On Sep 28, 10:55 am, Tim Bradshaw <t...@tfeb.org> wrote: > There's a large existing body of knowledge on dimensional analysis > (it's a very important tool for physics, for instance), and obviously > the answer is to do whatever it does. Raising to any power is fine, I > think (but transcendental functions, for instance, are never fine, > because they are equivalent to summing things with different > dimensions, which is obvious if you think about the Taylor expansion of > a transcendental function). > > --tim
Umm.. Not so. The terms in the Taylor series are made of repeated derivatives with respect to the same variable as the function's argument. That is, in the vicinity of the value a, f(x) = f(a) + f'(a)*(x-a)/1! + f''(a)*(x-a)^2/2! + f'''(a)(x-a)^3/3! + ... each of the derivatives has units that are the reciprocal of the units of the (x-a)^n terms, e.g. the second term's "units" would be "units of f per units of x" * "the units of x", which is simply "the units of f". It had better be true that each of the terms in the series has the same units. Otherwise, they could not be summed. That said, I'm having a hard time thinking of a transcendental function that doesn't take a dimensionless argument, e.g. what on earth would be the units of ln(4.0 ft)? --v -- http://mail.python.org/mailman/listinfo/python-list