Group Theory Quotes & Sayings

This success led my theoretical group to the chemical reactivity theory, extending more and more widely the range of compound and reactions that were discussed. — Kenichi Fukui

There is a mathematical underpinning that you must first acquire, mastery of each mathematical subdiscipline leading you to the threshold of the next. In turn you must learn arithmetic, Euclidian geometry, high school algebra, differential and integral calculus, ordinary and partial differential equations, vector calculus, certain special functions of mathematical physics, matrix algebra, and group theory. For most physics students, this might occupy them from, say, third grade to early graduate school - roughly 15 years. Such a course of study does not actually involve learning any quantum mechanics, but merely establishing the mathematical framework required to approach it deeply. — Carl Sagan

In theory, I'd like to work in a group. But the group I'd like to work in, all the musicians in them are long since dead. — Robert Wyatt

Limited government is not a means to liberty, it is an end. That is to say, there are always going to be a group of citizens who cannot meet their basic needs, and there most assuredly will always be politicians willing to promise that they will meet them. The difference between liberty and tyranny by popular support, or correctly termed "democratic despotism, " is little more than the vehicle a free society chooses to use in order to meet those needs. — Richard D. Baris

The application of group theory to physics became one of the main branches of physics that I specialized in. — Chen-Ning Yang

Bilderberg pulls the strings of every government and intelligence agency in the Western world. — James Morcan

A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of government as beyond its control, of itself as wholly controlled by government. Somewhere in between and In gradations is the group that has the sense that gov't exists for it, and shapes its consciousness accordingly. — Lionel Trilling

This, indeed, is the problem, the ultimate question, in neuroscience - and it cannot be answered, even in principle, without a global theory of brain function, one capable of showing the interactions of every level, from the micropatterns of individual neuronal responses to the grand macropatterns of an actual lived life. Such a theory, a neural theory of personal identity, has been proposed in the last few years by Gerald M. Edelman, in his theory of neuronal group selection, or neural Darwinism. — Oliver Sacks

Still, the belief in God was essentially a question of faith. Even for those, like Jeremy, who believed in the big bang theory, it said nothing about the creation of the sphere in the first place. Atheists would say the sphere was always there, those with faith might say that God created it, and there was no way ever to prove which group was right. That's why, Jeremy figured, it was called faith. Still, — Nicholas Sparks

From this failure to expunge the microeconomic foundations of neoclassical economics from post-Great Depression theory arose the "microfoundations of macroeconomics" debate, which ultimately led to a model in which the economy is viewed as a single utility-maximizing individual blessed with perfect knowledge of the future.
Fortunately, behavioral economics provides the beginnings of an alternative vision of how individuals operate in a market environment, while multi-agent modelling and network theory give us foundations for understanding group dynamics in a complex society. These approaches explicitly emphasize what neoclassical economics has evaded: that aggregation of heterogeneous individuals results in emergent properties of the group, which cannot be reduced to the behavior of any "representative individual." These approaches should replace neoclassical microeconomics completely. — Steve Keen

There's a theory that snoring at night in sleep is a subconscious defence reflex-a warning sound that frightened potential predators away from the mouth of the cave when our lower-paleolithic ancestors huddled in vulnerable sleep. That group of nomads, cameleers, sheep and goat herders, farmers, and guerilla fighters lent credibility to the idea, for they snored so thunderously and with such persistent ferocity through the long, cold night that they would've frightened a pride of ravenous lions into scattering like startled mice. — Gregory David Roberts

I have no idea who coined the term 'the New Journalism,' or when it was coined. I have never even liked the term. Any movement, group, party, program, philosophy or theory that goes under a name with 'new' in it is just begging for trouble, of course. — Tom Wolfe

There is, however, something odd about this pattern. Other than joining a political party, it is hard to think of any other sort of community that people join by agreeing to a set of principles. Imagine joining a knitting group. Does anyone go to a knitting group and ask if the knitters believe in knitting or what they hold to be true about knitting? Do people ask for a knitting doctrinal statement? Indeed, if you start knitting by reading a book about knitting or a history of knitting or a theory of knitting, you will very likely never knit. — Diana Butler Bass

We may as well cut out group theory. That is a subject that will never be of any use in physics. — James Jeans

Churchill admired the division of powers in the American government, but he thought they were copied from much older British practices. In 1950 he said: [T]he division of ruling power has always been for more than 500 years the aim of the British people. The division of power is the keynote of our parliamentary system and of the constitutions we have spread all over the world. The idea of checks and counter checks; the resistance to the theory that one man, or group of men, can by sweeping gestures and decisions reduce all the rest of us to subservience; these have always been the war cries of the British nation and the division of power has always been one of the war cries of the British people. And from here the principle was carried to America. The scheme of the American Constitution was framed to prevent any one man or any one lot, getting arbitrary control of the whole nation. — Larry P Arnn

There is a theory going around that the U.S.A. was and still is a gigantic Masonic plot under the ultimate control of the group known as the Illuminati. It is difficult to look for long at the strange single eye crowning the pyramid which is found on every dollar bill and not begin to believe the story, a little. Too many anarchists in 19th-century Europe - Bakunin, Proudhon, Salverio Friscia - were Masons for it to be pure chance. Lovers of global conspiracy, not all of them Catholic, can count on the Masons for a few good shivers and voids when all else fails. — Thomas Pynchon

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

Even today, I am in total awe of the following wondrous chain of ideas and interconnections. Guided throughout by principles of symmetry, Einstein first showed that acceleration and gravity are really two sides of the same coin. He then expanded the concept to demonstrate that gravity merely reflects the geometry of spacetime. The instruments he used to develop the theory were Riemann's non-Euclidean geometries-precisely the same geometries used by Felix Klein to show that geometry is in fact a manifestation of group theory (because every geometry is defined by its symmetries-the objects it leaves unchanged). Isn't this amazing? — Mario Livio

The theory of the "wisdom of crowds" says that if you aggregate many different opinions from a diverse group of people, you are much more likely to arrive at the best opinion than if you just listen to one specialist. — Simon Kuper

A story about the Jack Spratts of medicine [was] told recently by Dr. Charles H. Best, co-discoverer of insulin. He had been invited to a conference of heart specialists in North America. On the eve of the meeting, out of respect for the fat-clogs-the-arteries theory, the delegates sat down to a special banquet served without fats. It was unpalatable but they all ate it as a duty. Next morning Best looked round the breakfast room and saw these same specialists - all in the 40-60 year old, coronary age group - happily tucking into eggs, bacon, buttered toast and coffee with cream. — Richard Mackarness

Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics ... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory ... — Morris Kline

To reject any vast group of one's cultural ancestors in the cause of some current theory is not just arrogance; it's posthumous mass murder. It's the same kind of thinking that makes genocide possible. The masses (albeit the dead masses) and the pathetic little lives they lived are irrelevant compared to this greater purpose we have at hand. Write them out of the record. They never existed.
...
One could not judge things by the brief span of one's own lifetime. That was at the core of modern arrogance: only my lifetime counts. My lifetime is 'forever.' Time before it and time after it do not exist. Everything of importance must come to pass in my lifetime. This is what drives the frenzy for change. — Tony Hendra

Democracy can't work. Mathematicians, peasants, and animals, that's all there is
so democracy, a theory based on the assumption that mathematicians and peasants are equal, can never work. Wisdom is not additive; its maximum is that of the wisest man in a given group. — Robert A. Heinlein

In this book, you will encounter various interesting geometries that have been thought to hold the keys to the universe. Galileo Galilei (1564-1642) suggested that "Nature's great book is written in mathematical symbols." Johannes Kepler (1571-1630) modeled the solar system with Platonic solids such as the dodecahedron. In the 1960s, physicist Eugene Wigner (1902-1995) was impressed with the "unreasonable effectiveness of mathematics in the natural sciences." Large Lie groups, like E8-which is discussed in the entry "The Quest for Lie Group E8 (2007)"- may someday help us create a unified theory of physics. in 2007, Swedish American cosmologist Max Tegmark published both scientific and popular articles on the mathematical universe hypothesis, which states that our physical reality is a mathematical structure-in other words, our universe in not just described by mathematics-it is mathematics. — Clifford A. Pickover

The law of all modern states takes account of associations, whose members, in theory, pursue the common end with equal zeal. The experience of all associations proves, however, that this is not the case, and that a lively, constant and vigorous awareness of the end is found only in a minority of the associates; an association is really rather like a comet - a large tail of docile followers dragged along by a small dynamic head. — Bertrand De Jouvenel

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

Oh my God, does art engender humanity? It awakens your humanity. But humanity has nothing to do with political theory. Political theory is in the interests of one group of humanity, or one ideal for humanity. But humanity-my heavens, that's what proper art renders. We have a paradox. Going into the deepest aspects of inner space connects you with something that is the most vital for the outer realm. — Joseph Campbell

Creating consent (hegemony) is never a simple act. It is rather the result of the social structures and the cultural patterns that dictates for each group its behavior and for each institutions its practices. — Amine Zidouh

The importance of group theory was emphasized very recently when some physicists using group theory predicted the existence of a particle that had never been observed before, and described the properties it should have. Later experiments proved that this particle really exists and has those properties. — Irving Adler

the Eight Percent Rule to McCann. "It's really very simple," he said, using the same melodic voice he used to pet and stroke the jury. "I have to convince one juror out of twelve to vote with us. One of twelve is eight percent, give or take. Not that I need to convince him our client is innocent, understand. I just need to establish an intimate partnership with that one fellow or lady in a crowd who is contrary. The man or woman who has an ax to grind. My theory, and you saw it happen twice, is that in any group of people forced to be together, at least eight percent of them will go against the majority if for no other reason than to shove it up their ass - if they have an authority figure they can trust to be on their side. I am that leader in the courtroom. — C.J. Box

To learn theory by experimenting and doing.
To learn belonging by participating and self-rule.
Permissiveness in all animal behavior and interpersonal expression.
Emphasis on individual differences.
Unblocking and training feeling by plastic arts, eurythmics and dramatics.
Tolerance of races, classes, and cultures.
Group therapy as a means of solidarity, in the staff meeting and community meeting.
Taking youth seriously as an age in itself.
Community of youth and adults, minimizing 'authority.'
Educational use of the actual physical plant (buildings and farms) and the culture of the school community.
Emphasis in the curriculum on real problems and wider society, its geography and history, with actual participation in the neighboring community (village or city).
Trying for functional interrelation of activities. — Paul Goodman

I wrote my first textbook in 1970. It was called 'The Theory and Practice of Group Psychotherapy,' and over the years, many students told me that they enjoyed reading it because there were so many stories in there; often just a paragraph or a page of something that happened in a group session. — Irvin D. Yalom

I became intrigued with colour theory. The absurd pronouncements of the Colour Institute, a group that decides what colours are hot each year or season, amused me. — John Barton

When I first began examining the global-warming scare, I found nothing more puzzling than the way officially approved scientists kept on being shown to have finagled their data, as in that ludicrous "hockey stick" graph, pretending to prove that the world had suddenly become much hotter than at any time in 1,000 years. Any theory needing to rely so consistently on fudging the evidence, I concluded, must be looked on not as science at all, but as simply a rather alarming case study in the aberrations of group psychology. — Christopher Booker

Sexual objectification doesn't get oppressive until it is done consistently, and to a specific group of people, and with no regard whatsoever paid to their humanity. Then it ceases to become about desire and starts to be about control. Seeing another person as meat and fat and bone and nothing else gives you power over them, if only for an instant. Structural sexual objection of women draws that instant out into an entire matrix of hurt. It tells us that women are bodies first, idealised, subservient bodies, and men are not. — Laurie Penny

The instinct to survive is human nature itself, and every aspect of our personalities derives from it. Anything that conflicts with the survival instinct acts sooner or later to eliminate the individual and thereby fails to show up in future generations ... A scientifically verifiable theory of morals must be rooted in the individual's instinct to survive
and nowhere else!
and must correctly describe the hierarchy of survival, note the motivations at each level, and resolve all conflicts.
We have such a theory now; we can solve any moral problem, on any level. Self-interest, love of family, duty to country, responsibility toward the human race ...
The basis of all morality is duty, a concept with the same relation to group that self-interest has to individual. — Robert A. Heinlein

Governments do not necessarily act in the national interest, especially when making detailed microeconomic interventions. Instead, they are influenced by interest group pressures. The kinds of interventions that new trade theory suggests can raise national income will typically raise the welfare of small, fortunate groups by large amounts, while imposing costs on larger, more diffuse groups. — Paul Krugman

I do agree that the science is not settled on this. The idea that we would put American's economy at jeopardy based on scientific theory that's not settled yet, to me is just nonsense. Just because you have a group of scientists that stood up and said, this is the fact. Galileo got outvoted for a spell. But the fact is, to put America's economic future in jeopardy, asking us to cut back in areas that would have monstrous economic impact on this country, is not good economics, and I will suggest to you is not necessarily good science. — Rick Perry

One absolutely crucial change is that feminist film theory is today an academic subject to be studied and taught. "Visual Pleasure and Narrative Cinema" was a political intervention, primarily influenced by the Women's Liberation Movement and, in my specific case, a Women's Liberation study group, in which we read Freud and realised the usefulness of psychoanalytic theory for a feminist project. — Laura Mulvey

There's nothing about me on the jacket because I have no credentials. I majored in English at school, but I only took one creative writing class. I think I got a B. And I never really thought about getting an MFA. I'm too spiteful to take criticism constructively and I'm only comfortable being honest about people behind their backs, so workshops or group critiques were never what I was looking for. For years I just wrote in journals and didn't really worry about turning any of it into stories or stuff for other people to read, so I guess I developed my writing style by talking to myself, like some homeless people do. Only I used a pen and paper instead of just freaking out on the street. If they switched to a different medium they might be better off. It would probably help if they had someplace to live too. — Paul Neilan

What is missing from the policy analyst's tool kit
and from the set of accepted, well-developed theories of human organization
is an adequately specified theory of collective action whereby a group of principals can organize themselves voluntarily to retain the residuals of their own efforts. — Elinor Ostrom