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The proof is elegant and the result profound. Still, it is typical mathematics; so, it’s a good example to reflect upon. In doing so, we will begin to see the elements of the mathematical image, the standard conception of what mathematics is. Let’s begin a list of some commonly accepted aspects. By ‘commonly accepted’…
The response many organizations adopted then (and continue to pursue AF) is to provide overwhelming amounts of data to the public. This provided a two-fold defense. First, it allowed immediate deniability to any charge of withholding data. Second, the sheer volume of data available meant that almost any argument could…
A Cornell experiment in the 1960s polled a group of computer science students and divded them into those who liked to work with music in the background and those who didn't. They put 1/2 of each group together in a silent room, and the other 1/2 in a different room equipped with headphones and a musical selection. To…
The ship wherein Theseus and the youth of Athens returned [from Crete] had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing…
As we move from the "low" level to the "high", say from the domain of machine code all the way up to, for instance, a rich, expressive Ruby DSL, the question arises, as it does for all language: have we acquired a surplus of content that cannot be simply reduced to core rules? At this point things get less…
There is another species of progress, appertaining to the sciences in question, equally important; I mean, the improvement of their language, at present so vague and so obscure. To this improvement must they owe the advantage of becoming popular, even in their first elements. Genius can triumph over these…
In the midst of the decline of Greece, Athens, which, in the days of its power, had honoured philosophy and letters, owed to them, in its turn, the preserving for a longer period some remains of its ancient splendour. In its tribune, indeed, the destinies of Greece and Asia were no longer decided; it was, however, in…
As recorded in the stone carvings of Egypt and Mesopotamia, the history of worid society begins with humanity at large knowing nothing of physics. chemistry, or biology. Humans recognized but few safe edibles. Humans had witnessed many lethal poisonings by superficially attractive items plucked from the mysterious…
Scientists are trained to avoid rhetorical arguments, the "vulgar Induction" Bacon warned against, and let the chips of reality fall where they may. They highly prize this intellectual honesty because the stakes for them are very high. They know how value judgments, prejudices, and habits of thought can blind you to…
There is objective truth to be learned by observation, and the knowledge gained gives power that other "ways of knowing" have not. But the more dangerous problem with postmodernist thinking is its a priori nature. Not truth, but a political goal has to be served—in this particular case the goal of openness, or…
RULE I We are to admit no more causes of natural things, than such as are both true and sufficient to explain their appearances. To this purpose the philosophers say, that Nature does nothing in vain, and more is in vain, when less will serve; for Nature is pleased with simplicity, and affects not the pomp of…
Perhaps the essence of the Liberal outlook could be summed up in a new decalogue, not intended to replace the old one but only to supplement it. The Ten Commandments that, as a teacher, I should wish to promulgate, might be set forth as follows: 1. Do not feel absolutely certain of anything. 2. Do not think it worth…
There is one great difficulty with a good hypothesis. When it is completed and rounded, the corners smooth and the content cohesive and coherent, it is likely to become a thing in itself, a work of art. It is then like a finished sonnet or a painting completed. One hates to disturb it. Even if subsequent information…
It is rigid dogma that destroys truth; and, please notice, my emphasis is not on the dogma, but on the rigidity. When men say of any question, 'This is all there is to be known or said of the subject; investigation ends here,' that is death. It may be that the mischief comes not from the thinker but for the use made…
It has hitherto been a serious impediment to the progress of knowledge, that is in investigating the origin or causes of natural productions, recourse has generally been had to the examination, both by experiment and reasoning, of what might be rather than what is. The laws or processes of nature we have every reason…
A mathematician who can only generalise is like a monkey who can only climb UP a tree. ... And a mathematician who can only specialise is like a monkey who can only climb DOWN a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must…
The scientist, if he is to be more than a plodding gatherer of bits of information, needs to exercise an active imagination. The scientists of the past whom we now recognize as great are those who were gifted with transcendental imaginative powers, and the part played by the imaginative faculty of his daily life is as…
What the founders of modern science, among them Galileo, had to do, was not to criticize and to combat certain faulty theories, and to correct or to replace them by better ones. They had to do something quite different. They had to destroy one world and to replace it by another. They had to reshape the framework of…
Slavery in America was perpetuated not merely by human badness but also by human blindness. ... Men convinced themselves that a system that was so economically profitable must be morally justifiable. ... Science was commandeered to prove the biological inferiority of the Negro. Even philosophical logic was manipulated…
Artificial intelligence is based on the assumption that the mind can be described as some kind of formal system manipulating symbols that stand for things in the world. Thus it doesn't matter what the brain is made of, or what it uses for tokens in the great game of thinking. Using an equivalent set of tokens and…