I'm reading Ivar Ekeland's The Best of All Possible Worlds, and I can't resist posting this quotation:
We are a far cry from Plato, for instance, who taught that the objects we observe are but images, or shadows, of originals, the only true and real Objects, which exist in a world above one own, the world of Ideas. [...] Poincaré points out that science does not need that kind of belief: there is no need for objects to exist in any other way than to relate our sensations with common experience. Clearly there is no more room for metaphysics: science can be concerned with relating only facts, not things.
A residual Platonism often confuses natural science, mathematics, and computer science. Time to read Poincaré.
You sent me looking for an old Dover reprint of Science and Hypothesis by Poincaré.
From p 90
"1. There is no absolute space, and we only conceive of relative motion; and yet in most cases mechanical facts are enunciated as if there is an absolute space to which they can be referred.
"2. There is no absolute time. When we say that two periods are equal, the statement has no meaning, and can only acquire a meaning by a convention.
"3. Not only have we no direct intuition of the equality of two periods, but we have not even direct intuition of the simultaneity of two events occurring in two different places. I have explained this in an article entitled, Mesure du Temps,1
"4. Finally, is not our Euclidean geometry in itself only a kind of convention of language? Mechanical facts might be enunciated with reference to a non-Euclidean space which would be less convenient but quite as legitimate as our ordinary space; the enunciation would become more complicated, but it still would be possible.
"Thus, absolute space, absolute time, and even geometry are not conditions which are imposed on mechanics. All these things no more existed before mechanics than the French language can be logically said to have existed before the truths which are expressed in French..."
It is a bit off-subject but I was reminded of Feynman's position on the social sciences, which he considered to be pseudo-science with the potentail of being real (but not now).
After looking trhough some old books for a half hour, I decided to Google and found a video on youtube (!)
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