Parallel Lines Never Meet Quotes

We are all bumbling along,side by side, week in, week out, our paths similar in some ways and different in others, all apparently running parallel. But parallel lines never meet.

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.

As lines, so love's oblique, may well Themselves in every angle greet : But ours, so truly parallel, Though infinite, can never meet.

As lines, so loves oblique may well Themselves in every angle greet; But ours so truly parallel, Though infinite, can never meet. Therefore the love which us doth bind, But Fate so enviously debars, Is the conjunction of the mind, And opposition of the stars.

My task is to explain to you as quickly as possible my essence, that is, what sort of man I am, what I believe in, and what I hope for, is that right? And therefore I declare that I accept God pure and simple. But this, however, needs to be noted: if God exists and if he indeed created the earth, then, as we know perfectly well, he created it in accordance with Euclidean geometry, and he created human reason with a conception of only three dimensions of space. At the same time there were and are even now geometers and philosophers, even some of the most outstanding among them, who doubt that the whole universe, or, even more broadly, the whole of being, was created purely in accordance with Euclidean geometry; they even dare to dream that two parallel lines, which according to Euclid cannot possibly meet on earth, may perhaps meet somewhere in infinity. I, my dear, have come to the conclusion that if I cannot understand even that, then it is not for me to understand about God. I humbly confess that I do not have any ability to resolve such questions, I have a Euclidean mind, an earthly mind, and therefore it is not for us to resolve things that are not of this world. And I advise you never to think about it, Alyosha my friend, and most especially about whether God exists or not. All such questions are completely unsuitable to a mind created with a concept of only three dimensions. And so, I accept God, not only willingly, but moreover I also accept his wisdom and his purpose, which are completely unknown to us; I believe in order, in the meaning of life, I believe in eternal harmony, in which we are all supposed to merge, I believe in the Word for whom the universe is yearning, and who himself was 'with God,' who himself is God, and so on and so forth, to infinity. Many words have been invented on the subject. It seems I'm already on a good path, eh? And now imagine that in the final outcome I do not accept this world of God's, created by God, that I do not accept and cannot agree to accept. With one reservation: I have a childlike conviction that the sufferings will be healed and smoothed over, that the whole offensive comedy of human contradictions will disappear like a pitiful mirage, a vile concoction of man's Euclidean mind, feeble and puny as an atom, and that ultimately, at the world's finale, in the moment of eternal harmony, there will occur and be revealed something so precious that it will suffice for all hearts, to allay all indignation, to redeem all human villainy, all bloodshed; it will suffice not only to make forgiveness possible, but also to justify everything that has happened with men--let this, let all of this come true and be revealed, but I do not accept it and do not want to accept it! Let the parallel lines even meet before my own eyes: I shall look and say, yes, they meet, and still I will not accept it.

Though we met at the same station, we were but passing trains; on parallel lines, destined to never meet.

I am trying to explain as quickly as possible my essential nature, that is, what manner of man I am, what I believe in, and for what I hope, that's it, isn't it? And therefore I tell you that I accept God honestly and simply. But you must note this: If God exists and if He really did create the world, then, as we all know, He created it according to the geometry of only three dimensions in space. Yet there have been some very distinguished ones, who doubt whether the whole universe, or to speak more generally the whole of being, was only created in Euclid's geometry; they even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity. I have come to the conclusion that, since I can't understand even that, I can't expect to understand about God. I acknowledge humbly that I have no faculty for settling such questions, I have a Euclidian earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not. All such questions are utterly inappropriate for a mind created with a conception of only three dimensions. And so I accept God and am glad to, and what's more I accept His wisdom, His purpose - which are utterly beyond our ken; I believe in the underlying order and the meaning of life; I believe in the eternal harmony in which they say we shall one day be blended. I believe in the Word to Which the universe is striving, and Which Itself was "with God", and Which Itself is God and so on, and so on, to infinity.

The reason why everyone is not naturally enlightened is simply this: people have categorized the world into good and bad, God and Devil, high and low, sacred and filthy, pure and impure, heaven and hell. These are parallel lines that will never meet. Once

Two Metro lines, two trains, two carriages, two people walking in parallel streets, two lives, couples criss-crossing without seeing each other, potential encounters, meetings which shall never take place. The imagination rewrites history. It modifies the local directory and the roll-call of those who frequent a town, a street, a house, a woman. It transfixes reflections in the mirror for all eternity. It hangs entire portrait galleries from the wall of our future memory on which magnificent strangers use a sharp knife to engrave their initials and a date.

In one of his novels about a sterile and painful relationship, Aldous Huxley uses the expression, "the love of the parallels"--that hopeless love between two parallel lines which stretch out simultaneously but can never meet.

Newcomers to manuscripts sometimes ask what such books tell us about the societies that created them. At one level, these Gospel Books describe nothing, for they are not local chronicles but standard Latin translations of religious texts from far away. At the same time, this is itself extraordinarily revealing about Ireland. No one knows how literacy and Christianity had first reached the islands of Ireland, possibly through North Africa. This was clearly no primitive backwater but a civilization which could now read Latin, although never occupied by the Romans, and which was somehow familiar with the texts and artistic designs which have unambiguous parallels in the Coptic and Greek churches, such as carpet pages and Canon tables. Although the Book of Kells itself is as uniquely Irish as anything imaginable, it is a Mediterranean text and the pigments used in making it include orpiment, a yellow made from arsenic sulphide, exported from Italy, where it is found in volcanoes. There are clearly lines of trade and communication unknown to us.

Yet there have been and still are mathematicians and philosophers who doubt whether the whole universe, or to speak more widely, the whole of being, was only created in Euclid's geometry. They even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity.

For what is it you and I are trying to do now? What I'm trying to do is to attempt to explain to you as quickly as possible the most important thing about me, that is to say, what sort of man I am, what I believe in what I hope for - that's it isn't it? And that's why I declare that I accept God plainly and simply. But there's this that has to be said: if God really exists and if he really has created the world, then, as we all know, he created it in accordance with the Euclidean geometry, and he created the human mind with the conception of only the three dimensions of space. And yet there have been and there still are mathematicians and philosophers, some of them indeed men of extraordinary genius, who doubt whether the whole universe, or, to put it more wildly, all existence was created only according to Euclidean geometry and they even dare to dream that two parallel lines which, according to Euclid can never meet on earth, may meet somewhere in infinity. I, my dear chap, have come to the conclusion that if I can't understand even that, then how can I be expected to understand about God? I humbly admit that I have no abilities for settling such questions. And I advise you too, Aloysha, my friend, never to think about it, and least of all about whether there is a God or not. All these problems which are entirely unsuitable to a mind created with the idea of only three dimensions. And so I accept God, and I accept him not only without reluctance, but what's more, I accept his divine wisdom and his purpose- which are completely beyond our comprehension.

Whenever I try to forget you, Erick, something brings you back into my memory. And whenever I want to drive emotions away from me, they quickly return as thoughts or dreams . . . or the words of an old woman. Perhaps loneliness has forced me to hang on to the faint spectrum of your memory—kept my heart longing in painstaking eagerness. But no . . . no more, and not again. How long can my heart withstand the seesaw of emotions? If I had one wish, I would want you and me to be two parallel lines, either on flat or spherical earth . . . never to meet.

There have been and there still are mathematicians and philosophers, some of them indeed men of extraordinary genius, who doubt whether the whole universe, or, to put it more widely, all existence, was created only according to Euclidean geometry and they even dare to dream that wo parallel lines which, according to Euclid, can never meet on earth, may meet somewhere in infinity. I, my dear chap, have come to the conclusion that if I can’t understand even that, then how can I be expected to understand about God? I humbly admit that I have no abilities for settling such questions. I have a Euclidean, an earthly mind, and so how can I be expected to solve problems which are not of this world.

There have been and still are geometricians and philosophers, and even some of the most distinguished, who doubt whether the whole universe, or to speak more widely the whole of existence, was only created in Euclid's geometry; they even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity. I have come to the conclusion that, since I can't understand even that, I can't expect to understand about God. I acknowledge humbly that I have no faculty for settling such questions, I have a Euclidean earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not. All such questions are utterly inappropriate for a mind created with an idea of only three dimensions.

A consequence of Maxwell's theory of electromagnetism is that light rays move in straight lines. Thus it makes sense to use light rays when tracing the geometry of space. But if we adopt this idea, we see immediately that Einstein's theory has great implications. For light rays are bent by gravitational fields, which, in turn, respond to the presence of matter. The only conclusion to draw is that the presence of matter affects the geometry of space. In Euclidean geometry, if two straight lines are initially parallel, they can never meet. But two light rays that are initially parallel can meet in the real world, because if they pass on eachbside of a star, they will be bent toward each other. So Euclidean geometry is not true in the real world. Moreover, the geometry is constantly changing, because matter is constantly moving. The geometry of space is not like a flat, infinite plane. It is like the surface of the ocean-incredibly dynamic, with great waves and small ripples in it.

For example, the central idea in Einstein's theory of general relativity is that gravity is not some mysterious, attractive force that acts across space but rather a manifestation of the geometry of the inextricably linked space and time. Let me explain, using a simple example, how a geometrical property of space could be perceived as an attractive force, such as gravity. Imagine two people who start to travel precisely northward from two different point on Earth's equator. This means that at their starting points, these people travel along parallel lines (two longitudes), which, according to the plane geometry we learn in school, should never meet. Clearly, however, these two people will meet at the North Pole. if these people did not know that they were really traveling on the curved surface of a sphere, they would conclude that they must have experienced some attractive force, since they arrived at the same point in spite of starting their motions along parallel lines. Therefore, the geometrical curvature of space can manifest itself as an attractive force.

Parallel lines have so much in common.  It’s a shame they’ll never meet.

Parallel lines have so much in common. It's a shame they'll never meet.

Non-Euclidean' became a byword for non-absolute knowledge. It also served to illustrate most vividly the gap between mathematics and the natural world. Mathematics was much bigger than physical reality. There were mathematical systems that described aspects of Nature, but there were others that did not. Later, mathematicians would use these discoveries about geometry to discover that there were other logics as well. Aristotle's system was, like Euclid's, just one of many possibilities. Even the concept of truth was not absolute. What is false in one logical system can be true in another. In Euclid's geometry of flat surfaces, parallel lines never meet, but on curved surfaces they can. These discoveries revealed the difference between mathematics and science. Mathematics was something bigger than science, requiring only self-consistency to be valid. It contained all possible patterns of logic. Some of those patterns were followed by parts of Nature; others were not. Mathematics was open-ended, uncompleteable, infinite; the physical universe was smaller.

Rarely was Arabic used for physics, chemistry, or mathematics in any of the schools of Beirut, whose main curriculum has always been community conformity. It seems that Arabic is not considered a language for logic. A joke that used to make the rounds when I was a child, probably still going strong: the definition of parallel lines in geometry textbooks in Saudi Arabia is two straight lines that never meet unless God in all His glory wills it.

[Euclid's] second postulate, for example, says that any line segment may be extended indefinitely. That is difficult for even the most querulous to argue with. The fifth, on the other hand, states that if two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side (labelled a and b in the diagram below) is less than two right angles (i.e. 180°), then the two lines inevitably must intersect each other on that side if extended far enough. If, on the other hand, a and b do add up to 180°, the two lines never meet so are said to be parallel. To mathematicians, that looks less like a postulate and more like a theorem in need of proving.

The philosophy of "Karma" and "Destiny" are two parallel lines...which have never met, nor can they ever meet.

We are two parallel lines prolonged to infinity side by side but never to meet.

But when the marriage began to sour, he refined that mathematical image: “We are two parallel lines prolonged to infinity side by side but never to meet.

You’d always existed in a reality that ran parallel to my own, and I’d accepted the geometrical precept that parallel lines never meet.