On Tue, 5 Apr 2022 at 11:44, Steven D'Aprano <st...@pearwood.info> wrote: > > On Tue, Apr 05, 2022 at 04:36:24AM +1000, Chris Angelico wrote: > > > Some unit cancellations really do result in pure scalars. The ratio of > > a circle's circumference to its diameter isn't a unit of m/m any more > > than the ratio of a circle's area to that of a circumscribed square is > > a unit of m²/m². They're both just numbers. > > Of course it is a ratio. You said it yourself: it is a ratio of > circumference to diameter. > > That ratio is only numerically equal to π if the units you measure the > cicumference and diameter are the same. Otherwise it has units > "inches/cm" (or whatever units you used) and a completely different > numerical value. > > > On the other hand, a > > radian is a very real unit of distance/distance (based on its > > definition of arc length), and it's a unit of angle. > > The SI system defines both radians and steradians as dimensionless > derived units, previously known as "supplementary units". >
You're missing the point: these are ALL dimensionless values, yet they are incompatible. Regardless of the units used to measure the circumference and diameter, they will *by definition* cancel out and leave you with pi (case in point: using a pie as the unit https://www.youtube.com/watch?v=ZNiRzZ66YN0 ). But a radian and a steradian are not the same type of thing. Nor is an index of refraction.They're all dimensionless. They're NOT all fungible. The unit type "inches/cm" is meaningless, but the unit type "length/length" is very meaningful. And that's where the problem comes in. Please, stop being all caught up on one small error that I propagated, and look at the actual point? You're really good at this sort of thing. ChrisA _______________________________________________ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/EGZY7HIHZB7AHNYT7XQEFHDGA4A2RWWK/ Code of Conduct: http://python.org/psf/codeofconduct/
