The Circle and the Line: Part 2

In The Circle and the Line: Part 1 I wanted to show some examples of how patterns in the Observable Universe can be broken down into the fundamental pats of circles and lines. The general idea behind a binary like this is that the two parts are opposites, and if it isn't one, it is the other. But just like the opposite ends of the color spectrum can be blended and connected with magenta, circles and lines are connected as well. The focus of this essay is to show the various relationships between circles and lines.

The most famous connection between circles and lines is probably the ratio between a circle's circumference and its diameter: 3.14159 etc.... This number is known as Pi, and it is kind of a big deal. Pi could easily warrant its own essay, but I'm hoping you're already pretty familiar with it. The main thing about Pi in terms of the Looping Spectrum stuff is that if you have a circle, you can figure out its corresponding line, and vice versa. I also want to take the time to mention a lesser known ratio called Tau:

Tau is the ratio between a circle's radius and its circumference instead of its diameter and circumference. There is some debate among mathematicians about which is the "real" circle constant, but this seems silly to me because they are essentially two perspectives of the same thing; sometimes you use the radius, and other times the diameter makes more sense. Either way, the important thing is we have a way to find circles that correspond with lines and lines that correspond with circles.

Another way to connect circles and lines is to consider rotation. If a circle were to spin on one axis and you were looking at it from the side, it would look like a line twice during its rotation. (The importance of perspective is elaborated upon more in this essay.)

Rotating the circle would form a sphere, and this brings us from 2D to 3D. Thinking in terms of 3D is important because 3D is where "reality" is. (More about dimensions in this essay.) To sum things up, all the flat things we call 2D are actually made of 3D molecules and atoms, and we only experience the 4th dimension as memories of the past or thoughts about the future. So how do we upgrade the circle and the line to the third dimension? Circles relate to a few different forms, most notably spheres, rings, and discs, but what about the line? You could argue that a rectangular prism would make the most sense, but cylinders are more balanced, and they relate better to spinning.  Spinning is important because it seems to be what everything in the Universe loves to do, and obviously ties right back into circles.

(It may be helpful to think of strings or wires instead of cylinders, but it is the same idea.)

So there is the cylinder, a three dimensional line with a circle at each end. One of the 3D forms for the circle is the ring, (more on rings and the torus here) and if you were to move around inside a big enough ring it would just look like a cylinder, similar to how a road can look flat even though it is on the curved surface of the Earth. This sets up a bit of a "chicken and the egg" scenario (although I hate that example because unless you reject evolution the egg obviously came first.) So what came first, the circle or the line? Or if you bump things up to the third dimension you could ask what came first, the cylinder or the ring? This is a paradox, so the answer depends on your perspective and what you are trying to measure. I think the main point to realize here is that in geometric terms, circles and lines are the two building blocks of the Universe, and this sets up a balanced dynamic of opposites because one is not more important than the other.