Thanks Stan --

This looks really interesting. I hope you will be able to help make a
really great Squeak units facility happen.

Cheers,

Alan

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At 6:48 AM -0000 11/3/98, Stan Heckman wrote:
>I too am interested in a units package for squeak. I have implemented
>a units package in another language (Mathematica) that handles Sam's
>"general case which ends up with composite units like furlongs per
>cubic fortnight per dyne centimeter." I agree with Sam that "you
>then need an algebraic system with mappings for unit definitions (dyne
>cm = erg, etc) so these composite units could recognize whether they
>were compatible or not and if the units could be reduced or mapped to
>another unit."
>
>The only two "mathematical" functions I used from Mathematica
>to do this were one that told me whether a set of vectors was linearly
>independent, and one that returned combinations from a set, taken N at
>a time. I know squeak already has a function for returning combinations
>N at a time, so all we need is the linear independence checker. Can
>someone point me to a linear algebra library for squeak?
>
>Things that gave me grief before, and that would be good to do more simply
>this time, are non-absolute temperatures, lists and tensors, automatic
>unit simplification and functions other than (+ - * /).
>
>What's the problem with non-absolute temperatures? Well, when I say
>that I heated my dinner from 40 Fahrenheit to 400 Fahrenheit, I would
>like to keep the same units, and describe the temperature difference
>as 360 Fahrenheit. If I want the heat put into dinner, I multiply dinner's
>mass and heat capacity by 360. But if I let the oven cool 40
>degrees, and then want to compute the density of the air using the ideal
>gas law, I want not 360, but 360 + 459.67. As human beings we figure out
>the right thing to do in each case from context, but I don't think Squeak
>can be that smart. The resolution I've used before is to never use
>non-absolute temperature scales for temperature differences, only for
>temperatures. The Mathematica units package handles this automatically; I
>doubt that feature was really worth the complexity it cost.
>
>What's the problem with lists? One must either keep the units once per
>list, or once per element of the list. No matter which one chooses,
>half the time one wishes it were the other way. My bias is to keep the
>units of homogeneous lists only once per list, because this preserves
>the information that the list is dimensionally homogeneous, and
>without this I found my code became cluttered with checks to see
>whether a list was homogeneous.
>
>What's the problem with automatic simplification? Well, when I divide
>newtons per ampere squared by farads per meter, it's a very good bet
>that I want to see units of ohms squared. But when I divide miles by
>hours, I probably don't want to see this simplified to knots. Humans
>have a lot of heuristics for this, learned in years of classwork, and
>learned differently in different disciplines. I found that I could do
>a pretty good job of reproducing my own heuristics by simplifying only
>if I could reduce the total number of base units required, not introduce
>any fractional powers, and I restricted my base units to the set of
>units I started with plus joule, watt, pascal, newton, coulomb, volt,
>ohm, farad, henry, tesla, weber, and siemens. Using units in the original
>expression before the units above will usually keep absorbed dose in
>rads, instead of converting it to pascals.
>
>What's the problem with functions other than +, -, *, and /? The problem
>is that there are so many of them. :-) In the Mathematica package, I
>kept encountering functions that should work with dimensional quantities
>but didn't. See the functions section on the web page. If someone can
>figure out any way to avoid the same proliferation of tiny methods in
>the Squeak units package, that would be a very important contribution.
>
>An HTML version of my (Mathematica) units package is available at
>  http://stanheckman.com/a/98h/glimpsedotter/html/PhysicalUnits.html
>The (brute force) automatic simplification section might be
>interesting to someone implementing similar functionality in Squeak.
>
>--
>Stan