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Started by Unbeliever, October 18, 2006, 02:53:32 pm
Quote from: Winston Churchill, in [i]My Early Life[/i] (1930)Some of my cousins who had the great advantage of University education used to tease me with arguments that nothing had any existence except what we think of it....These amusing mental acrobatics are all right to play with. They are perfectly harmless and perfectly useless....I always rested on the following argument....We look up to the sky and see the sun. Our eyes are dazzled and our senses record the fact. So here is the great sun standing apparently on no better foundation than our physical senses. But happily there is a method, apart altogether from our physical senses, of testing the reality of the sun. It is by mathematics. By means of prolonged processes of mathematics, entirely separate from the senses, astronomers are able to calculate when an eclipse will occur. They predict by pure reason when a black spot will pass across the sun on a certain day. You go and look, and your sense of sight immediately tells you that their calculations are vindicated. So here you have the evidence of the senses reinforced by the entirely separate evidence of a vast independent process of mathematical reasoning. We have taken what is called in military map-making "a cross bearing". When my metaphysical friends tell me that the data on which the astronomers made their calculations, were necessarily obtained originally through the evidence of the senses, I say, "no". They might, in theory at any rate, be obtained by automatic calculating-machines set in motion by the light falling upon them without admixture of the human senses at any stage. When it is persisted that we should have to be told about these calculations and use our ears for that purpose, I reply that mathematical process has a reality and virtue in itself, and that once discovered it constitutes a new and independent factor. I am also at this point accustomed to reaffirm with emphasis my conviction that the sun is real, and also that it is hot - in fact hot as Hell, and that if the metaphysicians doubt it they should go there and see.
Quote from: Leonardo da Vinci, in [i]Treatise on Painting[/i] (1651)No human investigation can be called real science if it cannot be demonstrated mathematically.
Quote from: Albert Einstein, in [i]Sidelights on Relativity[/i] (1922)One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of all other sciences are to some extent debatable and in constant danger of being overthrown by newly discoverd facts.
Quote from: Havelock Ellis, in [i]The Dance of Life[/i] (1923)The mathematician has reached the highest rung on the ladder of human thought.
Quote from: Galileo Galilei, in [i]Opere il Sattiatore[/i] (1656)Philosophy is written in that great book which ever lies before our gaze - I mean the universe - but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is all triangles and circles and other geometrical figures, without the help of which it is impossible to conceive a single word of it, and without which one wanders through a dark labyrinth.
Quote from: Pierre Simon de Laplace, in [i]Men of Mathematics[/i] by E.T Bell (1965)All the effects of nature are only the mathematical consequences of a small number of immutable laws.
Quote from: Adolphe Quetelet, in [i]Eulogy of Quetelet[/i]by E. Mailly (1874)The more progress physical sciences make, the more they tend to enter the domain of mathematics, which is a kind of center to which they all converge. We may even judge of the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation.
Quote from: Bertrand Russell, "Mathematics and the Metaphysicians", [i]Mysticism and Logic[/i] (1917)Mathematics may be defined as the subject in which we never know what we are talking about, nor wheter what we are saying is true.
Quote from: Bertrand Russell, in "The Study of Mathematics", [i]Mysticism and Logic"[/i] (1917)Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of a sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
Quote from: William Thomson (Lord Kelvin), in a lecture at the Institution of Civil Engineers, May 3, 1883I often say that when you can measure what you are speaking about and express it in numbers you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.
Quote from: William Thomson (Lord Kelvin), in [i]The Life of Lord Kelvin[/i] by S.P. Thompson (1910)Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherialization of common sense.
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