A Quote by Werner Heisenberg
The discontinuous 'reduction of the wave packets' which cannot be derived from Schroedinger's equation is ... a consequence of the transition from the possible to the actual.
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But it is certainly not possible to insist on one hand that the formalism is complete and to insist on the other hand that its application to 'the actual' actually demands a step which cannot be derived from it.
Working in the digital domain, you're using approximations of things; the actual sound wave never enters the equation. You deal with sections of it, and you're able to do so much more by just reducing the information to a finite amount.
It is a curious historical fact that modern quantum mechanics began with two quite different mathematical formulations: the differential equation of Schroedinger and the matrix algebra of Heisenberg. The two apparently dissimilar approaches were proved to be mathematically equivalent.
By explanation the scientist understands nothing except the reduction to the least and simplest basic laws possible, beyond which he cannot go, but must plainly demand them; from them however he deduces the phenomena absolutely completely as necessary.
It was clear to me that the White House's solemn atmosphere would not civilize Trump. But the merciless nepotism with which he conducts politics, in which he places himself and his family above the law, I wouldn't have considered that possible. And on top of that there is this reduction of complex political decisions to 140 characters. When it comes to a U.S. president, I consider the reduction of politics to a tweet to be truly dangerous. Trump is a risk to his country and the entire world.
The transition from rebellion to acceptance has an extremely important consequence. . . in which we start seeing life as a training school, to teach us what we need to learn.
It takes creativity at every stage to make the discontinuous leap from one level of knowledge to the next. These discontinuous leaps of understanding lead to insights that in turn lead to value creation.
So briefly do we raise our heads, so quick sink back. For a moment we are lifted by a wave of time, are tossed up into the sunlight of consciousness We cannot see so far as where this wave began, but maybe we have waited some thousand years for it to come, and now it is on us. This is our moment, the wave is breaking. The crest which passes through us now in tumult was shaped by the past, and we in this moment are able to shape the crest which is to come.
Life cannot be calculated. That's the big mistake our civilization made. We never accepted that randomness is not a mistake in the equation -- it is part of the equation.
There has to be a consequence to failure. Schools in the inner cities cannot be told, 'Oh, we want you to teach every child to learn how to read and, incidentally, if you fail to do that there's no consequence,' .. There has to be a consequence to failure, and the Title I money needs to follow the child.
Mental pictures offer us an opportunity to practice new traits and attitudes, which otherwise we could not do. This is possible because again - your nervous system cannot tell the difference between an actual experience and one that is vividly imagined.
Since nothing can exist that does not fulfil the conditions which render its existence possible, the different parts each being must be co-ordinated in such a way as to render possible the existence of the being as a whole, not only in itself, but also in its relations with other beings, and the analysis of these conditions often leads to general laws which are as certain as those which are derived from calculation or from experiment.
Art is precisely that condition which pertains when, after all analysis and reduction to parts has taken place, there remains a 'quality' which is more than the sum of those parts, which could not exist in any other form, and which cannot be caught, or held, or contained.
Given certain known factors in an equation and the equation comprising a situation of absolute need - any form of need - you can predict the results. Leave a sick junkie in the back room of a drugstore and only one result is possible.
Basically, we convert the entire Web into a big equation, with several hundred million variables, which are the page ranks of all the Web pages, and billions of terms, which are the links. And we're able to solve that equation.
Correct is to recognize what diseases are and whence they come; which are long and which are short; which are mortal and which are not; which are in the process of changing into others; which are increasing and which are diminishing; which are major and which are minor; to treat the diseases that can be treated, but to recognize the ones that cannot be, and to know why they cannot be; by treating patients with the former, to give them the benefit of treatment as far as it is possible.
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