„Mathematical maturity is anyhow an uncertain concept, for the mind’s natural competence seems to change with age, its purview variable.“

Quelle: "Mathematical retrospections," 2013, p. 142

Letzte Aktualisierung 4. Juni 2020. Geschichte
Robert Langlands Foto
Robert Langlands
kanadischer Mathematiker 1936

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George Klir Foto

„Among the various paradigmatic changes in science and mathematics in this century, one such change concerns the concept of uncertainty.“

—  George Klir American computer scientist 1932 - 2016

In science, this change has been manifested by a gradual transition from the traditional view, which insists that uncertainty is undesirable in science and should be avoided by all possible means, to an alternative view, which is tolerant of uncertainty and insists that science cannot avoid it. According to the traditional view, science should strive for certainty in all its manifestations (precision, specificity, sharpness, consistency, etc.); hence, uncertainty (imprecision, nonspecificity, vagueness, inconsistency,etc.) is regarded as unscientific. According to the alternative (or modem) view, uncertainty is considered essential to science; it is not only an unavoidable plague, but it has, in fact, a great utility.
Quelle: Fuzzy sets and fuzzy logic (1995), p. 1.

Henri Bergson Foto

„A woman's will
Is changeful and uncertain still.“

—  John Conington British classical scholar 1825 - 1869

Quelle: Translations, The Aeneid of Virgil (1866), Book IV, p. 134

Lotfi A. Zadeh Foto

„A linguistic variable is a variable whose values are words or sentences in a natural or synthetic language.“

—  Lotfi A. Zadeh Electrical engineer and computer scientist 1921 - 2017

Variante: A linguistic variable is defined as a variable whose values are sentences in a natural or artificial language.
Quelle: 1970s, Outline of a new approach to the analysis of complex systems and decision processes (1973), p. 28

Eduard Jan Dijksterhuis Foto
Sheri S. Tepper Foto

„To my mind, the expression of divinity is in variety, and the more variable the creation, the more variable the creatures that surround us, botanical and zoological, the more chance we have to learn and to see into life itself, nature itself.“

—  Sheri S. Tepper American fiction writer 1929 - 2016

Locus interview (1998)
Kontext: To my mind, the expression of divinity is in variety, and the more variable the creation, the more variable the creatures that surround us, botanical and zoological, the more chance we have to learn and to see into life itself, nature itself. If we were just human beings, living in a spaceship, with an algae farm to give us food, we would not be moved to learn nearly as many things as we are moved by living on a world, surrounded by all kinds of variety. And when I see that variety being first decimated, and then halved — and I imagine in another hundred years it may be down by 90% and there'll be only 10% of what we had when I was a child — that makes me very sad, and very despairing, because we need variety. We came from that, we were born from that, it's our world, the world in which we became what we have become.

„It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws. Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members.
On the other hand, the mathematics of variable magnitudes—function theory or analysis—considers mathematical forms in their genesis. By writing the equation of the parabola, we express its law of generation, the law according to which the variable point moves. The path, produced before the eyes of the 113 student by a point moving in accordance to this law, is the parabola.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy. But it is exactly in this respect that our view of nature is so far above that of the ancients; that we no longer look on nature as a quiescent complete whole, which compels admiration by its sublimity and wealth of forms, but that we conceive of her as a vigorous growing organism, unfolding according to definite, as delicate as far-reaching, laws; that we are able to lay hold of the permanent amidst the transitory, of law amidst fleeting phenomena, and to be able to give these their simplest and truest expression through the mathematical formulas“

—  Christian Heinrich von Dillmann German educationist 1829 - 1899

Quelle: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 37.

Viktor Schauberger Foto
H.P. Lovecraft Foto

„I have no use for the machine age or any of its conceptions, methods, & ideals.“

—  H.P. Lovecraft American author 1890 - 1937

Letter to Frank Belknap Long (27 February 1931), in Selected Letters III, 1929-1931 edited by August Derleth and Donald Wandrei, p. 300
Non-Fiction, Letters, to Frank Belknap Long
Kontext: All I want is to know things. The black gulph of the infinite is before me... I have no use for the machine age or any of its conceptions, methods, & ideals. I have use only for abstract cognition without social or utilitarian connotations; the thing which Thales & Anaxagoras & Heraclitus went after, & which was clearly definable by the word philosophy until those pragmatical puffballs Socrates & Plato threw a monkey-wrench into the works & crippled human thought for the next two millennia. Now it is a matter of perfect indifference to me whether or not baser interests cluster round the search for truth & lick the molasses-drops that ooze out of the fact-barrel. This apelike parasitism of the herd means nothing either for or against the abstract is-or-isn't quest which Thales began, Democritus continued, & Einstein prolongs. If machine-culture chooses to worship "science", that's its own business. It doesn't imply that the abstract process of cognition-craving turns about & reciprocally worships machine-culture!... Cognition, as such, is completely without social or aesthetic implications except so far as it places certain obvious contradictions of natural laws, & certain pointless exaltations of empty trivialities, in a light so unfavourable as to encourage obsolescence. It is nobody's tool or handmaiden—it is itself alone. Practically speaking, the mind likely to worship pure cognition most sincerely is that most of all opposed to industrialism & standardisation. Cognition is that branch of human desire & celebration most antipodally removed from anything envisaged or wished by Thomas A. Edison, Henry Ford, & the late Charles P. Steinmetz. It is the enemy of urban civilisation as it is the enemy of all handicaps which cripple the free individualistic excursions of the disinterested intellect into unknown cosmic space. It is the sworn ally of beauty because it is itself one of the supreme forms of beauty—the catharsis of a primal, titanic urge which links man to the uttermost gulfs of dramatic immensity. It is one with the greatest music & the loftiest poetry—being perhaps a glimpse of the liberating & expanding reality which both are blindly seeking.

J.M.W. Turner Foto

„In our variable climate where [all] the seasons are recognizable in one day, where all the vapoury turbulence involves the face of things, where nature seems to sport in all: her dignity and dispensing incidents for the artist’s study.... how happily is the landscape painter situated, how roused by every change in nature in every moment, that allows no languor even in her effects which she places before him, and demands most peremptorily every moment his admiration and investigation, to store his mind with every change of time and place.“

—  J.M.W. Turner British Romantic landscape painter, water-colourist, and printmaker 1775 - 1851

Quote from Turner's lectures, 1811; as cited in Life and Work of J.M.W. Turner, Andrew Wilton; London: Academy Editions, 1979; as quoted in 'A brief history of weather in European landscape art', John E. Thornes, in Weather Volume 55, Issue 10 Oct. 2000, p. 367-368
In 1811 already Turner gave his first lectures as Professor of Perspective; in one of his lectures he spoke of the advantages of the British climate for landscape artists
1795 - 1820

Georg Cantor Foto
William James Foto

„Age is a very high price to pay for maturity.“

—  William James American philosopher, psychologist, and pragmatist 1842 - 1910

Maneka Gandhi Foto

„We are changing the law and I am personally working on it to bring 16-year-olds into the purview. According to the police, 50 per cent of the crimes are committed by 16-year-olds who know the Juvenile Justice Act. But now for premeditated murder, rape, if we bring them into the purview of the adult world, then it will scare them.“

—  Maneka Gandhi Indian politician and activist 1956

On the Juvenile Justice Act, as quoted in "Juveniles who commit rape should be tried as adults: Maneka Gandhi" http://ibnlive.in.com/news/juveniles-who-commit-rape-should-be-tried-as-adults-maneka-gandhi/485770-37-64.html, IBNLive (14 July 2014)
2011-present

Georg Cantor Foto
Cassius Jackson Keyser Foto

„The golden age of mathematics - that was not the age of Euclid, it is ours.“

—  Cassius Jackson Keyser American mathematician and journalist of pronounced philosophical inclinations 1862 - 1947

Quelle: The Human Worth of Rigorous Thinking: Essays and Addresses, p. 268

Joseph Addison Foto

„There is not so variable a thing in Nature as a lady's head-dress.“

—  Joseph Addison politician, writer and playwright 1672 - 1719

No. 98 (22 June 1711).
The Spectator (1711–1714)

Immanuel Kant Foto
George Klir Foto

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“