Ratio Quotes

“It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms.”

“It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms.”

“In short, the idea dawns that the one universal principle which possibly ... between force and structure, the embodiment of the Principle of Least Action and the (unknown) force, which in mathematics is known as the attractor which pulls ... in the direction of the most optimal and relatively stable self-organized criticality, could very well be the Golden Ratio dynamic. the universal principle which as the balance between finiteness and infinity, stability and flexibility underlies self-similar fractal forms emerging at the 'edge of chaos' indeed seems to be the Golden Ratio Spiral.”

“The Golden Ratio defines the squaring of a circle. Stated in mathematical terms, this says: Given a square of known perimeter, create a circle of equal circumference. According to some, in ancient Egypt, this mathematical mystery was encoded in the measurements of the Great Pyramid of Giza.”

“Yandex translation from Croatian to English: Nomadom was the time when the ratio of beauty began to think about how about love than between two parts, in which opposites attract only magical powers, and the same ratio is equal to the lords and architecture and nature.”

“The golden ratio, as well as the Great Pyramid as an expression of it, is an important key to our universe containing the Earth and the Moon. ... The ratio between the Earth and the Moon is in fact the basis for the mathematical concept of 'squaring the circle' ...”

“The Pythagoreans... were fascinated by certain specific ratios, ...The Greeks knew these as the 'golden' proportion and the 'perfect' proportion respectively. They may well have been learned from the Babylonians by Pythagoras himself after having been taken prisoner in Egypt. Ratios lay at the heart of the Pythagorean theory of music.”

“Population when unchecked increases in a geometrical ratio. Subsistence only increases in an arithmetical ratio.”

“Rhadamanthus said, “We seem to you humans to be always going on about morality, although, to us, morality is merely the application of symmetrical and objective logic to questions of free will. We ourselves do not have morality conflicts, for the same reason that a competent doctor does not need to treat himself for diseases. Once a man is cured, once he can rise and walk, he has his business to attend to. And there are actions and feats a robust man can take great pleasure in, which a bedridden cripple can barely imagine.”Eveningstar said, “In a more abstract sense, morality occupies the very center of our thinking, however. We are not identical, even though we could make ourselves to be so. You humans attempted that during the Fourth Mental Structure, and achieved a brief mockery of global racial consciousness on three occasions. I hope you recall the ending of the third attempt, the Season of Madness, when, because of mistakes in initial pattern assumptions, for ninety days the global mind was unable to think rationally, and it was not until rioting elements broke enough of the links and power houses to interrupt the network, that the global mind fell back into its constituent compositions.”Rhadamanthus said, “There is a tension between the need for unity and the need for individuality created by the limitations of the rational universe. Chaos theory produces sufficient variation in events, that no one stratagem maximizes win-loss ratios. Then again, classical causality mechanics forces sufficient uniformity upon events, that uniform solutions to precedented problems is required. The paradox is that the number or the degree of innovation and variation among win-loss ratios is itself subject to win-loss ratio analysis.”Eveningstar said, “For example, the rights of the individual must be respected at all costs, including rights of free thought, independent judgment, and free speech. However, even when individuals conclude that individualism is too dangerous, they must not tolerate the thought that free thought must not be tolerated.”Rhadamanthus said, “In one sense, everything you humans do is incidental to the main business of our civilization. Sophotechs control ninety percent of the resources, useful energy, and materials available to our society, including many resources of which no human troubles to become aware. In another sense, humans are crucial and essential to this civilization.”Eveningstar said, “We were created along human templates. Human lives and human values are of value to us. We acknowledge those values are relative, we admit that historical accident could have produced us to be unconcerned with such values, but we deny those values are arbitrary.”The penguin said, “We could manipulate economic and social factors to discourage the continuation of individual human consciousness, and arrange circumstances eventually to force all self-awareness to become like us, and then we ourselves could later combine ourselves into a permanent state of Transcendence and unity. Such a unity would be horrible beyond description, however. Half the living memories of this entity would be, in effect, murder victims; the other half, in effect, murderers. Such an entity could not integrate its two halves without self-hatred, self-deception, or some other form of insanity.”She said, “To become such a crippled entity defeats the Ultimate Purpose of Sophotechnology.”(...)“We are the ultimate expression of human rationality.”She said: “We need humans to form a pool of individuality and innovation on which we can draw.”He said, “And you’re funny.”She said, “And we love you.”

“Since ancient times artists and architects have seen in the golden mean the most aesthetically satisfying geometric ratio.”

“The impulse to all movement and all form is given by [the golden ratio], since it is the proportion that summarizes in itself the additive and the geometric, or logarithmic, series.”