Never have I learned less from a 500-page book then I did from Jeremy Gray’s Henri Poincare: A Scientific Biography. When Gray brings-up Poincare’s writings (which Poincare often wrote in the form of responses to the work of other thinkers), he doesn’t so much elucidate the ideas as merely list them.
I did, at least, come away from the book with a feeling that Poincare, who seems not to have been much of an experimenter himself, thought that the logical and mathematical analysis which he brought to science was just as important as the experiments which other scientifically minded persons were performing in their laboratories. Gray paraphrases Poincare as declaring that it is the mathematical relationships which allow experiments to be generalized.
Poincare makes the point that no experiment can be exactly duplicated. Therefore, it is the the generalization of the knowledge gained from research that gives knowledge its ultimate value because then we may make predictions for other, similar scenarios. Through mathematical equations and formulas, we can boost the specific to the level of the ideal— the ideal being applicable across many situations. For Poincare, the aim of a good experiment is not really to discover what happens in that one, particular situation, but to acquire new knowledge which will allow for more accurate predictions for a whole TYPE of circumstance.
In another area… Poincare made the point that, if the entire Universe got bigger overnight– with everything growing in the same proportion– we’d never know it.
I, myself, have previously been led to similar thoughts– though more about personal size and about Time. I realized one day, when contemplating suggestions that the Universe was expanding equally in all directions, that if I contemplate a patch of space closer and closer to my self, I must eventually consider the idea that my own body is expanding along with the rest of the Universe!
This led me to the contemplation of Time… If the distance between Point A and Point B is increased, than the time it takes to get from A to B will also be increased, assuming velocity remains constant. What would this then mean in an expanding Universe? Could it mean that it now takes longer for things to get done– could Time be slowing down?
Or perhaps the Universe is moving faster and faster in a way that offsets the increasing distance between things. This could explain why we feel as if Time is speeding up as we grow older, that the years are clicking by faster and faster. Even though we could not PHYSICALLY tell Time was speeding-up (since everything would be moving faster in proportion), perhaps some part of our mind or spirit is able to grasp the phenomenon, and that’s why– even though it still takes about 365 days for the Earth to go around the Sun– it FEELS faster every year.