Eric Temple Bell quote: “The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move …”

“You can see for what reason I commend the study of eloquence to you—because we can neither explain what we ourselves want, nor understand the surviving writing written by our ancestors, unless we have thoroughly studied a fixed rule for speaking. For my part, I do not see how there could be others who wish neither to explain what they think, nor to understand what is excellently said.”

Philip Melanchthon (1497–1560) German reformer

Source: Praise of Eloquence (1523), p. 64

“A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid.”

Freeman Dyson book Infinite in All Directions

Source: Infinite in All Directions (1988), Ch. 2 : Butterflies and Superstrings, p. 17
Context: Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid. This is what one means when one says that a point is a mathematical abstraction. The question, What is a point? has no satisfactory answer. Euclid's definition certainly does not answer it. The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry?... It cannot be answered by a definition.

“The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry? …It cannot be answered by a definition.”

Freeman Dyson book Infinite in All Directions

Source: Infinite in All Directions (1988), Ch. 2 : Butterflies and Superstrings, p. 17
Context: Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid. This is what one means when one says that a point is a mathematical abstraction. The question, What is a point? has no satisfactory answer. Euclid's definition certainly does not answer it. The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry?... It cannot be answered by a definition.

“I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect... Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

As quoted in Solid Shape (1990) by Jan J. Koenderink

“In string theory one studies strings moving in a fixed classical spacetime. …what we call a background-dependent approach. …One of the fundamental discoveries of Einstein is that there is no fixed background. The very geometry of space and time is a dynamical system that evolves in time. The experimental observations that energy leaks from binary pulsars in the form of gravitational waves—at the rate predicted by general relativity to the… accuracy of eleven decimal places—tell us that there is no more a fixed background of spacetime geometry than there are fixed crystal spheres holding the planets up.”

Lee Smolin (1955) American cosmologist

"Loop Quantum Gravity," The New Humanists: Science at the Edge (2003)

“The efforts of a multitude of writers have rather been directed towards producing alternatives for Euclid which shall be more suitable, that is to say, easier, for schoolboys. It is of course not surprising that, in these days of short cuts, there should have arisen a movement to get rid of Euclid and to substitute "a royal road to geometry"; the marvel is that a book which was not written for schoolboys but for grown men (as all internal evidence shows, and in particular the essentially theoretical character of the work and its aloofness from anything of the nature of "practical" geometry) should have held its own as a schoolbook for so long.”

Thomas Little Heath (1861–1940) British civil servant and academic

The Thirteen Books of Euclid's Elements (1908)

“For thousands of years people have been trying to force other people to think their way. Did they succeed? No. Will they succeed? No. Why? Because brute force is not an argument.”

Robert G. Ingersoll (1833–1899) Union United States Army officer

The trial of Charles B. Reynolds for blasphemy (1887)

“This intelligence-testing business reminds me of the way they used to weigh hogs in Texas. They would get a long plank, put it over a cross-bar, and somehow tie the hog on one end of the plank. They'd search all around till they found a stone that would balance the weight of the hog and they'd put that on the other end of the plank. Then they'd guess the weight of the stone.”

John Dewey (1859–1952) American philosopher, psychologist, and educational reformer

Quoted by Dorothy Canfield Fisher in Vermont Tradition http://books.google.com/books?id=K7wMAAAAYAAJ&q=%22This+intelligence-testing+business+reminds+me+of+the+way+they+used+to+weigh+hogs+in+Texas+They+would+get+a+long+plank+put+it+over+a+cross-bar+and+somehow+tie+the+hog+on+one+end+of+the+plank+They'd+search+all+around+till+they+found+a+stone+that+would+balance+the+weight+of+the+hog+and+they'd+put+that+on+the+other+end+of+the+plank+Then+they'd+guess+the+weight+of+the+stone%22&pg=PA380#v=onepage (1953)
Misc. Quotes

“Two other sciences in the same way will accurately treat of 'size': geometry, the part that abides and is at rest, [and] astronomy, that which moves and revolves.”

Nicomachus (60–120) Ancient Greek mathematician

Book I, Chapter III, p.184
Nicomachus of Gerasa: Introduction to Arithmetic (1926)

“'Twas the fifteenth anniversary of her twenty-second year,
So he smiled at her as sweetly as a hog
And asked what present she would like. And jestingly she said:
"Your green tie for my little yellow dog."”

Billy Bennett (1887–1942) British comedian

"The Green Tie on the Little Yellow Dog", line 13

“The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry.”

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Eric Temple Bell 14

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