Qabbalistic Oddments 01

The Decimal Basins

Operations of cumulation-decimation reach the following end states or fixed cycles.  

Basin-0 (0): 0 » 0 …

Basin-1 (9): 8 » (36) 9 » (45) 9 … 9 » (45) 9 …

Basin-2 (1): 1 » 1 … 4 » (10) 1 » 1 ... 7 » (28) 1 » 1 …

Basin-3 (3): 2 » 3 » 6 » (21) 3 … 3 » 6 » (21) 3 … 5 » (15) 6 » (21) 3 … 6 » (21) 3 …

Decimal numeracy contains four implicit digital equilibria. Any cumulation-decimation process will fall into one of these, and remain there. They can be framed as abstract sinks or basins of attraction.

Each exhibits distinctive characteristics.

These can be classified by their power of capture. What – and first of all how much – does each take beside itself?

The result is an assignment of values, 3, 2, 1, 0.

As a bonus, captivation values can be adopted as ordinal indices.

They then acquire informative (or non-arbitrary) tags.

Their names say what – or at least how much – they do.

Basin-0 captures nothing. From it nothing enters or leaves. Uniquely, it coincides with its own index. Singularity is not unity, but the subtraction of unity from the unit.

Basin-1 brings the octave to novelty. Unity has no place in it, unless in the difference between eight and nine.  

Basin-2, finally, reaches unity, in two ways. Four and seven both feed it.

Basin-3, the summit of captivation, draws what it catches into the triad. Two, five, and six arrive there.

In this way decimal number falls into four non-arbitrary categories. Echoes of the Tetraktys might be noted.