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.
Subatomic particles do not exist but rather show 'tendencies to exist', and atomic events do not occur with certainty at definite times and in definite ways, but rather show 'tendencies to occur'.
Crash programs fail because they are based on theory that, with nine women pregnant, you can get a baby in a month.
It is clear that Economics, if it is to be a science at all, must be a mathematical science ... simply because it deals with quantities... As the complete theory of almost every other science involves the use of calculus, so we cannot have a true theory of Economics without its aid.
When it comes to the things that people really want in science fiction - like space travel - the simplest things end up causing them not to happen. Humans are 100-pound bags of water, built to live on Earth.
As a Christian, but also as a scientist responsible for overseeing the Human Genome Project, one of my concerns has been the limits on applications of our understanding of the genome. Should there be limits? I think there should. I think the public has expressed their concern about ways this information might be misused.
Weve got to go [back to the moon]. But we dont want to stay too long. ... The ultimate goal is Mars.
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