The snark in that first reply is glorious.
this post was submitted on 11 Jan 2024
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That's surprisingly accurate, as people here are highlighting (it makes geometrical sense when dealing with complex numbers).
My nephew once asked me this question. The way that I explained it was like this:
- the friend of my friend is my friend; (+1)*(+1) = (+1)
- the enemy of my friend is my enemy; (+1)*(-1) = (-1)
- the friend of my enemy is my enemy; (-1)*(+1) = (-1)
- the enemy of my enemy is my friend; (-1)*(-1) = (+1)
It's a different analogy but it makes intuitive sense, even for kids. And it works nice as mnemonic too.
It’s a different analogy but it makes intuitive sense, even for kids.
Its good maths but terrible realpolitick.
I teach maths and one of the analogies is use is watching a film of someone walking forwards and backwards. If you play the film forwards (multiplying by positive), you can see the person walking forwards and backwards as normal. If you play the film backwards (multiplying by negative) you see the opposite. So multiplying by negative reverses whatever was happening before. Hard to put into words but the visuals (hopefully) seem to explain it well enough.
Lmao not gonna lie, this would be a very intuitive way of teaching a kid negative values.
How is multiplying akin to rotating?
Fun fact: exponents and multiplication DO work like rotation ... in the complex domain (numbers with their imaginary component). It's not a pure rotation unless it's scalar, but it's neat.
I know I explained that the worst ever, but 3blue1brown on YT talks about it and many other advanced math concepts in a lovely intuitive way.
“It absolutely, definitely makes sense”