Compliments of ProfPat's provided URL (excerpt): - A "whole" must consist of two opposite parts.
- These two opposite parts must be mutually exclusive.
- These two opposite parts are complementary to each other.
Seque to ___________________________ Compliments of Nobody's provided URLS: Another circular symbol of balance--though seemingly with no central point--is the classic tai chi symbol representing Taoism.
But what few people realize is that within the circle there are actually two circles within the larger circle, and the two dots define their centers.
The simple fact of circles within circles leads to some surprising mathematics, a peculiarity of this symbol. In the picture above, "r" designates the radius of the circle--the distance from the center of the circle to its perimeter, or circumference. The radius times two--in other words, the line from one side of the circle to the other--is called the diameter. Mathematics teaches us that the circumference of this circle is equal to pi (π=3.14) times the diameter, or:
πd which is the same as 2πr
Now look at the tai chi symbol again, and notice that the radius of the big circle is the diameter of the small circles.
Let's call the large circle "A" and the smaller ones "B" and "C." Let's say the diameter of Circle B equals 1. So the diameter of Circle A equals 2.
Then the circumferences of the two circles are:
A: 2πr=2x3.14x2=12.56 B: 2πr=2x3.14x1=6.28
And of course, even without a calculator, we can see that the circumference of Circle B is half that of Circle A. Since Circles B and C are equal in size, we can take half of the circumference of each to make one circle, right? And that is half of the length of the circumference of Circle A. So the red line and the blue line in this drawing are of equal length:
So what? Well, remember that in fact, you can put two circles inside each of Circles B and C, making four circles, whose half-circumferences also add up to the same:
And you can put two circle in each of those circles, and so on.
Notice now that the width of the yellow line from side to side--the amplitude of the wave, so to speak--is half that of the red line, which is half that of the blue line. So as each circle is divided in two, the line described by the half-circumferences becomes less and less wavy.
Do you see where this is going?
Take this down to the smallest level, with hundreds of circles lined up,
and their curvy half-circumferences
will define a straight line!
In other words, there is an extreme paradox here, because you will eventually get a line that is both 6.28 and 2...at the same time!
This is a fascinating illustration of one of the basic points of Taoism, that all the seeming "pairs of opposites" in the world are actually manifestations of the Tao--the One behind the Many.
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___________________ Hey Guys: We may be on to something, and something may be on to us. (Something about parallel, mutually exclusive but complementary universes: squared?) Either way, it's a mighty soberin' thought. Great contributions to this thread. You Folks are transcending Truly Yours, at his own initial consideration. Nobody is Somebody and ProfPat paramountly promotes herself. As for Michael. Well. He's a flocking Grand Master. Lovin' it. (Have a great Tao in the morning...) Best regards, - RP