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.
Interpretation
The quote highlights the beauty of understanding nature through mathematical analysis.
In this quote, Pierre-Simon Laplace expresses the idea that observing and analyzing natural phenomena reveals deeper intellectual truths, which is a source of fascination for those who engage in mathematical speculation. He suggests that the systematic nature of the universe, which is reflected through mathematics, enriches our understanding and appreciation of the world around us.
In practice
This quote can be shared in a lecture about the relationship between mathematics and the natural sciences.
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.
All the effects of Nature are only the mathematical consequences of a small number of immutable laws.
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.
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.
Any important disease whose causality is murky, and for which treatment is ineffectual, tends to be awash in significance.
So there he is at last. Man on the moon. The poor magnificent bungler! He can't even get to the office without undergoing the agonies of the damned, but give him a little metal, a few chemicals, some wire and twenty or thirty billion dollars and vroom! there he is, up on a rock a quarter of a million miles up in the sky.
People are going to buy cheap fertilizer so they can grow enough crops to feed themselves, which will be increasingly difficult with climate change.
Science is a way of getting knowledge. It's a method. It's a method that really relies on making mistakes. We propose ideas, they are usually wrong, and we test them against the data. Scientists do this in a formal way. It's a way that everyone can go through life; that's how we should be teaching science from a very young age.
I would give absolutely nothing for the theory of Natural Selection, if it requires miraculous additions at any one stage of descent.
Just as computer technology and the Internet created whole new industries and extraordinary benefits for people that extend into almost every realm of human endeavor from education to transportation to medicine, genetics will undoubtedly benefit people everywhere in ways we can't even imagine but know will surely occur.
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