alt Hacker News> You generally can’t apply functions to dimensional units.
Perhaps not in mathematics, but in programming that's clearly possible. I guess programming is more general than mathematics.
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podocarp • today at 9:18 AM
No, it's definitely possible in mathematics, they've left out some details as to what the units are doing that makes them unable to be assigned to functions. I mean a regular ODE that you get from newtons laws is a set of functions that take position and time as inputs, which all have units. What they mean should be "dimensionless functions cannot be applied to dimensional variables". These are commonly functions like sin cos exp log and so on.
This is precisely why (programming language) types are poor model of physics units, despite often being touted for this exact use case. 3m is not the same thing as "the value 3 of type meter". It is the multiplication of the dimensionless scalar 3 with the special "m" constant for meters.
That's why pow(3m, 2) = 9 m^2, and not `the value 9 of type meter`. Of course, you can define the type `square meter` as well, and define `pow -> meters -> positive integer -> square meters`. However this quickly becomes overwhelming once you start doing more complex expressions with multiple types. What is the type of `pow (3kg^2 * m/s, 3/2)`?
Edit to add: also, there is a simple fact that "sin(pi/2 kg)" is just not defined, in programming or math or physics or any other useful system. It's definitely not 1kg, just like sin ( (pi/2) * 2) is not sin (pi/2) * sin (2).