Theodorus of Cyrene and Theaetetus generalised the theory of irrationals, and we may safely conclude that a great part of the substance of Euclid's Book X. (on irrationals) was due to Theætetus. Theætetus also wrote on the five regular solids, and Euclid was therefore no doubt equally indebted to Theætetus for the contents of his Book XIII. In the matter of Book XII. Eudoxus was the pioneer. These facts are confirmed by the remark of Proclus that Euclid, in compiling his Elements, collected many of the theorems of Eudoxus, perfected many others by Theætetus, and brought to irrefragable demonstration the propositions which had only been somewhat loosely proved by his predecessors.
Thomas Little HeathRelated topics
book compiling contents demonstration doubt due euclid five great matter pioneer regular remark somewhat substance theory others elements factsRelated quotes
In this book I try to show how models of self-organization can be applied to many economic phenomena - how the principle of "order from instability," which explains the growth of hurricanes and embryos, can also explain the formation of cities and business cycles; how the principle of "order from random growth" can explain the strangely simple rules that describe the sizes of earth quakes, meteorites, and metropolitan areas. I believe that the ideas of self-organization theory can add substantially to our understanding of the economy; whatever their ultimate usefulness, these ideas are very exciting, and playing around with them is tremendous fun.
Paul Krugman
Not only is it possible to devise complete models of the economy on hypotheses other than rationality, but in fact virtually every practical theory of macroeconomics is partly so based. The price- and wage- rigidity elements of Keynesian theory are hard to fit into a rational framework, though some valiant efforts have been made. ... But if the Keynesian model is a natural target of criticism by the upholders of universal rationality, it must be added that monetarism is no better. I know of no serious derivation of the demand for money from a rational optimization. ... The use of rationality in these arguments is ritualistic, not essential.
Kenneth Arrow
I was 16 when I got saved and all the atheists in my city started coming after me, trying to get me converted away from Christianity. And I had some real problems believing some of the things in the Bible. They were showing me supposed contradictions and all that. [...] But I had to make a decision as a 16 year old new Christian. I said, "Lord, I'm going to believe your book until somebody can prove it's wrong." Some of my friends decided they're going to doubt the Bible until it's proven right. I think that's a mistake. I think I made the right decision. I said, "God, I'm going to believe you even for the things I don't understand." And he's proven himself on just about every one of them.
Kent Hovind
It is known that very distant nebulae, probably galactic systems like our own, show remarkably high receding velocities whose magnitude increases with the distance. This curious phenomenon promises to provide some important clues for the future development of our cosmological views. It maybe of advantage, therefore, to point out some of the principal facts which any cosmological theory will have to account for. Then a brief discussion will be given of different theoretical suggestions related to the above effect. Finally, a new effect of masses upon light will be suggested which is a sort of gravitational analogue of the Compton effect.
Fritz Zwicky
My theory has been to discover the modern synthesis by methods based upon science, methods based upon the theory of colors discovered by M. Chevreul, in conformity with the experiments of Maxwell and the measurements of N. 0. Rood; to substitute the optical mingling for the mingling of pigments; in other words, the decomposition of all the colors into their constituent elements; because the optical mingling excites much more intense luminosity than the mingling of pigments. As for the execution, we regard it as nothing; it is at any rate only unimportant, art having nothing to do with it. According to us, the sole originality consists in the character of the drawing and the vision individual to each artist.
Camille Pissarro
