Quotes by Mathematicians - Page 20

TO MAKE A LONG STORY SHORTTo make a long story shortI leave all my possessionsto the Municipal Slaughterhouseto the Special Unit of the Police Departmentto Lucky Dog LottoSo now if you want you can shoot

Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.

The habit of looking into the future and thinking that the whole meaning of the present lies in what it will bring forth is a pernicious one. There can be no value in the whole unless there is value in the parts.

The last thing one discovers in composing a work is what to put first.

Hadn't another wise man, the Buddha himself, warned about the evils of attachment?

As far as you can avoid it, do not give grief to anyone. Never inflict your rage on another. If you hope for eternal rest, feel the pain yourself; but don’t hurt others.

Little Alice fell d o w nthe hOle, bumped her head and bruised her soul

If we all told what we know of one another there would not be four friends in the world

I wish to propose for the reader's favourable consideration a doctrine which may, I fear, appear wildly paradoxical and subversive. The doctrine in question is this: that it is undesirable to believe a proposition when there is no ground whatever for supposing it true.

The philosophers make still another objection: "What you gain in rigour," they say, "you lose in objectivity. You can rise toward your logical ideal only by cutting the bonds which attach you to reality. Your science is infallible, but it can only remain so by imprisoning itself in an ivory tower and renouncing all relation with the external world. From this seclusion it must go out when it would attempt the slightest application.

If the ordinary wage-earner worked four hours a day, there would be enough for everybody and no unemployment -- assuming a certain very moderate amount of sensible organization. This idea shocks the well-to-do, because they are convinced that the poor would not know how to use so much leisure. In America men often work long hours even when they are well off; such men, naturally, are indignant at the idea of leisure for wage-earners, except as the grim punishment of unemployment; in fact, they dislike leisure even for their sons.

We one and all of us have an instinct to pray and this fact constitutes an invitation from God to pray.

I wish I hadn't cried so much!" said Alice, as she swam about, trying to find her way out. "I shall be punished for it now, I suppose, by being drowned in my own tears! That will be a queer thing, to be sure! However, everything is queer today.

Being a hero is the easiest way to meet a bullet with your name on it.

Advocates of capitalism like to appeal to the sacred principles of liberty, which are embodied in one maxim: The fortunate must not be restrained in the exercise of tyranny over the unfortunate.

We should not be ashamed to acknowledge truth and to assimilate it from whatever source it comes to us, even if it is brought to us by former generations and foreign peoples. For him who seeks the truth there is nothing of higher value than truth itself; it never cheapens or debases him who reaches for it but ennobles and honors him.

To ridicule philosophy is really to philosophize.

In this theater of man's life it is reserved only for God and angels to be lookers on.

If we were all given by magic the power to read each other’s thoughts, I suppose the first effect would be almost all friendships would be dissolved; the second effect, however, might be excellent, for a world without any friends would be felt to be intolerable, and we should learn to like each other without needing a veil of illusion to conceal from ourselves that we did not think each other absolutely perfect.

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.

Это не вина психологии романтиков, это их стандарт ценностей. Они восхищаются сильными страстями, безразлично какого рода и каковы бы ни были их социальные последствия. Романтическая любовь, особенно когда она несчастлива, достаточно сильна, чтобы заслужить их одобрение, но большинство сильнейших страстей разрушительно: ненависть, негодование и ревность, раскаяние и отчаяние, поруганная гордость и ярость несправедливо притесняемого, воинственный пыл и презрение к рабам и трусам. Следовательно, тип человека, поддерживаемый романтизмом, особенно в его байроновском варианте, – это склонный к насилию и антисоциальный, анархический бунтарь или побеждающий деспот.Причины того, что это мировоззрение обладает притягательной силой, лежат очень глубоко в природе человека и условиях его существования. Из чувства самосохранения человек стал стадным существом, но инстинктивно он остается в очень большой степени одиночкой; следовательно, необходимы религия и мораль, чтобы подкрепить этот инстинкт. Но привычка воздерживаться от удовольствий в настоящем ради преимуществ в будущем утомительна, и когда возбуждаются страсти, трудно держать себя в благоразумных рамках общественного поведения. Те, кто в такие моменты отбрасывает их, приобретают новую энергию и ощущение силы от прекращения внутреннего конфликта, и, хотя в конце концов они могут попасть в беду, они наслаждаются чувством божественной экзальтации, которое, хотя известно великим мистикам, никогда не может быть испытано теми, чье поведение не выходит за рамки прозаической добродетели. Индивидуалистическая сторона их природы утверждает себя, но, если сохраняется интеллект, это утверждение должно облекать себя в миф. Мистик пребывает наедине с Богом и, созерцая бесконечное, чувствует себя свободным от обязанностей по отношению к своему ближнему.

There is one quality more important than know-how.... This is know-how by which we determine not only how to accomplish our purposes but what our purposes are to be.

There is a widespread philosophical tendency towards the view which tells us that Man is the measure of all things, that truth is man-made, that space and time and the world of universals are properties of the mind, and that, if there be anything not created by the mind, it is unknowable and of no account for us. This view, if our previous discussions were correct, is untrue; but in addition to being untrue, it has the effect of robbing philosophic contemplation of all that gives it value, since it fetters contemplation to Self. What it calls knowledge is not a union with the not-Self, but a set of prejudices, habits, and desires, making an impenetrable veil between us and the world beyond. The man who finds pleasure in such a theory of knowledge is like a man who never leaves the domestic circle for fear his word might not be law.

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

Speak English!" said the Eaglet. "I don't know the meaning of half those long words, and, what's more, I don't believe you do either!" And the Eaglet bend down its head to hide a smile: some of the other birds tittered audibly.

The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, 'Seek simplicity and distrust it.

If you limit your actions in life to things that nobody can possibly find fault with you will not do much.

Certainty a strange Ferris wheel of a statement!

The heart has its reasons which reason knows nothing of.

How much more of the mosque, of prayer and fasting?Better go drunk and begging round the taverns.Khayyam, drink wine, for soon this clay of yoursWill make a cup, bowl, one day a jar.When once you hear the roses are in bloom,Then is the time, my love, to pour the wine;Houris and palaces and Heaven and Hell-These are but fairy-tales, forget them all.

There are no foolish questions and no man becomes a fool until he has stopped asking questions.

The total absence of humour from the Bible is one of the most singular things in all literature.

WHAT DOES AN OLD MAN GAIN BY EXERCISINGwhat will he gain by talking on the phonewhat will he gain by going after fame, tell mewhat does he gain by looking in the mirrorNothingeach time he just sinks deeper in the mudIt’s already three or four in the morningwhy doesn’t he try to go to sleepbut no--he won’t stop doing exercisewon’t stop with his famous long-distance callswon’t stop with Bachtt with Beethoventttt with Tchaikovskywon’t stop with the long looks in the mirrorwon’t stop with the ridiculous obsession about continuing to breathepitiful--it would be better if he turned out the lightRidiculous old man his mother says to himyou and your father are exactly alikehe didn’t want to die eithermay God grant you the strength to drive a carmay God grant you the strength to talk on the phonemay God grant you the strength to breathe may God grant you the strength to bury your motherYou fell asleep, you ridiculous old man!but the poor wretch does not intend to sleepLet’s not confuse crying with sleeping

There is no possibility of remembering what has been found and understood, and later repeating it to oneself. It disappears as a dream disappears. Perhaps it is all nothing but a dream.

The very comprehensibility of the world points to an intelligence behind the world. Indeed, science would be impossible if our intelligence were not adapted to the intelligibility of the world. The match between our intelligence and the intelligibility of the world is no accident. Nor can it properly be attributed to natural selection, which places a premium on survival and reproduction and has no stake in truth or conscious thought. Indeed, meat-puppet robots are just fine as the output of a Darwinian evolutionary process.

You cannot simply read the Quran,not if you take it seriously.You either have surrendered to it already or you fight it.It attacks tenaciously,directly,personally; it debates,criticizes,shames and challenges.From the outset it draws the line of battle, and I was on other side.

Contrariwise,' continued Tweedledee, 'if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.

Each religion makes scores of purportedly factual assertions about everything from the creation of the universe to the afterlife. But on what grounds can believers presume to know that these assertions are true? The reasons they give are various, but the ultimate justification for most religious people’s beliefs is a simple one: we believe what we believe because our holy scriptures say so. But how, then, do we know that our holy scriptures are factually accurate? Because the scriptures themselves say so. Theologians specialize in weaving elaborate webs of verbiage to avoid saying anything quite so bluntly, but this gem of circular reasoning really is the epistemological bottom line on which all 'faith' is grounded. In the words of Pope John Paul II: 'By the authority of his absolute transcendence, God who makes himself known is also the source of the credibility of what he reveals.' It goes without saying that this begs the question of whether the texts at issue really were authored or inspired by God, and on what grounds one knows this. 'Faith' is not in fact a rejection of reason, but simply a lazy acceptance of bad reasons. 'Faith' is the pseudo-justification that some people trot out when they want to make claims without the necessary evidence.But of course we never apply these lax standards of evidence to the claims made in the other fellow’s holy scriptures: when it comes to religions other than one’s own, religious people are as rational as everyone else. Only our own religion, whatever it may be, seems to merit some special dispensation from the general standards of evidence.And here, it seems to me, is the crux of the conflict between religion and science. Not the religious rejection of specific scientific theories (be it heliocentrism in the 17th century or evolutionary biology today); over time most religions do find some way to make peace with well-established science. Rather, the scientific worldview and the religious worldview come into conflict over a far more fundamental question: namely, what constitutes evidence.Science relies on publicly reproducible sense experience (that is, experiments and observations) combined with rational reflection on those empirical observations. Religious people acknowledge the validity of that method, but then claim to be in the possession of additional methods for obtaining reliable knowledge of factual matters — methods that go beyond the mere assessment of empirical evidence — such as intuition, revelation, or the reliance on sacred texts. But the trouble is this: What good reason do we have to believe that such methods work, in the sense of steering us systematically (even if not invariably) towards true beliefs rather than towards false ones? At least in the domains where we have been able to test these methods — astronomy, geology and history, for instance — they have not proven terribly reliable. Why should we expect them to work any better when we apply them to problems that are even more difficult, such as the fundamental nature of the universe?Last but not least, these non-empirical methods suffer from an insuperable logical problem: What should we do when different people’s intuitions or revelations conflict? How can we know which of the many purportedly sacred texts — whose assertions frequently contradict one another — are in fact sacred?

Faith is a sounder guide than reason. Reason can go only so far but faith has no limits.

Nature is pleased with simplicity. And nature is no dummy

Madam, I have just come from a country where people are hanged if they talk.

What goes up must come down.

An arguing couple spiraling into negativity and teetering on the brink of divorce is actually mathematically equivalent to the beginning of a nuclear war.

The virtue of a man ought to be measured not by his extraordinary exertions, but by his every-day conduct.

...It is necessary for the average citizen, if he wishes to make a living, to avoid incurring the hostility of certain big men. And these big men have an outlook - religious, moral, and political - with which they expect their employees to agree, at least outwardly.

Speak in French when you can’t think of the English for a thing--turn your toes out when you walk---And remember who you are!

I took especially great pleasure in mathematics because of the certainty and the evidence of its arguments.

Pure analysis puts at our disposal a multitude of procedures whose infallibility it guarantees; it opens to us a thousand different ways on which we can embark in all confidence; we are assured of meeting there no obstacles; but of all these ways, which will lead us most promptly to our goal? Who shall tell us which to choose? We need a faculty which makes us see the end from afar, and intuition is this faculty. It is necessary to the explorer for choosing his route; it is not less so to the one following his trail who wants to know why he chose it.

Real life is to most men a long second best a perpetual compromise between the ideal and the possible.

To make light of philosophy is to be a true philosopher.

The deepest definition of youth is life as yet untouched by tragedy.

Mortal as I am, I know that I am born for a day. But when I follow at my pleasure the serried multitude of the stars in their circular course, my feet no longer touch the earth.

The best mathematics is serious as well as beautiful—‘important’ if you like, but the word is very ambiguous, and ‘serious’ expresses what I mean much better

Бунт индивидуалистических инстинктов против социальных уз является ключом к пониманию философии, политики и чувств – не только того, что обычно называется движением романтизма, но и его последователей вплоть до наших дней. Философия под влиянием немецкого идеализма стала солипсистской, и самоусовершенствование было провозглашено основополагающим принципом этики. Что касается чувства, то должен был существовать неприятный компромисс между стремлением к изоляции и необходимостью удовлетворения страсти и экономических потребностей. В рассказе Д. Г. Лоуренса «Человек, который любил острова» герой постепенно все в большей степени пренебрегает таким компромиссом и в конце концов умирает от голода и холода, но наслаждаясь полной изоляцией. Однако такой последовательности не достигли писатели, которые превозносят одиночество. Отшельник не пользуется удобствами цивилизованной жизни, и человек, который хочет писать книги или создавать произведения искусства, должен принять помощь других, для того чтобы поддержать свое существование в то время, когда он работает. Для того чтобы продолжать чувствовать себя в одиночестве, он должен быть в состоянии предотвратить тех, кто служит ему, от покушения на его Я, что лучше всего достигается, если они являются рабами. Страстная любовь, однако, более сложное дело. Поскольку страстные любовники рассматриваются как люди, которые восстали против социальных оков, ими восхищаются. Но в реальной жизни отношения любви сами быстро становятся социальными оковами и партнера по любви начинают ненавидеть, и все более неистово, если любовь достаточно сильна, чтобы сделать узы такими, что их трудно разорвать. Следовательно, любовь начинают представлять как борьбу, в которой каждый стремится уничтожить другого, проникая сквозь защитительные барьеры его или ее Я. Эта точка зрения становится обычной в произведениях Стриндберга и еще больше Д. Г. Лоуренса.

Those who have never known the deep intimacy and the intense companionship of happy mutual love have missed the best thing that life has to give.

The reformative effect of punishment is a belief that dies hard chiefly I think because it is so satisfying to our sadistic impulses.

Man needs for his happiness not only the enjoyment of this or that but hope and enterprise and change.

Government can easily exist without laws, but law cannot exist without government.