Étienne Gilson quote: “Hume's skepticism, therefore, descends in a direct line from Cartesian mathematicism.”

“Every New Year is the direct descendant, isn't it, of a long line of proven criminals?”

Ogden Nash (1902–1971) American poet

"Good-by, Old Year, You Oaf or Why Don't They Pay the Bonus?" in The Primrose Path (1935)

“I'm descended from a long line of preachers and policemen.”

Tom Robbins (1932) American writer

High Times interview (2002)
Context: I'm descended from a long line of preachers and policemen. Now, it's common knowledge that cops are congenital liars, and evangelists spend their lives telling fantastic tales in such a way as to convince otherwise rational people that they're factual. So, I guess I come by my narrative inclinations naturally. Moreover, I grew up in the rural South, where, although television has been steadily destroying it, there has always existed a love of colorful verbiage.

“Scientists don't frighten me. They think in straight, predictable, directable, and therefore MISdirectable lines. It's children and conjurers who frighten me. Against scientists, I feel quite confident.”

James P. Hogan book Code of the Lifemaker

Code of the Lifemaker (1983)

“While the rest of the species is descended from apes, redheads are descended from cats.”

Mark Twain (1835–1910) American author and humorist

“[The computer is also the direct descendant of the telegraph as it enables one… to] "transmit information without transporting material"”

J. C. R. Licklider Libraries of the future

Source: Libraries of the future, 1965, p. 6 as cited in: Rodney James Giblett (2008) Sublime communication technologies. p. 175.

“Let the letters a b c denote the three angular points of a rectilineal triangle. If the point did move continuously over the lines ab, bc, ca, that is, over the perimeter of the figure, it would be necessary for it to move at the point b in the direction ab, and also at the same point b in the direction bc. These motions being diverse, they cannot be simultaneous. There-fore, the moment of presence of the movable point at vertex b, considered as moving in the direction ab, is different from the moment of presence of the movable point at the same vertex b, considered as moving in the same direction bc. But between two moments there is time; therefore, the movable point is present at point b for some time, that is, it rests. Therefore it does not move continuously, which is contrary to the assumption. The same demonstration is valid for motion over any right lines including an assignable angle. Hence a body does not change its direction in continuous motion except by following a line no part of which is straight, that is, a curve, as Leibnitz maintained.”

Immanuel Kant (1724–1804) German philosopher

Kant's Inaugural Dissertation (1770), Section III On The Principles Of The Form Of The Sensible World

“I freely admit that the remembrance of David Hume was the very thing that many years ago first interrupted my dogmatic slumber and gave a completely different direction to my researches in the field of speculative philosophy.”

Immanuel Kant book Prolegomena to Any Future Metaphysics

Variant translation: I freely admit: it was David Hume's remark that first, many years ago, interrupted my dogmatic slumber and gave a completely different direction to my enquiries in the field of speculative philosophy.
Prolegomena to Any Future Metaphysics (1783)

“Let the directions of your streets and alleys be laid down on the lines of division between the quarters of two winds. On this principle of arrangement the disagreeable force of the winds will be shut out from dwellings and lines of houses.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book I, Chapter VI, Sec. 7-8
Context: Let the directions of your streets and alleys be laid down on the lines of division between the quarters of two winds. On this principle of arrangement the disagreeable force of the winds will be shut out from dwellings and lines of houses. For if the streets run full in the face of the winds, their constant blasts rushing in from the open country, and then confined by narrow alleys, will sweep through them with great violence. The lines of houses must therefore be directed away from the quarters from which the winds blow, so that as they come in they may strike against the angles of the blocks and their force thus be broken and dispersed.

“Let us imagine that from any given point the system of shortest lines going out from it is constructed; the position of an arbitrary point may then be determined by the initial direction of the geodesic in which it lies, and by its distance measured along that line from the origin. It can therefore be expressed in terms of the ratios dx0 of the quantities dx in this geodesic, and of the length s of this line. …the square of the line-element is \sum (dx)^2 for infinitesimal values of the x, but the term of next order in it is equal to a homogeneous function of the second order… an infinitesimal, therefore, of the fourth order; so that we obtain a finite quantity on dividing this by the square of the infinitesimal triangle, whose vertices are (0,0,0,…), (x1, x2, x3,…), (dx1, dx2, dx3,…). This quantity retains the same value so long as… the two geodesics from 0 to x and from 0 to dx remain in the same surface-element; it depends therefore only on place and direction. It is obviously zero when the manifold represented is flat, i. e., when the squared line-element is reducible to \sum (dx)^2, and may therefore be regarded as the measure of the deviation of the manifoldness from flatness at the given point in the given surface-direction. Multiplied by -¾ it becomes equal to the quantity which Privy Councillor Gauss has called the total curvature of a surface. …The measure-relations of a manifoldness in which the line-element is the square root of a quadric differential may be expressed in a manner wholly independent of the choice of independent variables. A method entirely similar may for this purpose be applied also to the manifoldness in which the line-element has a less simple expression, e. g., the fourth root of a quartic differential. In this case the line-element, generally speaking, is no longer reducible to the form of the square root of a sum of squares, and therefore the deviation from flatness in the squared line-element is an infinitesimal of the second order, while in those manifoldnesses it was of the fourth order. This property of the last-named continua may thus be called flatness of the smallest parts. The most important property of these continua for our present purpose, for whose sake alone they are here investigated, is that the relations of the twofold ones may be geometrically represented by surfaces, and of the morefold ones may be reduced to those of the surfaces included in them…”

Bernhard Riemann (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

“Elizabeth II is a direct descendant of William the Conqueror. Yet it is quite probable that she bares not a single one of the old king's genes.”

Richard Dawkins book The Selfish Gene

Source: The Selfish Gene (1976, 1989), Ch. 11. Memes: the new replicators

“Hume's skepticism, therefore, descends in a direct line from Cartesian mathematicism.”

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Étienne Gilson 22

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