["Not quantity but quality"]--Greek maxim.

"Nothingness has no center, and its boundaries are nothingness." Leonardo da Vinci, Notebooks

"Apart from the finite, the infinite is devoid of meaning and cannot be distinguished from nonentity. The notion of the essential relatedness of all things is the primary step in understanding how finite entities require the unbounded universe [and] the search for such understanding is the definition of philosophy. It is the reason mathematics, which deals with finite patterns, is related to the notion to the Good and to the notion of the Bad. . . Mathematics is the most powerful technique for the understanding of pattern, and for the analysis of the relationships of patterns. Here we reach the fundamental justification for the topic of Plato's lecture ['Mathematics and the Good']. . . [But] evidently [Plato's] lecture was a failure; for he did not succeed in making evident to future generations his intuition of mathematics as elucidating the notion of the Good. Many mathematicians have been good men for example, Pascal and Newton. Also many philosophers have been mathematicians. But the peculiar association of mathematics and the Good remains an undeveloped topic, since its first introduction by Plato . . . . Throughout the various ages of European civilization, moral philosophy and mathematics have been assigned to separate departments of university life. " Alfred North Whitehead, A Philosopher Looks at Science

"The infinitude of data has a flattening effect," Mr. Biggs said. "It makes everything equal to everything else. And that's what the Web does in a funny sort of way." [from] Matthew Mirapaul, Impressionists in Cyberspace, Digital But Diverse http://www.nytimes.com/2001/08/06/arts/design/06ARTS.html

"For Camus, understanding the world goes deeper than it does for most of us. His problem is that the world cannot be comprehended by the intellect . . . Therefore it is absurd. Not ridiculous, not grotesque, but beyond reason. . . . Although striking, 'absurd' is a poor word for the concept, and has led to some misunderstandings. The idea is ultimately a mathematical one. The Greek thinkers who first worked on mathematics were impressed by the fact that numbers seemed to constitute an intelligible realm of their own . . . but they soon came on certain ratios which could not 'make sense' in this way. Why should the diameter of a circle give such an incomprehensible relation to its circumference as 3.1415926535897938426 and so on in a series as endless as the task of Sisyphus? Such a relation they called irrational, because it could not be fitted neatly into the category of reason. . . The Romans took over the concept 'irrational,' but translated it rather poorly as 'inharmonious,' in Latin absurdus, and thence it got into English and other languages." Gilbert Highet, Classical Papers

"In the absence of standards by which the quality of education might be judged, the quantity of education, the number of years spent in educational institutions and the number of degrees acquired, tended to become the mark of the educated man." Robert Maynard Hutchins, Some Observations on American Education

"Now our treatment of this science will be adequate, if it achieves that amount of precision which belongs to its subject matter. The same amount of exactness must not be expected in all departments of philosophy alike . . . The subjects studied by political science are Moral Nobility and Justice, but these conceptions involve much difference of opinion and uncertainty, so that they are sometime believed to be mere conventions and have no real existence in the nature of things. And a similar uncertainty surrounds the question of the Good, because it frequently occurs that good things have harmful consequences: people have before now been ruined by wealth, and in other cases courage has cost men their lives. We must therefore be content if we achieve the amount of precision possible . . . it is equally unreasonable to accept merely probable conclusions from a mathematician and to demand strict demonstrations from an orator." Aristotle, Ethics

". . . it is rare that mathematicians are intuitive, and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically, and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning." -- Blaise Pascal

"If you still want to hope for the stars, just remember that, at the current growth rate, in a few thousand years everything in the visible universe would be converted into people, and the ball of people would be expanding with the speed of light!" --Paul Ehrlich, The Population Bomb.

"I just wonder what it would be like to be reincarnated in an animal whose species had been so reduced in numbers that it was in danger of extinction. What would be its feelings toward the human species whose population explosion had denied it somewhere to exist . . . I must confess that I am tempted to ask for reincarnation as a particularly deadly virus." --HRH Prince Phillip

"You never see a number larger than ten to the hundred and twenty-fourth, for example. Why not?' Because there is nothing bigger than that. That is the volume of the universe in cubic fermis. A fermi is the smallest dimension that makes any sense to talk about--ten to the minus thirteen centimeters. That's about the diameter of an electron." John McPhee, The Curve of Binding Energy

"The Golden Mean (or Golden Section), represented by the Greek letter phi, is one of those mysterious natural numbers, like e or pi, that seem to arise out of the basic structure of our cosmos. Unlike those abstract numbers, however, phi appears clearly and regularly in the realm of things that grow and unfold in steps, and that includes living things. The decimal representation of phi is 1.6180339887499... . You can find it in a number of places . . .Number Series--If you start with the numbers 0 and 1, and make a list in which each new number is the sum of the previous two, you get a list like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... to infinity. This is called a 'Fibonacci series'. If you then take the ratio of any two sequential numbers in this series, you'll find that it falls into an increasingly narrow range: 1/0 = Whoa! That one doesn't count. 1/1 = 1; 2/1 = 2; 3/2 = 1.5; 5/3 = 1.6666...; 8/5 = 1.6;13/8 = 1.625; 21/13 = 1.61538...;34/21 = 1.61904...and so on, with each addition coming ever closer to multiplying by some as-yet-undetermined number. The number that this ratio is oscillating around is phi (1.6180339887499...). It's interesting to note that the ratio 21/13 differs from phi by less than .003, and 34/21 by only about .001 (less than 1/10 of one percent!), thus providing our less technically-advanced ancestors an easy way to derive phi on a large scale in the real world with a high degree of precision. [In] geometry The golden proportion: is .618 over 1; or 1.618 over ten. So if you have a rectangle with one side seven inches long, multiply seven by 1.618 to get the length of the other side which will be a golden rectangle.. . . If you have a rectangle whose sides are related by phi (say, for instance, 13 x 8), that rectangle is said to be a Golden Rectangle. It has the interesting property that, if you create a new rectangle by 'swinging' the long side around one of its ends to create a new long side, then that new rectangle is also Golden. In the case of our 13 x 8 rectangle, the new rectangle will be (13 + 8 =) 21 x 13 . . . and so on, with, again, each addition coming ever closer to multiplying by phi. . . . Ancient architecture [like the front of the Parthenon] is filled with Golden Rectangles. . . . [I]n the world of nature, things always grow by adding some unit, even if the unit is as small as a molecule. So it's not surprising that phi turns out to be an ideal rate of growth for things which grow by adding some quantity. Some examples:The Nautilus shell (Nautilus pompilius) grows larger on each spiral by phi; The sunflower has 55 (see number list) clockwise spirals overlaid on either 34 or 89 (see number list) counterclockwise spirals, a phi proportion." [citation lost].

"The rough formula for the relationship between sight lines and the curve of the earth is that the square root of the observer's altitude in feet will equal the number of miles over flat land or water between the observer and the horizon. A person lying on a beach nine feet above sea level can see three miles across the water . . . " John McPheee

"In these days of specialization the excellent custom which formerly prevailed at Oxford and Cambridge whereby men took honors in both classics and mathematics has gone by the board. It is now rare to find a classical scholar who has even an elementary knowledge of mathematics, and the mathematician's knowledge of Greek is usually confined to the letters of the alphabet." Editor's Preface to Greek Mathematics, in the Loeb Classical Library edition.

"The simplest problems which come up from day to day seem to me quite unanswerable as soon as I try to get below the surface. Each side, when I hear it, seems right till I hear the other. I have neither the time nor the ability to learn the facts, or to estimate their importance if I knew them; I am disposed to accept the decision of those charged with the responsibility of dealing with them." --Judge Learned Hand, Democracy: Its Presumptions and Realities.

"What is the answer? [silence] Then what is the question?" Gertrude Stein's last words on her deathbed.