this post was submitted on 11 Jan 2024
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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.