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 number line starts at 0, then goes to 1, then to 2, 3, 4, etc.. until you decide to stop counting and put and arrow at the end showing that it goes to infinity. So the number line begins with "nothing" and ends with "something that has no limit."
When considering numbers and what they represent, there seems to be something different about 0, 1, and Infinity verses numbers like 2, 3, 4, 5, and so on until you decide to stop counting. 0, 1, and Infinity deal with beginnings and endings, and I will refer to them from now on as the "value" numbers. Numbers greater than 1 but less than Infinity deal with a repeating pattern (known as counting) that is found between the beginning and the end, and I will refer to them as the "color" numbers. Before I go any further I am going to sort out some semantics:
Quantity: an amount of things.
Value: what something has in order to be considered a thing in the first place.
Alright, so, I don't think it is too hard to understand why 0 and Infinity are different from other numbers but I feel like I should explain anyway. To sum it up, they don't really represent a quantity, they represent a concept that is relative to a quantity. (0 represents the lack of quantity and Infinity represents a quantity without limit.) It is less obvious why I would include 1 with the value group, but it is because it is the first thing. You don't have to count your way up to one, it just pops into existence from nothing, and then you begin your counting. All numbers that come after one are the result of counting how many ones there are, and this counting has a frequency, making them the frequency numbers.
The value numbers are connected in some interesting ways, and I want to begin with the links between one and infinity. The best connection between these two is in the concept of a singularity. A singularity is a single point of infinity, so in other words, it is one and infinity at the same time, or an unbounded limit contained in a single spot. Singularities are a paradox like that: infinite and contained, bounded and unbounded. Since infinity has no limit it will eventually become everything, and something that is truly everything is actually just one thing when you see it as a whole. Another way of putting it is to consider that the Universe is infinite and covers everything, and there is only one Universe. (If there was more than one Universe, the word would lose its meaning, and we would need a new word to describe a group of Universes. We could call it a multiverse, but that is just the concept of infinity again. Besides, calling it a multiverse implies that there is just one, and we are back at the concept of one. Don't bother trying to call it multi multiverse, you know where that will lead you!) One and infinity are two sides of the same coin, and it creates a paradox known as a singularity.
When this connection between one and infinity is applied to the number line is would imply that when the line hits infinity, it loops back around to one making some kind of a number circle instead of a number line. From our perspective we can't really observe a loop like this, but there are other patterns that give us some evidence to make sense of this. Consider the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, etc -> to infinity. The way it starts is a little odd, going from 0 to 1, and then another 1, and then the pattern of adding the previous number to get the next one emerges. However, this makes more sense when you consider one and infinity to be two sides of the same coin, and going off to infinity starts you back at one. This would make the sequence look something like this: 1, 2, 3, 5, 8, 13, ->∞/1, 2, 3, 5, 8, 13, ->∞/1, 2, 3, 5, 8, 13, ->∞/1, 2, 3, 5, 8, 13, ->∞ and so on with no real beginning or end, much like the way a spiral behaves:
[fib spiral]
The value numbers are connected in some interesting ways, and I want to begin with the links between one and infinity. The best connection between these two is in the concept of a singularity. A singularity is a single point of infinity, so in other words, it is one and infinity at the same time, or an unbounded limit contained in a single spot. Singularities are a paradox like that: infinite and contained, bounded and unbounded. Since infinity has no limit it will eventually become everything, and something that is truly everything is actually just one thing when you see it as a whole. Another way of putting it is to consider that the Universe is infinite and covers everything, and there is only one Universe. (If there was more than one Universe, the word would lose its meaning, and we would need a new word to describe a group of Universes. We could call it a multiverse, but that is just the concept of infinity again. Besides, calling it a multiverse implies that there is just one, and we are back at the concept of one. Don't bother trying to call it multi multiverse, you know where that will lead you!) One and infinity are two sides of the same coin, and it creates a paradox known as a singularity.
When this connection between one and infinity is applied to the number line is would imply that when the line hits infinity, it loops back around to one making some kind of a number circle instead of a number line. From our perspective we can't really observe a loop like this, but there are other patterns that give us some evidence to make sense of this. Consider the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, etc -> to infinity. The way it starts is a little odd, going from 0 to 1, and then another 1, and then the pattern of adding the previous number to get the next one emerges. However, this makes more sense when you consider one and infinity to be two sides of the same coin, and going off to infinity starts you back at one. This would make the sequence look something like this: 1, 2, 3, 5, 8, 13, ->∞/1, 2, 3, 5, 8, 13, ->∞/1, 2, 3, 5, 8, 13, ->∞/1, 2, 3, 5, 8, 13, ->∞ and so on with no real beginning or end, much like the way a spiral behaves:
[fib spiral]
One and infinity are connected by the concept of a singularity, but the concept of 0 is a bit different. As I mentioned in the Numbers as Concepts essay link, 0 represents no things, or nothing. It ends up being like the opposite of one, because one is a thing, and zero is not a thing. And since one and infinity are connected the way they are, 0 ends up being the opposite of all numbers. A diagram like this should help explain what I mean:
[zero inf 1 inf diagram with numbers on the right loop, 0 on the left]
0 is a place holder. It represents the things that can't be represented, because they don't exist. It is an entire half of possibly the greatest binary there is: existence and non-existence. Zero is a value number along with One and Infinity because the three of them are not counted like the other numbers, they just are.
So the general idea here is value numbers make their own little loop of existence and non existence, and the frequency numbers exist between one and infinity, and deal with how many of those things exist in any given time or place. I think this set up may help give us a new perspective on the various patterns found in numbers, and perhaps the numbers themselves will shed some light on the mysteries of how something goes from not existing to existing.
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