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!666 ^ 777?

The presence of profound patterns of symmetry within the system of integers leads to an unexpected series of understandings and perspectives which change what numerism is and means for those willing to explore these matters deeply in a personal way. As one may imagine, changing one’s relationship to numerism radically affects how we perceive and assemble identity — the very basis of conscious and linguistic awareness.

As it turns out, the gates to this exploration are the numbers 3 and 9, long held to embody principles and perhaps understandings of transentient or transhuman origin. To begin the quest that will allow us access to these mysteries, we must see the incredibly suspicious relationship of 3, 7 and 9 to the series of integers, and particularly the decad, however we may choose to define it.


trineMath - a recombinant arithmetic

The first nine(ten) numeric entities in base 10
— Father’s mode.

[click to enlarge in a new window]

In the diagram above, we have organized the first 10 counting numbers vertically (we shall later explore some variations on this theme). For the sake of our experiment, we presume that each ‘set of 3 numbers’ is related. Thus, we circle them to indicate this relation. To the right of the circle, we write their sum, or, if they do not sum to a single-digit number, their digital root. This is the number obtained by summing the digits of the group; if the sum has multiple digits these are summed until a single-digit result is produced. Thus: 12 + 42 = 54, 5 + 4 = 9 (the digital root of 54).

Further to the right, is the number obtained from this operation ‘plus one’. This represents the act of ‘counting that which unifies the digits’ — in this case, our circle.

We sum the digits, top to bottom, extracting the digital root where necessary. When complete, the diagram above illustrates the relationships made visible by our experiment. Each set of 3 has a digital root of 6. This number becomes 7 when we count that which collects each digit into the equation (our circle). We then continue the process, adding these sums top to bottom. The digital root (when we begin at 1) is always 9. But as we proceed beyond the first decad, we find that the number that generates this root changes in a predictable, yet strangely meaningful way...

human: counts [5] 10
animal: counts [6] 18->9
angel: counts [7+] 21->3+

count all three at once


father’s math


mother’s math

no-one’s math

Notice that none of these patterns ever deviates in its sums? This implies an orderly affinity of trines throughout the natural numbers.

[click to explore any lineage]


This is the braid [the bracelets] expressed by the orderly unreduced sums of the mother/father trines.

A non-ordinary song of trinary symmetry — written into the entirety of the regular progression of integers:

[click to explore the ‘bracelets’]


Digital Roots

I realize that at first introduction this process appears non-mathematical — since it relies on the utility of digit-summing which is commonly considered to properly belong to numerology and kabbalah, rather than mathematics. Because this numeric device has nothing to do with accounting and is useless in enumerating the war-dead, we’ve been encouraged to conveniently neglect the living sources of the mathematical operations we guide our thought and technology with. Yet we must return to this ancient stage with new eyes — for within lies the key to travel of a form we cannot yet imagine — and perhaps an egress from 10000 years of atrocity inspired primarily by the broken dolls of what was once a celestial science.

The mathematics as we know and practice it is a minuscule and abstracted shaving of what our ancestors knew explored through the manifold lenses of numeric relation. Because we have developed profound sophistication in manipulating abstract entities we have forgotten that the stuff we manipulate is not now and never was abstract. There is no instance of an abstract number anywhere in the many universes — except in the human imagination.

Implicit in numeric reductions are a set of recombinant lenses which reveal mathematically demonstrable relationships — in a dimension of relation our species has thus far ignored — primarily because we rely upon linear methods which are insufficient to reveal these relationships. Methods ‘more like us’ are faster and more accurate — and they rely upon a multidimensional and multiply-scalar perspective to accomplish this seemingly impossible feat.

It is my hope that this essay may serve to re-inspire us to seek a relationship with numerism which is founded in the wise comprehension of multiple sources and ways of understanding — for in these seemingly primitive methods lie a vast and as yet undiscovered universe.


There is a 3 and 9-based symmetry in the natural numbers which requires the lens of digit-summing to adequately reveal or explore. In recognition of possible formal objections I ask you to favor with close attention three related facets of evidence which I have crafted in the hope of allaying these and other similar concerns:

1. The perfect numbers. In these trinary summing sieves developed around the natural divisors of the perfects, the digit ‘supporting the top’ always reduces via digit-summing to 9.

2. The reflective elements in the sums of the trines, expressed as fractions where double, and explored to their repeating-points. The symmetry of 9 is omnipresent in these perspectives.

3. The sequence of all integer-based bubbleForms of this nature [2-12] over the range of 0-1000. Each produce startling symmetries formed only upon trines and nines.

o:O:o : o:O:o : o:O:o

[ s ym~me trined-angle ]


to the mathematekoi, the akousimatics...

The School at Athens — Raphael

contents and concept © d. de stefano, 2004