Two Kinds of Numbers

When describing light there are two sides to consider: value link and color. link I think the intertwined relationship shared by value and color can serve as a metaphor for other things in the Universe, including the number line, and that is the topic of this essay.

There are other essays on this site to talk about color and value, but I am going to do a quick review here. Colors are frequencies of light, and to make them lighter or darker, you need to add or subtract value. Values are amplitudes of light (like black, white, and gray) and represent how much light there is to make colors brighter or darker. Values are often lumped in with color, but they work in different ways. The main thing to understand for this essay is in additive color mixing, all of the colors combine into white and can be separated from white, and in subtractive color mixing the same is true for black.

[color mixing graphic]

In this way, it could be said that value is the "beginning" and "end" of color, and this talk of beginnings and ends is what leads us to the number line:

[numberline graphic]

The Diagram

You might have already noticed the diagram that goes along with this Looping Spectrum idea, but here it is again in case you missed it:

I don't have a formal name for this symbol yet, I've mostly just been calling it "the diagram." This essay is to explain how I came up with these shapes in this arrangement. 

Numbers as Concepts

The goal of this essay is to explain certain numbers as ideas or concepts, and not just a quantity. (I already brought this up a bit in The Circle and the Line: Part 1 link by relating shapes to numbers.)

In the Looping Spectrum Paradox, the numbers needed to explain everything are 1, 2, 3, 4, and 5. There is also 0 and infinity to consider, but let us start with the number one:

1

The number 1 represents a singularity, a single thing. In terms of geometry, it would be a single point. It is pretty hard to talk about the concept of one because if it really is just one, there is nothing else around to compare it to. You could say it is like one apple, but then what does that even mean? One apple where? In your hand? One apple in a basket? If it is just an apple, then you couldn't even be there to say that there is one apple because then there would be two things; you and the apple. This brings us to the concept of 2, which is a lot easier to comprehend.

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:

The Circle and the Line: Part 1

The reason the idea is called "Looping Spectrum" is because it seems everything in the Observable Universe can be reduced to pattern made from circles and the lines. (The circle is the loop and the line is the spectrum.)

The first thing to examine is geometry, with the goal being to find the most fundamental shape. If you associate numbers with shapes and consider shapes with fewer sides to be more fundamental than those with many sides, then squares would be more fundamental than pentagons, and triangles would be more fundamental than squares. In fact, triangles are the most fundamental polygon because all other polygons are actually just a bunch of triangles stuck together.

Color Theory: Part 2

In the first color theory essay I talked about the primary colors and how magenta is a bit different than the other colors. There is more to color than just what is going on in the rainbow though, and that brings us to the topics of this essay: value and florescence.

Value is an element of design separate from color but very closely related, similar to how shape and line are easily grouped together. Value is where we get the lightness and darkness of a color, and where we find black, white, and gray. So here is an important point: black and white are NOT colors, they are values. It is convenient for us to refer to values like black and white as colors when we are asked what color our car or shirt is, but value and color are two different things.

Color Theory: Part 1

     There are two really important lessons about color that don't seem to be common knowledge:

     1. There are TWO sets of primary colors, and red blue and yellow isn't even one of them.
     2. Magenta is a color we can see but we can not measure it physically.

     It concerns me a bit that I took a color theory class in college for my art degree and neither of these things were mentioned. It concerns me even more that across the world art teachers are telling students the primary colors are red, blue, and yellow, which turns out to be a less than accurate way to explain the color wheel. There are actually two sets of three primary colors, one for additive color and one for subtractive color.

Additive color mixing looks like this: