Multiplicity: The Idea of One (One Circle, Many Circles)
Ilexa Yardley 15 November 2009
One thing we can agree on as observers: there is multiplicity in (of, within) observation. Some call multiplicity variety. There is a multiplicity of multiplicity, or a variety of variety, all around us.
Where does this multiplicity or variety come from?
One is two is the basis for multiplicity as any reproduction clearly shows. That is, to make one you need two, at least most of the time, where two is normally thought of as two ones.
Two can also be thought of as a proxy for many. That is, once you have two, you will necessarily have many. (Most of the time can be all of the time if we decide to observe this as another two as one.)
There is one man and there are many men. There is man and there is woman. So, there are two (at least) kinds of multiplicities. Man, men, woman, women, are symbols for the idea of multiplicity which is eventually variety (many men and women, all species).
One is two and two is many and many is one. A circle (and also a line). We can view any line as the diameter of a hidden but mandatory circle, and any circle as the circumference of a hidden but mandatory line. Either the circle or line is one with the other a two (or many).
In order to observe multiplicity, the idea of more than one, we must agree, at first, or as a foundation, or basis, to (on) one. Without one we cannot have more than one. So, one and not one go together. They are in a mandatory (circular) relationship.
Normally we think of one and not one in a linear relationship.
That is, we think that in order to have more than one you start with one and then you continue on ad infinitum into infinity: one, two, three… This would make one an absolute, not a relativity. Counting, the way we normally do it, is linear. That is zero is not infinity.
So one big question is: is not one always zero? Another is: is not one always infinity?
Most would say, no, not one can be zero or not zero, or any other number, or idea, or symbol, as long as it is not one. But a smart aleck might come along and say, you can join any group into one (any multiple) by calling it (observing it as) one.
For example, a couple can be viewed as (observed as) one. A city can be viewed as (observed as) one. So in order to observe multiplicity we must have one but we are not relegated to (stuck with) one.
And one and not one may not necessarily progress in a mandatory line; they share a linear and a circular relationship. Because the line is always the diameter of a circle, a two is always one, and, because all two relationships are circular, a one is always a two. So what is one and where does one come from?
There is a circle (mandatory) between one and not one. There is also this same circle between any two any-things (every two every-things). We may not be able to see this circle. It may be totally invisible to us (as observers).
However, closer examination reveals circle (even when it is not present) is the foundational (only) observer. Circle, then is one.
This means one in a circle with not one mandates circle as the relationship between zero and infinity.
That is, from the circle’s point of view, or, if the circle is observer, zero and infinity are (is) the same.
This makes one a relativity (purely).
Any and all observers and observations, then, begin and end where zero is infinity (pi). This is how we end up with multiplicity and (or) variety (unlimited number of entities comes from an extremely limited entity (pi)).
Circle is a name given to a geometric entity which is also found as a line because it takes a line to make a circle and a line is also the diameter of a circle.
A line can be open or closed, wiggly or straight, but a line is always, eventually, both a circumference and a diameter of a circle. A line connects two circles (also known as points). The idea of point, if it is real, has to be circle (any point must have a diameter making it a circle).
So this means there are no lines without circles and no circles without lines and point is another word for circle which is another word for line.
Without the invention of mathematics we would not know circle (line) (point). Without the invention of mathematics we would also not know two (one) (zero, infinity). And, similarly, without the invention of mathematics we would not know one (not one) (many).
We take counting for granted because our culture and our history is based on counting. Counting is based on man’s ability to separate one entity from another. That is, if we could not separate X from Y there would be no counting (and no men).
To separate X from Y we need an observer (you). To separate X from Y we must join them.
In science terminology:
X ≠ Y, X = Y, X o Y
0 ≠ ∞, 0 = ∞, 0 o ∞
Different symbols say the same thing:
X > Y, X < Y, X <>Y
0 > ∞, 0 < ∞, 0 <> ∞
We can call X and Y you and me (or we and I) (or any two names). The name is totally irrelevant, even though we have cast names onto all kinds of things. We take the naming process for granted (that is, we believe in our names). We ignore the notion of one (circle, line, point) when we surrender to a name; however, name is dependent on the notion (idea) of one.
Language, like mathematics, is a symbolic system that is useful to man (and to all entities). Ordinarily we think only man invents (and understands) language and mathematics (symbols). However we have no way of proving this.
Animals and plants make noise, and animals and plants can also separate themselves from their enemies (and friends, other animals, plants, etc.). So animals and plants also use language and numbers, even though their language and numbers is indiscernible to us (we can never be the animals and plants we observe, or we can never fully understand our observations once we separate ourselves from them).
Language and mathematics are conveniences, but they are also based on something. So what is this something? Again, it is circle.
We can see the circle as a basis for both language and mathematics because the circle is a basic unit which shows up (must be) between any symbol and the entity (or process) it represents. That is a name comes from the entity it describes and the entity it describes comes from the name (it is impossible to say for certain what comes first because they are in a circular as well as a linear relationship).
Any linear relationship must also (always) be circular.
The line is also a unit, and the line, as diameter of a circle, can be viewed as (observed as) a circle. So we can stick with circle as a convenience, the same way we use the idea of one as a convenience.
When we name something, we are assigning an idea to a symbol for convenience.
When we agree on a name we are joining a two into one. The naming process is circular. That is, there is no name without entity and no entity without name and the name and entity are joined (and separated) via circle. So circle is the basic name (number) beneath all others. Circle is the basis for naming.
This is obvious, even though, at first, it is not at all obvious. There is a multiplicity of names. We never agree on a name fully (we invent our own names for things, called thinking, and then writing or speaking). That is, we move and make noise in a certain way and then we give it a name (a symbol). All entities do this (it is their process) (they make noise).
We are given the right and the responsibility to name things in our own way by the circle. That is, there is a mandatory circle between us and our observations, whatever we name them. A multiplicity of names comes from one name. Circle is one name for many. It is a descriptive name because it is foundational (it is real).
When we create a name (language, mathematics) we are assigning a symbol to an idea (entity or process). The symbol is a short cut or an abstraction or a representation for an approximate entity or process (the only accurate name for any entity or process is circle).
Circle is the only real idea. Within circle lies circumference, diameter, pi. Pi holds the circle and its diameter together. This is where we begin our one into two idea (entity, process). It is also what joins (separates) a name to (from) its entity. It is also what produces a line (separation, joining).
Multiple (two) is the only one (we are mandated into multiplicity or variety because there is no one without two). So, therefore, duplicity (multiplicity) is singularity. Duplicity (multiplicity) is the singularity we search for (and have now found). This all comes from circle (one circle, all circles) (one circle, many circles).
Because diameter is circumference and they are held together by pi, multiple is singular and singular is multiple. One cannot occur without two and two is a proxy for multiple.
Multiplicity (duality, singularity) is reality (many circles one circle). Multiplicity (duality) is singularity.
Circle is singularity, duality, multiplicity (one, two, three; circumference, diameter, pi).
All symbols (words, numbers) are names (multiple) for circle. Any name can be changed into any other name (via circle).
If there is one there is necessarily many. If there are many there is necessarily one. There is a circle (and line) between many and one. Many comes from one. One comes from many. This can occur in one or two directions. You (the observer) must decide (determine, observe).
Pi (circle, line) is the only observer (you, I).
(There is a mandatory circle between any observer and observation making circle the only observer (observation)).
Observation (observer) produces multiplicity.