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)

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

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Related quotes

As the natural sciences have developed to encompass increasingly complex systems, scientific rationality has become ever more statistical, or probabilistic. The deterministic classical mechanics of the enlightenment was revolutionized by the near-equilibrium statistical mechanics of late 19th century atomists, by quantum mechanics in the early 20th century, and by the far-from-equilibrium complexity theorists of the later 20th century. Mathematical neo-Darwinism, information theory, and quantitative social sciences compounded the trend. Forces, objects, and natural types were progressively dissolved into statistical distributions: heterogeneous clouds, entropy deviations, wave functions, gene frequencies, noise-signal ratios and redundancies, dissipative structures, and complex systems at the edge of chaos.

Nick Land

Every development of truths which relate to human nature, and more especially its active manifestations, is attended with a wish to see worked out in practice what theory has shown us to be just and good. To man, whose mind is seldom satisfied with the calmly beneficent influence of abstract ideas, this desire is perfectly natural, and it increases in liveliness with the spirit of benevolent sympathy in social happiness and well-being. But, however natural in itself, and however noble in its origin, this desire has not unfrequently led to hurtful consequences,-nay, often to greater evils than the colder indifference, or (as from the very opposite cause the same effect may follow) the glowing enthusiasm, which, comparatively heedless of reality, delights only in the pure beauty of ideas.

Wilhelm von Humboldt

He was one of the few judges who could occasionally poke fun at himself. He told me that once he was sitting at a dinner at the Cambridge University where a number of distinguished persons had been invited. Next to him was an elderly gentleman whose identity he did not know. There was some discussion about the theory of relativity and he aired his own views with a certain measure of authority. His neighbour told him that his views were interesting and invited him for a cup of tea in the next two or three days. Later on he found out that he had been talking to the world renowned physicist Sir Arthur Eddington who was reputed as one of the few persons apart from Einstein who understood the theory of relativity. He never picked up the courage to go for that cup of tea and face Sir Arthur Eddington.

Mohammad Hidayatullah

P. Bernays has pointed out on several occasions that, since the consistency of a system cannot be proved using means of proof weaker than those of the system itself, it is necessary to go beyond the framework of what is, in Hilbert's sense, finitary mathematics if one wants to prove the consistency of classical mathematics, or even that of classical number theory. Consequently, since finitary mathematics is defined as the mathematics in which evidence rests on what is intuitive, certain abstract notions are required for the proof of the consistency of number theory.... In the absence of a precise notion of what it means to be evident, either in the intuitive or in the abstract realm, we have no strict proof of Bernays' assertion; practically speaking, however, there can be no doubt that it is correct...

Paul Bernays

We don't have much time left. We are moving towards temperature increases of around two degrees Celsius, which is going to have consequences in the tropics, and we will loose things like glaciers. That's not a theory; it's happening right now. It's not a prediction; it's happening right now. But you just sightsee near those glaciers. But the glaciers are a big source of water. And on the questions of water, in California we store our water in a snowpack. When that's gone, the rain will be the same but it won't accumulate. With warming temperatures the snowpack will now work. It might be possible to substitute with dams, but that's complicated. This is conjoined with a big energy problem and I think that we really have to encourage development in this area. Just waiting for technological improvement won't work. We need to encourage it.

Kenneth Arrow