Duality – A Principle of Numbers

Shiva the Mountain worshipped by Nanda – with thanks to Deepak

We begin with 1. The Great Collective. Nothing exists outside the One. Everything is contained within the One and measured by the One. There’s only One of you and only One of me. Yet somehow we are One in one another.

As soon as number begins it divides into two parts. Odd Numbers and Even Numbers.

1 2 3 4 5 6 7 8 9 10 11 12

Every number is either odd or even. It cannot be both. It is one or the other. After this come many divisions into types, Evenly Even, 2, 4, 8; Oddly Even, 6, 10, 14; Evenly Odd, 12, 20, 24, 28 and the like.

Odd numbers also have divisions but really there are only two types of odd numbers, Prime numbers, divisible only by One and the number itself, and all the other odd numbers. Prime numbers start a new series in numbers, they bring a new pattern to order.

But this duality springs deeper. Arithmetic gives rise to two applications of number, measure and comparison, or Geometry and Ratio.

When we turn to Geometry we find the square is delineated by four corners. A square of one has no centre. It is an entirety of itself. The square of 2 has four corners , but it also has four midpoints, one on each side, and another in the centre where the four corners meet. This makes 9 which is the next square in sequence.

A Square of One has no centre, A square of two does.

When we look at 9 we find it has 16 points, or corners.

Square of 3 (9) with 16 loci

And so the pattern repeats the odd numbered squares have an even number of points, or corners to the constituent squares, totalling the next square number in sequence. The even squares similarly have an odd number of points totalling the next square above that one in sequence.

So just like numbers themselves the sequence of square numbers bounces from being even to odd or with a central square or a central point. An odd numbered square has a central square, an even numbered has only a point.

A series of cubes, 1, 2 and 3 with corners

The same is true for cubes. The cube of two is 8, and 8 has 27 corners, points or loci delineating it. I will leave the rest for you to fathom.

So it is the Universe breathes in and out between Being and Becoming. Being present or absent. It breathes and expands.

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