3 ms·

School teaching tends to be authoritarian, so that's a reaction I felt too. "Less than no apples? Minus times minus is plus? What the hell is this and who order

School teaching tends to be authoritarian, so that's a reaction I felt too. "Less than no apples? Minus times minus is plus? What the hell is this and who ordered it?" I wish it'd been explained like: counting numbers like 1, 2, 3 obey certain laws, e.g. adding in different ways gets the same result. If you relax just a few of the laws in the right way, you can find a broader class of things obeying the shared logic. In the case of complex numbers, we're dropping ordering, and finding that takes us from 1-d sliding and stretching (adding and multiplying) to 2-d, where the stretching becomes stretching and turning.

quacked 5y ago
I think the biggest problem with authoritarian thinking about math is that math is not a discovered set of authoritarian principles, but rather a colossal project to make up weird relationships that satisfy the rules of the weird relationships that were already made up. Approaching imaginary numbers as: > "Eventually, mathematicians got sick of not being able to achieve a negative result through multiplication, so Rafael Bombelli finally made up imaginary numbers using the work of other Italians and even some Greeks. Unfortunately for him, most people thought his idea and rule set was stupid until about two hundred years later. We will now learn what sorts of nonsense he made up--those of you who are interested in electricity had better listen close--" will inevitably lead to a different mindset about math than: > "Today's lesson is that the square root of negative one is i. Write that down, because it WILL be on the test."
caf 5y ago
I feel like they could have explained "minus times minus is a plus" using the distributive law. -1 x -1 = -1 * (0 - 1) = (-1 * 0) - (-1 * 1) Presumably at this point you were happy with "anything times zero is zero" and "anything times unity is itself", so: = 0 - (-1) and now we can just use the additive laws of negative numbers, which hopefully were intuitive enough: = 1

quacked 5y ago

I think the biggest problem with authoritarian thinking about math is that math is not a discovered set of authoritarian principles, but rather a colossal project to make up weird relationships that satisfy the rules of the weird relationships that were already made up. Approaching imaginary numbers as: > "Eventually, mathematicians got sick of not being able to achieve a negative result through multiplication, so Rafael Bombelli finally made up imaginary numbers using the work of other Italians and even some Greeks. Unfortunately for him, most people thought his idea and rule set was stupid until about two hundred years later. We will now learn what sorts of nonsense he made up--those of you who are interested in electricity had better listen close--" will inevitably lead to a different mindset about math than: > "Today's lesson is that the square root of negative one is i. Write that down, because it WILL be on the test."

caf 5y ago

I feel like they could have explained "minus times minus is a plus" using the distributive law. -1 x -1 = -1 * (0 - 1) = (-1 * 0) - (-1 * 1) Presumably at this point you were happy with "anything times zero is zero" and "anything times unity is itself", so: = 0 - (-1) and now we can just use the additive laws of negative numbers, which hopefully were intuitive enough: = 1