Quotes & Sayings About Number Theory

At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate. — Terence Tao

In the work of Ramanujan, the number 24 appears repeatedly. This is an example of what mathematicians call magic numbers, which continually appear, where we least expect them, for reasons that no one understands. Miraculously, Ramanujan's function also appears in string theory. The number 24 appearing in Ramanujan's function is also the origin of the miraculous cancellations occurring in string theory. In string theory, each of the 24 modes in the Ramanujan function corresponds to a physical vibration of the string. Whenever the string executes its complex motions in space-time by splitting and recombining, a large number of highly sophisticated mathematical identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan. (Since physicists add two more dimensions when they count the total number of vibrations appearing in a relativistic theory, this means that space-time must have 24 + 2 = 26 space-time dimensions.) — Michio Kaku

The usefulness of the models in constructing a testable theory of the process is severely limited by the quickly increasing number of parameters which must be estimated in order to compare the predictions of the models with empirical results. — Anatol Rapoport

The number of public policies that hinge on whether you believe in evolution - or which theory of evolution you subscribe to - are few to none. — Anonymous

The notion of mental accounts is absent in traditional economic theory, which holds that wealth in general, and money in particular, should be fungible: That is, $100 in roulette winnings, $100 in salary, and a $100 tax refund should have the same significance and value to you, since each C-note could buy the same number of downloads from iTunes or the same number of burgers at McDonald's. Likewise, $100 kept under the mattress should invoke the same feelings or sense of wealth as $100 in a bank account or $100 in U.S. Treasury securities (ignoring the fact that money in the bank, or in T-bills, is safer than cash under the bed). If money and wealth are fungible, there should be no difference in the way we spend gambling winnings or salary. — Gary Belsky

In the 19th century, smallpox was widely considered a disease of filth, which meant that it was largely understood to be a disease of the poor. According to filth theory, any number of contagious diseases were caused by bad air that had been made foul by excrement or rot. — Eula Biss

The number of games went up or down according to the brutal, elegant logic of the economics of fun:
a certain amount of difficulty
plus
a certain amount of your friends
plus
a certain amount of interesting strangers
plus
a certain amount of reward
plus
a certain amount of opportunity
equaled
fun — Cory Doctorow

All disciplines of science are built on the causality of the relationships governing related events. Yet the theory of evolution is built upon the idea of accidental changes that resulted in complex living systems. I was unable to comprehend how the notion that an infinite number of random accidents systematically happened to produce living species, and kept improving these beings, is justified. — T.H. Janabi

His Theory of the Universe seems to have been, that it consisted solely of a multitude of objects which could be weighed, numbered, and measured; and the vocation to which he considered himself called was, to weigh, number and measure as many of those objects as his allotted three-score years and ten would permit. This conviction biased all his doings, alike his great scientific enterprises, and the petty details of his daily life. — George Wilson

Two centuries ago Carl Friedrich Gauss, one of the greatest mathematicians and a founder of number theory, described his brainchild as "the queen of mathematics." Queens are regal, but they are also largely decorative, and this nuance was not lost on Gauss. — Ian Stewart

One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory. — Hermann Weyl

This anchoring to a number is the reason people do not react to their total accumulated wealth, but to differences of wealth from whatever number they are currently anchored to. This is the major conflict with economic theory, as according to economists, someone with $1 million in the bank would be more satisfied than if he had half a million. But — Nassim Nicholas Taleb

No number of sightings of white swans can prove the theory that all swans are white. The sighting of just one black one may disprove it. — Karl Popper

While an increasing number of male academic, political, and cultural figures have felt comfortable enough in recent years to proclaim themselves feminists, absorbing aspects of feminist politics and theory into their thinking, their gestures are most often built on an essentialized and static dichotomy between men and women. But men must do more than admit their complicity in patriarchy; they must begin to rethink the very boundaries that shape and define what it means to be a man.

Conversely, women must play an important part in this reevaluation, an idea suggest by Eve Kosofsky Sedgwikc's admonition that "when something is about masculinity, it isn't always 'about men'." Far from being just about men, the idea of masculinity engages, inflects, and shapes everyone. — Maurice Berger

There is that wish, in the name of democracy, to level down, because high cultural standards are despised and rejected, and even feared, in our Western Democracies. Don't let anyone else have what I've not got, or can't enjoy! - is the secret theory. A very large number of writers in the British and American popular press profess to be preaching democracy when in fact they are only trying to make envy respectable! — Ann Bridge

I dug the untraceable phone Patch had given me out of my handbag and dialled his number.
"I have a free couple of hours," I told him, walking toward my car, which was parked on the next block. "There's a very dark, very secluded barn in Lookout Hill Park behind the carousel. I could be there in fifteen minutes."
I heard the smile in his voice."You want me bad."
"I need and an endorphin boost."
"And making out in an abandoned barn with me will give you one?"
"No, it will probably put me in an endorphin coma, and I'm more than happy to test the theory. — Becca Fitzpatrick

The principle of conservation of boson number inside a system is seen to follow directly from the Abstraction Model. The IBMs are seen to obey the Laws of Physical Transaction that follows from Zero-Postulation. The chaotic superfields at the requisite scaling-ratio yields necessary equation-parameters needed to describe them at that given scaling-ratio. This is seen to be independent of the choice of scale, but at smaller scaling-ratios, we have less loss of information. At a higher scale, we seem to have less number of parameters required to describe them. — Subhajit Ganguly

One possible solution to the grandfather paradox is the theory of multiverse originally set forth by Hugh Everett. According to multiverse theory, every version of our past and future histories exists, just in an alternate universe.

For every event at the quantum level, the current universe splits into multiple universes. This means that for every choice you make, an infinite number of universes exist in which you made a different choice.

The theory neatly solves the grandfather paradox by posting separate universes in which each possible outcome exists, thereby avoiding a paradox.

In this way we get to live multiple lives.

There is, for example, a universe where Samuel Kingsley does not derail his daughter's life. A universe where he does derail it but Natasha is able to fix it. A universe where he does derail it and she is not able to fix it. Natasha is not quite sure which universe she's living in now. — Nicola Yoon

Phineas Gage's case is not the only important
historical source in the effort to understand the neural basis of
reasoning and decision making ... [to understand the effect of] prefrontal damage ... The Hebb-Penfield and Ackerly-Benton shared a number
of personality traits ... They are bereft of a theory of
their own mind and of the mind of those with whom they interact — Antonio R. Damasio

The NSF study projected a shortfall of 675,000 scientists and engineers without considering the future demand for such individuals in the marketplace. It simply observed a decline in the number of 22-year-olds and projected that this demographic trend would result in a huge shortfall. This could be termed the supply-side theory of labor market analysis. But making labor market projections without considering the demand side of the equation doesn't pass the laugh test with experts in the field. — Howard Wolpe

The advantage of this interpretation is that we can drop condition number three, the collapse of the wave function. Wave functions never collapse, they just continue to evolve, forever splitting into other wave functions, in a never-ending tree, with each branch representing an entire universe. The great advantage of the many worlds theory is that it is simpler than the Copenhagen interpretation: it requires no collapse of the wave function. The price we pay is that now we have universes that continually split into millions of branches. — Michio Kaku

Military population that has a disproportionate number of young people with a history of sexual abuse. One theory for this holds that military service is an easy way for young people to get out of their home, and so the military will disproportionally draw recruits from troubled families. According to a 2014 study in the American Medical Association's JAMA Psychiatry, men with military service are now twice as likely to report sexual assault during their childhood as men who never served. This was not true during the draft. Sexual abuse is a well-known predictor of depression and other mental health issues, and the military suicide rate may in part be a result of that. Killing — Sebastian Junger

I am a physicist, not a biologist. ... But I am very much excited by your article in May 30th Nature, and think that brings Biology over into the group of "exact" sciences. ... If your point of view is correct each organism will be characterized by a long number written in quadrucal (?) system with figures 1, 2, 3, 4 standing for different bases. ... This would open a very exciting possibility of theoretical research based on combinatorix and the theory of numbers! ... I have a feeling this can be done. What do you think? — James Gleick

It is going to be necessary that everything that happens in a finite volume of space and time would have to be analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition [that physics is computer-simulatable] is right, physical law is wrong. — Richard P. Feynman

I believe, Jack, there are two kinds of people in the world. Killers and diers. Most of us are diers. We don't have the dispoisiton, the rage or whatever it takes to be a killer. We le death happen. We lie down and die. But think what it's like to be a killer. Think how exciting it is, in theory, to kill a person in direct confrontation. If he dies, you cannot. To kill him is to gain life-credit. The more people you kill, the more credit you store up. It explains any number of massacres, wars, executions. [ ... ] In theory, violence is a form of rebirth. The dier passively succumbs. The killer lives on. What a marvelous equation. - Murray (WN 290) — Don DeLillo

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts. — Adrien-Marie Legendre

True, the Standard Model does explain a very great deal. Nevertheless it is not yet a proper theory, principally because it does not satisfy the physicists naive faith in elegance and simplicity. It involves some 17 allegedly fundamental particles and the same number of arbitrary and tunable parameters, such as the fine-structure constants, the muon-electron mass ratio and the various mysterious mixing angles. — Sheldon L. Glashow

Prefect had always found hardest to understand about humans was their habit of continually stating and repeating the very very obvious, as in It's a nice day, or You're very tall, or Oh dear you seem to have fallen down a thirty-foot well, are you all right? At first Ford had formed a theory to account for this strange behavior. If human beings don't keep exercising their lips, he thought, their mouths probably seize up. After a few months' consideration and observation he abandoned this theory in favor of a new one. If they don't keep on exercising their lips, he thought, their brains start working. After a while he abandoned this one as well as being obstructively cynical and decided he quite liked human beings after all, but he always remained desperately worried about the terrible number of things they didn't know about. "Yes," he agreed with — Douglas Adams

Renormalization is just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr's orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number. — Paul Dirac

Topology and number theory are my faves. — Janna Levin

Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers. — Vladimir Arnold

The Hindu religion is the only one of the world's great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths.
It is the only religion in which the time scales correspond to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long. Longer than the age of the Earth or the Sun and about half the time since the Big Bang. — Carl Sagan

My work on prime gaps lead to lots of media coverage, some good, some bad, some ugly, and some merely ridiculous. For example, a reporter of our university newspaper, who admitted that he is still learning English, wrote that "Prof. Goldston solved one of the most controversial problems in the prime number theory last month with support from his Turkish partner." — Daniel Goldston

If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos. — Gary William Flake

Number theorists say that number theory is too complicated, so let's pretend that there is only one prime number, and then let's combine all these results. Surprisingly, sometimes it works. — Saharon Shelah

But just in proportion as this process of extermination has acted on an enormous scale, so must the number of intermediate varieties, which have formerly existed, be truly enormous. Why then is not every geological formation and every stratum full of such intermediate links? Geology assuredly does not reveal any such finely graduated organic chain; and this, perhaps, is the most obvious and serious objection which can be urged against the theory. The explanation lies, as I believe, in the extreme imperfection of the geological record. — Charles Darwin

a controversial theory," Claire said, "that proposes that dark matter, which we know is invisible in our universe, is ordinary matter from another universe. There's also a theory that our Big Bang resulted from a collision between two parallel universes and that this was only one in perhaps an infinite number of Big Bangs to occur in the multiverse. So maybe the two theories are compatible. Maybe dark matter, like the dark matter in the Grail, came to us from another bubble. — Glenn Cooper

So, in one slightly technical line, here's the mathematical skinny. There's an equation in string theory that has a contribution of the form (D-10) times (Trouble), where D represents the number of spacetime dimensions and Trouble is a mathematical expression resulting in troublesome physical phenomena, such as the violation of energy conservation mentioned above. As to why the equation takes this precise form, I can't offer any intuitive, nontechnical explanation. But if you do the calculation, that's where the math leads. Now, this simple but key observation is that if the number of spacetime dimensions is ten, not the four we expect, the contribution becomes 0 times Trouble. And since 0 times anything is 0, in a universe with ten spacetime dimensions the trouble gets wiped away. That's how the math plays out. Really. And that's why string theorists argue for a universe with more than four spacetime dimensions. — Brian Greene

[On Sophie Germain] When a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men ... succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of [number theory], then without doubt she must have the noblest courage, quite extraordinary talents and superior genius. — Carl Friedrich Gauss

The likelihood of the formation of life from inanimate matter is 1 to a number with 40,000 noughts after it (1040,000) ... It is big enough to bury Darwin and the whole theory of evolution. There was no primeval soup, neither on this planet nor any other, and if the beginnings of life were not random, they must therefore have been the product of purposeful intelligence. — Fred Hoyle

Filibusters should require 35 senators to ... make a commitment to continually debate an issue in reality, not just in theory. The number of votes needed to overcome a filibuster should be reduced to 55 from 60. — Evan Bayh

From time to time. You do not count your steps any more. For the simple reason they number each day the same. Average day in day out the same. The way being always the same. You keep count of the days and every tenth night multiply. And add. Your father's shade is not with you any more. It fell out long ago. You do not feel your footfalls any more. Unhearing unseeing you go your way. Day after day. The same way. As if there were no other any more. For you there is no other any more. You used never to halt except to make your reckoning. So as to plod from nought anew. This need removed as we have seen there is none in theory to halt any more. Save perhaps a moment at the outermost point. To gather yourself together for the return. And yet you do. As never before. — Samuel Beckett

[The] structural theory is of extreme simplicity. It assumes that the molecule is held together by links between one atom and the next: that every kind of atom can form a definite small number of such links: that these can be single, double or triple: that the groups may take up any position possible by rotation round the line of a single but not round that of a double link: finally that with all the elements of the first short period [of the periodic table], and with many others as well, the angles between the valencies are approximately those formed by joining the centre of a regular tetrahedron to its angular points. No assumption whatever is made as to the mechanism of the linkage. Through the whole development of organic chemistry this theory has always proved capable of providing a different structure for every different compound that can be isolated. Among the hundreds of thousands of known substances, there are never more isomeric forms than the theory permits. — Nevil Vincent Sidgwick

I became a little alarmed at the number of my readers who took the meme more positively as a theory of human culture in its own right - either to criticize it (unfairly, given my original modest intention) or to carry it far beyond the limits of what I then thought justified. This was why I may have seemed to backtrack. — Richard Dawkins

You could consider the idea of the multiverse, and think of it as something like a tree - that is, the universe we live in is one of an uncountable number of branches of possible universes, created by random chance and the decisions of sentient beings. So, for instance, when I rang you up in the morning, there was a possible future universe in which you answered the phone, and another in which you did not, and by answering the phone you put us in one universe and not the other. In that instance the time traveler doesn't just move from the future to the past and back to the future: he moves down one branch of the universe, toward the root that's back at the beginning of time, and back up another branch. — Dexter Palmer

By the eighteenth century the most reliable way to get a bath was to be insane. Then they could hardly soak you enough. In 1701, Sir John Floyer began to make a case for cold bathing as a cure for any number of maladies. His theory was that plunging a body into chilly water produced a sensation of "Terror and Surprize" which invigorated dulled and jaded senses. — Bill Bryson

Cardinal Arithmetics is much older than Number Theory. People used to exchange things way before there were numbers. Expressing numbers like 762 is already a sign of a very advanced civilization. — Saharon Shelah

Shepherd Book: What are we up to, sweetheart?
River: Fixing your Bible.
Book: I, um ... What?
River: Bible's broken. Contradictions, false logistics - doesn't make sense.
Shepherd Book: No, no. You-you-you can't ...
River: So we'll integrate non-progressional evolution theory with God's creation of Eden. Eleven inherent metaphoric parallels already there. Eleven. Important number. Prime number. One goes into the house of eleven eleven times, but always comes out one. Noah's ark is a problem.
Shepherd Book: Really?
River: We'll have to call it early quantum state phenomenon. Only way to fit 5000 species of mammal on the same boat.
Shepherd Book: River, you don't fix the Bible.
River: It's broken. It doesn't make sense.
Book: It's not about making sense. It's about believing in something, and letting that belief be real enough to change your life. It's about faith. You don't fix faith, River. It fixes you. — Ben Edlund

If women patronize the wheel the number of buyers will be twice as large. If women ride they must, when riding, dress more rationally than they have been wont to do. If they do this many prejudices as to what they may be allowed to wear will melt away. Reason will gain upon precedent and ere long the comfortable, sensible, and artistic wardrobe of the rider will make the conventional style of woman's dress absurd to the eye and unenduring to the understanding. A reform often advances most rapidly by indirection. An ounce of practice is worth a ton of theory; and the graceful and becoming costume of woman on the bicycle will convince the world that has brushed aside the theories, no matter how well constructed, and the arguments, no matter how logical, of dress-reformers. — Frances E. Willard

I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar's time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded. — James Sanborn

Among top grandmasters the Dutch is a rare defense, which is good reason to play it! It has not been studied very deeply by many opponents, and theory, based on a small number of 'reliable' games, must be rather unreliable. — Bent Larsen

Those colors of hers really begin their attack on me now, ripping through my skin, electrifying my bloodstream, sending sparks zapping around in my stomach. I take a long pull on my whisky but I can't keep a hard-on from starting. I only mention this because I have a theory that the hard-on is the number one reason for sexism down through history. I mean, it is seriously impossible to really soak in a girl's ideas, no matter how deep or true, when you have a stiffy coming on. — Tim Tharp

If someone were to propose that the planets go around the sun because all planet matter has a kind of tendency for movement, a kind of motility, let us call it an 'oomph,' this theory could explain a number of other phenomena as well. So this is a good theory, is it not? No. It is nowhere near as good as the proposition that the planets move around the sun under the influence of a central force which varies exactly inversely as the square of the distance from the center. The second theory is better because it is so specific; it is so obviously unlikely to be the result of chance. It is so definite that the barest error in the movement can show that it is wrong; but the planets could wobble all over the place, and, according to the first theory, you could say, 'Well, that is the funny behavior of the 'oomph. — Richard Feynman

Recreational number theory [ ... ] is that part of number theory that is too difficult to study. — Hendrik Lenstra

I think actually if you take the analogy with other areas of engineering, and increasingly of science and even mathematics, you can see people do not have to learn the vast number of formulae they used to learn. Instead, they have to learn to use the computer effectively. This frees them, I feel, to understand concepts and the foundations while they're learning the mechanics of the application of the theory. — C.A.R. Hoare

One consequence of this formulation is that a physical principle that unites many smaller physical theories must autoomatically unite many seemingly unrelated branches of mathematics. This is precisely what string theory accomplishes. In fact, of all physical theories, string theory unites by far the largest number of branches of mathematics into a single coherent picture. Perhaps one of the by-products of the physicists' quest for unification will be the unification of mathematics as well. — Michio Kaku

Last is D, the number of spatial dimensions. Due to interest in M-theory, physicists have returned to the question of whether life is possible in higher or lower dimensions. — Michio Kaku

After preliminary work by a number of other distinguished mathematicians and economists, game theory as a systematic theory started with von Neumann and Morgenstern's book, 'Theory of Games and Economic Behavior,' published in 1944. — John Harsanyi

From the dawn of civilization, human beings have tried to find out order in the chaotic world surrounding them. It has however never been easy to find a solution to explain a given system while being a part of that system. The best bet is to find out the most fundamental components within the system and building a theory round these. In other words, a theory that is able to describe the world in totality has to keep the number of basic postulates it depends upon to zero or near zero. — Subhajit Ganguly

For [Wolfgang] Pauli the central problem of electrodynamics was the field concept and the existence of an elementary charge which is expressible by the fine-structure constant ... 1/137. This fundamental pure number had greatly fascinated Pauli, .... For Pauli the explanation of the number 137 was the test of a successful field theory, a test which no theory has passed up to now. — Charles P. Enz

In network theory, the value of a system grows as approximately the square of the number of users of the system. — Robert Metcalfe

The whole action of the laws tended to increase the number of consumers of food and to diminish the number of producers, was due the invention of the Malthusian theory of population. — Henry Charles Carey

Music is part of Number Theory. Nowadays when a number-theorist applies for a grant, he says that it is good for security, but in those days, way before America, he would say that it's good for music. I will not comment whether we have progressed ... — Hendrik Lenstra

The overwhelming number of teachers ... are unable to name or describe a theory of learning that underlies what they do. — Alfie Kohn

As soon as science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a system of thought a theory. The theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the 'truth' of the theory lies. — Albert Einstein

I was lucky enough to build on the work of a number of people who had already run laps around this theory-building track. The original classification scheme, years ago, distinguished radical from incremental change. The theory said that established firms managed incremental change well, but would be expected to founder when their industry encountered a radical change. — Clayton Christensen

Although it is hard to visualize a landscape in a space of high dimensions, the more the number of parameters, the more likely it is that a walk of any finite distance, taken in a random direction from a place near the summit of a mountain, will go down rather than up. Thus, we may conclude that, if the hypotheses made here are true, most changes in the parameters of the laws of physics will decrease the rate at which black holes are produced in our universe. Because of this, the theory I am sketching here is actually subject to observational test. — Lee Smolin

Political philosophy reaches for the best regime, a regime so good that it can hardly exist. Political science advances a theory - in fact, a number of theories - that promises to bring agreement and put an end to partisan dispute. — Harvey Mansfield

Egoism holds, therefore, is that each man's happiness is the sole good--that a number of different things are each of them the only good thing there is--an absolute contradiction! No more complete and thorough refutation of any theory could be desired. — G.E. Moore

I think US/UK genre has become more open to "diverse" writers and writing; there's a genuine interest in reading work from countries outside the US/UK and hearing voices that have been historically shut out, but at the same time, people are quite lazy. That sounds harsh, but I include myself in it - your tastes are shaped by what you've read and watched before, and it takes a little effort to understand stories that use a different voice, that follow different storytelling conventions, that are trying to subvert the dominant paradigm. There's a quite large group of people who are "yay diversity" in theory, but I think the number of people who have then said to themselves, "OK, if I'm committed to this, I need to start reading outside my comfort zone and making an effort" is maybe a little smaller. — Zen Cho

All index-number systems, so far as they are intended to have a greater significance for monetary theory than that of mere playing with figures, are based upon the idea of measuring the utility of a certain quantity of money. The object is to determine whether a gramme of gold is more or less useful to-day than it was at a certain time in the past. As far as objective use-value is concerned, such an investigation may perhaps yield results. We may assume the fiction, if we like, that, say, a loaf of bread is always of the same utility in the objective sense, always comprises the same food value. It is not necessary for us to enter at all into the question of whether this is permissible or not. — Ludwig Von Mises

But it is not at all certain that this superiority of the many over the sound few is possible in the case of every people and every large number. There are some whom it would be impossible: otherwise the theory would apply to wild animals- and yet some men are hardly any better than wild animals. — Aristotle.

To the extent that we even understand string theory, it may imply a massive number of possible different universes with different laws of physics in each universe, and there may be no way of distinguishing between them or saying why the laws of physics are the way they are. And if I can predict anything, then I haven't explained anything. — Lawrence M. Krauss

Facts are of not much use, considered as facts. They bewilder by their number and their apparent incoherency. Let them be digested into theory, however, and brought into mutual harmony, and it is another matter. — Oliver Heaviside

To sum up: all nature-spirits are not the same as fairies; nor are all fairies nature-spirits. The same applies to the relationship of nature-spirits and the dead. But we may safely say that a large proportion of nature-spirits became fairies, while quite a number of the dead in some areas seem to take on the character of nature-spirits. We cannot expect any fixity of rule in dealing with barbaric thought. We must take it as it comes. It bears the same relationship to "civilized" or folk-lore theory as does the growth of the jungle to a carefully designed and meticulously labelled botanical garden. As Victor Hugo once exclaimed when writing of the barbaric confusion which underlies the creative function in poetry: 'What do you expect? You are among savages! — Lewis Spence

Of course, the set of logically consistent mathematical structures is many times larger than the set of physical principles. Therefore, some mathematical structures, such as number theory (which some mathematicians claim to be the purest branch of mathematics), have never been incorporated into any physical theory. Some argue that this situation may always exist: Perhaps the human mind will always be able to conceive of logically consistent structures that cannot be expressed through any physical principle. However, there are indications that string theory may soon incorporate number theory into its structure as well. — Michio Kaku

Being spiritual-but-nonreligious sounds good in theory - at least it's better than attending antiquated religious institutions. We can do that. And we have. A growing number of us identify as spiritual-but-nonreligious. — Gudjon Bergmann

In theory, there is nothing the computer can do that the human mind can not do. The computer merely takes a finite amount of data and performs a finite number of operations upon them. The human mind can duplicate the process — Isaac Asimov

Here is a quilted book about mathematical practice, each patch wonderfully prepared. Part invitation to number theory, part autobiography, part sociology of mathematical training, Mathematics without Apologies brings us into contemporary mathematics as a living, active inquiry by real people. Anyone wanting a varied, cultured, and penetrating view of today's mathematics could find no better place to engage. — Peter Galison

The substance of what I have to say to the disadvantage of the theory and practice of universal suffrage is that it tends to invert what I should have regarded as the true and natural relation between wisdom and folly. I think that wise and good men ought to rule those who are foolish and bad. To say that the sole function of the wise and good is to preach to their neighbors, and that everyone indiscriminately should be left to do what he likes, should be provided with a ratable share of the sovereign power in the shape of the vote, and that the result of this will be the direction of power by wisdom, seems to me the wildest romance that ever got possession of any considerable number of minds. — James Fitzjames Stephen

In his ... 'Geometrical peculiarities of the Pyramids', Ballard shows the relationship between the equal area theory and the golden number. After checking Herodotus' statement via dimensions Ballard concludes: 'I have therefore the authority of Herodotus to support the theory which I shall subsequently set forth, that this pyramid was the exponent of lines divided in mean and extreme ratio. — Roger Herz-Fischler

If you take Darwin's theory and extend it to its logical end, it can be used to justify a number of very horrendous things. — Kirk Cameron

Mimetic theory explains the presence of disabilities and infirmities in a great many mythical stories. When there is no ground for making a victim of someone - because he isn't guilty of anything - people act as children do and make a scapegoat of someone who is physically unattractive, or who is an outsider. The number of outsiders in myths is quite extraordinary. And why are so many victims lame? My work is scientific because it tries to solve the puzzle constituted by these clues, to explain why outsiders, many of them handicapped, are made into victims and forcibly expelled from a community. The burden falls on anyone who doubts my theory to supply a better explanation, or else to adopt mine for want of a more satisfactory one. — Rene Girard

My number-one theory in life is that style is proportional to your lack of resources - the less you have, the more stylish you're likely to be. — Beth Ditto

The theory that can absorb the greatest number of facts, and persist in doing so, generation after generation, through all changes of opinion and detail, is the one that must rule all observation. — Adam Smith

The historian Arthur Schlesinger has pointed out that people tend to get interested in politics again every 30 years. The universe moves in cycles of three. The number figures in everything from Pythagoras's theory that the universe is based on three to the Father-the-Son-and-the-Holy- Ghost to the three-sided pyramidal shapes that intersect in the Jewish Star of David. The notion of the mystical three, metaphysically, spiritually, and even politically, is quite interesting to me. — Marianne Williamson

The truth and value of a theory does not depend on the number of people who are interested in it - otherwise you might compare the number of people who follow the predictions of astrologers in the daily press with those who attend lectures by Einstein, and conclude that astrology was more valuable and true than physics. — Dorothy L. Sayers

We can invent as many theories we like, and any one of them can be made to fit the facts. But that theory is always preferred which makes the fewest number of assumptions. — Albert Einstein

The pattern recognition theory of mind that I articulate in this book is based on a different fundamental unit: not the neuron itself, but rather an assembly of neurons, which I estimate to number around a hundred. The wiring and synaptic strengths within each unit are relatively stable and determined genetically - that is the organization within each pattern recognition module is determined by genetic design. Learning takes place in the creation of connections between these units, not within them, and probably in the synaptic strengths of the interunit connections. — Ray Kurzweil

There are about 250,000 different species of fossil plants and animals known . In spite of this large quantity of information, it is but a tiny fraction of the diversity that [according to the theory] actually lived in the past. There are well over a million species living today and . [it is] possible to predict how many species ought to be in our fossil record. That number is at least 100 times the number we have found. — David M. Raup

Unlike other features on OkCupid, there is no visual component to match percentage. The number between two people only reflects what you might call their inner selves - everything about what they believe, need, and want, even what they think is funny, but nothing about what they look like. Judging by just this compatibility measure, the four largest racial groups on OkCupid - Asian, black, Latino, and white - all get along about the same.1 In fact, race has less effect on match percentage than religion, politics, or education. Among the details that users believe are important, the closest comparison to race is Zodiac sign, which has no effect at all. To a computer not acculturated to the categories, "Asian" and "black" and "white" could just as easily be "Aries" and "Virgo" and "Capricorn." But this racial neutrality is only in theory; things change once the users' own opinions, and not just the color-blind workings of an algorithm, come into play. — Christian Rudder

Understanding a theory has, indeed, much in common with understanding a human personality. We may know or understand a man's system of dispositions pretty well; that is to say, we may be able to predict how he would act in a number of different situations. But since there are infinitely many possible situations, of infinite variety, a full understanding of a man's dispositions does not seem to be possible. — Karl Popper

She'd heard theories in her time regarding the number-one enemy of everything, ranging from Osama bin Laden to premarital sex. The dust theory she liked. — Barbara Kingsolver

However, The haven-Slocum Theory also points out that this course is not without risk. An even greater number of people dwelling on The Navidson Record have shown an increase in obsessiveness, insomnia, and incoherence: Most of those who chose to abandon their interest soon recovered. A few, however, required counseling and in some instances medication and hospitalization. Three cases resulted in suicide. — Mark Z. Danielewski

If even in science there is no a way of judging a theory but by assessing the number, faith and vocal energy of its supporters, then this must be even more so in the social sciences: truth lies in power. — Imre Lakatos

The only goal of science is the honour of the human spirit, and a question in number theory is worth a question concerning the system of the world. — Serge Lang

It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms. — Richard A. Dunlap

If goodness were only a theory, it were a pity it should be lost to the world. There are a number of things, the idea of which is a clear gain to the mind. Let people, for instance, rail at friendship, genius, freedom, as long as they will -the very names of these despised qualities are better than anything else that could be substituted for them, and embalm even the most envenomed satire against them. — William Hazlitt

It turns out to be very difficult to devise a theory to describe the universe all in one go. Instead, we break the problem up into bits and invent a number of partial theories. Each of these partial theories describes and predicts a certain limited class of observations, neglecting the effects of other quantities, or representing them by simple sets of numbers. It may be that this approach is completely wrong. If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution by investigating parts of the problem in isolation. Nevertheless, it is certainly the way that we have made progress in the past. — Stephen Hawking

a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation. — Stephen Hawking