Quotes by Mathematicians - Page 17

It is the preoccupation with possessions, more than anything else, that prevents us from living freely and nobly.
Bertrand Russell
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.
P.D. Ouspensky
In the Second World War he took no public part, having escaped to a neutral country just before its outbreak. In private conversation he was wont to say that homicidal lunatics were well employed in killing each other, but that sensible men would keep out of their way while they were doing it. Fortunately this outlook, which is reminiscent of Bentham, has become rare in this age, which recognizes that heroism has a value independent of its utility. The Last Survivor of a Dead Epoch
Bertrand Russell
I hate the world and almost all the people in it. I hate the Labour Congress and the journalists who send men to be slaughtered, and the fathers who feel a smug pride when their sons are killed, and even the pacifists who keep saying human nature is essentially good, in spite of all the daily proofs to the contrary. I hate the planet and the human race—I am ashamed to belong to such a species.
Bertrand Russell
War grows out of ordinary human nature.
Bertrand Russell
Imagination is the only weapon in the war against reality.
Lewis Carroll
In the outworks of our lives, we were almost strangers, but we shared a certain outlook on human life and human destiny, which, from the very first, made a bond of extreme strength . . . . At our very first meeting, we talked with continually increasing intimacy. We seemed to sink through layer after layer of what was superficial, till gradually both reached the central fire. It was an experience unlike any other that I have known. We looked into each other's eyes, half appalled and half intoxicated to find ourselves together in such a region. The emotion was as intense as passionate love, and at the same time all-embracing. I came away bewildered, and hardly able to find my way among ordinary affairs.
Bertrand Russell
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.
Bertrand Russell
O friend, for the morrow let us not worryThis moment we have now, let us not hurryWhen our time comes, we shall not tarryWith seven thousand-year-olds, our burden carry
Omar Khayyám
Few friendships would survive if each one knew what his friend says of him behind his back
Blaise Pascal
Never forget you are the successful product of a harsh universe; the simple fact that you exist, whence trillions of other organisms do not, is a mathematical miracle.
Matt Parker
She generally gave herself very good advice (though she very seldom followed it), and sometimes she scolded herself so severely as to bring tears into her eyes;
Lewis Carroll
SIMPLICIO: ... You have to [learn to] walk before you can run.SALVIATI: No, you have to have something you want to run toward.
Paul Lockhart
Cat: Where are you going?Alice: Which way should I go?Cat: That depends on where you are going.Alice: I don’t know.Cat: Then it doesn’t matter which way you go.
Lewis Carroll
Love is something far more than desire for sexual intercourse; it is the principal means of escape from the loneliness which afflicts most men and women throughout the greater part of their lives. There is a deep-seated fear, in most people, of the cold world and the possible cruelty of the herd; there is a longing for affection, which is often concealed by roughness, boorishness or a bullying manner in men, and by nagging and scolding in women. Passionate mutual love while it lasts puts an end to this feeling; it breaks down the hard walls of the ego, producing a new being composed of two in one.
Bertrand Russell
What do you call yourself?" the Fawn said at last. Such a soft sweet voice it had!"I wish I knew!" thought poor Alice. She answered, rather sadly, "Nothing, just now.""Think again," it said: "that won't do."Alice thought, but nothing came of it. "Please, would you tell me what you call yourself?" she said timidly, "I think that might help a little.""I'll tell you, if you'll come a little further on," the Fawn said. "I can't remember here."So they walked on together through the wood, Alice with her arms clasped lovingly round the soft neck of the Fawn, till they came out into another open field, and here the Fawn gave a sudden bound into the air, and shook itself free from Alice's arms. "I'm a Fawn!" it cried out in a voice of delight. "And dear me, you're a human child!" A sudden look of alarm came into its beautiful brown eyes, and in another moment it had darted away at full speed.
Lewis Carroll
Let it be considered that what is more wholesome than any particular belief is integrity of belief and that to avoid looking into the support of any belief from a fear that it may turn out rotten is quite as immoral as it is disadvantageous.
Charles Sanders Peirce
Neither a man nor a crowd nor a nation can be trusted to act humanely or to think sanely under the influence of a great fear.
Bertrand Russell
Conquer the world by intelligence, and not merely by being slavishly subdued by the terror that comes from it.
Bertrand Russell
Collective fear stimulates herd instinct, and tends to produce ferocity toward those who are not regarded as members of the herd.
Bertrand Russell
Fear is the main source of superstition, and one of the main sources of cruelty. To conquer fear is the beginning of wisdom.
Bertrand Russell
Without books, God is silent, justice dormant, natural science at a stand, philosophy lame, letters dumb, and all things involved in darkness.
Thomas Bartholin
that the grace of fable stirs the mind"...and..."that the perusal of excellent books is, as it were, to interview with the noblest men of past ages
René Descartes
And what is the use of a book," thought Alice, "without pictures or conversation?
Lewis Carroll
Where should I go?" -Alice. "That depends on where you want to end up." - The Cheshire Cat.
Lewis Carroll
The reading of all good books is like conversation with the finest men of past centuries.
René Descartes
... who can forget the amazement of a child balancing an adult on a see-saw, simply by being placed at the right position. How could this be? Where did all that extra force come from!?The only wonder nowadays is that a physics student is unlikely to produce a satisfactory answer to this question. Perhaps we will be offered a few mumblings about moments, force times distance, laws of the lever perhaps even the "principle of virtual work". But we probably won't get an answer that seems to explain where that extra force comes from; and it is highly unlikely that we will get an answer that begins by establishing principles about rigid bodies, even though the rigidity of the lever is an absolute necessity for it to work.In fact, the whole path from Newton's Laws, which basically concern "point masses", to bodies whose shape and extent are significant, is often rather dubiously traversed, even though elementary physics courses blithely pose such problems of the most diverse sorts.
Michael Spivak
For many years I have been saying that I would like to write a book (or series of books) called Physics for Mathematicians. Whenever I would tell people that, they would say, “Oh good, you're going to explain quantum mechanics, or string theory, or something like that”. And I would say, “Well that would be nice, but I can't begin to do that now; first I have to learn elementary physics, so the first thing I will be writing will be Mechanics for Mathematicians”. So then people would say, “Ah, so you're going to be writing about symplectic structures”, or something of that sort. And I would have to say, “No, I'm not trying to write a book about mathematics for mathematicians, I'm trying to write a book about physics for mathematicians”; …… it's elementary mechanics that I don't understand. … I mean, for example, that I don't understand this – lever.... Most of us know the law of the lever, but this law is simply a quantitative statement of exactly how amazing the lever is, and doesn't give us a clue as to why it is true, how such a small force at one end can exert such a great force at the other. Now physicists all agree that Newton's Three Laws are the basis from which all of mechanics follows, but if you ask for an explanation of the lever in terms of these three laws, you will almost certainly not get a satisfactory answer.
Michael Spivak
Probability theory is nothing more than common sense reduced to calculation. -1819
Pierre-Simon Laplace
Everything is what it is because it got that way.
D'Arcy Wentworth Thompson
My work has always tried to unite the True with the Beautiful and when I had to choose one or the other, I usually chose the Beautiful.
Hermann Weyl
And every science, when we understand it not as an instrument of power and domination but as an adventure in knowledge pursued by our species across the ages, is nothing but this harmony, more or less vast, more or less rich from one epoch to another, which unfurls over the course of generations and centuries, by the delicate counterpoint of all the themes appearing in turn, as if summoned from the void.
Alexandre Grothendieck
Science is a river with two sources, the practical source and the theoretical source.
Alfred North Whitehead
If I have been able to see further than others, it is because I have stood on the shoulders of giants
Isaac Newton
It may be asked how I know that there are any Reals. If this hypothesis is the sole support of my method of inquiry, my method of inquiry must not be used to support my hypothesis. The reply is this: 1. If investigation cannot be regarded as proving that there are Real things, it at least does not lead to a contrary conclusion; but the method and the conception on which it is based remain ever in harmony. No doubts of the method, therefore, necessarily arise from its practice, as is the case with all the others. 2. The feeling which gives rise to any method of fixing belief is a dissatisfaction at two repugnant propositions. But here already is a vague concession that there is some one thing which a proposition should represent. Nobody, therefore, can really doubt that there are Reals, for, if he did, doubt would not be a source of dissatisfaction. The hypothesis, therefore, is one which every mind admits. So that the social impulse does not cause men to doubt it. 3. Everybody uses the scientific method about a great many things, and only ceases to use it when he does not know how to apply it. 4. Experience of the method has not led us to doubt it, but, on the contrary, scientific investigation has had the most wonderful triumphs in the way of settling opinion. These afford the explanation of my not doubting the method or the hypothesis which it supposes; and not having any doubt, nor believing that anybody else whom I could influence has, it would be the merest babble for me to say more about it. If there be anybody with a living doubt upon the subject, let him consider it.
Charles Sanders Peirce
To satisfy our doubts . . . it is necessary that a method should be found by which our beliefs may be determined by nothing human, but by some external permanency -- by something upon which our thinking has no effect. . . . Our external permanency would not be external, in our sense, if it was restricted in its influence to one individual. It must be something which affects, or might affect, every man. And, though these affections are necessarily as various as are individual conditions, yet the method must be such that the ultimate conclusion of every man shall be the same. Such is the method of science. Its fundamental hypothesis, restated in more familiar language, is this: There are Real things, whose characters are entirely independent of our opinions about them; those Reals affect our senses according to regular laws, and, though our sensations are as different as are our relations to the objects, yet, by taking advantage of the laws of perception, we can ascertain by reasoning how things really and truly are; and any man, if he have sufficient experience and he reason enough about it, will be led to the one True conclusion. The new conception here involved is that of Reality. It may be asked how I know that there are any Reals. If this hypothesis is the sole support of my method of inquiry, my method of inquiry must not be used to support my hypothesis. The reply is this: 1. If investigation cannot be regarded as proving that there are Real things, it at least does not lead to a contrary conclusion; but the method and the conception on which it is based remain ever in harmony. No doubts of the method, therefore, necessarily arise from its practice, as is the case with all the others. 2. The feeling which gives rise to any method of fixing belief is a dissatisfaction at two repugnant propositions. But here already is a vague concession that there is some one thing which a proposition should represent. Nobody, therefore, can really doubt that there are Reals, for, if he did, doubt would not be a source of dissatisfaction. The hypothesis, therefore, is one which every mind admits. So that the social impulse does not cause men to doubt it. 3. Everybody uses the scientific method about a great many things, and only ceases to use it when he does not know how to apply it. 4. Experience of the method has not led us to doubt it, but, on the contrary, scientific investigation has had the most wonderful triumphs in the way of settling opinion. These afford the explanation of my not doubting the method or the hypothesis which it supposes; and not having any doubt, nor believing that anybody else whom I could influence has, it would be the merest babble for me to say more about it. If there be anybody with a living doubt upon the subject, let him consider it.
Charles Sanders Peirce
That is the essence of science: ask an impertinent question, and you are on the way to the pertinent answer.
Jacob Bronowski
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.
Euclid
We are nature's unique experiment to make the rational intelligence prove itself sounder than the reflex. Knowledge is our destiny
Jacob Bronowski
One of the most curious consequences of quantum physics is that a particle like an electron can seemingly be in more than one place at the same time until it is observed, at which point there seems to be a random choice made about where the particle is really located. Scientists currently believe that this randomness is genuine, not just caused by a lack of information. Repeat the experiment under the same conditions and you may get a different answer each time.
Marcus du Sautoy
Personally I do not agree with sex being brought into science at all. The idea of 'women and science' is entirely irrelevant. Either a woman is a good scientist, or she is not; in any case she should be given opportunities, and her work should be studied from the scientific, not the sex, point of view
Hertha Ayrton
To understand this new frontier, I will have to try to master one of the most difficult and counterintuitive theories ever recorded in the annals of science: quantum physics. Listen to those who have spent their lives immersed in this world and you will have a sense of the challenge we face. After making his groundbreaking discoveries in quantum physics, Werner Heisenberg recalled, "I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?" Einstein declared after one discovery, "If it is correct it signifies the end of science." Schrödinger was so shocked by the implications of what he'd cooked up that he admitted, "I do not like it and I am sorry I had anything to do with it." Nevertheless, quantum physics is now one of the most powerful and well-tested pieces of science on the books. Nothing has come close to pushing it off its pedestal as one of the great scientific achievements of the last century. So there is nothing to do but to dive headfirst into this uncertain world. Feynman has some good advice for me as I embark on my quest: "I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' because you will get 'down the drain,' into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.
Marcus du Sautoy
Scientists rightly resist invoking the supernatural in scientific explanations for fear of committing a god-of-the-gaps fallacy (the fallacy of using God as a stop-gap for ignorance). Yet without some restriction on the use of chance, scientists are in danger of committing a logically equivalent fallacy-one we may call the “chance-of-the-gaps fallacy.” Chance, like God, can become a stop-gap for ignorance.
William A. Dembski
eorum omnium actiones in se invicem
Isaac Newton
If non-linear leaps in intelligence and ability are possible, why haven't these effects been observed in our schools? I believe the answer lies in the profound inertia of human thought: when an entire society believes something is impossible, it suppresses, by its very way of life, the evidence that would contradict that belief.
John Mighton
[I]n any profession the highest order of work is achieved, not by fussy empirical demands for 'something to be done,' but by patient study of the eternal laws.
Henry Whitehead
A good scientist is a person with original ideas. A good engineer is a person who makes a design that works with as few original ideas as possible.
Freeman Dyson
Constrained optimization is the art of compromise between conflicting objectives. This is what design is all about. To find fault with biological design - as Stephen Jay Gould regularly does - because it misses some idealized optimum is therefore gratuitous. Not knowing the objectives of the designer, Gould is in no position to say whether the designer has proposed a faulty compromise among those objectives.
William A. Dembski
Even if the intelligent design of some structure has been established, it still is a separate question whether a wise, powerful, and beneficent God ought to have designed a complex, information-rich structure one way or another. For the sake of argument, let's grant that certain designed structures are not simply, as Gould put it, "odd" or "funny," but even cruel. What of it? Philosophical theology has abundant resources for dealing with the problem of evil, maintaining a God who is both omnipotent and benevolent in the face of evil.
William A. Dembski
With great power comes great dissipation.
Timothy Poston
Before you can ask 'Is Darwinian theory correct or not?', You have to ask the preliminary question 'Is it clear enough so that it could be correct?'. That's a very different question. One of my prevailing doctrines about Darwinian theory is 'Man, that thing is just a mess. It's like looking into a room full of smoke.' Nothing in the theory is precisely, clearly, carefully defined or delineated. It lacks all of the rigor one expects from mathematical physics, and mathematical physics lacks all the rigor one expects from mathematics. So we're talking about a gradual descent down the level of intelligibility until we reach evolutionary biology.
David Berlinski
Even if we have a reliable criterion for detecting design, and even if that criterion tells us that biological systems are designed, it seems that determining a biological system to be designed is akin to shrugging our shoulders and saying God did it. The fear is that admitting design as an explanation will stifle scientific inquiry, that scientists will stop investigating difficult problems because they have a sufficient explanation al
William A. Dembski
We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.
Roger Penrose
If after hearing my songs just one human being is inspired to say something nasty to a friend or perhaps to strike a loved one it will all have been worth the while.
Tom Lehrer
To establish evolutionary interrelatedness invariably requires exhibiting similarities between organisms. Within Darwinism, there's only one way to connect such similarities, and that's through descent with modification driven by the Darwinian mechanism. But within a design-theoretic framework, this possibility, though not precluded, is also not the only game in town. It's possible for descent with modification instead to be driven by telic processes inherent in nature (and thus by a form of design). Alternatively, it's possible that the similarities are not due to descent at all but result from a similarity of conception, just as designed objects like your TV, radio, and computer share common components because designers frequently recycle ideas and parts. Teasing apart the effects of intelligent and natural causation is one of the key questions confronting a design-theoretic research program. Unlike Darwinism, therefore, intelligent design has no immediate and easy answer to the question of common descent.Darwinists necessarily see this as a bad thing and as a regression to ignorance. From the design theorists' perspective, however, frank admissions of ignorance are much to be preferred to overconfident claims to knowledge that in the end cannot be adequately justified. Despite advertisements to the contrary, science is not a juggernaut that relentlessly pushes back the frontiers of knowledge. Rather, science is an interconnected web of theoretical and factual claims about the world that are constantly being revised and for which changes in one portion of the web can induce radical changes in another. In particular, science regularly confronts the problem of having to retract claims that it once confidently asserted.
William A. Dembski
The meaning of world is the separation of wish and fact.
Kurt Gödel
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.
William A. Dembski
How came the bodies of animals to be contrived with so much art, and for what ends were their several parts?Was the eye contrived without skill in Opticks, and the ear without knowledge of sounds?...and these things being rightly dispatch’d, does it not appear from phænomena that there is a Being incorporeal, living, intelligent...?
Isaac Newton
Blind metaphysical necessity, which is certainly the same always and every where, could produce no variety of things. All that diversity of natural things which we find suited to different times and places could arise from nothing but the ideas and will of a Being, necessarily existing.
Isaac Newton
Whenever explaining an event, we must choose from three competing modes of explanation. These are regularity, chance, and design... To attribute an event to design is to say that it cannot reasonably be referred to either regularity or chance.
William A. Dembski