Analysis of Map
The structure or collocations of the admittedly crude map - of Figure 1
- can be explained or justified. As I proceed with this exposition, which
unavoidably will be superficial and speculative at times, always remember
two things: that because "Branching" and "Oscillation, Rhythms, Cycles"
were the two scalors, the architecture of the entire map - either patently
or subtly - must somehow depend upon them; and that the unitary concern
of the mapping is with the simplest 2-D interrelatedness of canonical causes
of form.
North
In the north of the map, {V - Interference} occurs near {g - Oscillations
| Rhythm | Cycle | Reversion} because of the recurrent and often periodic
character of interference (e.g. qua wave interference patterns), especially
when the two are thought of in terms of the role they might play, and behavior
exhibit, in the genesis of shape. One can similarly understand the presence
in that cartographic neighborhood of {Y - Interweaving | Plexure}, which
has analogical and homological relationships to, and indeed interrelationships
with, both {g} (e.g. qua cyclical braiding and because the finite manifold
of interweaving tends to entrain finitary behavior) and {V} (e.g. interweaving
at once resembles and conduces to interference; in turn, interference often
triggers weaving and interweaving). The reason {Y} neighbors {L - Boundary
conditions | Boundaries | Limits} may lie in the role of the latter in
the exploratory searching and optimizing adaptations of a helically interlacing
strand, streamline, or generative singularity; and in the inverse derivability
of {L} from {Y}. {Z - Inversion} has both cyclic {g} and antisyzygial {G}
aspects.
East
Further east, {J - Averaging | Integration | Smoothing} might be near {L
- Boundary...} through the fact that it is in a sense what the latter is
all about. {d - Maximization} is often the product of the physical integration,
etc of a set of elements, forces, tendencies, effects, or the like (the
same could be said of {A - Adaptation | Facilitation}). Maximization is
an extreme whose significance is relative, and it causes form through its
very relationship to what is less or least, and hence through {G - Antisyzygies
(meetings of opposites)}. By definition {U - Interdifferentiation} is antisyzygial
{G}. Again, the nature of {N - Catalysis | Critical factors} lies in the
sufficiency of a small or minimal thing to trigger a large, maximal, holistic,
or total transformation. The same theme is operative in explaining the
propinquity of {a - Laws | Nomogenesis (the evolution of law or laws)},
since one thinks of laws in terms of a dominating invariant, or a mere
quality catalyzing or governing a quantity, or a dimensionless universal
of paradoxically or antinomically ubiquitous effect or reexpression (whereas
nomogenesis is but the piling up, discontinuous precipitation, supersedure,
self-action, or antisyzygial dialectics of such petty tyrants or godlike
qualities); and of {O - Chance | Circumstances | Randomness}, wherein infinitesimals
or mere coincidents may have all the catalytic power of a law. Another
reason why {O - Chance...} and {a - Laws...) occurred together, as supposedly
interrelated, may have been the very fact that the former is the exception
that proves the rule; what lies beyond law is chance, and it must be the
contingent residue of the universe - if it is anything - which law governs,
or at least constrains and limits; again, chance induces shape by violating
or permuting a normal or general law.
Incidentally, the location of {a - Laws...} at a point co-opposite to
the scalors, {g} and {M}, might be supremely appropriate, given that the
illustrative dyadic concept of unbranched stability suggests the very essence
of a law or the mode of action of a law in producing shape.
Of great interest is the fact that it was here, in the southeast sector
of the map of the Causes of Forms, that {Q - Information} and {R - Initial
conditions | Predispositions | Tendencies | Statistics} chose to appear
and that the two items materialized at one and the same point. Was this
for the trivial reason that both are perhaps minimally related to the two
scalors, {M} and {g}; or because of the rather more interesting possibility
that they are both NEGATIVELY related to the scalors; or because of the
even more interesting possibility that they are unexpectedly, and maybe
profoundly, INTERRELATED - in their nature, effect, or causation of form?
Certainly the contribution of information to the genesis of form may lie
in its ironically at once chance-like and law-like insignificance, background
criticality, or catalytic effect, or in its figure-ground duality. Information
disposes, it creates a tendency, it is perhaps the voice of a statistical
trend - though here we are back at the bathetic. Laws and randomness and
statistics and anomalies, even anisotropy: to be sure there is at least
one clear voice - one lacing melody - in this jungle.
Why Information?
Let me pause for a moment to comment on the nature of one item, {Q -Information},
which may be a source of some perplexity. Why have I included information
at all in what is supposed to represent a universal typology of the causes
of form? Isn't it a fundamentally unrelated category of thing? Or isn't
its role at least limited to cases where supervenient intelligence guides
its technological application or contemplates its transcendental relevance;
or to where eons of biological evolution have managed to make it meaningful
within the specialized systems of organisms?
The whole concept of information, in its technical formulation, is new
to science, being mere decades old. Even now, or especially now, we have
no idea what it is essentially or what its full scope or real limits may
be. Is it a method, a metaphor, a useful or misleading fiction, a way of
looking at things, an index of human knowledge or memory; or might it be
something more, perhaps even a natural phenomenon, a physical process,
or even the basic or quintessential stuff of the universe, being, mind,
or reality?
A. L. Mackay has attempted to relax, extend, and generalize the entire
idea of structure, and has drawn up a long list of transitions that are
currently unfolding from the classical concepts of crystallography to modern
concepts of a general science of structure. A table of these transitions
appears in the book "Symmetry through the Eyes of a Chemist", by Istvan
and Magdolna Hargittai (1987 VCH). It is so ideonomic, and relevant to
the causes of form in general, that I have a convenient excuse for reproducing
the whole of it, as Table 2:
Table of Classical vs. Modern Concepts in Structure
| CLASSICAL CONCEPTS |
MODERN CONCEPTS |
| Absolute identity of components. |
Substitution and nonstoichiometry. |
| Absolute identity of the environment of each unit. |
Quasi-identity and quasi-equivalence. |
| Operations of infinite range. |
Local elements of symmetry of finite range. |
| "Euclidean" space elements. Plane sheets, straight lines. |
Curved space elements. Membranes, micelles, helices. Higher structures
by curvature of lower structures. |
| Unique dominant minimum in free energy configuration space. |
One of many quasi-equivalent states; METASTABILITY RECORDING ARBITRARY
INFORMATION (PATHWAY); PROGRESSIVE SEGREGATION AND SPECIALIZATION OF INFORMATION
STRUCTURE. |
| Infinite number of units. Crystals. |
Finite numbers of units. Clusters; "crystalloids". |
| Assembly by incremental growth (one unit at a time). |
Assembly by intervention of other components ("crystalase" enzyme).
INFORMATION-CONTROLLED ASSEMBLY. Hierarchic assembly. |
| Single level of organization (with large span of level). |
Hierarchy of levels of organization. Small span of each level. |
| Repetition according to symmetry operations. |
Repetition according to program. Cellular automata. |
| Crystallographic symmetry operations. |
General symmetry operations (equal "program statements"). |
| Assembly by a single pathway in configuration. |
Assembly by branched lines in configuration space. BIFURCATIONS GUIDED
BY "INFORMATION", i.e., LOW-ENERGY EVENTS OF THE HIERARCHY BELOW. |
Note the four remarks I've put in uppercase, particularly the last.
These hint at a point of view which is also very much my own: that information
is really a UNIVERSAL NATURAL PHENOMENON, and one which may play a major,
overlooked role in morphogenesis and morphology. Actually this heterodoxy
is supported by many new discoveries, and much new thinking, in fields
ranging from theoretical physics and cosmology to chemistry, computer science,
and biology. So-called information seems to have something to do with the
fine-grain structure of the world, and with its large-scale structure and
laws as well; something very fundamental.
South
We have passed to the southwest now, where forms arise because things {X
- Intersect | Collide | Transect | Penetrate}; which is no doubt why we
are still shadowed by {F - Anomalies | Deviation | Discrepancy}. Forms
arise here because things and forms intersect, collide, overlap - interconnect
and bridge {T} - with one another and with the world; or simply owing to
{b - Leakage}. Even when intersection is prevented - because convergence
is insufficient or truncated, or divergence is excessive - forms may be
caused by simple {D - Angles}.
West
The MOST EXTREME angles may have or confer the shape of {C - Anastomosis}
or {M - Branching}. A thing or shape may turn into or away from itself;
or a set of things or forms may turn away from or back into one another.
The possibility of this occurring repeatedly nudges the causation of form
back toward the north of the map, with its oscillatory, cyclic, reversionary
pole {g}.
Of course branching can lead to anastomosis, and the latter presupposes
the former. Related to all this and to each other are {K - Bending} and
{I - Attraction}; e.g. the attractive causation of form tends to induce
bending, and when things bend together we at least SPEAK of attraction.
Likewise semi-equivalent are attraction and {S - Input | Addition | Gain
| Acquisition}.
The effect of the existence of {H - Asymmetry} is apt to be {P - Mathematical
chaos}, {e - Metastabilities}, {W - Interruptions | Gaps | Voids}, and
{B - Alternation}. Moreover, all are realistically and formally associated
with {V - Interference} and the scalor {g - Oscillations | Rhythms | Cycles
| Reversion}. For instance, let there be cyclic {W - Interruptions | Gaps
| Voids} and there may also be {M - Branching} or {C - Anastomosis}.
Here we have come full circle and the organic structure of the map is
now apparent in its complex and simple entirety.
Note on Scaling Method
You may have noticed that each upper or lower case letter labling one of
the 33 variables in Figure 1, has had appended to it a tiny pair of numbers.
What this set of 2 x 33 = 66 numbers represents is the set of decisions
I originally made as to the overall degree of RELATEDNESS, on a 9-point
linear scale of subjective weights, of a set of thirty-three Causes-of-Forms
to two of themselves in particular: namely {M - Branching} and {g - Oscillations
| Rhythm | Cycle}. The first number in each pair gives my estimate of the
relatedness of the variable to {M}; the second or superscripted number,
to {g}. It was only by the INVERTIVE expedient of treating {M} and {g}
as though they were scalors rather than scalees, and the original scalors
as being thirty-three scalees, that I was able to compute the adumbrative
graph. A rough VERBAL translation of the 0-8 NUMERICAL degrees of relatedness
on this scale would be: 0 = NONE/MINIMAL; 1 = VERY LOW; 2 = LOW/WEAK; 3
= FAIR; 4 = MODERATE/MEDIUM; 5 = GOOD; 6 = HIGH/STRONG; 7 = VERY HIGH;
8 = EXTREME/MAXIMAL. I often use this scale because it has what I consider
to be, at least from a cognitive point of view, an optimal set symmetries:
the triad of triads [(0,1,2),(3,4,5),(6,7,8)]. The effect of this meta-triad
is to lubricate intuition or to give maximal self-illumination to judgment
through a hierarchic, fractal, and group-theoretic device. It's exquisitely
meaningful, in short, and what the self-referential nature of consciousness
and intelligence seems to demand.
So the pairs of numbers enable one to instantly consult what is fundamentally
governing the map and to directly see the interweaving influence of the
two variables in the mutual dispositions of all of the thirty-three universal
generic Causes-of-Form.