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A classic of science, this famous essay by "the Newton of France" introduces lay readers to the concepts and uses of probability theory. It is of especial interest today as an application of mathematical techniques to problems in social and biological sciences.
Generally recognized as the founder of the modern phase of probability theory, Laplace here applies the principlesA classic of science, this famous essay by "the Newton of France" introduces lay readers to the concepts and uses of probability theory. It is of especial interest today as an application of mathematical techniques to problems in social and biological sciences.
Generally recognized as the founder of the modern phase of probability theory, Laplace here applies the principles and general results of his theory "to the most important questions of life, which are, in effect, for the most part, problems in probability." Thus, without the use of higher mathematics, he demonstrates the application of probability to games of chance, physics, reliability. of witnesses, astronomy, insurance, democratic government and many other areas.
General readers will find it an exhilarating experience to follow Laplace's nontechnical application of mathematical techniques to the appraisal, solution and/or prediction of the outcome of many types of problems. Skilled mathematicians, too, will enjoy and benefit from seeing how one of the immortals of science expressed so many complex ideas in such simple terms....more
Paperback, 224 pages
Published January 18th 1996 by Dover Publications (first published December 13th 1994)
Pierre-Simon Laplace (23 March1749 – 5 March1827) was a French mathematician and astronomer, discoverer of the Laplace transform and Laplace's equation.
- "On voit, par cet Essai, que la théorie des probabilités n'est, au fond, que le bon sens réduit au calcul; elle fait apprécier avec exactitude ce que les esprits justes sentent par une sorte d'instinct, sans qu'ils puissent souvent s'en rendre compte."
- Translation: "One sees, from this Essay, that the theory of probabilities is basically just common sense reduced to calculus; it makes one appreciate with exactness that which accurate minds feel with a sort of instinct, often without being able to account for it."
- From the Introduction to Théorie Analytique des Probabilités, second and later editions; also published separately as Essai philosophique sur les Probabilités (1814). Œuvres complètes de Laplace, tome VII, p. cliii, Paris: Gauthier-Villars, 1878-1912.
- Also reported as: "The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which ofttimes they are unable to account."
- Or as: "Probability theory is nothing but common sense reduced to calculation."
- "Les questions les plus importantes de la vie ne sont en effet, pour la plupart, que des problèmes de probabilité."
- "La dernière chose que nous attendions de vous, Général, est une leçon de géométrie !"
- Translation: "The last thing we expect of you, General, is a lesson in geometry!"
- Laplace to Napoléon, after the latter had reported on some new elementary geometry results
- "Ce que nous connaissons est peu de chose, ce que nous ignorons est immense."
- Translation: "What we know is not much. What we do not know is immense."
- Allegedly his last words, reported in Joseph Fourier's "Éloge historique de M. le Marquis de Laplace" (1829) with the comment, "This was at least the meaning of his last words, which were articulated with difficulty." Quoted in Augustus De Morgan's Budget of Paradoxes (1866).
- "L'homme ne poursuit que des chimères."
- Translation: "Man follows only phantoms."
- His true last words, according to Augustus De Morgan's Budget of Paradoxes (1866).
- Compare Edmund Burke's famous remark, after a parliamentary candidate's sudden death, about "what shadows we are, and what shadows we pursue".
- "Lisez Euler, lisez Euler, c'est notre maître à tous."
- Translation: "Read Euler, read Euler, he is the master of us all." (Sometimes freely translated as: "Read Euler: he is our master in everything.")
- Reported by Gugliemo Libri in the Journal des Savants, January 1846, p. 51: « ...ces paroles mémorables que nous avons entendues de sa propre bouche : "Lisez Euler, lisez Euler, c'est notre maître à tous". »
- "Nature laughs at the difficulties of integration."
- Quoted in I. Gordon and S. Sorkin, The Armchair Science Reader, New York, 1959.
- "Il est facile de voir que..."
- Translation: "It is therefore obvious that..."
- Frequently used in the Traité de mécanique céleste when he had proved something and mislaid the proof, or found it clumsy. Notorious as a signal for something true, but hard to prove.
- It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit.But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
- Quoted in H Eves Return to Mathematical Circles (Boston 1988).
Philosophical Essay on Probabilities (1902)
- source, translated by Frederick Wilson Truscott from Théorie Analytique des Probabilités (originally published 1812) 6th ed.
Ch. 1 Introduction
- The most important questions of life... are indeed for the most part only problems of probability. Strictly speaking it may even be said that nearly all our knowledge is problematical; and in the small number of things which we are able to know with certainty, even in the mathematical sciences themselves, the principal means for ascertaining truth—induction and analogy—are based on probabilities.
Ch. 2 Concerning Probability
- Imaginary causes have gradually receded with the widening bounds of knowledge and disappear entirely before sound philosophy, which sees in them only the expression of our ignorance of the true causes.
- Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes. The human mind offers, in the perfection which it has been able to give to astronomy, a feeble idea of this intelligence. Its discoveries in mechanics and geometry, added to that of universal gravity, have enabled it to comprehend in the same analytical expressions the past and future states of the system of the world.
- All these efforts in the search for truth tend to lead it [the human mind] back continually to the vast intelligence... but from which it will always remain infinitely removed. This tendency peculiar to the human race is that which renders it superior... and their progress in this respect distinguishes nations and ages and constitutes their true glory.
- Let us recall that formerly, and at no remote epoch... all the unusual phenomena were regarded as so many signs of celestial wrath.
- The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought.
- It is to the influence of the opinion of those whom the multitude [the populous] judges best informed, and to whom it has been accustomed to give its confidence in regard to the most important matters of life, that the propagation of those errors is due, which in times of ignorance, have covered the face of the earth. Magic and astrology offer us two great examples. These errors... having for a basis only universal credence, have maintained themselves during a very long time; but at last the progress of science has destroyed them in the minds of enlightened men, whose opinion consequently has caused them to disappear... through the power of imitation and habit which had so generally spread them... This power, the richest resource of the moral world, establishes and conserves in a whole nation ideas entirely contrary to those... elsewhere... What indulgence ought we not then to have for opinions different from ours, when this difference often depends only upon the various points of view where circumstances have placed us! Let us enlighten those whom we judge insufficiently instructed; but first let us examine critically our own opinions, and weigh with impartiality, their respective probabilities.
Quotes about Laplace
- Whenever I meet in La Place with the words "Thus it plainly appears," I am sure that hours, and perhaps days, of hard study will alone enable me to discover how it plainly appears.
- Laplace made many important discoveries in mathematical physics... Indeed, he was interested in anything that helped to interpret nature. He worked on hydrodynamics, the wave propagation of sound, and the tides. In the field of chemistry, his work on the liquid state of matter is classic. His studies of the tension in the surface layer of water, which accounts for the rise of liquids inside a capillary tube, and of the cohesive forces in liquids, are fundamental. Laplace and Lavoisier designed an ice calorimeter (1784) to measure heat and measured the specific heat of numerous substances; heat, to them, was still a special kind of matter. Most of Laplace's life was, however, devoted to celestial mechanics.
- Morris Kline, Mathematical Thought from Ancient to Modern Times (1972)
- Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature.
- Morris Kline, Mathematical Thought from Ancient to Modern Times (1972)
- This is another important dispute in the history of how we think about being wrong: whether error represents an obstacle in the path toward truth, or the path itself. The former idea is a conventional one. The latter... emerged during the Scientific Revolution and continued to evolve throughout the Enlightenment. But it didn't really reach its zenith until the early nineteenth century, when... Pierre Simon Laplace refined the distribution of errors, illustrated by the now-familiar bell curve. ...Laplace used the bell curve to determine the precise orbit of the planets. ...By using the normal distribution to graph... individually imperfect data points, Laplace was able to generate a far more precise picture of the galaxy. ...aggregate enough flawed data, and you get a glimpse of the truth.
- Laplace had taken Newton's science and turned it into philosophy. The universe was a piece of machinery, its history was predetermined, there was no room for chance or for free will. The cosmos was indeed an ice-cold clock.
- Brian L. Silver, The Ascent of Science (1998)
- "[Sire,] je n'ai pas eu besoin de cette hypothèse."
- De Morgan, Augustus (January 1872). Sophia Elizabeth De Morgan ed. A Budget of Paradoxes, London: Longmans, Green, and Co. As found in http://www-history.mcs.st-andrews.ac.uk/~history/Quotations/Laplace.html, accessed February 13, 2006.
- Translation: "[No, Sire,] I had no need of that hypothesis."
- Reputed reply to Emperor Napoleon I, who had asked why he hadn't mentioned God in his discourse on secular variations of the orbits of Saturn and Jupiter ("Mais où est Dieu dans tout cela?"/'But where is God in all this?').
- The exchange is reported by Victor Hugo (who in turn was citing François Arago) as:
- "Comment, vous faites tout le système du monde, vous donnez les lois de toute la création et dans tout votre livre vous ne parlez pas une seule fois de l'existence de Dieu !"
- Translation: "How can this be! You made the system of the world, you explain the laws of all creation, but in all your book you speak not once of the existence of God!"
- Alternate translation: "You have written this huge book on the system of the world without once mentioning the author of the universe!"
- Alternate translation: "How is it that, although you say so much about the Universe, you say nothing about its Creator?"
- "[Sire,] je n'avais pas besoin de cette hypothèse-là."
- Translation: "I did not need to make such an assumption."
- Lagrange, also present (or to whom Napoleon repeated Laplace's reply, in another version), then commented: "Ah ! C’est une belle hypothèse; ça explique beaucoup de choses."
- Translation: "Ah! That is a beautiful assumption; it explains many things."
- Alternate translation: "Ah, but that is such a good hypothesis. It explains so many things!"
- Sometimes (as in Félix Blanchet's preface to his edition of the Œuvres complètes de Lucrèce. Paris: Garnier, 1861, p. xx) this comment is attributed to Laplace himself.
- Wikipedia recounts research about this much-cited episode.