Book/Science and Method

Poincare, Henri; Maitland, Francis (2007). Combinatorial Physics. local page: New York : Cosimo Classics, ©. ISBN 9781602064485. 

Preface

Henri Poincare was, by general agreement, the most eminent scientific man of his generation -- more eminent, one is tempted to think, than any man of science now living.

On comprehensiveness of outlook, and minute, patient analysis:

Since Leibniz, I do not know of any philosopher who has possessed both: broadly speaking, British philosophers have excelled in analysis, while those of the Continent have excelled in breath and scope. In this respect, Poincare is no exception: in philosophy, his mind was intuitive and synthetic; wonderfully skillful, it is true, in analysing a science until he had extracted its philosophical essence, and in combining this essence with those of other sciences, but not very apt in those further stages of analysis which fall within the domain of philosophy itself. He built edifices with the philosophic materials that he found ready to hand, but he lacked the patience and the minuteness of attention required for the creation of new materials.

In the last paragraph of this Preface.

To be always right is no possible in philosophy; but Poincare's opinions, right or wrong, are always the expression of a powerful and original mind with a quite unrivaled scientific equipment; a masterly style, great wit, and a profound devotion to the advancement of knowledge. Through these merits, hs books supply, better than any others known to me, the growing need for a generally intelligible account of the philosophic outcome of modern science.

— Bertrand Russell

Introduction

The scientific method consists in observation and experiment. If the scientist had an unfinity of time at this disposal, it would be sufficient to say to him, "Look , and look carefully." But, since he has not time to look at everything, and above all to look carefully, and since it is better not to look at all than to look carelessly, he is forced to make a selection.

I. The Scientist and Science

But scientists believe that there is a hierarchy of facts, and that a judicious selection can be made. They are right, for other wise there would be no science, and science does not exist. ... if they had not been preceded by disinterested fools who died poor, who never thought of the useful, and yet had a guide that was not their own caprice. What these fools did, as Mach has said, was to save their successors the trouble of thinking. If they had worked solely in view of an immediate application, they would have nothing behind them, and in face of a new requirement, all would have had to be done again.

The Selection of Facts

TOLSTOI explains somewhere in his writings why, in his opinion, "Science for Science's sake" is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection; and that being so, can this selection be governed by the mere caprice of our curiosity? Is it not better to be guided by utility, by our practical, and more especially our moral, necessities? Have we not some better occupation than counting the number of lady-birds in existence on this planet?

The scientists does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worthy knowing, and life would not be worthy living. ... What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp. It is this that gives a body a skeleton, so to speak, to the shimmering visions that flatter our senses, and without this support the beauty of these fleeting dreams would be imperfect, because it would be indefinite and ever elusive. Intellectual beauty, on the contrary is self-sufficing, and it is for it, more perhaps than for the future good of humanity, that the scientists condemns himself to long and painful labours.

On Page 23,

Thus we see that care for the beautiful leads us to the same selection as care for the useful. Similarly economy of thought, that economy of effort which, according to Mach, is the constant tendency of science, is a source of beauty as well as a practical advantage. The buildings we admire are those in which the architect has succeeded in proportioning the means to the end, in which the columns seem to carry the burdens imposed on them lightly and without effort, like the graceful caryatids of the Erechtheum.

Talking to Yuan Xun on the subject matter of collision detection, I realized that the mechanism of collision detection is relevant to the notion of selecting relevant content or paging of content. The paging structure of content can be thought of as a Bounding volume hierarchy.

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Authored by:Henri Poincare