A Quote by Omar Khayyam
Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.
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Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.
On the geometric level, we see certain physical elements repeated endlessly, combined in an almost endless variety of combinations. It is puzzling to realize that the elements, which seem like elementary building blocks, keep varying, and are different every time that they occur. If the elements are different every time that they occur, evidently then, it cannot be the elements themselves which are repeating in a building or town; these so-called elements cannot be the ultimate "atomic" constituents of space.
Now, everybody knows the basic erogenous zones. You got one, two, three, four, five, six, and seven. ... OK, now most guys will hit one, two, three and then go to seven and set up camp. ... You want to hit 'em all and you wanna mix 'em up. You gotta keep 'em on their toes. ... You could start out with a little one. A two. A one, two, three. A three. A five. A four. A three, two. Two. A two, four, six. Two, four, six. Four. Two. Two. Four, seven! Five, seven! Six, seven! Seven! Seven! Seven! Seven! Seven! Seven! Seven! Seven! Seven! [holds up seven fingers]
In the old physics, three times two equals six and two times three equals 6 are reversible propositions. Not in quantum physics. Three times two and two times three are two different matters, distinct and separate propositions.
The Syllogism consists of propositions, propositions consist of words, words are symbols of notions. Therefore if the notions themselves (which is the root of the matter) are confused and over-hastily abstracted from the facts, there can be no firmness in the superstructure. Our only hope therefore lies in a true induction.
Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define.
The propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as "All bachelors are unmarried," but they also share the complete lack of empirical content which is associated with that certainty: The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.
There is a difference between a book of two hundred pages from the very beginning, and a book of two hundred pages which is the result of an original eight hundred pages. The six hundred are there. Only you don't see them.
I work on one book at a time. And yes, I am immersed. Six days a week for four to six hours a day. In between books, I stop writing for as much as two to three months, but during that time, I do research and think, plot and plan the book.
Life consists Of propositions about life. The human Revery is a solitude in which We compose these propositions, torn by dreams, By the terrible incantations of defeats And by the fear that the defeats and the dreams are one. The whole race is a poet that writes down The eccentric propositions of its fate.
What we have to understand that we have to believe into things which can be proved. Now the time has come that Divine itself has to be proved. That God Almighty has to be proved. That Christ as a son of God has to be proved, that His birth as immaculate conception has to be proved. Not by argument, not by reasoning, nor by blind faith but by actualization on your central nervous system.
There are different interpretations of the problem of universals. I understand it as the problem of giving the truthmakers of propositions to the effect that a certain particular is such and such, e.g. propositions like 'this rose is red'. Others have interpreted it as a problem about the ontological commitments of such propositions or a problem about what those propositions mean.
That is, a system starts with a group of interrelated propositions which involve reference to empirical observations within the logical framework of the propositions in question.
I take facts about reasons to be fundamental in two ways. First, I believe that facts about reasons are not reducible to or analyzable in terms of facts of other kind, such as facts about the natural world. Second, I believe that reasons are the fundamental elements of the normative domain, and other normative notions, such as goodness and moral right and wrong can be explained in terms of reasons.
Within the human consciousness is the unique ability to perceive the transparency between absolute, permanent relationships, contained in the insubstantial forms of a geometric order, and the transitory, changing forms of our actual world. The content of our experience results from an immaterial, abstract, geometric architecture which is composed of harmonic waves of energy, nodes of relationality, melodic forms springing forth from the eternal realm of geometric proportion.
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