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[Phys-l] Types of scalars



I've been reflecting on fundamental mathematics that I gloss over in
my introductory physics classes, and it occurred to me that there are
actually three types of scalars that we use in introductory physics:
1) Never-negative scalars, like mass or length or distance.
2) Scalars which can be negative, and the zero is significant: like
charge or flux or current, or changes in temperature, or vector
components.
3) Scalars which can be negative, and the zero is not significant:
like temperature (in Celsius) and potential energy.

I am thinking it would be convenient to make this distinction to my
introductory students, because they behave in different ways (for
example, Category-3 scalars are never multiplied). Has anyone seen
these distinctions made before? I think all physicists are aware of
these categories, but I don't know that anyone ever explained them to
me.

More importantly, are there NAMES for these three categories?

They can be broken up even further if one has a mind:
1a) Quantities like mass or length or duration, which can be added and
subtracted directly.
1b) Vector magnitudes like speed, which probably can't be added
without going back to the original vector.
2a) Fluxes like current or work: the sign indicates direction of flow.
2b) Surpluses, like charge (or bank accounts): the sign indicates
presence or absence.
2c) Changes in quantities, like ∆T: the sign indicates increase or decrease.
3) I can't think of any subcategories of this one.

Too many categories may be more confusing than helpful, however.


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:@-) Scott
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