Pierre-Simon Laplace Quotes (1749-1827)

“The curve described by a single molecule of air or vapor is regulated in a manner just as certain as the planetary orbits; the only difference between them that which comes from our ignorance.”

“Hesiod, the oldest author to have written on theogony, asserted that the gods and men are created by unknown natural forces. We can therefore consider paganism as a superstitious form of atheism.”

“The theory of probabilities is basically only common sense reduced to a calculus. It makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it.”

“Said the great and magnanimous Laplace: 'It is India that gave us the ingenious method of expressing all numbers by ten symbols, each 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, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.'”

“Plus one, minus one, plus one, minus one, etc. By adding the first two terms, the next two, and so forth, the result is converted into another for which each term is zero. Grandi, the Italian Jesuit, had concluded the possibility of creation from this series; because the result is always equal to ½, he saw the unborn fraction of infinitely many zeros, or nothingness. It was thus that Leibnitz saw in his binary arithmetic the image of creation. He imagined that Unity represented God, and Zero the void; and that the Supreme Being drew all beings from the void, just as unity and zero express all numbers in this system of numeration. This conception was so pleasing to Leibnitz that he communicated it to the Jesuit, [Claudio Filippo] Grimaldi, president of the Chinese tribunal for mathematics, in the hope that this emblem of creation would convert the Emperor of China, since he was very fond of the sciences, to Christianity. I mention this merely to show how childhood prejudices may lead astray even the greatest men.”

“Plus one, minus one, plus one, minus one, etc. By adding the first two terms, the next two, and so forth, the result is converted into another for which each term is zero. Grandi, the Italian Jesuit, had concluded the possibility of creation from this series; because the result is always equal to ½, he saw the unborn fraction of infinitely many zeros, or nothingness. It was thus that Leibnitz saw in his binary arithmetic the image of creation. He imagined that Unity represented God, and Zero the void; and that the Supreme Being drew all beings from the void, just as unity and zero express all numbers in this system of numeration. This conception was so pleasing to Leibnitz that he communicated it to the Jesuit, [Claudio Filippo] Grimaldi, president of the Chinese tribunal for mathematics, in the hope that this emblem of creation would convert the Emperor of China, since he was very fond of the sciences, to Christianity. I mention this merely to show how childhood prejudices may lead astray even the greatest men.”

“Induction, analogy, hypotheses founded upon facts and rectified continually by new observations, a happy tact given by nature and strengthened by numerous comparisons of its indications with experience, such are the principal means for arriving at truth. If one considers a series of objects of the same nature one perceives among them and in their changes ratios which manifest themselves more and more in proportion as the series is prolonged, and which, extending and generalizing continually, lead finally to the principle from which they were derived. But these ratios are enveloped by so many strange circumstances that it requires great sagacity to disentangle them and to recur to this principle: it is in this that the true genius of sciences consists. Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity. It is difficult to appreciate the probability of the results of induction, which is based upon this that the simplest ratios are the most common; this is verified in the formulae of analysis and is found again in natural phenomena, in crystallization, and in chemical combinations. This simplicity of ratios will not appear astonishing if we consider that all the effects of nature are only mathematical results of a small number of immutable laws. Yet induction, in leading to the discovery of the general principles of the sciences, does not suffice to establish them absolutely. It is always necessary to confirm them by demonstrations or by decisive experiences; for the history of the sciences shows us that induction has sometimes led to inexact results.”

“Induction, analogy, hypotheses founded upon facts and rectified continually by new observations, a happy tact given by nature and strengthened by numerous comparisons of its indications with experience, such are the principal means for arriving at truth. If one considers a series of objects of the same nature one perceives among them and in their changes ratios which manifest themselves more and more in proportion as the series is prolonged, and which, extending and generalizing continually, lead finally to the principle from which they were derived. But these ratios are enveloped by so many strange circumstances that it requires great sagacity to disentangle them and to recur to this principle: it is in this that the true genius of sciences consists. Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity. It is difficult to appreciate the probability of the results of induction, which is based upon this that the simplest ratios are the most common; this is verified in the formulae of analysis and is found again in natural phenomena, in crystallization, and in chemical combinations. This simplicity of ratios will not appear astonishing if we consider that all the effects of nature are only mathematical results of a small number of immutable laws. Yet induction, in leading to the discovery of the general principles of the sciences, does not suffice to establish them absolutely. It is always necessary to confirm them by demonstrations or by decisive experiences; for the history of the sciences shows us that induction has sometimes led to inexact results.”

“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.”

“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.”

“With respect to the cohesion and capillary action of liquids, I have had the good fortune to anticipate Mr. Laplace in his late researches, and I have endeavoured to show, that my assumptions are more universally applicable to the facts, than those which that justly celebrated mathematician has employed.”