That makes a lot of sense. Thank you.

Great question. I see squaring terms as turning line segments (which can be oriented in a direction) into area (which typically doesn't have a directional orientation). So you are converting something where direction matters into something where it doesn't. In a way, squaring a line moves us into measuring the "self-similarity". For two distinct objects, we can't compare them directly, but we can compare how similar they are to themselves. You might like this: https://betterexplained.com...