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On Nov 29, 2010, at 4:22 PM, John Denker wrote:
... F is a vector. That is sufficient (indeed more than sufficient) to
guarantee that we can write it as the sum of three other forces
F1, F2, and F3.
I hate to belabor the obvious, but the acceleration a is also a
vector. That means we can write it as the sum of three other
accelerations a1, a2, and a3.
We can start with the obvious possibility a1=F1/m, a2=F2/m, and a3=F3/m
... but there is an infinitude of other ways of writing a as the sum
of three vectors ... not to mention an additional infinitude of ways of
writing a as the sum of four vectors, et cetera. ...
Yes indeed. We invented many ways of predicting outcomes of experiments. In other words, we invented many useful models. Some are more useful than others. Does Mother Nature (reality) use our models (words, sentences, vectors, algebra, calculus and other products of human intellect)?. Probably not. A net force is applied to an object and acceleration (along the direction of that force) is always observed, at the same time. Distinction between reality and models is worth emphasizing, as often stated on this list. Yes, I am also belaboring the obvious.
The "if A then B" reasoning, the concept of symmetry, etc. belong to modeling; we have no evidence that outcome of experiments depend on reasoning. They just happen to be consistent with reasoning invented and accepted by scientists. Isn't this fascinating?