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The overall answer to this one is, "It depends." That is where the conundrum comes into play because it does depend on circumstances along with beliefs, philosophies and both perceptions and concepts. The question alone can trigger a mind boggling set of answers all dependent on, "It depends."
The overall answer to this one is now, “What limitations are you going to put on the answer?”
It can be said a circle, closed, has only one side and that is the side on the outer aspect that makes a circle. Some may assume that inside a circle does not exist but if it does then there are two sides to a circle.
It can be said that a circle is made of of degrees and that if we conceive each degree of the circle is a place holder for a person to stand than each degree becomes a side so there are 360 sides to each circle and if that is possible then each degree on the inside of the circle gives us 720 sides.
Of course if you use the four points of the globe, i.e., north, south, east and west, much like in the ancient classics then you have only four sides to that circle and there are not inner sides because the four points of north, south, east and west would not exist making the inner part of the circle - void. Thinking this way one who applies martial skills and methodologies does not have a way to apply those skills to the inner part of the opponent unless you can allow the inner part of the circle to have substance, i.e., likened to one’s psychological side of the mind then one can apply certain psychological princples and methodologies to an adversary’s mind to enhance those outer physical skills and methodologies to defeat the opponent in the conflict often coming with violence - both physical as the outer circle and mental as the inner side or sides of the circle.
You see, so far, that without any additional qualifications to the question thereby narrowing down all the possibilities there is often no end to the responses you can provide when applying thought and creativity to a karate koan such as “How many sides on a circle?” If you don’t qualify it like this, “How many literal sides are on a drawn one dimensional circle?” Then you have limitations and obstacles and restrictions to guide you toward a more direct and literal answer.
This once again adds to the last answer because now we know that depending on things this circle now has multi-directional capabilities beyond a singular, one dimensional drawn circle so that 360 degree now also has 360 more degrees at every original degree mark leaving us with an almost, seemingly, infinite set of sides or possibilities making the basic concept of, “It depends,” even more complex in its simplicity.
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