There is also the significance of fours, as in four dimensional timespace. Some string theorists believe that string theory can be accurately described in four dimensions.
Every number has as much significance as can be subscribed to it. Two is just easier to see.
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Originally Posted by xepherys
I would think, in it's context, that an anti-circle would, in fact, be all area not encompassed by said circle. It's equation would take all of existance and subtract from it the area of the known circle.
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But if a circle has area, wouldn't an anti-circle necessarily have no area? The point is that when it comes to opposites one must pick and choose which characteristics to focus on. What makes a circle a circle? Roundness? Pi? Area? What is the opposite of round? Pi? Area?
Duality can perhaps be interesting, but as a means of organizing the world i find it to be woefully inadequate.