Re: "dimensional analysis"?

Evan Kirshenbaum <kirshenbaum@xxxxxxxxxx> wrote:

nospam@xxxxxxxxxxxxxxxx (J. J. Lodder) writes:

Evan Kirshenbaum <kirshenbaum@xxxxxxxxxx> wrote:
The OED's first citation is Bridgman's 1922 book, but the Wikipedia
entry (dimension=grain of salt) has an earliest citation of Edgar
Buckingham's 1914 "On Physically Similar Systems; Illustrations of
the Use of Dimensional Analysis", _Physical Review_ 4: 345.

Ah. The salt is justified. The actual subtitle is "Illustrations
of the Use of Dimensional *Equations*". Looking at the paper, it
does seem to cover the idea of dimensional analysis, even if it
didn't use the term.

It must have been used implicitly by the 19th century giants. After
all, it is just analysis of the scaling behaviour.

Brigdman's contribution is mainly to give it a name, and to
formalise it.

From my cursory scan of Buckingham's paper, it appears that he was
trying to formalize it. I don't have a copy of Bridgman's book
(either on-line or physically--the library at HP Labs doesn't have a
copy, which somewhat surprises me) so I can't tell whether Buckingham
is cited. Do you have one?

No, sorry, I don't own a copy,
and the library is too far away.

Unfortunately, his choice was a bad one, since it invites confusion
with the dimensions of space.

Whatever space you're working in. (These days, I routinely work in
spaces ranging from one to several thousand dimensions.)

To late to do something about it now.

Yeah. Not being a physics person, my first encounter with dimensional
analysis was in the early '90s when I started working on architectures
for test systems. It became clear that a large number of program bugs
could have been caught early on if the type systems required you to
specify units. This would allow the programmer to be told "Wait! That
can't be right" at compile time (or, if it was right, force them to be
explicit about it by putting in the appropriate unit conversion
factor).

But that's not what dimensional analysis does for you.
With inches, and pounds you (may) have the same system of dimensions.
What dimensional analysis does tell you is
that when you scale length by a factor of 25.4
you have to scale volume with (25.4)^3

Unfortunately, it's some 15 years later, and people are still
essentially forced to relegate such information to documentation (if
it's mentioned anywhere).

Non-SI engineering handbooks often have formulas
with the unit to be used in square brackets behind each quantity.
(like = constant . Heat[BTU] . Mass[lb] . ...)
Good practice,
but this doesn't translate easily into computerese.

Best,

Jan

.

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