From: Deane Yang (deane_yang_at_[hidden])
Date: 2004-01-14 10:33:47
Andy Little wrote:
>>The "logic" of dimensional analysis has been quite cogently described by
>> Deane Yang.
> (Understating) I find this remark slightly odd. Deane has several times
> asked myself and others to explain the concepts of physical quantities. In
> much of his writing he confuses quantities,dimensions and units. (Like Deane
> you would like to 'make up' your own dimension/units system....this may be
> what you are saying.)
OK. (takes a deep breath). Here's one more try. I have NEVER said I do
not understand dimensional analysis. I understand it extremely well and
have in fact figured out how to describe it in purely mathematical
terms. I understand perfectly well the difference between units and
dimensions. And a key point that seems to be missed by some is the
dimensional analysis is NOT part of physics; it is a part of mathematics
that was discovered and exploited by physicists. In some sense
mathematicians also use it (abstract linear algebra), but mathematicians
do not call it "dimensional analysis".
Why is a mathematician's perspective useful here? Because it helps
us distinguish clearly by what aspects of physical dimensions follow
by purely mathematical principles and deductive logic and what aspects
are "man-made" (i.e., ad hoc conventions). My impression is that the
better programmers on this list have understood many of the points I
have tried to make.
What I did not understand is how physicists decided that there were
only seven fundamental dimensions and how they decided, among all
possible dimensions, which ones were "fundamental".
That is what I asked you.
Basically, based on upon the responses received from various physicists,
it appears that the decision was
completely ad hoc. This was an acceptable answer to me, because
physics is an empirical science and therefore different from
mathematics, where we're locked into deductive logic. Unfortunately,
I sometimes forget this.
I'd appreciate it if you tried to read my writing a little more carefully.
I do however accept the criticism of others that I have not provided
enough code samples. I will try to do better there.
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