The differential equation of the first order \frac {dy}{dx} = f(x, y) ... prescribes the slope \frac {dy}{dx} at each point of the plane (or at each point of a certain region of the plane we call the field").... a differential equation of the first order... can be conceived intuitively as a problem about the steady flow of a river: Being given the direction of the flow at each point, find the streamlines.... It leaves open the choice between the two possible directions in the line of a given slope. Thus... we should say specifically "direction of an unoriented straight line" and not merely "direction."
George PólyaRelated topics
call certain choice differential direction equation field find flow given leaves line open order plane point possible problem region river should straight thusRelated quotes
As an advocate of birth control I wish ... to point out that the unbalance between the birth rate of the 'unfit' and the 'fit,' admittedly the greatest present menace to civilization, can never be rectified by the inauguration of a cradle competition between these two classes. In this matter, the example of the inferior classes, the fertility of the feeble-minded, the mentally defective, the poverty-stricken classes, should not be held up for emulation.... On the contrary, the most urgent problem today is how to limit and discourage the over-fertility of the mentally and physically defective.
Margaret Sanger
Always mystify, mislead, and surprise the enemy, if possible; and when you strike and overcome him, never let up in the pursuit so long as your men have strength to follow; for an army routed, if hotly pursued, becomes panic-stricken, and can then be destroyed by half their number. The other rule is, never fight against heavy odds, if by any possible maneuvering you can hurl your own force on only a part, and that the weakest part, of your enemy and crush it. Such tactics will win every time, and a small army may thus destroy a large one in detail, and repeated victory will make it invincible.
Stonewall Jackson
A certain region in the field becomes crucial, is focused; but it does not become isolated. A new, deeper structural view of the situation develops, involving changes in functional meaning, the grouping, etc. of the items. Directed by what is required by the structure of a situation for a crucial region, one is led to a reasonable prediction, which like the other parts of the structure, calls for verification, direct or indirect. Two directions are involved: getting a whole consistent picture, and seeing what the structure of the whole requires for the parts.
Max Wertheimer
Carnap calls such concepts as point, straight line, etc., which are given by implicit definitions, improper concepts. Their peculiarity rests on the fact that they do not characterize a thing by its properties, but by its relation to other things. Consider for example the concept of the last car of a train. Whether or not a particular car falls under this description does not depend on its properties but on its position relative to other cars. We could therefore speak of relative concepts, but would have to extend the meaning of this term to apply not only to relations but also to the elements of the relations.
Hans Reichenbach
Nature has always been recorded by artists, from prehistoric cave paintings to twentieth-century landscape photography. I too wanted to make nature the subject of my work, but in new ways. I started working outside using natural materials like grass and water, and this evolved into the idea of making a sculpture by walking ... My first work made by walking, in 1967, was a straight line in a grass field, which was also my own path, going ‘nowhere'. In the subsequent early map works, recording very simple but precise walks on Exmoor and Dartmoor, my intention was to make a new art which was also a new way of walking: walking as art.
Richard Long