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Sunday, 30 June 2013 12:24

Where do numbers come from?

The short answer is where everything else comes from.

For a longer explanation we have to start with the concept of origin. The most comprehensive, expansive/compressive concept possible must be in the form of a sphere; it is undifferentiated and concentric without scale. The sphere is unity, it is whole without qualification, without inner or outer boundary, in all direction. Unity contains units, where each unit inherently contains unity.

Two arbitrary diametrically opposite point locations on a unit sphere of any size, when compressed towards each other creates tension inward and movement outward at 90 degrees to the direction of movement retaining spherical volume. A sphere to circle transformation reveals differentiation without adding or taking anything away. This can be demonstrated by rolling a ball of clay and squishing it flat using your hand.

In this spherical transformation there appear three congruent circle planes; top, bottom, and the circle ring connecting the two. When considering individual parts there are two edges connecting the three planes making five individual congruent circle parts. There are seven properties to the disc when considering the internal volume and the space surrounding the circle unit. The concept of a unified whole suggest no surrounding space, no taking apart or separation, only expanding potential into and out from any location. Nothing is added or removed through compression, only a flattening spherical displacement showing form differentiation.

The sphere to compressed disc from which an image is then drawn loses the dynamics of spherical force to the 2-D symbol, a static stand-in to which we assign meaning. Images that appear on paper or screens are always a representation of something else. A holographic image projected into space does not embody energy uniqueness, the dynamics resides with the original. A reproduction will never be the original no matter what means of sophisticated technologies are used.

 

 

                                         yinyang2c

 

Circle/sphere origin is pattern to countless multiple copies from which are formed expressions of all kinds; it is a process of divisional revelation. The circle disc is a dynamic self-referencing system of spherical unity with infinite symmetry. Numbers have not appeared, only multiplicity of structural pattern in-formed with differences.

Working backward from the image towards spherical origin gives another perspective. Draw a circle and cut it away from the paper making a 3-D circle disc. It becomes dynamic that can be rolled and spun revealing countless rotational axis. Curving the circle around and touching any two points on the circumference will form a curved open conical plane. When the two points touching are diametrically opposite each other the curved plane becomes an open cylinder; a special cases cone.

Regardless of which two points are used when touching, crease the circle flat. Alignment occurs dividing the circles equally into halves. Rotating on the crease in both directions reveals a spherical pattern of movement reflecting origin. Any fold less than half (two points on circumference not touching) will lack alignment to origin.

Alignment shows duality in unity of three (1+2=3.) These numbered parts do no happen separate from the circle. The crease is a line of symmetry, a diameter, an axis of rotation; a multifunctional straight line with two end points on the circumference; a tri-unity system of three individually identifiable parts, four points, six relationships revealing a tetrahedron pattern of movement, and much more if you include all five circles. This all happens simultaneously. Numbers are used to spatially separate partial events.

This folded straight line crease is the symbol of our first number (1). Number one is the first mark of self-referencing movement of unity. From one line of symmetry we surmise an infinite number of  symmetries and countless relationships in combinations and arrangements. All possible combinations of number functions are coded into the relationship of one straight line and one circle (the first of an infinite number of folds.)

Without unity of the circle the idea of one isolated from context is non existent. Yet separation is used to develop abstract relationships by adding, then subtracting, multiplying, and dividing to get a larger and smaller segmented number scale. We teach a unitized system of separated numbers in sequential ordering from simple to complex. We have assumed this is how it is.

Addition, subtraction, multiplication and division carries the assumption of building from nothing, zero (O) to one unit towards developing complex system of calculated functions using multiple units. We accept units coming from nothing with little understanding about how and why or there being no logic.

In retracing the process from sphere to circle then first fold we see an opposite sequence of functions to what we are taught. First is circle/sphere unity, wholeness through compression shows origin and with first movement is a folded division that generates a multiplication of individualized units that can be subtracted from and added to each other. Unity has not been destroyed, there is no separation.

Division, multiplication, subtraction and addition are observed when starting with unity where a process of ongoing interrelated complexity is revealed all within the circle. Through observation and thinking about what we see about what we do when folding the circle, numbers are then symbols signifying inherent differences that are acted upon in relationship to each other.     

Nothing exist in separation; only in context. One is an abstraction. Two in separation does not exist. Only in context does relationship of two ones become three. Starting with unity the one line of division is not separate from the act of dividing in two parts. In context there is no separate between one and two, they are three; structural pattern. Traditionally we abstract one and two from three using the circle as a symbol for nothing from which numbers mysteriously emerge.

There is no conflict; one illustrates the abstraction of 2-D and the other reflects 3 dimensional reality. Both systems are correct. One is part of the other. Both taught early at the same time would advance understanding of geometry and mathematics with benefit to other disciplines. By introducing unity into a unit based system would expand thinking towards a more comprehensive way of understanding the nature of where we are, who we are and maybe get closer to why we are.

Looking at a larger picture is simply a bigger unit. The syntheses of many units of all sizes is not unity. There is no summation that gains the Whole. When you start with the whole it is all there, mostly unrealized and through a principled process of generation potential is endlessly revealed within unity.

There is no ultimate boundary, no conditions of confinement to circle unity. The circle demonstrates, order, structural relationship, and principles that are foundational to all subsequent evolving of information. This does not happen with polygons or polyhedra, no amount of numbers can account for it.

We can say we invented numbers, or maybe discovered them, possibly they are inherent in how the mind keeps track, or it is an abstraction of what occurs before number recognition later constructed as language, maybe numbers were given through higher insight, or by creatures from off of this planet coming from other worlds. Nobody now was around for the first couple of numbers so it is pretty much guess work about what it is that fits the accepted version of the number story. It is demonstrated that numbers have a context. How do we substantiate they came from nothing?

Where do your numbers come from?

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