Yes, I do think you are wrong. The concept of 'exact' is context sensitive,
but not altogether meaningless. This is an issue which causes scientists to
have a great problem communicating with the scientifically illiterate world.
For practical purposes, I would call an exact analysis/calculation one whose
errors can be specified. "Exact" means that the results which we state are
less than the precribed error. If you insist that the error go right down to
zero, then there is nothing in the world that can be specified that precisely
(this is the uncertainty principle in action). Does that mean that we totally
abandon the concept of exact? Let me give some familiar examples.
Suppose I go into a high-precision laboratory and measure the voltage across
the terminals of a standard cell and report it as 1.376899 volts +/-.000001
volt (this is doable.) Are you rejecting this as non-exact because I cannot
get closer than 1uVolt?
The degree of error is the whole gist of exactness, and in practice, we refer
to measurments, calculations, etc. as 'exact' if their error is very low. How
low? That requires judgement and adherence to convention.
In the case which I stated (a power supply calculation) I was making a fairly
specific statement which would be understood by most experienced design
engineers. Namely, before the computer became a desktop tool for every single
person on the planet, many conceptually simple problems were never solved
exactly. The most important category of same is problems involving non-linear
elements, which are not well described by standard physical laws and
formulas. Pre-computer power supply design was based upon picewise-linear
approximations to linear circuits, which means that even if the mathematics
were done exactly, the results would still be approximate. But with a
computer, you can easily solve the necessary circuit equations to any degree
of precision, limited only by how many significant figures of precision you
seek. In practice, we don't need 10 or 100 sig. figures to feel that the
result is exact.
So in that respect, when I tell you that I have done an exact solution, what
I am really saying (this is understood to those who do this kind of
calculation) is I will calculate the results for you to any specified degree
of precision. You CANNOT make that statement based on an old-style
(non-numeric) calculation which invokes approximations in the basic circuit
equations themselves (e.g. piecewise-linear models). That is the difference.
Eric vonValtier K8LV
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