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Without the capacity to provide its own information, the mind drifts into randomness.

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Pierre-Simon Laplace

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.

Ignorance, Knowledge, Observe, Occur, Science
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We are so far from knowing all the forces of nature and their various modes of action that it would be unworthy of the philosopher to deny phenomena simply because they are inexplicable at the present state of our knowledge. The more difficult it is to acknowledge their existence, the greater the care with which we must study these phenomena.

Acknowledge, Care, Deny, Knowing, Philosophical, Study

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.

Celestial, Distance, Moving, Relations, Science, Time

Such is the advantage of a well constructed language that its simplified notation often becomes the source of profound theories.

Advantage, Becomes, Language, Math, Profound

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.

Correspondence, Examples, Intellectual, Interesting, Law, Science

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.

Comets, Ignorance, Knowledge, Regulated, Science, Vapour
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