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.
If you study science deep enough and long enough, it will force you to believe in God.
It is hardly possible to maintain seriously that the evil done by science is not altogether outweighed by the good. For example, if ten million lives were lost in every war, the net effect of science would still have been to increase the average length of life.
I can now state that I have succeeded in operating a motive device by means of [cosmic rays]. I will tell you in the most general way, the cosmic ray ionizes the air, setting free many charges - ions and electrons. These charges are captured in a condenser which is made to discharge through the circuit of the motor.
In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.
Tune your television to any channel it doesn't receive and about 1 percent of the dancing static you see is accounted for by this ancient remnant of the Big Bang. The next time you complain that there is nothing on, remember that you can always watch the birth of the universe.
In spite of the opinions of certain narrow-minded people who would shut up the human race upon this globe, we shall one day travel to the Moon, the planets, and the stars with the same facility, rapidity and certainty as we now make the ocean voyage from Liverpool to New York.
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