Group Theory Quotes

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

It is the dull and elementary parts of applied mathematics, as it is the dull and elementary parts of pure mathematics, that work for good or ill. Time may change all this. No one foresaw the applications of matrices and groups and other purely mathematical theories to modern physics, and it may be that some of the 'highbrow' applied mathematics will become 'useful' in as unexpected a way; but the evidence so far points to the conclusion that, in one subject as in the other, it is what is commonplace and dull that counts for practical life. ~ G.H. Hardy

A good example of the archetypal ideas which the archetypes produce are natural numbers or integers. With the aid of the integers the shaping and ordering of our experiences becomes exact. Another example is mathematical group theory. ...important applications of group theory are symmetries which can be found in most different connections both in nature and among the 'artifacts' produced by human beings. Group theory also has important applications in mathematics and mathematical physics. For example, the theory of elementary particles and their interactions can in essential respects be reduced to abstract symmetries.
[The Message of the Atoms: Essays on Wolfgang Pauli and the Unspeakable] ~ Kalervo V. Laurikainen

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

Galois's ideas, with all their brilliance, did not appear out of thin air. They addressed a problem whose roots could be traced all the way back to ancient Babylon. Still, the revolution that Galois had started grouped together entire domains that were previously unrelated. Much like the Cambrian explosion-that stunning burst of diversification in life forms on Earth-the abstraction of group theory opened windows into an infinity of truths. Fields as far apart as the laws of nature and music suddenly became mysteriously connected. The Tower of Babel of symmetries miraculously fused into a single language. ~ Mario Livio

Group theory has been called by the noted mathematics scholar James R. Newman "the supreme art of mathematical abstraction." It derives its incredible power from the intellectual flexibility afforded by its definition. ~ Mario Livio

The progress of the sciences toward theories of fundamental unity, cosmic symmetry (as in the unified field theory) - how do such theories differ, in the end, from that unity which Plato called "unspeakable" and "indiscribable," the holistic knowledge shared by so many peoples of the earth, Christians included, before the advent of the industrial revolution made new barbarians of the peoples of the West? In the United States, before spiritualist foolishness at the end of the last century confused mysticism with "the occult" and tarnished both, William James wrote a master work of metaphysics; Emerson spoke of "the wise silence, the universal beauty, to which every part and particle is equally related, the eternal One . . ."; Melville referred to "that profound silence, that only voice of God"; Walt Whitman celebrated the most ancient secret, that no God could be found "more divine than yourself. ~ Peter Matthiessen

Despite its name, the big bang theory is not really a theory of a bang at all. It is really only a theory of the aftermath of a bang. ~ Alan Guth

Read an article about a group of mathematicians who developed a financial model to accurately compare apples and oranges. I was stunned. Never thought I'd see the day. Preliminary indications are that the model allows any two kinds of fruit to be compared, although guava still causes minor rounding errors. Further testing is ongoing.
Gomez Porter, blogspace entry ~ Graham Parke

It is not possible to starve an organised terrorist group because it is number one a state, so it levies taxation inside the territory that is controlled by Islamic State. But also the activity, for example the smuggling of oil, is taking place in an area which is a war zone. So of course people will buy that oil because they don't have any alternative. So even if we wanted to stop that kind of trade, it will be very, very difficult to do that. ~ Loretta Napoleoni

The most important moments in a trial are often not seen by a jury. That is because it's one of the judge's main responsibilities to screen what they see and hear, lest they be prejudiced. It's the "you can't unring a bell" theory; once the jury hears something they shouldn't have heard, th trial is forever tainted.
If the damage is great enough, a mistrial is the result. Judges basically prefer nuclear war to mistrials. ~ David Rosenfelt

The official independence celebration was going to be held over four or five days, and a group of journalists from all over the world was allowed to fly in, because Angola was closed otherwise. ~ Ryszard Kapuscinski

Whichever theory we adopt to give a rational explanation of human existence, that theory must take into account and explain the mental nature we see at work in all modern communities. ~ Arthur Keith

In other words, I'd say the whole story of Bob Dylan is one man's search for God. The turns and the steps he takes to find God are his business. I think he went to a study group at the Vineyard, and it created a lot of excitement. ~ T Bone Burnett

how unordered atoms could group themselves into ever more complex patterns until they ended up manufacturing people. ~ Richard Dawkins

San Narciso was a name; an incident among our climatic records of dreams and what dreams became among our accumulated daylight, a moment's squall-line or tornado's touchdown among the higher, more continental solemnities - storm-systems of group suffering and need, prevailing winds of affluence. There was the true continuity, San Narciso had no boundaries. No one knew yet how to draw them. She had dedicated herself, weeks ago, to making sense of what Inverarity had left behind, never suspecting that the legacy was America. ~ Thomas Pynchon

'Boyz-n-the-Hood' was actually supposed to be written for Eazy's group. He had a group out in New York called Home Boys Only, called HBO. One of them looked like LL Cool J. Eazy wanted to write a song for them, a street song, like what we were doing on the mix tapes. So when I wrote it, it was too West Coast for them. ~ Ice Cube

In the democratic, egalitarian spirit of our day, we hold in suspicion positions of social authority, yet we submit to the power of peers. Social anxiety, peer group pressure, and competition all dictate our lives. Many are more afraid of offending their friends than they are of offending figures of authority. We have moved from a culture based upon hierarchy to a peerarchy. Ironically we flee from relational distinctions and boundaries, yet without these traditions and boundaries we become mired in codependency. ~ Mark Sayers

Think of how it all started: America was founded by slave owners who informed us, "All men are created equal." All "men," except Indians, niggers, and women. Remember, the founders were a small group of unelected, white, male, land-holding slave owners who also, by the way, suggested their class be the only one allowed to vote. To my mind, that is what's known as being stunningly
and embarrassingly
full of shit. ~ George Carlin

The profit orientation is only one orientation of a person. The same people who are interested in profit-making are also selfless. I am not saying that capitalist theory is wrong. I am saying that it has not been interpreted and practiced fully. ~ Muhammad Yunus

I always say Manny [Ramirez] is a strange guy. Outwardly, he's happy-go-lucky. On the inside, he's got a lot of conspiracy theories going on. I would say Manny might be one of these guys when he's 50 years old, he might be in his house with all the blinds shut kind of looking out like the CIA's out there. You don't know, man. I mean, you don't know what's going on in the interior with him. So you don't worry about it. ~ Bronson Arroyo

The large majority of teenagers who attend Higgs are soulless, conformist idiots. I have successfully integrated myself into a small group of girls who I consider to be "good people," but sometimes I still feel that I might be the only person with a consciousness, like a video game protagonist, and everyone else are computer-generated extras who have only a select few actions, such as "initiate meaningless conversation" and "hug. ~ Alice Oseman

Despite the popularity of this view, the DeValoises felt it was only a partial truth. To test their assumption they used Fourier's equations to convert plaid and checkerboard patterns into simple wave forms. Then they tested to see how the brain cells in the visual cortex responded to these new wave-form images. What they found was that the brain cells responded not to the original patterns, but to the Fourier translations of the patterns. Only one conclusion could be drawn. The brain was using Fourier mathematics - the same mathematics holography employed - to convert visual images into the Fourier language of wave forms. 12 The DeValoises' discovery was subsequently confirmed by numerous other laboratories around the world, and although it did not provide absolute proof the brain was a hologram, it supplied enough evidence to convince Pribram his theory was correct. Spurred on by the idea that the visual cortex was responding not to patterns but to the frequencies of various wave forms, he began to reassess the role frequency played in the other senses. It didn't take long for him to realize that the importance of this role had perhaps been overlooked by twentieth-century scientists. Over a century before the DeValoises' discovery, the German physiologist and physicist Hermann von Helmholtz had shown that the ear was a frequency analyzer. More recent research revealed that our sense of smell seems to be based on what are called osmic frequencies. Bekesy's work had clearly d ~ Michael Talbot

No one has yet been found so firm of mind and purpose as resolutely to compel himself to sweep away all theories and common notions, and to apply the understanding, thus made fair and even, to a fresh examination of particulars. Thus it happens that human knowledge, as we have it, is a mere medley and ill-digested mass, made up of much credulity and much accident, and also of the childish notions which we at first imbibed. ~ Francis Bacon

Isabelle took out her invitation and waved it like a white flag. "I have an invitation. These" - she indicated the rest of the group with a grand wave of her arm - "are my friends."
Magnus plucked the invitation out of her hand and looked at it with fastidious distaste. "I must have been drunk," he said. He threw the door open. "Come in. And try not to murder any of my guests."
Jace edged into the doorway, sizing up Magnus with his eyes. "Even if one of them spills a drink on my new shoes?"
"Even then." Magnus's hand shot out, so fast it was barely a blur. He plucked the stele out of Jace's hand - Clary hadn't even realized he was holding it - and held it up. Jace looked faintly abashed. "As for this," Magnus said, sliding it into Jace's jeans pocket, "keep it in your pants, Shadowhunter. ~ Cassandra Clare

If pondering whether something is appropriate to post online, ask yourself: Would I tell this to a large group of people in-person? If the answer is "no" or "maybe not," do not post it. ~ Erik Qualman

It was my mom and I against the world. We lived in New York in this bohemian lifestyle where an extended group of artists and photographers were like my aunts and uncles. ~ Brooke Shields

While Five lingers at the back of the group looking nervous to be meeting so many new people, John strides right towards me. A grin splits my face - it's more than just being united with my best friend, it's the feeling that we're going to be part of something great together. We're going to save the world. ~ Pittacus Lore

Sports constantly make demands on the participant for top performance, and they develop integrity, self-reliance and initiative. They teach you a lot about working in groups, without being unduly submerged in the group. ~ Byron White

I may have had a prejudice against agnosticism as a body of thought: sort of a fence-sitting theory, where you can't make up your mind one way or another. ~ S.T. Joshi

Mr Hall's hypothesis has its cause for subsidence, but none for the lifting of the thickened sunken crust into mountains. It is a theory for the origin of mountains, with the origin of mountains left out. ~ James Dwight Dana

To have a group of cloistered clinicians away completely from the broad current of professional life would be bad for teacher and worse for student. The primary work of a professor of medicine in a medical school is in the wards, teaching his pupils how to deal with patients and their diseases. ~ William Osler

In South America euphemism appears to be the grisly preserve of violent power. 'Liberty' was the name of the biggest prison in Uruguay under the military dictatorship, while in Chile one of the concentration camps was called 'Dignity.' It was the self-styled 'Peace and Justice' paramilitary group in Chiapas [Mexico] that in 1997 shot 45 peasants in the back, nearly all of them women and children, as they prayed in a church. What have the souls of the south done over the past few decades to deserve quite so much liberty and dignity and peace and justice? ~ Isabel Fonseca

You would think that if any group in America had 20% to 25% unemployment, it would generate all kinds of attention. The Labor Department would understandably and necessarily begin to concentrate on what can we do to reduce this level of unemployment. Congress would give great time on the floor for debate on what can be done. ~ Emanuel Cleaver

All the theories of conspiracy were always a way to escape our responsibilities. It is a very important kind of social sickness by which we avoid recognizing reality such as it is and avoid our responsibilities. ~ Umberto Eco

If democracy brings an undemocratic group to power, is that a victory for democracy? ~ Richard Engel

I feel passionately about issues, and I don't hide my emotions from people. I am not a focus group-tested, blow-dried candidate or governor. Now that has always made some people, you know, uneasy. Some people like that style, some people don't ... But I am not a bully. ~ Chris Christie

His theory was that non-fiction could be as artful as fiction. ~ Gerald Clarke

All the theories mess you up inside. ~ Paul Cezanne

It used to be that if someone was to get involved in feminism, it was probably because they were already interested. They were already interested in feminism; they were already interested in being an activist, and they found their way to like a NOW meeting or to a consciousness-raising group or something like that. ~ Jessica Valenti

We have created a society in which the rich become richer and the poor become poorer, and in which we are so caught up in our own immediate problems that we cannot afford to be aware of what is going on with the rest of the human family or our planet Earth. In my mind I see a group of chickens in a cage disputing over a few seeds of grain, unaware that in a few hours they will all be killed. ~ Thich Nhat Hanh

It really is a nice theory. The only defect I think it has is probably common to all philosophical theories. It's wrong. ~ Saul Kripke

I never wanted to do the same kind of movies over and over anyway, so my theory on it all is I'm just gonna try and dodge the label and keep doing what I am doing. ~ Matt Damon

I've been an inveterate reader of literary magazines since I was a teenager. There are always discoveries. You're sitting in your easy chair, reading; you realize you've read a story or a group of poems four times, and you know, Yes, I want to go farther with this writer. ~ Marilyn Hacker

There is, in fact, no need to drag politics into literary theory: as with South African sport, it has been there from the beginning. I mean by the political no more than the way we organize our social life together, and the power-relations which this involves; and what I have tried to show throughout this book is that the history of modern literary theory is part of the political and ideological history of our epoch. From Percy Bysshe Shelley to Norman N. Holland, literary theory has been indissociably bound up with political beliefs and ideological values. Indeed literary theory is less an object of intellectual enquiry in its own right than a particular perspective in which to view the history of our times. Nor should this be in the least cause for surprise. For any body of theory concerned with human meaning, value, language, feeling and experience will inevitably engage with broader, deeper beliefs about the nature of human individuals and societies, problems of power and sexuality, interpretations of past history, versions of the present and hopes for the future. It is not a matter of regretting that this is so - of blaming literary theory for being caught up with such questions, as opposed to some 'pure' literary theory which might be absolved from them. Such 'pure' literary theory is an academic myth: some of the theories we have examined in this book are nowhere more clearly ideological than in their attempts to ignore history and politics altogether. Literary theor ~ Terry Eagleton

Birds chirped and hawked in the distance. A group of them, maybe vultures, circled the sky. Rae glanced at the blanket. Those damn birds could probably smell Marissa, and the second everyone left, they'd pounce on her. ~ Yawatta Hosby

Why do people wage war? Why do hundreds of thousands, even millions of people group together and try to annihilate each other? Do people start wars out of anger? Or fear? Or are anger and fear just two aspects of the same spirit? ~ Haruki Murakami

The theory of science which permits and encourages the exclusion of so much that is true and real and existent cannot be considered a comprehensive science. ~ Abraham Maslow

The last thing I need is more high school drama but a support group that doesn't dig into my personal business sounds good. They can keep the drama for themselves. ~ Nikki Godwin

For the law, the clarity of language and the finality of judgment is crucial, because you have to decide a case one way or another - whether it is criminal or civil or whatever. In ordinary life, you do not have to decide things with absolute finality. You do not have to decide on a theory in order to behave in a certain way towards other people. ~ Talal Asad