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:
It's a different analogy but it makes intuitive sense, even for kids. And it works nice as mnemonic too.
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.
That's exactly what eventually helped me understand it.
To multiply the negative by a negative is like an instruction to "reverse the circumstance that created the negative and then keep 'reversing' forward", so to speak.
You come across a hole in the ground. You see a shovel and 5 piles of dirt. That hole in the ground represents where that dirt used to be.
You can "add" more depth to the hole by digging, i.e. continuing to remove dirt and create more piles.
But you can also reverse what was done by "un-digging", I.e. putting the dirt back into the hole.
So if you "un-dug" the hole with the 5 piles of dirt, you'd have 0 piles, and 0 holes.
But if you "un-dug" the hole 5 times in a row, you've filled the hole and started creating a pile on top of it with dirt from somewhere else.
Its good maths but terrible realpolitick.
Realpolitik is terrible no matter what.
My math teacher in middle school explained it with love/hate, but same set up.
If you hate to love you're a hater If you love to hate you're a hater
Oh this is a really cool way to think about it! Thanks for sharing
I mean, you can negotiate a peace agreement and free trade deals, you don't have to be enemies.
This is basically the staple way of explaining the topic in my country. It was a very bizzare concept for 13 year old me so it made understanding it a lot easier.
Sorry for the question, but where are you from? I learned this with my mother, so I don't know if it's something common here (Brazil) or something that she picked from her Polish or Italian relatives.