Quotes & Sayings About Bifurcation

Bifurcation occurs when the environment of a potentially chaotic system destabilizes due to stress over time, or to some inciting disturbance, explosive or catastrophic. When perturbation occurs, an attractor draws the trajectories of the disturbance and, at the point of transition, the system bifurcates and is propelled to a new order of self-organization, or else it disintegrates. — Wally Lamb

At the highest level, there is the general Subject-Self metaphor, which conceptualizes a person as bifurcated. The exact nature of this bifurcation is specified more precisely one level down, where there are five specific instances of the metaphor. These five special cases of the basic Subject-Self metaphor are grounded in four types of everyday experience: (1) manipulating objects, (2) being located in space, (3) entering into social relations, and (4) empathic projection-conceptually projecting yourself onto someone else, as when a child imitates a parent. The fifth special case comes from the Folk Theory of Essences: Each person is seen as having an Essence that is part of the Subject. The person may have more than one Self, but only one of those Selves is compatible with that Essence. This is called the "real" or "true" Self. — George Lakoff

I find it really liberating to be in a place where I am a foreigner in every way. I've lived with this all my life - this divide, this bifurcation. And in Italy, I don't feel it. There's none of that tension, only the expectation I place on myself to speak the language well. I find it relaxing. Something drops away, and I observe. — Jhumpa Lahiri

Explosive bifurcation is the sudden transition that wrenches the system out of one order, and into another. — Wally Lamb

Feminism is itself a challenge. Feminism is a challenge to the way things are in the world. It is by definition an oppositional movement, because it's trying to accomplish something. I've never felt like feminism was a consciousness raising effort in isolation. Everything about feminism is about getting something in the world to get better for women, and to get the world to be less stupid on gender bifurcation terms. I think that feminism over time gets better, or it gets better and worse and better and worse at achieving the goals that it's trying to achieve, but the overall mission stays the same. I guess I don't think of it as feminism versus anti-feminism; I sort of think of it as feminism versus the world. I don't think of it as a competition; there's no winning. In feminism, you're always trying to make stuff better. It's opposition to which you cannot attribute a tally. — Rachel Maddow

When systems come to be far from points of equilibrium, they reach bifurcation points, wherein multiple, as opposed to unique, solutions, to instability become possible. — Immanuel Wallerstein

I have noticed a curious bifurcation in outcome in the way romances are written by women et written by men - Love Story, The Bridges of Madison County, every James Bond tale ever penned, even the film named above - end with the woman either lost or dead. And the man free to love, or at least to have sex, again. Romances (in the modern genre sense) written by women end with the couple alive, together, and in a committed and at least potentially fertile relationship, ready to turn to the work of their world. In other words, men's romances are about love and death; women's romances are about love and life. — Lois McMaster Bujold

In a dynamical system, or a massively complex dynamical system such as we live in, when there is a moment of bifurcation, which is the technical mass jargon for "the snap", that is the only time you get to do anything about the evolution of the system. So according to this self-inflating view, we live at an especially important special moment in history where when we think something or do something it has actually an enormous effect on the future. What we do has some influence on the creation of the future more than at other times in history. — Ralph Abraham

A bifurcation of loyalties that requires religious to put canon law above civil law and moral law puts us in a situation where the keepers of religion may themselves become one of the greatest dangers to the credibility - and the morality - of the church itself. — Joan D. Chittister

Though blessed with the enviable properties of a mink coat - graceful, unreasonable, and impractical no matter what she was draped over - she was nevertheless one of those people whose personality proved to be the bane of modern mathematicians. She was neither a flat nor solid shape. She showed no symmetry at all. Trigonometry, Calculus and Statistics all proved useless. Her Pie Chart was a muddle of arbitrary wedges, her Line Graph, the silhouette of the Alps. And just when one listed her under Chaos Theory - Butterfly Effects, Weather Predictions, Fractals, Bifurcation diagrams and whatnot - she showed up as an equilateral triangle, sometimes even a square. — Marisha Pessl

One of my frustrations is that we in society generally have this bifurcation in how we see the world. That's probably a little less true with business audiences, but in general, there tends to be this view that for-profit companies are greedy, and nonprofits are noble. It's absolutely more complicated than that. — Nicholas Kristof

We seem to be in the midst of a process of cascading bifurcations that may last some 50 more years. We can be sure some new historical order will emerge. We cannot be sure what that order will be. Concretely, we may symbolize the first bifurcation as the effect of the world revolution of 1968 which continued up to and including the so-called collapse of the communisms in 1989, the social bifurcation. — Immanuel Wallerstein

One way to find food for thought is to use the fork in the road, the bifurcation that marks the place of emergence in which a new line of development begins to branch off. — William Irwin Thompson

The Buddha, in recovering his capacity for nonsensual joy, learned that this joy was limitless. He found that if he got himself out of the way, his joy completely suffused his mindful awareness. This gave him the confidence, the stability, the trust, and the means to see clearly whatever presented itself to his mind. In the curious bifurcation of consciousness that meditation develops, where we can be both observer and that which is being observed, the quality of joy that he recovered did not remain an internal object. It was not only a memory or merely a feeling to be observed; it was also a quality of mind that could accompany every moment of mindfulness. The more he accepted the presence of this feeling and the more it toggled between being object and subject, the closer the Buddha came to understanding his true nature. — Mark Epstein

There is a second but not so obvious truth. "I am the Bread of Life," said Jesus. "He who comes to Me will never go hungry, and he who believes in Me will never be thirsty." Notice the power implicit in the claim. At the heart of every major religion is a leading exponent. As the exposition is studied, something very significant emerges. There comes a bifurcation, or a distinction, between the person and the teaching. Mohammed, to the Koran. Buddha, to the Noble Path. Krishna, to his philosophizing. Zoroaster, to his ethics. Whatever we may make of their claims, one reality is inescapable. They are teachers who point to their teaching or show some particular way. In all of these, there emerges an instruction, a way of living. It is not Zoroaster to whom you turn. It is Zoroaster to whom you listen. It is not Buddha who delivers you; it is his Noble Truths that instruct you. It is not Mohammed who transforms you; it is the beauty of the Koran that woos you. By — Ravi Zacharias

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