Warning: serious linguistic hacking follows. I tried to be careful in
writing, please be careful in reading. Corrections welcome.
Ethan Furman writes:
> On 4/9/22 21:17, Stephen J. Turnbull wrote:
>
> > if 12*u.mm * 42*u.MFr == 502*u.foo:
> > print('Well done!')
>
> Part of the argument as well, I think, is that the top expression
> would be parsed as:
>
> ((12 * u.m) * 42) * u.MFr
>
> which, if actually equal to 502*u.foo, is dumb luck.
It's actually equal to 504*u.foo, I shouldn't do multiplications
larger than 12 * 12 in my head. But yes, the correct answer is
(12 * 42) * u.foo, if I could only do arithmetic on integers!
I guess you could call the associative law of multiplication "dumb
luck", but most mathematicians will consider that hate speech. If the
unit class is designed correctly (the units package is designed
correctly), both the associative and commutative laws of
multiplication hold.
The only gotcha as far as the value is concerned is that if you put in
divisions such as u.m/u.s, then you often will need parentheses. But
that's true for ordinary arithmetic as well. There would be a problem
if the LHS were 12*u.mm / 42*u.MFr. That's actually nonsense in a
units-aware world. Parentheses are required: 12*u.mm / (42*u.MFr).
The "we demand syntax" crowd wants the "add unit" operation to have
higher precedence than numerical multiplication and division. Hmm,
unfortunately both '@' and '%' have the same precedence as '*' and
'/', but we could make the precedence more natural by using '**' at
the cost of the intuition that a unit is just a quantity (object with
both value and unit attributes) with value 1.
I'm not sure that intuition helps the "we demand syntax" crowd,
though. Another way to put the issue is that libraries like units
don't provide units, they provide quantities. You can create a
quantity foo that acts like a unit by giving it the value 1, but
10*foo is of the same type as foo. It just has value attribute 10.
Again, that doesn't bother me, but I suspect that the "we demand
syntax" crowd will feel queasy about the idea that 'nm' *is* '1 nm'.
For them, 'nm' needs to be notated with a value to be a quantity.
I don't want to put words in anybody's mouth. If Brian or Rickey
disclaims that interpretation, they're right. If they think it has
expressive value but needs to be amended, they're right. I'm just
trying to provide words to express what the need is here.
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