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Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is…
Mathematics is one of humanity’s great achievements. By enhancing the capabilities of the human mind, mathematics has facilitated the development of science, technology, engineering, business, and government. Mathematics is also an intellectual achievement of great sophistication and beauty that epitomizes the power…
Geometry enlightens the intellect and sets one's mind right. All its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this…
Religion is still parasitic in the interstices of our knowledge which have not yet been filled. Like bed-bugs in the cracks of walls and furniture, miracles lurk in the lacunae of science. The scientist plasters up these cracks in our knowledge; the more militant Rationalist swats the bugs in the open. Both have their…
Philosophy is written in that great book which ever lies before our gaze—I mean the universe—but we cannot understand if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language, and the symbols are triangles, circles and Other geometrical…
For the things of this world cannot be made known without a knowledge of mathematics. For this is an assured fact in regard to celestial things, siDce two important sciences of mathematics treat of them, namely theoretical astrology and practical astrology. The first. . . gives us definite information as to the number…
The famous Canadian physician William Osler once wrote, “In science the credit goes to the man who convinced the world, not to the man to whom the idea first occurs.” When we examine discoveries in science and mathematics, in hindsight we often find that if one scientist did not make a particular discovery, some other…
Benoit Mandelbrot asked his famous question “How long is the coast of Britain?” long before this symposium was written, but it perfectly captures the sort of puzzle people in this crowd love. The question seems simple. Just look it up in the encyclopedia. But as Mandelbrot observed, the length of the coast of Britain…
Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful…
Now these numbers can be appreciated in many different ways. From the standpoint of calculation, they're as easy to understand as one plus one, which is two. Then one plus two is three, two plus three is five, three plus five is eight, and so on. Indeed, the person we call Fibonacci was actually named Leonardo of…
The selfish gene theory is Darwin's theory, expressed in a way that Darwin did not choose but whose aptness, I should like to think, he would instantly have recognized and delighted in. It is in fact a logical outgrowth of orthodox neo-Darwinism, but expressed as a novel image. Rather than focus on the individual…
Getting ready for the assumed inexorable Armageddon, each applied science and all of the great scientific specialization capabilities only toward weaponry, thus developing the ability to destroy themselves totally with no comprehensively organized oppositional thinking capability and initiative powerful enough to…
Kakeru Seki: A fact is somehow related to another fact. Unless you understand these relationships, you won't be a real reporter. Noriko Hikima: True journalism! Kakeru Seki: Well, you majored in the humanities. Noriko Hikima: Yes! That's true--I've studied literature since I was in high school. Kakeru Seki: You havea…
Surveillance serves not just as a legal and historical record but as a record of rep: proof that you’ve done what you say you’ve done. You bark, and anyone on the mesh can search to see if you also bite. It’s the foundation of the reputation economy. It’s not just video, of course, but surveillance of all types…
Phrases like “things are looking up” and “look at the upside” once meant something like “consider the good in the situation,” but they went through an ironic shift in the solar system’s early spacecolonial culture, mutating in the microgravity of early tin-can stations to mean a variety of practically sarcastic…
Occasionally he made a comment similar to Archimedes' "Eureka!" about a discovery, as he did when he wrong T T T=N. This is part of number theory, the field that Gauss called the Queen of Mathematics. A triangular number T is a number that you can get by adding up a string of consecutive whole numbers beginning with…
Life began in water, and every single function of life takes place in an aqueous environment. A profound way of classification in chemistry is the relation and interaction between molecules, or groups within molecules, and water. Molecules (or parts of molecules) can attract water in which case they are called…
actuarial escape velocity is defined as occurring when a year of medical research adds more than a year’s worth of longevity to the total population. Nothing even close to this has ever been achieved, and emerging signs of an asymptotic curve in progress suggest this velocity may never
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…
Rational mechanics soon became a vast and profound science. The true laws of the collision of bodies, respecting which Descartes was deceived, were at length known. Huyghens discovered the laws of circular motions; and at the same time he gives a method of determining the radius of curvature for every point of a given…