Pierre-Simon Laplace Quotes About Science
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[Science] dissipates errors born of ignorance about our true relations with nature, errors the more damaging in that the social order should rest only on those relations. TRUTH! JUSTICE! Those are the immutable laws. Let us banish the dangerous maxim that it is sometimes useful to depart from them and to deceive or enslave mankind to assure its happiness.
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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 of times they are unable to account.
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What we know is not much. What we do not know is immense.
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The telescope sweeps the sky without finding God.
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All the effects of Nature are only the mathematical consequences of a small number of immutable laws.
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I see with much pleasure that you are working on a large work on the integral Calculus ... The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics.
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It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.
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[It] may be laid down as a general rule that, if the result of a long series of precise observations approximates a simple relation so closely that the remaining difference is undetectable by observation and may be attributed to the errors to which they are liable, then this relation is probably that of nature.
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The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time.
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If an event can be produced by a number n of different causes, the probabilities of the existence of these causes, given the event (prises de l'événement), are to each other as the probabilities of the event, given the causes: and the probability of each cause is equal to the probability of the event, given that cause, divided by the sum of all the probabilities of the event, given each of the causes.
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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.
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However, the small probability of a similar encounter [of the earth with a comet], can become very great in adding up over a huge sequence of centuries. It is easy to picture to oneself the effects of this impact upon the Earth. The axis and the motion of rotation changed; the seas abandoning their old position to throw themselves toward the new equator; a large part of men and animals drowned in this universal deluge, or destroyed by the violent tremor imparted to the terrestrial globe.
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Without any doubt, the regularity which astronomy shows us in the movements of the comets takes place in all phenomena. The trajectory of a simple molecule of air or vapour is regulated in a manner as certain as that of the planetary orbits; the only difference between them is that which is contributed by our ignorance. Probability is relative in part to this ignorance, and in part to our knowledge.
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The simplicity of nature is not to be measured by that of our conceptions. Infinitely varied in its effects, nature is simple only in its causes, and its economy consists in producing a great number of phenomena, often very complicated, by means of a small number of general laws.
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The mind has its illusions as the sense of sight; and in the same manner that the sense of feeling corrects the latter, reflection and calculation correct the former.
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Man follows only phantoms.
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The word 'chance' then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge.
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