— Horace Mann American politician 1796 - 1859
The Common School Journal, Vol. V, No. 18 (15 September 1843)
Book II, Chapter 1, "The Rival Conceptions of God"
Mere Christianity (1952)
Context: My argument against God was that the universe seemed so cruel and unjust. But how had I got this idea of just and unjust? A man does not call a line crooked unless he has some idea of a straight line. What was I comparing this universe with when I called it unjust?
— Horace Mann American politician 1796 - 1859
The Common School Journal, Vol. V, No. 18 (15 September 1843)
„It seemed that this poor ignorant Monarch — as he called himself — was persuaded that the Straight Line which he called his Kingdom, and in which he passed his existence, constituted the whole of the world, and indeed the whole of Space. Not being able either to move or to see, save in his Straight Line, he had no conception of anything out of it.“
Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 13. How I had a Vision of Lineland
Context: Describing myself as a stranger I besought the King to give me some account of his dominions. But I had the greatest possible difficulty in obtaining any information on points that really interested me; for the Monarch could not refrain from constantly assuming that whatever was familiar to him must also be known to me and that I was simulating ignorance in jest. However, by persevering questions I elicited the following facts:It seemed that this poor ignorant Monarch — as he called himself — was persuaded that the Straight Line which he called his Kingdom, and in which he passed his existence, constituted the whole of the world, and indeed the whole of Space. Not being able either to move or to see, save in his Straight Line, he had no conception of anything out of it. Though he had heard my voice when I first addressed him, the sounds had come to him in a manner so contrary to his experience that he had made no answer, "seeing no man", as he expressed it, "and hearing a voice as it were from my own intestines." Until the moment when I placed my mouth in his World, he had neither seen me, nor heard anything except confused sounds beating against — what I called his side, but what he called his INSIDE or STOMACH; nor had he even now the least conception of the region from which I had come. Outside his World, or Line, all was a blank to him; nay, not even a blank, for a blank implies Space; say, rather, all was non-existent.His subjects — of whom the small Lines were men and the Points Women — were all alike confined in motion and eye-sight to that single Straight Line, which was their World. It need scarcely be added that the whole of their horizon was limited to a Point; nor could any one ever see anything but a Point. Man, woman, child, thing — each was a Point to the eye of a Linelander. Only by the sound of the voice could sex or age be distinguished. Moreover, as each individual occupied the whole of the narrow path, so to speak, which constituted his Universe, and no one could move to the right or left to make way for passers by, it followed that no Linelander could ever pass another. Once neighbours, always neighbours. Neighbourhood with them was like marriage with us. Neighbours remained neighbours till death did them part.Such a life, with all vision limited to a Point, and all motion to a Straight Line, seemed to me inexpressibly dreary; and I was surprised to note the vivacity and cheerfulness of the King.
„The materialists say, it is by means of a series of straight lines more or less perfect that one imagines the perfect straight line as an ideal limit. That is right, but the progression in itself necessarily contains what is infinite; it is in relation to the perfect straight line that one can say that such and such a straight line is less twisted than some other. … Either one conceives the infinite or one does not conceive at all.“
— Simone Weil French philosopher, Christian mystic, and social activist 1909 - 1943
Source: Lectures on Philosophy (1959), p. 87
— Marvin Minsky American cognitive scientist 1927 - 2016
K-Linesː A Theory of Memory (1980)
Context: When you "get an idea," or "solve a problem," or have a "memorable experience," you create what we shall call a K-line. This K-line gets connected to those "mental agencies" that were actively involved in the memorable event. When that K-line is later "activated," it reactivates some of those mental agencies, creating a "partial mental state" resembling the original.
— Ralph Waldo Emerson American philosopher, essayist, and poet 1803 - 1882
— Antoni Gaudí Catalan architect 1852 - 1926
The real author seems to be Pierre Albert-Birot https://books.google.com/books?id=3Ul51CwjUOcC&pg=PA290&dq=%22the+curved+line+that+belongs+let%27s+say+to+God+and+the+straight+line+that+belongs+to+man%22&hl=de&sa=X&redir_esc=y#v=onepage&q=%22the%20curved%20line%20that%20belongs%20let%27s%20say%20to%20God%20and%20the%20straight%20line%20that%20belongs%20to%20man%22&f=false.
— Helen Thomas American author and journalist 1920 - 2013
Interview by Adam Holdorf for Real Change News, (18 March 2004).
„The line has in itself neither matter nor substance and may rather be called an imaginary idea than a real object; and this being its nature it occupies no space. Therefore an infinite number of lines may be conceived of as intersecting each other at a point, which has no dimensions and is only of the thickness (if thickness it may be called) of one single line.“
— Leonardo Da Vinci Italian Renaissance polymath 1452 - 1519
The Notebooks of Leonardo da Vinci (1883), II Linear Perspective
„But if some mind very different from ours were to look upon some property of some curved line as we do on the evenness of a straight line, he would not recognize as such the evenness of a straight line; nor would he arrange the elements of his geometry according to that very different system, and would investigate quite other relationships as I have suggested in my notes.
We fashion our geometry on the properties of a straight line because that seems to us to be the simplest of all. But really all lines that are continuous and of a uniform nature are just as simple as one another. Another kind of mind which might form an equally clear mental perception of some property of any one of these curves, as we do of the congruence of a straight line, might believe these curves to be the simplest of all, and from that property of these curves build up the elements of a very different geometry, referring all other curves to that one, just as we compare them to a straight line. Indeed, these minds, if they noticed and formed an extremely clear perception of some property of, say, the parabola, would not seek, as our geometers do, to rectify the parabola, they would endeavor, if one may coin the expression, to parabolify the straight line.“
— Roger Joseph Boscovich Croat-Italian physicist 1711 - 1787
"Boscovich's mathematics", an article by J. F. Scott, in the book Roger Joseph Boscovich (1961) edited by Lancelot Law Whyte.
"Transient pressure analysis in composite reservoirs" (1982) by Raymond W. K. Tang and William E. Brigham.
"Non-Newtonian Calculus" (1972) by Michael Grossman and Robert Katz.
„Criticism, like so many other things, keeps to what has been said before and does not get out of the rut. This business of the 'Beautiful' some see it in curved lines, some in straight lines, but all persist in seeing it as a matter of line. I am now looking out of my window and I can see the most lovely countryside; lines just do not come into my head: the lark is singing, the river sparkles with a thousand diamonds, the leaves are whispering; where, I should like to know, are the lines that produce delicious impressions like these? They refuse to see proportion or harmony except between two lines: all else they regard as chaos, and the dividers alone are judge.“
— Eugène Delacroix French painter 1798 - 1863
Quote from a letter to Léon Peisse, 15 July 1949; as cited in Letters of the great artists – from Blake to Pollock, Richard Friedenthal, Thames and Hudson, London, 1963, p. 68
this quote refers to Delacroix's refusal to use the line as boundary of the form in his painting art, as a too sharp dividing force in the picture - in contrast to the famous classical painter in Paris then, Ingres
1831 - 1863
„By what name shall we call this animating principle of the universe, this source of all phenomana? Some call it Force or Energy or Mind, others call it God. Some call this idea a working hypothesis, others call it Faith.“
— Kirby Page American clergyman 1890 - 1957
Source: Something More, A Consideration of the Vast, Undeveloped Resources of Life (1920), p. 15
„Like drawing a straight line – you draw a straight line and it's crooked and you draw another straight line on top of it and it's crooked a different way and then you draw another one and eventually you have a very rich thing on your hands which is not a straight line. If you can do that the it seems to me you are doing more than most people. The thing is, it is very difficult to know oneself whether one is doing that or not, whether you mean what you do; and there is the other problem of the way you do it and whether sometimes you do more than you mean or you do less than you mean. It's very good if you can establish a language where it's clear that that is what you are doing – that you do what you mean to do.“
— Jasper Johns American artist 1930
interview at John's studio, Billy Klüver, March 1963, as quoted in Jasper Johns, Writings, sketchbook Notes, Interviews, ed. Kirk Varnedoe, Moma New York, 1996, p. 85
— Ani DiFranco musician and activist 1970
In or Out
„In the field of non-Euclidean geometry, Riemann… began by calling attention to a distinction that seems obvious once it is pointed out: the distinction between an unbounded straight line and an infinite line. The distinction between unboundedness and infiniteness is readily illustrated. A circle is an unbounded figure in that it never comes to an end, and yet it is of finite length. On the other hand, the usual Euclidean concept of a straight line is also unbounded in that it never reaches an end but is of infinite length.
…he proposed to replace the infiniteness of the Euclidean straight line by the condition that it is merely unbounded. He also proposed to adopt a new parallel axiom… In brief, there are no parallel lines. This … had been tried… in conjunction with the infiniteness of the straight line and had led to contradictions. However… Riemann found that he could construct another consistent non-Euclidean geometry.“
— Morris Kline American mathematician 1908 - 1992
Source: Mathematical Thought from Ancient to Modern Times (1972), p. 454
„Proposition 14. The straight line joined from the centre of the earth to the centre of the moon has to the straight line cut off from the axis towards the centre of the moon by the straight line subtending the (circumference) within the earth's shadow a ratio greater than that which 675 has to 1.“
— Aristarchus of Samos ancient Greek astronomer and mathematician
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)
— Thomas Mann German novelist, and 1929 Nobel Prize laureate 1875 - 1955
— Robert Henri American painter 1865 - 1929
„Israel says, quite correctly, that changing Israel’s ethnicity would change the idea of Israel. Well, changing America’s ethnicity changes the idea of America, too. Show me in a straight line why we can’t do what Israel does. Is Israel special? For some of us, America is special, too.“
— Ann Coulter author, political commentator 1961
2015, Adios, America: The Left's Plan to Turn Our Country into a Third World Hellhole (2015)