it really bothers me how loosely most people--students, educators, and researchers alike--treat units
@BatElite when doing math. A lot of people seem to just strip the units off, do the math, and then stick on the units again at the end
@Felthry Ah in that sense.
I've never learned anything other than to strip off the units. IDK how you'd do it otherwise.
@BatElite Units are quantities that you can do math to too. A newton times a meter *is* a joule. SI prefixes multiply like exponents; μ times k is m, for instance. You do math to the units too, not just to the numbers, and it helps _so much_ with keeping things straight and not making simple mistakes because if you do all your math and then the units work out to give you kilograms when you expected a speed, you know you did something wrong
@BatElite I guess most people don't think of things like this but it's so incredibly confusing to us... I can't understand how it makes sense for people to strip the units off before doing math
@Felthry AFAIK what you talk about makes sense, but I've learned to treat the two groups as separate equations.
Like, the numbers separately gives the value you're looking for.
You can then do the conversions and math stuff on the units to get an eventual value, potentially with a value to scale what you got earlier. (which in metric is often a power of ten) But that scaling is usually sort of half-implicit??
(I might be simplifying, not using any advanced maths in my current life. ^^;)
@BatElite Yeah, but the separation just doesn't make sense to me, because it's not "ten", it's "ten meters"
@Felthry I wonder if this sort of thing is why it took me years to realize that displacement, velocity and acceleration in physics are literally just differentiation/integration.
@BatElite There are a _lot_ of strange-looking equations in physics that people memorize but then most people never realize that they come from integrals or derivatives of more basic ideas. Like, the entire reason the formula for kinetic energy (½m·v²) has the factor of ½ is because it's an integral over velocity.
@Felthry In our case at least, that formula was taught before we ever had integration. And I think in practice our physics stuff was more about solving stuff and getting an answer than understanding the relationship mathematically. Only in the maths-backed reasoning sense? IDK