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[from the Synergetics on the Web site:
http://www.teleport.com/~pdx4d/synhome.html]

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                  Synergetics
                    Versus
             HyperCross Dogmatics

               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 
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. 

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. 
                                        
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 HyperCross Dogmatics: 

4-D Dreams: Flatland and Star Trek? 
Quest for Utopia 
The Fourth Dimension by Cliff Pickover (is God 4-D?) 
We cannot see the multidimensional reality because our senses 
    are limited to three dimensions 
The tesseract animation on Tom Getty's page really is fine 
    (you don't need to join a religion to appreciate its great 
    works of art) 

For further reading: 

The meaning of 4D in Synergetics 
FTP: On Redefining "Dimension" in Synergetics (rich text format) 
     or MS Word 6.0 format
More on "Dimension" at the Swarthmore Math Forum 
Let's End the Reign of Hypercross Dogmatics (newsgroup posting) 
Re "engineering mathematics" within the Fuller School 
      (Swarthmore Math Forum) 
The Geometry Junkyard (lots of links to hypercross junk) 
A short review of Life by the Numbers (book and PBS TV series) 
Flatland by Edwin A. Abbott 
Investigations into Linear Algebra Concepts... 
Hypertoon Synergetics 
GST: Proposed New Low Level Associations for the �System� Concept

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[original version with graphics and activated hyperlinks at
http://www.teleport.com/~pdx4d/hypercross.html]


---------------------------------------------------------
Kirby T. Urner  http://www.teleport.com/~pdx4d/kirby.html
4D Solutions    http://www.teleport.com/~pdx4d/  [PGP OK]
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