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
@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
Probably bad(ly explained) maths
@Felthry I know sort of what you mean though, for example we learned to convert metres per second to kilometres per hour by deviding/multiplying by 3,6. since
1km = 1000m
1h = 3600s
So while m/s is a fraction of (1/1 = 1), km/h converted to m/s is (1000/3600 = 1/3,6). I can't explain well, bleh. :<
Which is very simple for both of us I'm sure (I wonder if I could manage the kind of maths you do. :P)
re: Probably bad(ly explained) maths
@BatElite The kinds of math we do are frequently more calculus than arithmetic, so it depends on whether you think calculus is doable or not I suppose!
re: Probably bad(ly explained) maths
@Felthry I'm fairly certain I can get pretty far in calculus (except that I've not bothered with it for months if not more), as long as you don't ask about probability or permutations because I never learned any of that.
But guess what about 90% of programming challenges are about. :|
re: Probably bad(ly explained) maths
@BatElite Statistics is a mess that we're glad not to have to work with
@Felthry @BatElite the only times I've ever seen (or done) this is when the units are the same going in and out, and everything being plugged in is pure scalars. The moment you start multiplying or dividing units, or having to ask if you can add these units together, you need them to be in the dang math.