thus the wild strike as a prairie fire may spring over to other enterprises and involve ever greater masses.
Antonie Pannekoek
In the production under common ownership the bookkeeping is a public matter; it lies open to all. The workers have always a complete view of the course of the whole process. Only in this way they are able to discuss matters in the sectional assemblies and in the shop-committees, and to decide on what has to be done. The numerical results are made visible, moreover, by statistical tables, by graphs and pictures that display the situation at a glance. This information is not restricted to the personnel of the shop; it is a public matter, open to all outsiders. Every shop is only a member in the social production, and also the connection of its doings with the work outside is expressed in the book-keeping. Thus insight in the production going on in every enterprise is a piece of common knowledge for all the producers.
Antonie Pannekoek
