Perturbation Quotes
The divine tape recorder holds a million scenarios, each perfectly sensible. Little quirks at the outset, occurring for no particular reason, unleash cascades of consequences that make a particular feature seem inevitable in retrospect. But the slightest early nudge contacts a different groove, and history veers into another plausible channel, diverging continually from its original pathway. The end results are so different, the initial perturbation so apparently trivial.
Stephen Jay Gould
It was found [in the 1970s], unexpectedly and without anyone really having a concept for it, that the rules of perturbation theory can be changed in a way that makes relativistic quantum gravity inevitable rather than impossible. The change is made by replacing point particles by strings. Then Feynman graphs are replaced by Riemann surfaces, which are smooth - unlike the graphs, which have singularities at interaction vertices. The Riemann surfaces can degenerate to graphs in many different ways. In field theory, the interactions occur at the vertices of a Feynman graph. By contrast, in string theory, the interaction is encoded globally, in the topology of a Riemann surface, any small piece of which is like any other. This is reminiscent of how non-linearities are encoded globally in twistor theory.
Edward Witten
Replacing particles by strings is a naive-sounding step, from which many other things follow. In fact, replacing Feynman graphs by Riemann surfaces has numerous consequences: 1. It eliminates the infinities from the theory. ...2. It greatly reduces the number of possible theories. ...3. It gives the first hint that string theory will change our notions of spacetime. Just as in QCD, so also in gravity, many of the interesting questions cannot be answered in perturbation theory. In string theory, to understand the nature of the Big Bang, or the quantum fate of a black hole, or the nature of the vacuum state that determines the properties of the elementary particles, requires information beyond perturbation theory... Perturbation theory is not everything. It is just the way the [string] theory was discovered.
Edward Witten
There is little doubt that the planetary patina-including ourselves-is autopoietic. Life at the surface of the Earth seems to regulate itself in the face of external perturbation, and does so without regard for the individuals and species that compose it. More than 99.99 percent of the species that have ever existed have become extinct, but the planetary patina, with its army of cells, have continued for more than three billion years. ...trillions of communicating, evolving microbes. The visible world is a late-arriving, overgrown portion of the microcosm, and it functions only because of its well-developed connection with the microcosm's activities.
Lynn Margulis
In excited states of the public mind they have scarcely a discretion at all; the tendency of the public perturbation determines what shall and what shall not be dealt with. But, upon the other hand, in quiet times statesmen have great power; when there is no fire lighted, they can settle what fire shall be lit. And as the new suffrage is happily to be tried in a quiet time, the responsibility of our statesmen is great because their power is great too.
Walter Bagehot
Ideas and techniques known in quantum electrodynamics have been applied to the Bardeen-Cooper-Schrieffer theory of superconductivity. In an approximation which corresponds to a generalization of the Hartree-Fock fields, one can write down an integral equation defining the self-energy of an electron in an electron gas with phonon and Coulomb interaction. The form of the equation implies the existence of a particular solution which does not follow from perturbation theory, and which leads to the energy gap equation and the quasi-particle picture analogous to Bogolyubov's.
Yoichiro Nambu
