Discuss. I've just seen this and I've never thought of this calculations in this way. My mind is pretty much blown. (for the record, I'm not a scientist and have never taken any course in science/maths/etc after high school).
https://www.youtube.com/watch?v=F_0yfvm0UoU
>>7687926
>reported for being underage
>>7687930
I'm 27
>>7687926
Yeah, mathematics isn't just numbers, buddy
You ever work with vectors?
That's just one-dimensional vector arithmetic which is isomorphic to your standard field arithemtic.
>>7687926
Another reason to think math teachers in elementary/middle/high schools should be mathematicians... otherwise we get grown ups with less math actual knowledge than people of the last two centuries...
I honestly think this happens in most science fields: biology, chemistry, history, philosophy, even shit that people like to make fun of like geology/geography...
>>7687926
So you were probably taught just to memorize things rather than being taught how to visualize stuff.
>>7689698
>Is there a logical order to learn these in, or does it not really matter?
This.
Sucked at math growing up. Got good grades up through calculus but that was just effort and memorization. Then I learned to draw. After that, I looked at math again; things that I barely understood because obvious because learning to draw had taught me to visualize concepts. I was suddenly able to actually build the intuition behind concepts and proofs naturally, whereas, looking back, I was only able to grasp them using verbal rather than spatial thinking.
Thinking about why that is, it's prolly just because I was never taught math properly. I was taught to think about it as moving symbols around according to rules that stuck together using language-bound logic. Math, to me, shifted from being something resembling a word puzzle (all men are mortal; socrates is man; therefore socrates is a man - that kinda thing) to a bunch of pictures.
(Also this was probably mostly my fault. I never listened to me teachers growing up and actually dropped outta highschool before shaping up and eventually finishing my bachelors.)
>>7687926
Basic transformations - taught in middle school.
>>7689698
>So you were probably taught just to memorize things rather than being taught how to visualize stuff.
story of my life.
I went up to phd, but then I abandoned, since I know that it is too late to visualize.
>>7687926
Addition is consequential application, multiplication is nested application.
add m n f x = m f (n f x)
mul m n f x = m (n f) x
exp m n f x = (n m f) x
where
0 f x = x
s n f x = n f (f x)
