The concept of "dimension" varies with the namespace, and is often difficult to get a handle on. We get used to it in connection with a box having a heighth, width and a breadth, where these names are interchangeable (forget about "this side up" for now).
Greek metaphysics encourages us to atomize these attributes of a box into conceptually separable, standalone qualities, such that just-two- or just-one- dimensional worlds might have conceptual content.
But then every cartoon about a 2D flatland ends up with the usual observer/observed relationship (i.e. a viewpoint in a volume), because even if
their hypothetical world is flat,
ours never is.
So maybe it's time to do the Kantian thing and admit that "conceptual" and "volumetric" aren't that easily pried apart? Our idea of "dimension"
begins in volume, ab initio, shall we say.
So how might we make this more intelligible? Why not make the tetrahedron do the work of the cube in the 3D scenario, and why not say this most primitive system's topology is 4D, based on its prominent 4ness, in terms of both faces and vertices (the tetrahedron is its own dual, the paradigm inside-outer in Synergetics)?
This was Bucky's (
's) move (his way of getting 4D phased in to his namespace).
527.702 Geometers and "schooled" people speak of length, breadth, and height as constituting a hierarchy of three independent dimensional states__"one-dimensional," "two-dimensional," and "three-dimensional"__which can be conjoined like building blocks. But length, breadth, and height simply do not exist independently of one another nor independently of all the inherent characteristics of all systems and of all systems' inherent complex of interrelationships with Scenario Universe.
RBF made his 4D be "prefrequency", meaning no energy involvement, meaning eternal in that mathematical kind of way (the same way XYZ gets hall of fame status).
Then, any
real polyhedron, like a metal or wooden one you might kick or carve, gets to have all these
extra dimensions (a more physical spin
), the encompassing one being Frequency, otherwise known as time/size (with no strong difference between them, since Einstein), otherwise known as energy (convergent as matter, divergent as radiation). Specialcase events might be considered
4D++ i.e. "more than 4D".
This alternative namespace never become global to traditional physics or mathematics, i.e. there was no hostile takeover, either planned or accomplished. Mainstream mathematics had and still has ways to make topology work using the traditional 3D Space idea (with Time left to the physicists).
The physicists, meanwhile, picked up on Time (considered necessary for energy events), and got into complex coordinates (imaginary numbers), per the Einsteinian model and its progeny.
So both metaphysical nD-ism, and physio-energetic relativity (special and general), kept the 4D meme operational semi-autonomously from the U = (M)(P) = (4D)(F**3) synergetics meaning and namespace (F**3 signifies 3rd powering, and is canonically signified by a growing/shrinking tetrahedron, not a cube).
Which is and was just fine.
So long as we're clear on the namespace, we're unlikely to experience name collisions, i.e. alien memes
, lost and without a map, trying to get back home (how
a buckaneer might feel if transplanted to one of these other communities and left without friends).
Although 4D Studios is clearly vested in the Synergetics.4D concept, don't feel you need an advanced degree in the Humanities (e.g. philosophy) to play in our sandbox. We're not "anti mainstream" and traffic in other meanings of 4D quite successfully.
Just remember we might not be native speakers of your lingo, when you show up with your pet model, all prepared to explain it. So please have patience with us.
For futher reading:
http://worldgame.blogspot.com/2004/11/matrix.html