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.

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:

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. |

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.

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.