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discovered: 01.02.04 Last Edit: 07.22.09

dedicated to those whose eyes will see...

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

A: 1 + 2 + 3 + 4 = 10

B: ([3 + 3 + 3] + [3 + 3 + 3] + [3 + 3 + 3]) = 27 = 9

C: 1 + 2 + 3 = 6
[the first perfect number]

D: ... : 4 / 3 = 1.333... : 3 / 2 = 1.5 : 2 / 1 = 1 : ...

E: [ get recombinantly transcalar ]


” The Tetraktys [also known as the decad] is an equilateral triangle formed from the sequence of the first ten numbers aligned in four rows. It is both a mathematical idea and a metaphysical symbol that embraces within itself — in seedlike form — the principles of the natural world, the harmony of the cosmos, the ascent to the divine, and the mysteries of the divine realm. So revered was this ancient symbol that it inspired ancient philosophers to swear by the name of the one who brought this gift to humanity — Pythagoras.”

— Attributed to Iamblichus


It might not seem like much of a feat to draw a triangle and make some dots on it, but knowing what to do and teach with such a toy is an entirely different matter. Long ago, this seemingly simple figure engendered a cognitive explosion in those able to understand its mysteries, and that explosion led to entirely new ways and speeds of learning. Properly understood — it still does.

We don’t have a decent concept for the explosive change that comes from intimacy with this and similar toys — it blows things together, magnifying their wonder and practical potentials in our understanding and experience. They act like enhancements to one’s general intelligence, rather than enhancing a specific branch of formal knowledge-prowess. This process proceeds exponentially — gaining velocity and profundity in phase-leaps without giving sign of having any ‘end’.

There are ways of learning near at hand that render the wildest hopes of human education impoverished in comparison, and we are meant to have common access to them together, in our moment-to-moment lives and experience. When our free access to these ways and toys of learning is missing or obscured by mimics, our experience of human unity, hope, liberty and understanding are always missing with them — and the perennial outcome of this state is atrocity.


There are a lot of invisible dimensions whose primary function is transconnective, and where we tend to experience the physicality of ‘things’ as the arbiter of separation — the reverse is actually more generally true. The appearance of physical separation is secondary to re-unification result — yet this is difficult to detect. ‘The internet’ is one example: we ‘use’ the connectivity of many machines in series, without knowing anything about the machines we touch, or the connections — we only ‘notice’ the product: web pages like the one you’re reading. But ‘the internet’ doesn’t exist as a static entity — at all. It’s about a new way of access — and this way makes grand use of diversity of members — what we call separation.

By demonstrating novel ways into noticing these invisible ‘living dimensions’, the tetraktys offers a foothold in a universe that exists between, around, beneath, above, before, behind with(in) and after the dimensions we are familiar with. This ‘place of between and before’ is actually a unified being, comprised of forms of intelligent life we have no reasonable names for — yet. Some have called them angels, but to mathematicians they are angles — obviously we are at least moderately confused about them.

In physical experience, our senses are direct, and grant meaning-precedence to separation, local identity and specificity — whereas the the senses we have in connectivity domains are oblique, and grant meaning-precedence to unification and generality. The tetraktys aids us in gaining access to and understanding of these oblique senses, and offers us a further expansion: re-unifying these two universes to awe-inspiring effect.

The result is a transentient transport directly to the heart of a living library older than the physical universe. No joke.


Being a toy of generalization, the tetraktys is a visual hypostasis of a holophore — a playful model of ‘everything at once’, which has the power of unifying dimensions of knowledge we normally consider separate: numerism, music, geometry, dialectic, and the study of bodies in motion. Effectively, Pythagoras discovered the unified field theorem’s sources — and was determined to see that they were not lost once we had access. As a teaching-model, the power of this toy lies not in what it brings, but what it takes away — it removes divisions between multiple simultaneous domains of knowledge and learning, by providing an exceptionally general stage upon which various shape-based parables of the various perspectives on relativity may be extemporaneously demonstrated.

One of the most important functions of the tetraktys is to provide a visual metaphor of emanative processes which, while appearing abstract — are not. Its structure conserves a model of ‘Four Special Dimensions’ — three of which simultaneously ‘emerge’ as the universe we exist in and perceive — almost as if their ongoing song caused physical, cognitive and temporal manifestation as a kind of magical living ‘exhaust’. These dimensions are represented by the four rows of dots in the tetraktys:

The first is ‘totally unified’, and all possible dimensions emanate from it in a manner akin to the exhaust of a musically intelligent explosion. This is a position we might call ‘a transentity’. One of the things it may be modeled to represent is a meta-being who exists as a living record of the summed experience of every moment of every organism in all of time (including the future).
It would in this case also represent every possible combination of these moments, as symmetries (groups).

The second dimension, an organ of the first, is the primeval source of the essences of polarity. This is the first three points, top down — a trined angle.

The third, an organ of the first and second, is an explosive interpenetration between the first two — which exists in a single dimension. This dimension has a body and and a polarity rod. This is the third row, which exists as if the first three points were pressed into a single dimension, becoming a line, the top one in the middle.

And the fourth, which is an organ of the unity of the first three emanations, is our universe — the universe of matter, or mother. In our universe, spherical entities arise as a result of seemingly impossible forms of ‘rod spinning’.


Understand this: extremely generalizeable models of reality are what science claims to be seeking — but once we start naming things and making laws — we’re trapped in the opposite universe: specificity. And it’s a universe of eye-doll-o-trees. The dolls of human ideation are made to dominate the (relatively) miraculous reality of Nature. The cognitive effect of this game is analogous to the outcome of me preferring a sketch of my wife over actually knowing and relating with her.


learning toys

I think that human beings used to be more commonly aware that the stuff we call knowledge is a toy, that some toys are better than others — and that some species are inherently dangerous.

There are ways of knowing which mimic sophistication when their only real function is a form of more or less predatory self-preservation — and nearly all of these modes are incredibly aggressive in multiple dimensions. With a few circumstantial exceptions, ways that aren’t aggressive can’t compete — and thus inherently crippling ways of knowing have come to own and essentially dominate our world and our human experience. I am fairly confident this has long been the basis of the relationship between animals and formal knowledge in general, and between our species and representational sentience in particular — however I am not convinced that this is necessity, or even the nature of the relationship. The idea that this is ‘human nature’ or somehow intrinsic to us as cognitive organisms and groups seems absurd to me due to the fact that individuals and groups rarely evade the social and cognitive obligations implicit in their shared culture long enough for us to determine ‘what their nature is’.

In crafting and teaching the tetraktys, Pythagoras was correct in believing he had discovered an antidote to this problem, and he was onto something with this innocuous toy. His goal was to undo and surpass the problems of naming and dogma, without necessitating the sacrifice of poetics that is the common activity of science. By asking us to set emotion aside, science becomes a mechanical hypostasis inviting the consistent martyrdom of meaning and connectivity for the sake of formal knowledge in a given system. When Pythagoras finally found his way beyond the traps which had already too long bound our species, his response was to return with a key that would itself become explosive. There is, after all, a wise way of learning which can grow faster in human populations than its mimic. Without being warlike, this way can overwhelm the opposition through a strategy of terrain-denial. He knew that if he ever succeeded in planting even two or three seeds that could survive together, those two or three would have the power to rescue not only the planet, but all of human history.

What he was gave us is nothing like what it at first appears to be. This is why people were swearing by his name for having brought this simple diagram into the world of human experience: a toy which none could own, and anyone with a stick and some dirt could instantly play with. It requires no manufacture — it cannot not be stolen or co-opted, and ‘giving it away’ causes the giver and the gifted to become ‘exponentially more wealthy’ — in ongoing progressions.

Imagine that.



It should be noted that the tetraktys, as a model of reality (and beyond) is akin to the Tree of Life, which we associate with the branch of knowledge referred to as Kabbalah. I am uncertain whether Pythagoras took the basis of the Tree of Life and generalized it into the tetraktys, or whether this toy arose from his own travels and experiences across the veil.

One thing that is clear is that anyone who makes this journey comes back with something similar — yet entirely unique to their person and nature — thus one person could return with ‘The Tree of Life’ as a toy of the mysteries across the veil, and another with ‘the tetraktys’.

Each model is unique, and each has useful features. The tetraktys is so simple in basis that it avoids many dogmatic traps. There are no words or dogmas — it’s simply there. We can thus recombinantly paint upon it in a way that is definitely not allowed when the ‘jewels’ are ‘already filled’ with meanings or relationships — as in the Tree of Life.

A brief but insightful essay on the tetraktys can be found here. HipBone games offers novel learning toys incorporating tetraktyk principles.

The School at Athens — Raphael

”Sisters and brothers in quest, I implore you to righteously perceive that without the C the Supernal Decad is Dead.

Seeing this is so, we must discover together the meaning and precedence of this strange C.

It is light — but a form that moves and breathes — lives, and knows. A way of moving, in unity — through all beings, places, times, speeds and forms — at once.

The Achad (unity) shows us that C emanates from the Trine of A and becomes the Breath of the One — H in the Center. From this is born the Achad-e-my — the Uni-ver(se)-City — oneSongCity — which we here endeavor to give birth to and sustain in the experience of the people of our world. Never allow this C to be removed from the Decad! — for this is the road to blindness, death and despair for the children of Terra.

The C, you see, is the Center of the Decad itself — remove it and all Collapses — just as any person shall Collapse if ye stifle or deny their soul. Being the Center — it is the place from which all else emanates, just as the 3 invisible dimensions which give rise to the symmetry of trees, waters, , numerism, words and flowers.

This C plays a marvelous and Crucial game — it Chases itself, as though attempting to reCapture the first instant of all universes, again, in any instant of any universe. Creator, Center, Crucis, Chalice, and Crown — all emanate forth from the source of this C.

And yet we have not begun to understand, and all we have surveyed are but toys with which we hope to gain the necessary speed. Let us never Cease at any one token or toy — but employ them only to surpass all that hath come before. Let them dissolve during our wise pursuit of their sources, for having led us far beyond our expected destinations.”


Ci v iC

contents and concept © d. de stefano, 2004