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