Hypercross Dogmatics

HyperCross Dogmatics

by Kirby Urner
Originally posted: August 11, 1997
Last updated: November 13, 1997

image Synergetics does not buy into hypercross dogmatics.

The standard curriculum "ball of wax" you need to grasp, if you want to sound well trained in late 20th Century western (meta)physics, includes hypercross dogmatics, by which I mean the preaching that human sensory apparatus, with or without instrumental enhancements, is, by some flaw in its design, locked out of certain critical perceptual realms knowable only vicariously via sophisticated hypercross mathematics. Hypercross mathematics posits a fourth axis perpendicular to the three already mutually orthogonal X, Y, and Z axes.

On the face of it, this proposition of a fourth orthogonal appears patently nonsensical, positively absurd, but the hypercross dogmatists say this initial skepticism is a knee-jerk manifestation of a human failing, that because of our fallen state we simply have no experiential access to the mysterious "fourth dimension" (a space of four mutually orthogonal axes), nor to the many additional hyperdimensional realms, each characterized by yet one more nonexperiential perpendicular. The brutal truth, we are told, is we are perceptually trapped in "three dimensions". To understand what this means, we are to read a favorite tract of the hypercross dogmatists: Flatland by Edwin A. Abbott.

monk.gif - 1.6 KMathematics, on the other hand, is clearly able to demonstrate the "reality" of these hyperdimensional realms, and those with special powers do have a kind of privileged and intuitive access to hyperdimensional truth. People like Einstein and Penrose are known for their uncanny ability to perform as guides to these ethereal trans-experiential domains. So if you want to be acknowledged for your academic prowess and authoritative metaphysics (physics with an inventive, yet acceptable spin), you must school your imagination to accept this hard core orthodoxy of the hypercross, otherwise you will be banned from the inner sanctum.

As stated at the outset, Synergetics does not buy in to hypercross dogmatics.

Synergetics doesn't buy the standard "dimension talk" at all, let alone its hyperinflated, dogmatic versions. Once down to primitive conceptual volume, no further paring away of dimensionality is conceivable -- we don't have fewer dimensions than it takes to think of volume. Points, lines and planes all occur within this identical shared context -- are nonexperiential without it. And in Synergetics, the emphasis is on experiences, on special case phenomena, as the front and center means by which we come to grips with the generalized, exceptionless principles.

We simply have no experience of "Flatland" and all our attempts to experience it start with an irreducible, primordial sense of being observers within a containment -- observers with memories and an awareness of otherness and interaction.

But what about hyperdimensional sphere packing and its already proved relevance to many branches of science and mathematics? Surely we don't mean to throw out decades of useful research into higher dimensional polytopes.

The algebra and symbolic processing behind all the hyperdimensional sphere packing talk is useful programming, designed to operate with discrete locations in computer memory. Computer memory may be mapped using any kind of addressing logic, n-tuples, URLs, street names... with class methods defined to work in coordination with whatever invented schema. So to expand 3-tuple XYZ addressing to n-tuples, along with analogous definitions of 'sphere adjacency' (a term that remains operationally meaningful relative to methods for working with a 'dim 5' or 'dim 10' memory scheme) is not a problem, as long as we recognize the importance of metaphor and analogy within our operational mathematics.

The problem starts when we become fixated on the "literal reality" of hyperdimensional sphere packings and begin beating ourselves (or our students) over the head with the dogma that we are dumb or inferior creatures because we cannot physically see the "dim 24" spheres that our computer programs seem to suggest are "really there" somewhere.

image Locations in a logical space may have any number of addressing elements (i.e. coordinates) -- and the analogy between such a "logical space" and the space of visual-tactile experiences is embedded in metaphors. Connections between any two experiences, regardless of when-where they occurred, are edges, to which edges the properties of tension (pull) and compression (push) may be applied. A tetrahedron, in principle, consists of any four events no matter when or where these occur. So Synergetics certainly retains our sense of intervals, connections, relationships and of a logical space, a memory, wherein any number of data storage and retrieval schemes get used to identify and characterize the interconnected, discrete, special-case events.

Primitive System

The space of web pages is metaphorically such a polyvertexial structure of edges (links) and vertices (pages) -- a topology, a network. Synergetics is certainly not without its networks, its websites, its grand centrals, with connections converging-diverging everywhichway. But none of this experiential geometry of thinking requires us to buy that human experience is "trapped in 3D", or that the addressing schemes we require to spread our nets of hyperlinks throughout Universe must center around the hypercross: four or more mutual orthogonals.

In fact, Synergetics suggests that we not base our simplest spatial thinking on perpendiculars at all, let alone more than three. The paradigm network containment with the fewest edges and vertices is the tetrahedron, which is more suggestive of 60 degrees than 90 degrees, although it is true that opposite edges of the regular tetrahedron run at 90 degrees to one another (without intersecting).

Because Synergetics is a work in the humanities, semi-metaphorical verities are its bread and butter. Students trained in Synergetics are able to write and use computer programs which expand the usual 3-tuple XYZ addressing schema via n-tuples without getting so superstitious about the "hidden realities" which such operational mathematics is supposedly accessing altogether outside our powers to sensorially and experientially comprehend them. On the contrary, our senses are expanded by metaphor just as our mathematics is expanded by analogy and extrapolation. Our powers to visualize and otherwise experience are not being left in the dust owing to failings in the human design, but are keeping pace, because we recognize the symbolic nature of mathematics is not different in kind from the symbolic nature of the humanities, wherein hyperlinks have long sustained our stream of consciousness, even as our experiential networks have grown increasingly complicated and intricate.

Synergetics consists of hyperlink networks minus any investment in hypercross dogmatics. Synergetics is polemical against the standard "dimension talk" and therefore is free-standing outside the whole standard "ball of wax" which places such dogmatics at its core.

Exhibits re Belief in the HyperCross:

For further reading:

Synergetics on the Web
maintained by Kirby Urner