All the effects of Nature are only the mathematical consequences of a small number of immutable laws.
Interpretation
Nature operates according to fundamental mathematical laws that remain constant.
Pierre-Simon Laplace's quote reflects the idea that the complexities and phenomena we observe in nature can ultimately be traced back to a handful of unchanging mathematical principles. It suggests that beneath the surface of the natural world lies a structured and predictable framework governed by these immutable laws, emphasizing the relationship between mathematics and the natural sciences.
In practice
This quote can be used in a discussion about the predictability of natural phenomena in a science class.
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.
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.
The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.
Throughout history, people have studied pure science from a desire to understand the universe rather than practical applications for commercial gain. But their discoveries later turned out to have great practical benefits.
False facts are highly injurious to the progress of science, for they often endure long; but false views, if supported by some evidence, do little harm, for every one takes a salutary pleasure in proving their falseness.
It at once struck me that under these circumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed.
Chemistry... is like the maid occupied with daily civilisation; she is busy with fertilisers, medicines, glass, insecticides ... for she dispenses the recipes.
Testing shows the presence, not the absence of bugs.
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