Customer Reviews

Science and Hypothesis

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Poincare wrote the essays in this book about a hundred years ago, in 1905. That was the landmark period after Maxwell and before special relativity. I was fascinated to read this snapshot from such an exciting era in scientific thought.

This first-person view is set in the era when the all-encompassing ether was still considered seriously. People had recent memory of debates about whether electrons were real. There was no unification of rays from uranium and radium with cathode rays, x-rays, and ultraviolet.

The intellectual seeds of modern science had been sown, though. Experiments with ultraviolet foretold Einstein's photoelectric effect. Lorentz had already stated some of the invariants that led to relativity. Probability was just entering mainstream scientific thought, preparatory to statistical mechanics, quantum theory, and Heisenberg.

As Poincare covers the science of his day, he does so in the style of his day. He is quite unashamed in describing the British scientific temperament as boldly intuitive, but informal and sometimes spotty. By contrast, he describes the French as rigorous and inclusive, although maybe a bit too staid. Not just the science, but the social attitudes of the day come through in the pleasant little book. If you study the history of science and are partial to primary sources, I recommend this highly.

While not mathematical, the approach is so informed by a mathematician's way of looking at the world that some may find this wonderful book less exciting than it truly is. This is one of "the important books" in the philosophy of science.

Geometry and experience (IV). Changes in our sensory impressions attributable to geometrical change (change in position) are distinguished from other types of change in that they can be cancelled by an "internal" change on the part of the observer (moving his body). Corollary 1: an immobile being could not develop geometry. Corollary 2: if there were no solid bodies there would be no geometry.

No experiment can decide whether space is Euclidean or non-Euclidean (V). It does not suffice to measure the angle sum of a large triangle (V.3), for such experiments speak only of relations between specific triangles, meter sticks, etc., not space itself. Nor can the matter be decided by constructions that are impossible in one geometry but possible in the other, such as the non-existence in non-Euclidean geometry of regular hexagons with radius = side length (V.7), for the same reasons. For example, the experiment can come out the opposite way if the measuring sticks involved dilate with temperature.

The above is a special case of Poincaré's more general thesis of so-called structural realism (esp. X): only sensory impressions, not reality in itself, is accessible to us; relations (structures) among these impressions are the true content of scientific theories, not what the theory stipulates about mind-independend reality.

Newton's laws. The law of inertia is not an experimental fact (pp. 91-97). "Have there ever been experiments on bodies acted on by no forces? and, if so, how did we know that no forces were acting? The usual [empirical illustration] is that of a ball rolling for a very long time on a marble table; but why do we say that it is under the action of no force?" And conversely, let's say that the ball does deviate from its path, and that we cannot find any force to blame this on. Does that falsify the law of inertia? No, it only means that we do not understand the force in question. A force was acting on the ball by definition, since force is mass times acceleration. There is no way to define force independent of F=ma (pp. 97-101). Thus the law of inertia is true by definition, as is F=ma. But to define force as mass times acceleration we first need to know what mass is. For this we need to assume the law of equality of action and reaction so that we can define (ratios of) masses from ma=ma for two bodies acting on each other. "This would do very well if the two bodies were alone and could be abstracted from the action of the rest of the world; but this is by no means the case" (p. 101), a difficulty from which "there is no escape" except the following definition, "which is only a confession of failure: Masses are co-efficients which it is found convenient to introduce into calculation" (p. 103). Thus, analogous to the situation in geometry, the laws of mechanics amount to convention. "This convention, however, is not absolutely arbitrary; it is not the child of our caprice. We admit it because certain experiments have shown us that it will be convenient" (p. 136).

it is philosophy,precisely it is positivism(with slightly revised)! people who like read Henri Poincare might compare his with Ernst Mach.

I, a dedicated science lover, did not enjoy this book thoroughly. While it does provide some useful information, it is sometimes inaccurate and dull.