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.


2

The number 2 represents a binary, or two things. In terms of geometry, it would be two points, and these two points would have a line between them, forming a line segment. The concept of two is the bread and butter of easy to understand simplicity. Things like on or off, male or female, good or evil, yes or no, liberal or conservative, are all very common examples of binary concepts. The concept of two also gives you the option of a frame of reference, so we can say things like an apple on the table, or a crater on Mars, or a bone in your hand etc…

3

The concept of 3 is where things start to get interesting and a bit more complicated. It represents a ternary, or three things. In terms of geometry, it would be three points, and these points could form a triangle, or they could all be on the same line and represent a spectrum, with a point at the beginning, a point at the end, and some point in between. With the additive color spectrum red and blue would be the binary points at the end and green would be the in between. With good or evil it would be neutral, with yes or no it would be maybe, with liberal or conservative it would be someone who is politically apathetic, and with male or female it would be someone or something without a gender.  The concept of three is a more realistic portrayal of things in the Universe because we know things aren't as simple as one or the other; the shades of gray and neutrality in between also matter. 

4

The concept of 4 is where things start to get loopy, and I mean that both figuratively and literally. Four represents four things, and in geometry these four points would form a quadrilateral, like a square or rectangle. The four points could also be in a straight line, but in the Looping Spectrum Paradox, it is the 4th point that connects the opposite ends of the spectrum to form a loop, or a circle, just like in the color wheel:

In the color wheel, red and blue are the two opposites and they establish the binary. (It is really important to point out that it doesn't matter which is one and which is two; whatever one comes first is a matter of perspective. link) Once the binary is established we can consider green to be 3 for being neutral, since it is neither red nor blue. That leaves the 4th point as magenta, and this is where things get to be a bit of a paradox, because the 4th point is the two opposites at the same time.

With good or evil it would be something both good and evil at the same time instead of just neutral. With yes or no it would be maybe because you want both options, instead of being maybe because you don’t know enough to decide. With male or female, the fourth point could be represented by transgender, hermaphrodites, or androgyny. With politics, the 4th point would be a political philosophy that combines the liberal and conservative ideas into something new. Because it is a combination of two extreme opposites, the fourth point allows you to view the entire spectrum instead of being stuck as a third point somewhere between two extremes. In other words, the fourth point allows the spectrum to spin like a balanced wheel instead going back and forth like a balanced see saw.

5

The concept of 5 represents five things, but the geometrical references aren't really needed at this point. In terms of the Looping Spectrum Paradox, the 5th point would be anything inside or outside of the loop. In other words, the 5th point is needed to reference something that doesn't fit in to the nice little package that is set up in the color wheel. I figure this 5th point would itself be the start of a new wheel, with its own set of 4 points, and the whole thing would start all over again. This makes it a bit of a paradox, because from the perspective of the first four points, this would seem like a fifth point, but since it is separate it could be viewed to be on its own, and therefore it would go back to the concept of one. (In fact, any point could be considered to be a singular point, and anything more than that would be relative to other points.)

At this point I think it is worth noting that 3 is sort of the “most common” number here. 1 and 5 are basically the same thing, and can’t really be defined without some kind of frame of reference. 2 is useful for talking about things in basic terms, but as I said earlier, we know things are realistically more complicated than “one or the other.” 4 is awesome because it lets you complete a spectrum and see the whole thing as a circle, but you need to have a spectrum in the first place. That is where 3 comes along. 3 is a spectrum; it is the beginning, the middle, and the end. 3 is the magic number, it represents things like:

-past, present and future

-length, width and depth

-protons, neutrons and electrons

-it shows up as significant in most, if not all, major religions

-and every polygon is actually just a bunch of triangles stuck together.

Now, there are two more very important numbers (numerical concepts), and those are Zero, and Infinity.

0

The concept of Zero represents no things, or nothing. It has no geometric shape; no points, no angles, no sides, nothing at all! It is impossible to define the concept of Zero without something to compare it to. In other words, you need to have something to be able to describe nothing. Something and Nothing is a binary concept though, not a Zero concept. There is no such thing as a true nothing, because there would be nothing there to even say it was nothing. Even the word Zero is a thing, and therefore goes against the very nature of the concept of nothing.

∞

The concept of Infinity represents something without limit. In other words, it goes on forever. It doesn't have a traditional geometric shape, but it does have a symbol. (You probably know the symbol as an 8 laying down.) The concept of Infinity is familiar and has a well thought out mathematical definition, but we're still left wondering where the end of the limit could be, and it brings up some philosophical questions like "how could it go on forever, but then how could it just stop?"  In physics, when something reaches a limit, it tends to go the other way (such as with parabolas and oscillatory motion) but if there is no limit, it just keeps going. Considering how important spinning and cycles are in the Observable Universe, I think it is fair to consider that something that goes on "forever" would eventually find itself back where it started, much like walking around the globe would eventually lead you back to the start even though you only ever moved in one direction. When applying this to a number line, infinity would loop back around to the beginning and include every number. (this would make a number circle instead of a number line.) I feel like once it completed this loop, it would need a new name to describe it (perhaps eternity?), but the idea is that infinity is something without limit, and something without limit would eventually become everything.

The concepts of 1, 0, and Infinity have something in common; you can't define them without resorting to the concept of 2. (1 can only be defined if there is a second thing to give it a frame of reference, 0 can only be defined when referencing something that does exist, and if infinity becomes everything, it be defined by both the beginning AND the end.) This is because 1, 0, and Infinity are not like the other numbers. They deal with beginnings and ends, while the other numbers deal with quantity. This is a tough concept to explain, so it gets its own essay here. link