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.
Life began three and a half billion years ago, necessarily about as simple as it could be, because life arose spontaneously from the organic compounds in the primeval oceans.
Imagine a survivor of a failed civilization with only a tattered book on aromatherapy for guidance in arresting a cholera epidemic. Yet, such a book would more likely be found amid the debris than a comprehensible medical text.
Extinguished theologians lie about the cradle of every science as the strangled snakes beside that of Hercules; and history records that whenever science and orthodoxy have been fairly opposed, the latter has been forced to retire from the lists, bleeding and crushed if not annihilated; scotched, if not slain.
A full understanding of what happens in our everyday lives needs to take into account what happened at the Big Bang. And not only is that intrinsically interesting and just kind of cool to think about, but it's also a mystery that is not given much attention by working scientists; it's a little bit underappreciated.
The radiations that pour upon the earth cause the biosphere to take on properties unknown to lifeless planetary surfaces, and thus transform the face of the earth. Activated by radiation, the matter of the biosphere collects and redistributes solar energy, and converts it ultimately into free energy capable of doing work on earth.
I cannot give any scientist of any age better advice than this: the intensity of a conviction that a hypothesis is true has no bearing over whether it is true or not.
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