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Hierarchical structure is most obvious in organic and higher systems . Cyril Stanley Smith discussed hierarchical order in
inorganic
systems. In a historical note he said that one of the most surprising results from applying
x-ray diffraction to the study of crystals in 1912 was that:
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Most inorganic solids contain no molecules, or rather that the whole crystal is the
molecule, In sodium chloride, for instance, there is no specific pairing of sodium and
chlorine atoms any more than there is in solution; the atomic ratios called for by that
masterly summary of Daltonian principles, the law of simple combining proportions,
are in most cases due to the exigencies of charge and the geometric limitations
imposed by the crystal lattice, not to the formation of molecules.
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Since that time, our knowledge of crystaline structure has increased greatly and with it a new
vision of crystals has emerged. In a typical crystal, he explained, "The outlines of the crystal
grains are more reminiscent of the froth on a glass of beer than of geometric polyhedra." He
went on to explain why that is:
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Here it should be noted that a single individual, whether an atom, a crystal, or anything
else, can take whatever shape is natural to it, but in an aggregate, the individuals each
share an interface with another one in a zone of mutual conformity. Moreover, unless
some action occurs across this interface which results in an internal change in the
structure of both of the contacting units there is no basis for structural aggregation.
Although atoms may appear as "hard and shinly balls" when viewed on a large enough
scale, they attract each other only because they possess an internal structure that is
directly influenced by their external environment. This interaction between inside and
outside as seen by an individual is the very basis of a hierarchy of any kind whatever.
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Grain boundary is not recognizable in groups of a few atoms. It is the property only of an
aggregate large enough for divergent group properties to emerge. In any sufficiently large
array there will be areas of local departure from order (due to entropy or to the randomness of
its history), At a high scale of resolution the boundaries are fuzzy, their existence a question of
definition involving connections beyond the normal field of the viewer. At a lower
magnification the boundaries will appear sharp and distinct, at still lower magnification they
disappear again. Smith continued:
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In systems of any kind, change depends on the formation and/or movement of
interfaces. A polycrystalline aggregation can arise in a thermodynamically unstable
environment from either the discontinuous nucleation of new crystals and the
enlargement of these until they impinge upon each other, or from the gradual
condensation of imperfections to leave more perfect regions.
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The former change is a first order or high energy change, the second, a relatively low energy
change. The result, however, may be indistinguishable since the process ends by the
boundaries adjusting to their own needs. Smith gave two examples:
In a pure metal the first corresponds to the growth of crystals from the liquid or from
another (unstable) crystalline form, the latter to the recovery of a cold-worked
material, in which the imperfections (dislocations and vacancies) which are at first
widely scattered throughout the volume of the strained crystal collect together to form
a network of sub-grain boundaries. The sub-grain boundaries themselves may further
condense, but often they are swept away by the movement through them of the major
boundaries (recrystallization)--a process that on a large scale appears as a nucleation
and growth process. In most cases when the grains have reached composition
equilibrium throughout their volumes, further geometric change occurs simply by
movements of the grain to decrease their area and hence the energy of the system.
He proposed several principles of the hierarchies that deal particularly with inorganic
structure.
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The world is complex and understanding is simple; however,.there is always some
scale on which significant interaction involves relatively few units.. The newú
structures that seem to emerge as aggregates on a larger scale are partly illusory: It is
less of a characteristic of the structure itself than of the limited resolution of our
perception (whether visual or conceptual). Each level is what we see at certain
resolutions, and corresponds to the matching of only those structural elements that can
be resolved without too much detail at a single effect viewing distance.
1. An assembly of units will not form a coherent aggregate unless the parts interact in
such a way as to modify their internal structure and energy. An organism is an
aggregate in which there is a dominant center of organization and significant internal
communication. (A physically unconnected assembly can be related intellectually as a
structure in the mind of an observer.)
2, An aggregate that is neither completely ordered nor completely disordered must
have hierarchical aspects, but the perception of the levels of the hierarchy requires the
recognition of a two-dimensional surface to define each three-dimensional unit
according to Euhler's law. In general, the surface is defined by interactions between
discontinuities of the coordination of the parts on the next lower level; discontinuities
not so connectable constitute merely internal features. The number of imperfections,
and hence the number of possible interfaces, increases with size for simple reasons of
entropy.
3 Each scale of structure has a type and energy of interaction appropriate to it.
Structure and energy are inseparable. Though the strongest interactions between any
units are those between neighbors on the same scale, residual effects extend
downwards for a fewú and upwards through many levels--but not indefinitely, for
beyond a certain point complexity becomes irresolvable and merges again with
homogeneity. A human being is not far from the point of maximum significant
complexity that can be usefully associated with quantum interaction between chemical
atoms, while the planets and their satellites are not far from the smallest
gravitationally-determined structures.
4. Complex structures cannot originate instantaneously but are formed in time; they
must have a, history. A complex structure is both a partial record of past history and a
framework within which future changes occur by the operation of physical laws.
5. Structural change occurs by the formation of interfaces and/or by their movement.
New interfaces can form internally by the progressive condensations of imperfections
causing the self-enhancements of fluctuations until the gradients are sharp enough to
become definable interfaces, The external growth of an individual unit occurs by
acretion wúhich causes the translation of an existing interface. The latter is typical of
crystal growth, the former of spinodal transformation, biological cell division,
convection cells and stream-bed formation.
6, A complex aggrúegate may contain superimposed several different structural
hierarchies (each corresponding to a different type of interaction between units, based
on different aspects of internal strvcture). The hierarchies may be partially independent
or their various levels may interfere constructively or destructively with each other. In
organic aggregates all interactions, not necessarily those between adjacent atoms, are
those quantized photons transmitting electrical or magnetic fields, In biological
organisms there are superimposed more complex interactions based on mass transfer
of chemical messengers wúhich react only wúith specific complex local arrangements;
in intellectual or social systems small and large thought patterns interlock and new
patterns arise in the constructive mismatching of communicated parts of the old.
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In conclusion Smith stated that historically it was the artists who discovered the symmetries
that arise in the repetition of identical motifs regardless of their shape. They have a greater
sense of the relationship of parts to wholes than most scientists, "Perhaps the scientists
concern with accuracy of statements, which by its very nature must be limited, needs to be
tempered a little more than it has been in recent years with the artists awareness of larger scale
interactions,"
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