Sharpness Quotes (9 quotes)
Curves that have no tangents are the rule. … Those who hear of curves without tangents, or of functions without derivatives, often think at first that Nature presents no such complications. … The contrary however is true. … Consider, for instance, one of the white flakes that are obtained by salting a solution of soap. At a distance its contour may appear sharply defined, but as we draw nearer its sharpness disappears. The eye can no longer draw a tangent at any point. … The use of a magnifying glass or microscope leaves us just as uncertain, for fresh irregularities appear every time we increase the magnification. … An essential characteristic of our flake … is that we suspect … that any scale involves details that absolutely prohibit the fixing of a tangent.
(1906). As quoted “in free translation” in Benoit B. Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 7.
Hot things, sharp things, sweet things, cold things
All rot the teeth, and make them look like old things.
All rot the teeth, and make them look like old things.
In Poor Richard's Almanack (1734).
Magic and all that is ascribed to it is a deep presentiment of the powers of science. The shoes of swiftness, the sword of sharpness, the power of subduing the elements, of using the secret virtues of minerals, of understanding the voices of birds, are the obscure efforts of the mind in a right direction.
From 'History', collected in The Complete Works of Ralph Waldo Emerson (1903), 34.
My earliest impressions of wildlife and its pursuit retain a vivid sharpness of form, color, and atmosphere that half a century of professional wildlife experience has failed to obliterate or improve on.
In 'Red Legs Kicking', A Sand County Almanac, and Sketches Here and There (1949, 1987), 120.
Painting the desert, sun-setting the tone
Starving backstage, morning-stars are jaded
The moonshine murmur still shivers alone
Curved slice of sliver, shear breath shadows stone
Suspending twilight shiny and shaded
Painting the desert, sun-setting the tone
Carving solace into silver in June
On horizons’ glow from forgotten gold
The moonshine’s’ shilling delivers alone
Gleaming duels of knights, pierce deathly silence
Steel tines of starlight, clashing swords they hold
Painting the desert, sun-setting the tone
Dimples aware, sparkle sand on the dune
Winking at comets, after tails are told
The moon-sand whispers, sift rivers alone
Sharpness they hone, filing skills onto stone
Starlight dazzles, its own space created
Painting the desert, sun-setting the tone
From owls’ talon, moonlight shimmers alone
Starving backstage, morning-stars are jaded
The moonshine murmur still shivers alone
Curved slice of sliver, shear breath shadows stone
Suspending twilight shiny and shaded
Painting the desert, sun-setting the tone
Carving solace into silver in June
On horizons’ glow from forgotten gold
The moonshine’s’ shilling delivers alone
Gleaming duels of knights, pierce deathly silence
Steel tines of starlight, clashing swords they hold
Painting the desert, sun-setting the tone
Dimples aware, sparkle sand on the dune
Winking at comets, after tails are told
The moon-sand whispers, sift rivers alone
Sharpness they hone, filing skills onto stone
Starlight dazzles, its own space created
Painting the desert, sun-setting the tone
From owls’ talon, moonlight shimmers alone
…...
The apodictic quality of mathematical thought, the certainty and correctness of its conclusions, are due, not to a special mode of ratiocination, but to the character of the concepts with which it deals. What is that distinctive characteristic? I answer: precision, sharpness, completeness,* of definition. But how comes your mathematician by such completeness? There is no mysterious trick involved; some ideas admit of such precision, others do not; and the mathematician is one who deals with those that do.
In 'The Universe and Beyond', Hibbert Journal (1904-1905), 3, 309. An editorial footnote indicates “precision, sharpness, completeness” — i.e., in terms of the absolutely clear and indefinable.
The most striking characteristic of the written language of algebra and of the higher forms of the calculus is the sharpness of definition, by which we are enabled to reason upon the symbols by the mere laws of verbal logic, discharging our minds entirely of the meaning of the symbols, until we have reached a stage of the process where we desire to interpret our results. The ability to attend to the symbols, and to perform the verbal, visible changes in the position of them permitted by the logical rules of the science, without allowing the mind to be perplexed with the meaning of the symbols until the result is reached which you wish to interpret, is a fundamental part of what is called analytical power. Many students find themselves perplexed by a perpetual attempt to interpret not only the result, but each step of the process. They thus lose much of the benefit of the labor-saving machinery of the calculus and are, indeed, frequently incapacitated for using it.
In 'Uses of Mathesis', Bibliotheca Sacra (Jul 1875), 32, 505.
The popular and scientific views of “race” no longer coincide. The word “race,” as applied scientifically to human groupings, has lost any sharpness of meaning. To-day it is hardly definable in scientific terms, except as an abstract concept which may, under certain conditions, very different from those now prevalent, have been realized approximately in the past and might, under certain other but equally different conditions, be realized in the distant future.
Co-author with British anthropologist Alfred Cort Haddon (1855-1940).
Co-author with British anthropologist Alfred Cort Haddon (1855-1940).
In Julian S. Huxley and A.C. Haddon, We Europeans: A survey of “Racial” Problems (1935), 107.
This ability to incorporate the past gives the sharpest diagnostic tool, if one asks whether a body of knowledge is a science or not. Do present practitioners have to go back to an original work of the past? Or has it been incorporated? … Science is cumulative, and embodies its past.
'The Case of Leavis and the Serious Case’, Times Literary Supplement (9 Jul 1970), 737-740. Collected in Public Affairs (1971), 95.