XI
Project Gutenberg EPUB3 edition
Poincaré, Henri and Halsted, George Bruce
Another difficulty; have we really the right to speak of the cause of a phenomenon? If all the parts of the universe are interchained in a certain measure, any one phenomenon will not be the effect of a single cause, but the resultant of causes infinitely numerous; it is, one often says, the consequence of the state of the universe a moment before. How enunciate rules applicable to circumstances so complex? And yet it is only thus that these rules can be general and rigorous.
Not to lose ourselves in this infinite complexity, let us make a simpler hypothesis. Consider three stars, for example, the sun, Jupiter and Saturn; but, for greater simplicity, regard them as reduced to material points and isolated from the rest of the world. The positions and the velocities of three bodies at a given instant suffice to determine their positions and velocities at the following instant, and consequently at any instant. Their positions at the instant t determine their positions at the instant t + h as well as their positions at the instant t − h.
Even more; the position of Jupiter at the instant t, together with that of Saturn at the instant t + a, determines the position of Jupiter at any instant and that of Saturn at any instant.
The aggregate of positions occupied by Jupiter at the instant t + e and Saturn at the instant t + a + e is bound to the aggregate of positions occupied by Jupiter at the instant t and Saturn at the instant t + a, by laws as precise as that of Newton, though more complicated. Then why not regard one of these aggregates as the cause of the other, which would lead to considering as simultaneous the instant t of Jupiter and the instant t + a of Saturn?
In answer there can only be reasons, very strong, it is true, of convenience and simplicity.