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.
Interpretation
This quote highlights how chance reflects our limited understanding of the causes behind events, linking probability to both ignorance and knowledge.
In this quote, Pierre-Simon Laplace expresses the idea that what we often attribute to chance is a manifestation of our ignorance regarding the true causes of observable phenomena. He suggests that our understanding of probability is not just a reflection of randomness but is also influenced by the extent of our knowledge about the underlying processes that generate these events. This means that as our knowledge increases, our perception of chance decreases, illustrating the intricate relationship between uncertainty, knowledge, and probability in science.
In practice
In a lecture about probability theory, I would use this quote to illustrate how our understanding can change over time.
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.
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.
All the effects of Nature are only the mathematical consequences of a small number of immutable laws.
Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eye.
The weight of evidence for an extraordinary claim must be proportioned to its strangeness.
Probability theory is nothing but common sense reduced to calculation.
We have genuflected before the god of science only to find that it has given us the atomic bomb, producing fears and anxieties that science can never mitigate.
Nothing is so dangerous to the progress of the human mind than to assume that our views of science are ultimate, that there are no mysteries in nature, that our triumphs are complete and that there are no new worlds to conquer.
An alleged scientific discovery has no merit unless it can be explained to a barmaid.
The artificial products do not have any molecular dissymmetry; and I could not indicate the existence of a more profound separation between the products born under the influence of life and all the others.
Science is organized common sense where many a beautiful theory was killed by an ugly fact.
As a physicist, I've always found cosmology to be a rational elixir; it distances me from ordinary concerns.
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