Yet there are infinitessimally smaller numbers than one, and infinitely larger numbers than one. I guess this means we always need to keep context in mind, if we want to understand anything.
Science is seeking a GUT -- a grand universal theory that presumably will correlate and consolidate the insights and discoveries of Newton, Einstein, and the great quantum theorists (Bohr, Born, Schroedinger, Planck, others). Einstein's Relativity didn't repudiate Newton. It has been said that Newtonian mechanics is a fine theory and eminently reliable predictor of events that take place in the world of "ordinary" space and time. That Einstein's theories are descriptions of the world of the very, very large; and QM of the world of the very, very small. No one of them displaces or falsifies any other: They are descriptions of different aspects or "scales" of the Universe and it seems to me that at some ultimate level they must all work together. The string theorists, following Klein and Kaluza, are trying to figure out how to "tie them all together."
We live in such fascinating times, donh!
Thank you so much for your thoughtful reply.
What fascinating times, indeed.
I suggest that a universe in which the twins paradox exists is different from Newton's fixed-frame universe so radically that it is misleading to think of it as an adjustment in the trailing digits of the decimal place, most particularly for the discussion at hand.
Newton's and Einstien's universes could not be more radically different at their fundament. That both produce satisfactory answers for most purposes is NOT an argument in favor of an objective universe science is refining itself toward. The refinements produce better utility--they do not produce evidence narrowing ever closer to the True Truth.
Or, putting it another way: "one is a small number" isn't an objectively true statement for which there is an ineffable presence in the universe for science to seek out. It is a human invention to help us think about stuff.
I couldn't agree more.