Status Updates From La science selon Henri Poin...

Poincare talks about the crisis in mathematical physics of his day. Radium which gives off mysterious energy, recoil due to light, Brownian motion where particles move in zig-zag motion indefinitely and negative result on detection of ether. In the next half century, physicists will find answer to these questions. Currently in 21st century, similar crisis can be seen in string theory and subatomic models.

The role of astronomy as the frontrunner of physical sciences is brought out. The things stars and nebulae have taught us have left humankind far more enriched in its knowledge. Further, it has helped in bringing forth the fact that nature has order and everything is unified by connections.

A brief history of electromagnetism is given. How the experiments of Ampere and others slowly converged towards Maxwell's theory which unified electricity, magnetism and light. The terms Poincare uses are obsolete and obscure. Any advanced student who has modern textbooks would find it difficult to trace the terms. Further, it might seem childish. Though it should be remembered that atomic theory was still far away.

Hamilton’s principle of least action can be used to get the equations of a mechanical system. Applying it to electromagnetism, we have electrostatic charges for the potential energy and their movement as the kinetic energy. Though a unique "mechanical" representation of EM phenomena is not possible.

Probability requires subtle reasoning to validate its use in science. Poincare also tries to give an idea about the kind of hypothesis conjured from experimental data. Earlier, it was believed that simple continuous relations existed between data points. But it has been refuted slowly. Another weird area of science - the theory of errors. [This section needs rereading as it was very obscure]

Hypothesis are of different types(neutral, general). Care should be taken while choosing hypotheses to prove/disprove from an experiment. As time, material and human resources are limited; experiments should have maximum yield in terms of scientific knowledge. Differential equations in time and space work because immediate past and nearby distances affect elementary phenomena.

Poincaré analyses every single assumption, convention and definition that goes into mathematical and scientific theories. The writing is hard to follow as I am not accustomed to such long sentences. Anyway, the author's thinking gives an idea about the mind that has thought so much and in so many directions. Will follow discipline and complete the text. Need to re-read it after a couple of years.