Cycles and Fixed Points - Counting Permutations By Number of Fixed Points

Famous quotes containing the words counting, permutations, number, fixed and/or points:

“Is it not manifest that our academic institutions should have a wider scope; that they should not be timid and keep the ruts of the last generation, but that wise men thinking for themselves and heartily seeking the good of mankind, and counting the cost of innovation, should dare to arouse the young to a just and heroic life; that the moral nature should be addressed in the school-room, and children should be treated as the high-born candidates of truth and virtue?”
—Ralph Waldo Emerson (1803–1882)

“Motherhood in all its guises and permutations is more art than science.”
—Melinda M. Marshall (20th century)

“No Government can be long secure without a formidable Opposition. It reduces their supporters to that tractable number which can be managed by the joint influences of fruition and hope. It offers vengeance to the discontented, and distinction to the ambitious; and employs the energies of aspiring spirits, who otherwise may prove traitors in a division or assassins in a debate.”
—Benjamin Disraeli (1804–1881)

“Our live experiences, fixed in aphorisms, stiffen into cold epigrams. Our heart’s blood, as we write it, turns to mere dull ink.”
—F.H. (Francis Herbert)

“He is the best sailor who can steer within the fewest points of the wind, and extract a motive power out of the greatest obstacles. Most begin to veer and tack as soon as the wind changes from aft, and as within the tropics it does not blow from all points of the compass, there are some harbors which they can never reach.”
—Henry David Thoreau (1817–1862)