This stumped humanity for centuries, so don’t be too hard on yourself. Not sure if i can manage it, but let’s see.
I love trying to break down complicated ideas
The key here is how you conceptualize
This stumped humanity until the 7th century, and Europeans until the 16th, so don’t be too hard on yourself.
I love trying to distill down gnarly concepts, so let’s try to explain it with an example.
If I twice give you 16 pencils, you own 32 more pencils.
If I twice give you 16 pencil I O U’s, you own 32 fewer pencils.
If I twice take 16 pencils from you, you own 32 fewer pencils. But if you started with none, you can just owe me.
If I twice take 16 Pencil IOU’s from you, you own 32 more pencils.
Here’s another way of thinking about how a negative times a negative equals a positive:
If i film myself giving you 16 pencils (+) then play back that film forwards (+) twice (2x) the result looks like you have 32 pencils. If I play it backwards twice (-) it looks like you have 32 fewer pencils. But if i film myself taking 16 pencils (-) and then play it backwards twice (-2x), it looks like you now should have 32 more pencils!