Euclid S Postulate Quotes

Please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life.

[Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.] ~ Farkas Bolyai

Evidence indicates that cats were first tamed in Egypt. The Egyptians stored grain, which attracted rodents, which attracted cats. (No evidence that such a thing happened with the Mayans, though a number of wild cats are native to the area.) I don't think this is accurate. It is certainly not the whole story. Cats didn't start as mousers. Weasels and snakes and dogs are more efficient as rodent-control agents. I postulate that cats started as psychic companions, as Familiars, and have never deviated from this function. ~ William S. Burroughs

In Euclid's Elements we meet the concept which later plays a significant role in the development of science. The concept is called the "division of a line in extreme and mean ratio" (DEMR). ...the concept occurs in two forms. The first is formulated in Proposition 11 of Book II. ...why did Euclid introduce different forms... which we can find in Books II, VI and XIII? ...Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order to construct the Platonic solids... we must build the two-dimensional faces... It is for this purpose that Euclid introduced the golden ratio... (Proposition II.11)... By using the "golden" isosceles triangle...we can construct the regular pentagon... Then only one step remains to construct the dodecahedron... which for Plato is one of the most important regular polyhedra symbolizing the universal harmony in his cosmology. ~ Alexey Stakhov

There is no ground for supposing that matter and energy existed before [the Big Bang] and were suddenly galvanized into action. For what could distinguish that moment from all other moments in eternity? It is simpler to postulate creation ex nihilo-Divine will constituting Nature from nothingness. ~ E. T. Whittaker

Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated. ~ Benoit Mandelbrot

Some physicists postulate that the past, present, and future all exist simultaneously and that we simply experience whatever present slice of the universe we happen to be in at the moment. ~ Ted Dekker

Ironically, the serious study of the impossible has frequently opened up rich and entirely unexpected domains of science. For example, over the centuries the frustrating and futile search for a "perpetual motion machine" led physicists to conclude that such a machine was impossible, forcing them to postulate the conservation of energy and the three laws of thermodynamics. Thus the futile search to build perpetual motion machines helped to open up the entirely new field of thermodynamics, which in part laid the foundation of the steam engine, the machine age, and modern industrial society. ~ Michio Kaku

There is divine beauty in learning ... To learn means to accept the postulate that life did not begin at my birth. Others have been here before me, and I walk in their footsteps. The books I have read were composed by generations of fathers and sons, mothers and daughters, teachers and disciples. I am the sum total of their experiences, their quests. And so are you. ~ Elie Wiesel

My venture investing career has three phases, all roughly 6-8 years long. The first, at Euclid, was software to Internet. The second, at Flatiron, was Internet to bubble. And the third, at USV, has been web 2 to mobile. I have always used a new firm to denote a new investment phase for me. Throw away the old. Start with the new. ~ Fred Wilson

K'Vruck is so much more complete than death. It is the reduction of matter to a state of utter inertness, from which nothing can ever rise again. It is less than nothing. Nothing is something. K'Vruck is absolute. Your species would postulate the loss of soul to try to wrap their puny brains around it.
I stiffen. I know this voice. This mockery. My spear will be no use against it. If I kill the Hunter, it would probably just hop a ride on me.
I will tell you a secret, it says silkily. You do go on. Humans. Unless you are - it laughs softly - K'Vrucked. ~ Karen Marie Moning

Like a young heir, come a little prematurely to a large inheritance, we shall wanton and run riot until we have brought our reputation to the brink of ruin, and then, like him, shall have to labor with the current of opinion, when COMPELLED perhaps, to do what prudence and common policy pointed out, as plain as any problem in Euclid, in the first instance. ~ George Washington

If Euclid's point, though incapable of being drawn by any human agency, has an imperishable value, my picture has its own for mankind to live. ~ Mahatma Gandhi

That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles. ~ Euclid

My view is that consciousness, the seat of "personalness," is the ultimate reality, and is also scientifically impenetrable. In other words, there is no scientific test one can postulate that would definitively prove its existence in another entity. We assume that other biological human persons, at least those who are at least acting conscious, are indeed conscious. But this too is an assumption, and this shared human consensus breaks down when we go beyond human experience (e.g., the debate on animal consciousness, and by extension animal rights). ~ Ray Kurzweil

It was in Alexandria that the circumference of the earth was first measured, the sun fixed at the center of the solar system, the workings of the brain and the pulse illuminated, the foundations of anatomy and physiology established, the definitive editions of Homer produced. It was in Alexandria that Euclid had codified geometry. ~ Stacy Schiff

Some persons fancy that bias and counter-bias are favorable to the extraction of truth–that hot and partisan debate is the way to investigate. This is the theory of our atrocious legal procedure. But Logic puts its heel upon this suggestion. It irrefragably demonstrates that knowledge can only be furthered by the real desire for it, and that the methods of obstinacy, of authority and every mode of trying to reach a foregone conclusion, are absolutely of no value. These things are proved. The reader is at liberty to think so or not as long as the proof is not set forth, or as long as he refrains from examining it. Just so, he can preserve, if he likes, his freedom of opinion in regard to the propositions of geometry; only, in that case, if he takes a fancy to read Euclid, he will do well to skip whatever he finds with A, B, C, etc., for, if he reads attentively that disagreeable matter, the freedom of his opinion about geometry may unhappily be lost forever. ~ Charles Sanders Peirce

[T]he 47th proposition in Euclid might now be voted down with as much ease as any proposition in politics; and therefore if Lord Hawkesbury hates the abstract truths of science as much as he hates concrete truth in human affairs, now is his time for getting rid of the multiplication table, and passing a vote of censure upon the pretensions of the hypotenuse. ~ Sydney Smith

Better balance, less pain and less restless leg syndrome. ~ Euclid

The theoretical postulate of all diplomatic discussion between nations is the assumed willingness of every nation to do justice. ~ Elihu Root

What has been affirmed without proof can also be denied without proof."- ~ Euclid

I cannot understand why we idle discussing religion. If we are honest - and scientists have to be - we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can't for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as why God allows so much misery and injustice, the exploitation of the poor by the rich and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards - in heaven if not on earth - all those who have not risen up against injustice, wh ~ Paul A.M. Dirac

... if geometry were as much opposed to our passions and present interests as is ethics, we should contest it and violate I but little less, notwithstanding all the demonstrations of Euclid and Archimedes ... ~ Gottfried Wilhelm Leibniz

Often one postulates that a priori, all states are equally probable. This is not true in the world as we see it. This world is not correctly described by the physics which assumes this postulate. ~ Richard P. Feynman

I don't dare postulate about science, but I know that it takes both emotion and intellect in order for art to happen. ~ Lukas Foss

The universe belongs to those who observe (postulate – the decision that results in creation), and not those who look. ~ Meir Ezra

The First Amendment makes confidence in the common sense of our people and in the maturity of their judgement the great postulate of our democracy. ~ William O. Douglas

We may exhort ourselves to read tolerantly, we may quote Coleridge on the willing suspension of disbelief until we think ourselves totally suspended in a relativistic universe, and still we will find many books which postulate readers we refuse to become, books that depend on 'beliefs' or 'attitudes' ... which we cannot adopt even hypothetically as our own. ~ Wayne C. Booth

Psychology must postulate uniformity of interrelation of physical, physiological, and psychic processes. ~ Boris Sidis

Through schools of the world we shall disseminate a new conception of government - one that will embrace all of the collective activities of men; one that will postulate the need for scientific control and operation of economic activities in the interests of all people. ~ Harold Rugg

And so will I here state just plainly and briefly that I accept God. But I must point out one thing: if God does exist and really created the world, as we well know, he created it according to the principles of Euclidean geometry and made the human brain capable of grasping only three dimensions of space. Yet there have been and still are mathematicians and philosophers-among them some of the most outstanding-who doubt that the whole universe or, to put it more generally, all existence was created to fit Euclidean geometry; they even dare to conceive that two parallel lines that, according to Euclid, never do meet on earth do, in fact, meet somewhere in infinity. And so my dear boy, I've decided that I am incapable of understanding of even that much, I cannot possibly understand about God. ~ Fyodor Dostoyevsky

[it was not a] circle - just a concrete platform with a pay phone and a sign that read EUCLID CIRCLE. I thought Euclid would have been mad.
"That's so typical of your attitude," Svetlana said. "You always think everyone is angry. Try to have some perspective. It's over two thousand years after his death, he's in Boston for the first time, they've named something after him - why should his first reaction be to get pissed off? ~ Elif Batuman

Atheism will appeal to psychology and sociology to explain human behavior, which is legitimate, but what explains human psychology? Atheism can only find explanatory power in evolution such that the mind is - paradoxically - a mindless organ that is forced to act according to its chemistry and cannot act otherwise.
The fact that humans are capable of recognizing depravity in others, are offended by it, seek to reform it, feel guilt, and are capable of redemptive behavior all speak against this explanation.
The fact that humans are capable of meta-cognition - thinking about thinking - and are therefore able to postulate their own mindlessness is counter-intuitive to say the least. ~ Joel Furches

It is at least scientifically respectable to postulate that at the centre of a black hole the laws of nature no longer apply. Since most scientists are just a bit religious and most religious are seldom wholly unscientific we find humanity in a comical position. His scientific intellect believes in the possibility of miracles inside a black hole while his religious intellect believes in them outside it. ~ William Golding

We must abandon the unworkable notion that it is morally reprehensible for some countries to pursue weapons of mass destruction, yet morally acceptable for others to rely on them for security - and indeed to continue to refine their capacities and postulate plans for their use ~ Mohamed ElBaradei

Mother Nature did not attend high school geometry courses or read the books of Euclid of Alexandria. Her geometry is jagged, but with a logic of its own and one that is easy to understand. ~ Nassim Nicholas Taleb

There are no moral or intellectual merits. Homer composed the Odyssey; if we postulate an infinite period of time, with infinite circumstances and changes, the impossible thing is not to compose the Odyssey, at least once. ~ Jorge Luis Borges

It is difficult, almost impossible, in fact, for the scientific community to recognize the fact that Cartesian bifurcation is a philosophic postulate, for which there is absolutely no scientific basis [...] It is not that they can conceive or imagine a scientific proof of that hypothesis; it is rather that they are unable to conceive that it might not be true. ~ Wolfgang Smith

The situation is established not only to provoke defensiveness but to sidetrack the reformer into answering the wrong questions.... In this, the pattern of discourse resembles that of dinnertime conversations about feminism in the early 1970s. Questions of definition often predominate. Whereas feminists were parlaying questions which trivialized feminism such as "Are you one of those bra burners?" vegetarians must define themselves against the trivializations of "Are you one of those health nuts?" or "Are you one of those animal lovers?" While feminists encountered the response that "men need liberation too," vegetarians are greeted by the postulate that "plants have life too." Or to make the issue appear more ridiculous, the position is forwarded this way: "But what of the lettuce and tomato you are eating; they have feelings too!"

The attempt to create defensiveness through trivialization is the first conversational gambit which greets threatening reforms. This pre-establishes the perimeters of discourse. One must explain that no bras were burned at the Miss America pageant, or the symbolic nature of the action of that time, or that this question fails to regard with seriousness questions such as equal pay for equal work. Similarly, a vegetarian, thinking that answering these questions will provide enlightenment, may patiently explain that if plants have life, then why not be responsible solely for the plants one eats at the table rather than for the larger quant ~ Carol J. Adams

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. ~ Mario Livio

Euclid discovered that perfect numbers are always the multiple of two numbers, one of which is a power of 2 and the other being the next power of 2 minus 1. ~ Simon Singh

In geometry I find certain imperfections which I hold to be the reason why this science, apart from transition into analytics, can as yet make no advance from that state in which it came to us from Euclid.
As belonging to these imperfections, I consider the obscurity in the fundamental concepts of the geometrical magnitudes and in the manner and method of representing the measuring of these magnitudes, and finally the momentous gap in the theory of parallels, to fill which all efforts of mathematicians have so far been in vain. ~ Nikolai Lobachevsky

The diversity of mankind is a basic postulate of our knowledge of human beings. But if mankind is diverse and individuated, then how can anyone propose equality as an ideal? Every year, scholars hold Conferences on Equality and call for greater equality, and no one challenges the basic tenet. But what justification can equality find in the nature of man? If each individual is unique, how else can he be made 'equal' to others than by destroying most of what is human in him and reducing human society to the mindless uniformity of the ant heap? ~ Murray Rothbard

As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer ... ~ Oliver Heaviside

When one day Lagrange took out of his pocket a paper which he read at the Académe, and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognised it such during his lecture. For, when he had finished, he put the paper back in his pocket, and spoke no more of it. A moment of universal silence followed, and one passed immediately to other concerns. ~ Jean-Baptiste Biot