A Quote by Alfred North Whitehead
There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.
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I made an asylum application to Ecuador in this embassy, because of the U.S. extradition case, and the result was that after a month, I was successful in my asylum application. The embassy since then has been surrounded by police: quite an expensive police operation which the British government admits to spending more than £12.6 million.
We feel certain that the extraterrestrial message is a mathematical code of some kind. Probably a number code. Mathematics is the one language we might conceivably have in common with other forms of intelligent life in the universe. As I understand it, there is no reality more independent of our perception and more true to itself than mathematical reality.
There was, I think, a feeling that the best science was that done in the simplest way. In experimental work, as in mathematics, there was "style" and a result obtained with simple equipment was more elegant than one obtained with complicated apparatus, just as a mathematical proof derived neatly was better than one involving laborious calculations. Rutherford's first disintegration experiment, and Chadwick's discovery of the neutron had a "style" that is different from that of experiments made with giant accelerators.
The only thing that one really knows about human nature is that it changes. Change is the one quality we can predicate of it. The systems that fail are those that rely on the permanency of human nature, and not on its growth and development. The error of Louis XIV was that he thought human nature would always be the same. The result of his error was the French Revolution. It was an admirable result.
The life and soul of science is its practical application, and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.
We must understand that the fact of error, demonstrated in subsequent work, does not suggest that ethical lapses are responsible. It is more likely that the source of error is, as the advertisement says, a reflection of the fact that "its dangerous to trifle with Mother Nature".
Many persons who are not conversant with mathematical studies imagine that because the business of [Babbage’s Analytical Engine] is to give its results in numerical notation, the nature of its processes must consequently be arithmetical and numerical, rather than algebraical and analytical. This is an error. The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact it might bring out its results in algebraical notation, were provisions made accordingly.
This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due to the binary nature of mathematical perception. Either you have no inkling of an idea, or, once you have understood it, the very idea appears so embarrassingly obvious that you feel reluctant to say it aloud.
The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena. The verbal interpretation, on the other hand - i.e., the metaphysics of quantum theory - is on far less solid ground. In fact, in more than forty years physicists have not been able to provide a clear metaphysical model.
There is a certain point of unity within the self, and between the self and its world, certain complicity and magnetic mating, a certain harmony, that conscious mind and will cannot direct. Perhaps analysis and the separate mastery of each element are required before the instincts are ready to assume command, but only at first. Command by instinct is swifter, subtler, deeper, more accurate, more in touch with reality than command by conscious mind. The discovery takes one's breath away.
I have way more bravery than common sense, but you always assume things are going to be so difficult, and then when you're actually faced with them, you prevail. It's human nature.
When one admits that nothing is certain one must, I think, also admit that some things are much more nearly certain than others. It is much more nearly certain that we are assembled here tonight than it is that this or that political party is in the right. Certainly there are degrees of certainty, and one should be very careful to emphasize that fact, because otherwise one is landed in an utter skepticism, and complete skepticism would, of course, be totally barren and completely useless.
Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows no more uniformity than mathematics. Nevertheless, programming languages do bring a different perspective. [...] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation.
It may well happen that what is in itself the more certain on account of the weakness of our intelligence, which is dazzled by the clearest objects of nature; as the owl is dazzled by the light of the sun. Hence the fact that some happen to doubt about articles of faith is not due to the uncertain nature of the truths, but to the weakness of human intelligence; yet the slenderest knowledge that may be obtained of the highest things is more desirable than the most certain knowledge obtained of lesser things.
Nothing in all Nature is more certain than the fact that no single thing or event can stand alone. It is attached to all that has gone before it, and it will remain attached to all that will follow it. It was born of some cause, and so it must be followed by some effect in an endless chain.
History has taught us: never underestimate the amount of money, time, and effort someone will expend to thwart a security system. It's always better to assume the worst. Assume your adversaries are better than they are. Assume science and technology will soon be able to do things they cannot yet. Give yourself a margin for error. Give yourself more security than you need today. When the unexpected happens, you'll be glad you did.
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