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Re: [Phys-L] backwards units



On 05/03/2015 08:37 AM, rjensen@ualberta.ca wrote:

'quantity calculus'.

Excellent point. As Philip Keller wrote on 04/15/2015 10:21 AM

Once you know the magic word, google does the rest!

https://www.google.com/search?q=%22quantity+calculus%22

There are professional metrologists doing current
research on this topic:
https://scholar.google.com/scholar?as_ylo=2014&q=%22quantity+calculus%22

A useful formalism is the Factor Label method. There are
tons of pedagogical resources on this:
https://www.google.com/search?q=%22factor+label%22+method

A useful reference is the International Vocabulary of
Metrology (VIM). It shows how professionals think
about this stuff. I find it reassuring, because it is
pretty much consistent with how I like to do things:
http://www.nist.gov/pml/div688/grp40/upload/International-Vocabulary-of-Metrology.pdf

================

I like to point out that getting the units wrong might
cost you 328 million dollars
http://mars.jpl.nasa.gov/msp98/gif/m98patch.gif

================

When dealing with old-school computer languages, I said the
part about implicit SI was optional. If you prefer to be
fully explicit, that's fine. In that case, the previous
example becomes:
in__m = 0.0254;
ft__m = 12 * in__m;
yd__m = 3 * ft__m;
L__m = 10 * yd__m;
L__ft = L__m / ft__m;

That's less concise but more bullet-resistant.

================

When explaining it to non-experts, I draw the picture:

Length of hallway /divided/ into yards:

+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+


Length of hallway /divided/ into feet:

+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

This is one of those all-too-rare cases where the
language of English aligns with the language of
algebra: The length is /divided/ by the units as
surely as a pizza is divided into slices.

This is yet another way of explaining why the "f = 3 y" is
perverse. The concept of /divide/ is crucial here, so we
should write
L/ft = 3 L/yd
with the units in the denominator.