A glimpse of some of the miraculously reflective and self-referencing
symmetries of 9, seen over the multiples through 360. We might
call this the first circle of the weave.
The wonderful and well-nigh magical nature of this number signifies
that it and 3 are the best numberse to base early education upon,
for the mysteries of either will quicken the curiosity of the
student and the sage alike, being equal in every way to their
unique ways and needs.
1.
Contrary Motion:
Some of us are taught to recognize that the multiples of 9 proceed
by establishing a unique bi-directional motion, yet this is not
even the beginning of the wonders of 9’s weavings.
Given the list of the 1st 10 multiples, inclusive of of 9 [left
side of diagram]:
a: Counting down the left-side digits yields the list of integers,
in order. 1-9.
b: Counting up the right-side digits yields the same list, ‘upside-down’.
0-9.
c: The list of 10 multiples can be ‘divided in the middle’,
and it produces two reflective ‘twin lists’ of the
integers in order, following a U-shape. This implies the lemniscate,
the symbol of infinity
d: This contrary motion continues along the list of multiples.
In each set of 10, there is a ‘countdown digit’ [beginning
with the first 9] which ‘predicts’ which digit will
later be doubled where the lists meet. Thus ‘9 is prophetic’,
for it ‘always knows which will repeat in the list, long
before the repetition arises’. The predictor and the twins
it predicts are colored red in the left and right-side diagrams,
to illustrate this principle. The ‘doubled number’
is always 9 multiples away from its predictor.
e: The list implies a symmetry inversion between 45 and 54.
f: The musical and incredibly complex nature of this contrarian
interweaving cannot be over-emphasised,. for there is no end to
the unique ways in which this number will astound those wise enough
to persue it beyond the dimensions of structure, into those of
meaning.
2.
Reflective symmetries:
The central figure exposes some of the superficial reflective
symmetries in the muliples — by using a trineMath
toy where we sum each three multiples and examine the resulting
entities for their relation to the list that spawns them. Because
of the small sample-size, only the first few entities are traced
through their reflectives in the list.
Again we see the scalarly reflective rings revealed in trineMath,
and again the ‘two forms’ — one seemingly emerging
from between two multiples, and the other emerging from ‘the
place between the digits’ of a repeating self-reflecting
multiple — i.e: 144 — where the ‘inversion’
is between 4 and 4 — or 333.
3.
More than Meets the Eye:
There are a wide variety of extremely interesting occurances of important measures which ‘sum to 9’:
The number of seconds in one day: 86,400 = 1/10 the Sun’s diameter (864,000).
The value of the numbers in the Greek spelling of Pythagoras: 864.
Moon’s Diameter: 2,160 miles.
Mean Distance between the Earth and Moon: 216,000 Miles.
Approximate speed of the Sun as it travels through the interstellar medium: 21,600 mph.
Measure of the Platonic Month or Zodiacal Age: 2,160 years.
Measure of the ‘Great Year’ (one cycle of the precession of Equinoxes): 25,920 years.
All of these numbers sum to 9. But perhaps the most interesting of all is the ‘fine structure constant’ — approximately 1/137 of the angular momentum of protons and electrons remains uncomitted. This produces a fraction with the repeating decimal of 00729927, which of course sums to 9. The precise version of this fraction is known to differ according to various methods of deducing and applying it.
•••
Divide any whole number (which is not a multiple of 7) by 7 and you get a repeating fraction. The set of those numbers will sum to a number (27) which, when digit-summed will be 9. This demonstrates a unique relationship between 7 and 9.
i.e:
-15/7 = 2.142857 : 1+4+2+8+5+7 = 27 : 2+7 = 9
3275/7 = 467.857142 : 8+5+7+1+4+2 = 27 : 2+7 = 9
It appears that the same digits always appear in the fraction, and they always appear in the same order, however the order may begin on different digits.
