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.
I had a bet with Gordon Kane of Michigan University that the Higgs particle wouldn't be found.
To understand the universe in the state that it began in, the so-called Big Bang, we need laws of physics that work better than our current set of rules and procedures, which break down when we try to push them back to the beginning.
Information: the negative reciprocal value of probability.
A time will however come (as I believe) when physiology will invade and destroy mathematical physics, as the latter has destroyed geometry.
Cancer cells have had so many other things go wrong with them, genetic, non-genetic changes, that those cells, one of the things they then get selected for is that they have lots of telomerase because now the telomeres in those cells get maintained.
Better understanding of the natural world not only enhances all of us as human beings, but can also be harnessed for the better good, leading to improved health and quality of life.
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