General Ontology
Cosmos and Nomos

Theory of Ontological Layers and Complexity Layers

Part XXIX (Sequel-35)

Crystals and Organisms

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The discovered fact that not only organisms have a promorph, but also crystals, is one of the starting points of the crystal analogy, i.e. the investigation of the analogies between crystals and organisms (and more generally, between the inorganic and the organic).
This was in the year 2005, and still (2010) holds. And because all the previous documents in effect already contain all the elements of a crystal-analogy, we had [2005] decided to postpone the intended systmatic summary of all these elements. After all, the reader could do it her- or himself, and perhaps add or subtract certain such elements.
Meanwhile, it is the year 2010. In the intervening years I have in Fifth, but especially in Sixth Part of Website studied organic evolution (as exemplified by the Class of Insects). And this turned out to be very fertile ground for developing further the theory of the Explicate and Implicate reality Orders. All the facts and theories of evolution, the possibilities of monophyletic or polyphyletic development in organisms, the status of the "functional" in morphology and its special relation with the Implicate Order, and much more, has shaped my ideas about the precise role played by the Implicate Order in the constitution of, especially, the Organic World as we see it in the Explicate Order, and resulted in a fine overall metaphysical theory of form-generation (organic and inorganic).
In addition to all this, I am now [2010] enquiring into still deeper layers of material Reality, in fact into the very ground-work of Reality itself (ultimately includung the Explicate and Implicate Orders). I have found that the aspect of spatial extensivity, typically constitutive of the Explicate Order (an aspect that is in the Implicate Order replaced by dimensions of intensity), is the direct effect of the ultimate structure of "space", in fact of that which has "space" (spatiality) as its effect. Studies of the alleged nature of "infinity" have convinced me that "space", as medium and element of the Explicate Order (together with "time"), cannot be a true continuum. "Space", not as a receptaculum of things, but as the spatiality of the latter themselves, as being a "continuum" evokes contradictions, and cannot, as continuum, form a spatial extensum at all. The latter must be based on the presumed fact that the very groundwork of (explicate) reality must contain indivisible elements of extensionality already all by itself, meaning that "space" (or better, the "spatial") is (voidlessly)  d i s c r e t e.  Extensionality does not come from non-extensionality (for example not from the concatenation of extensionless points). And so we now assume that extensionality is based on a non-zero minimum (spatial and thus purely geometric) distance between every two geometric points of that ultimate groundwork of (explicate Reality). This minimum distance, being the absolute indivisible unit of spatial extension, is determined by geometry only. In determining this non-zero minimum distance between every two points, these points
only as geometric points do play a role. And although we assume these points to have, each one of them, a qualitative content (in the form of a "primitive quality"), this quality is assumed to exert not any influence whatsoever on the determination of the minimum distance between every two such points (whereas in crystals it does so). The result of all this is that the groundwork of the Explicate Order is in fact a regular (and universal) point-net :  It is regular because of the constancy of the minimum distance between every two points. For a two-dimensional space this net would consist of points arranged in equilateral triangles, and so constituting a hexagonal network. Generally taken, we will call it the "universal point-net", constituting discrete space, which has, consequently, its own geometry -- discrete geometry. Each point of this net has its elementary qualitative content, the "primitive quality". All "usual" qualities, such as color, are each constituted from a mixture of such primitive qualities and thus are patches of large quantities of net-points.
The whole of these net-points -- points, separated by the minimum distance -- together form the "display" of, what I may call, the "World Cellular Automaton" (World CA), an idea ("information mechanics") as such (and no more) already held by Edward Fredkin in the 1960's. According to a vast set of CA-transformation-rules having their seat in the Implicate Order, the display in the Explicate Order will change from moment to moment :  These rules, namely, make the next primitive quality of a net-point (i.e. its quality in the next moment), a net-point in the Explicate Order, to depend upon the qualities of the immediately surrounding net-points, etc.

And all this will change our emphasis in developing a crystal-analogy (crystals-organisms), i.e. the nature of the analogy will become somewhat different than the foregoing documents might suggest, despite the fact that I can still consider the content of all these documents to be true and relevant. Only the emphasis (in selecting the factors that constitute the analogy) will change, resulting in a different nature and degree of the analogy. After having found out that an "organic lattice" does not exist in organisms, and thus forbidding to entertain a crystal analogy, the "discovery" of the overall universal point-lattice (discrete space) may revive the crystal analogy, despite the fact that that universal point-lattice is not confined solely to crystals (with their crystallographic point-lattice on top of it) and organisms (both being genuine Substances in the metaphysical sense), but is present in all of explicate Reality including all non-substances. And of course -- and that is the important result of the foregoing documents about crystals and organisms -- in the "final crystal-analogy" to be given in the present document, dendritic (i.e. branched) crystals, as we find them in snow, will, together with the mentioned universal point-lattice, play a pivotal role in the very nature of the analogy between crystals and organisms.
The extended theory of the Implicate and Explicate Orders can be found, as it is developing, in  Fifth Part of Website  and especially in  Sixth Part of Website,  while the theory of the universal point-net is developed from Sixth Part of Website part XVk onwards (in the series on NATURAL PHILOSOPHY) in Sixth Part of Website.

The Crystal Analogy

( And in a broader sense :  The Inorganic-Organic Analogies )

In order not to lose sight of the essence of the crystal-analogy, we again repeat in what respects crystals and organisms may be compared to one another :

Let us now start the exposition of the "final" crystal-analogy.

The ability to generate structures (including shapes) which are (1) ordered, (2) macroscopic, and (3) can have genuine (i.e. morphological) antimers (i.e. morphological counterparts), may, in organisms, if we let us guide by the nature of dendritic crystals, be based on a kind of "exploitation" of the universal point-net itself (and thus not, as in dendritic cystals, of some secondary point-net, i.e. a crystallographic lattice). The fact that this form-generation does not take place everywhere in the explicate groundwork of reality, although the universal point-net is supposed to be everywhere (i.e. underlying all of explicate reality), must find the following 'explanation' in the case of organisms :  It is precisely there and only there in the overall universal point-lattice (the display-window of the World CA) where organic form-generation takes place, where we have to do with the presence or creation of an organic Substance (in the metaphysical sense). So in this case the universal point-net spatially extends, it is true, also beyond the region where the Substance is (developing), but there is still a sense of "accretion" of "matter" onto the developing Substance (and also of internal change) thanks to the qualitative change of neighboring (or internal) net-points and their assimilation onto and into the (developing) Substance. So a developing Substance (also when it is a crystal) is a local event in the universal point-net, i.e. a local event in discrete space. We must realize that the discretion of space is only evident at the lowest level of explicate reality, i.e. on the level of geometric minimal distance of geometric points. So "practically", i.e. macroscopically, and even at the level of molecules, we have, in the case of true Substances, to do with (heterogeneous) continua.
We must expound how we arive at such a conclusion, equating in a sense organisms and dendritic crystals.
Let us detect what precisely the consecutive order of things is in terms of "condition ==> conditioned". We shall do this by expounding the nature of (1) the universal point-lattice, (2) the dendritic crystal, (3) the non-dendritic crystal, (4) the nature of Substance (in the metaphysical sense), (5) the nature of dissipative structures, and (6) the nature of an organism.  And on the basis of these expositions we can then finally and definitively compare organisms with dendritic crystals.

From these six (view)points we shall now, more closely, compare (dendritic) crystals and organisms :

A dendritic crystal contains  morphological  determinants. This is a new "nexus-category". There is here an analogue with thermodynamic potentials such as entropy and free energy :  a Form-potential. And spontaneous motion (change, process) is always heading toward an extreme, in this case to that of the Form-potential. If this is reached, then the system or structure is in  morphological  equilibrium. This is accomplished by the mentioned long-distance correlations of parts of the dendritic crystal :  here we can speak in terms of a "morphic resonance" between the arms of the crystal, resulting in a mutual morphological equality of the six (as in snow crystals) arms of a same crystal. The system of a (fast) growing dendritic crystal will be subjected to crystallographic defects, lattice dislocations, increasing its morphological potential [referring to the possible diversity of forms and shapes, and not to confuse with the just mentioned Form-potential.]. The dendritic crystal has a lattice, a secondary lattice, superimposed onto the omnipresent universal point-net, a lattice, defined and determined by the quality (i.e. by the qualitative features) of the constituent particles (atoms or molecules) determining the minimal distance between them and consequently the form and size of the crystallographic unit-cell (and thus guaranteeing local [i.e. at sites inside the crystal] thermodynamic equilibria [while the dendritic crystal as a whole remains a far from equilibrium structure] )  and so determining the type of lattice consisting of these translatively repeating crystallographic unit-cells having, in addition to a specific geometric shape, a specific qualitative content (determining that shape). This crystallographic lattice is macroscopically superimposed upon the ultra-microscopic universal network of quality-points directly based on the geometric unit-distance of discrete space.
The dendritic crystal can be viewed as a Substance (in the metaphysical sense) based on the presence of long-distance correlation of its parts (morphologic resonance of its parts), expressing itself in the course of the crystal toward morphologic equilibrium. The dendritic crystal can moreover be viewed as a Substance based upon its degree of individuality and upon the repeatability (under certain defined conditions) of its qualitative pattern. Such a repeatability is in principle also possible in non-Substances, aggregates, but here the conditions must be 'infinitesimally' identical (which, in the real world, never happens), whereas in the case of a true Substance there is a certain range of conditions within which a same structure of such a Substance will appear. However, in dendritic crystals this range can be expected to be vey narrow indeed, but nevertheless not 'infinitesimally' so. And it is safe to say that every morphological structure actually encountered in at least dendritic snow crystals is not chaotic or random, but looks very determined, specific, and orderly. So we can safely speak of "specific constancy" of the intrinsic qualitative pattern of a dendritic crystal. All this, like it is in organisms.
The dendritic crystal has, like in organisms, genuine morphological antimers indicated by the arms. It is, just like organisms, a far-from-thermodynamic-equilibrium system, a dissipative system, which means that the system is still far away from an extreme of whatever thermodynamic potential :  no maximum entropy, because entropy is continually exported out of the system into the environment (that's why it is called a dissipative system). The amount of free energy is not the lowest possible. There is no maximal relaxation. Only morphologically the system is in equilibrium, the arms of the crystal develop equally, creating identical morphologies. All this, like it is in organisms. Also like in organisms, a dendritic crystal has long-distance correlations (between the arms of a same crystal), also rendering the dendritic crystal to be a Substance.
A liquid analogue of a dendritic crystal is the "splash", caused by the falling of a drop into a bowl filled with the same liquid. Subsequent upon falling, a circular rim rises up from the liquid. A rim, however, which becomes unstable and then giving off radially oriented 'spikes', and thus resulting in a radiate figure (i.e. a figure with 'antimers') just as in dendritic crystals. Such a "splash" most probably may be considered to be a dissipative system by reason of the mentioned instability to take place during the process. So here we have an example of a Form with antimers, which lacks un underlying (secondary) lattice structure. The splash is ephemeral though, but in other areas there exist "figures of impact" which are more persisting, i.e. leaving behind traces (visible, for instance, in many impact-craters on the moon). But all such figures do not have the intricate morphology as we see them in dendritic crystals. They are not more than analogous to them as to their global morphology, but surely are still interesting and important.
The only true difference, relevant to the present discussion, a difference between dendritic crystals and organisms, is that the latter do not have a crystallographic lattice of any kind. All conceptual attempts of mine and others to demonstrate at least the possibility of an "organic lattice" in organisms (a lattice, macroscopically superimposed, just like a true crystal lattice, upon the universal point-net of explicate reality), to demonstrate it without having to introduce unacceptable ad hoc constructions, have failed :  An organism is not a crystal, albeit that it displays many analogies with it, especially with a dendritic crystal.
But because a dendritic crystal does have a lattice (over and above the universal point-net), it might be that the possession of any lattice whatsoever is indeed needed for any solid or semi-solid medium to be able to generate a true morphological structure with antimers. And because organisms do not possess a secondary lattice or network, they must exploit the omnipresent universal point-net, at least as soon as in organic evolution solid or semi-solid organisms are about to appear. And, as to the morphology :  there are only few organisms primarily lacking antimers, they are of the promorphological category called "Anaxonia" (organismic shapes lacking any geometric axis), and, in a sense, [they are of the promorphological categories of] the "Monaxonia" (organismic shapes having only one single geometric axis) and the "Homaxonia" (spherical organisms, with all geometric axes equal). The Monaxonia and Homaxonia are, respecively, cylindrical, conical, or spherical forms, which might morphologically be viewed as either lacking antimers entirely or having infinitely many (i.e. undetermined finite) of them. Speaking of organismic morphologies with antimers, we must not only look at whole organisms but also at functional parts of them such as leaves and flowers in plants. These latter substructures are morphologically fairly independent of the morphology of the whole plant. Most leaves consist of two antimers, while many flowers have five, others four or two antimers.
A second difference between dendritic crystals and organisms is their state-of-aggregation, not, it is true, [this difference] consisting of the contrasting pair "solid-liquid", but of the pair "solid-semiliquid (or semi-solid), where the semi-liquid condition in organisms consists in the colloidal type of dispersion. But as to their state of aggregation, dendritic crystals and (most) organisms together differ from most other dissipative systems, which are liquid (they may be represented by chemical reaction mixtures in the laboratory, or, almost so, by the many primitive organisms in the ocean which are almost exclusively sea-water). And as to the capability of true morphological form-generation, this might mean that they indeed need to adopt a lattice structure (as done by [dendritic] crystals) or exploit one that is already present (as done by organisms). However, if, such a lattice is, in the case of organisms, the omnipresent universal point-net, we have, in assuming this, the problem that this point-net is present not only in organisms, but is present everywhere in explicate reality, while certainly not everywhere morphologies with antimers are being formed. We may more or less solve this problem by holding that a lattice or point-net is a necessary condition for such morphologies (as present in dendritic crystals and in most organisms) to be developed, but not a sufficient condition. In the case of organisms alone (alone, because in the case of dendritic crystals there clearly is already a difference between the area where their (secundary) lattice is and where it is not), two additional conditions must be satisfied :

For the development of non-dendritic crystals, on the other hand, the first of these additional conditions is not needed, because non-dendritic crystals thermodynamically are equilibrium structures.
But as to organisms : Only if we stipulatively add these two conditions to that of the presence of a lattice (as these two extra conditions are indeed satisfied in dendritic crystals and in organisms), a macroscopic morphological structure with true antimers can actually be formed and maintained.
If the system (a particular area of the universal point-net) is a Substance, then by definition there is a difference between system and surroundings. Given qualitative net-points either do belong to that individual Substance or do not. And when, subsequently, more and more qualitative net-points from the immediate surroundings are going to belong to that individual Substance, we may say that that particular Substance is "growing", like a crystal is growing. We even can say that evermore "unit-cells" of the universal point-net join this Substance [Considering exclusively the two-dimensional aspect, which is hexagonal, of the three-dimensional universal point-net, we can say that the addition of any single net-point to the Substance (not that it actually  moves  to that Substance, but that it is going to  b e l o n g  to that Substance) is in effect the addition of an equilateral triangle of discrete space to (that of) the Substance.]. So here indeed we have an organism without a (secondary) crystallographic lattice, but an organism that nevertheless grows in a way analogous to that of crystals. And, in contrast to crystals, where, as is known, internal changes are rare, in organisms there are, in addition to external changes, internal changes. And these are accomplished by replacement of given primitive qualities of certain net-points (in the organism) by other such qualities. This accounts for the qualitative diversity and "dynamics" in the organism, whereas in crystals such changes can only be accomplished by the rare internal and local changes and by crystallographic defects.
The structure of a dendritic crystal is formed and maintained by a particular crystallization law, being the, relative simple, dynamical law of such a crystal species and situated in the Implicate Order, whereas the structure and internal dynamics of an organism is governed by the dynamical law of precisely that particular organismic species, a law, also laid down in the Implicate Order, but now as a noëtic description of an existential strategy, as expounded in  Sixth Part of Website.  And if we consider all these laws to be part of one single transformation-law, the qualitative "flicker" of the points of the universal network in explicate reality can be supposed to be governed by one single, but complex, CA-transformation-rule residing in the Implicate Order, i.e. the rule of the "World Cellular Automaton".

This is about how far we may extend the crystal-analogy (crystals-organisms).

So organisms are not crystals, but do show, structurally and thermodynamically, much similarity with, especially, dendritic crystals. But the underlying network in organisms is not a secondary crystallographic lattice but the 'naked' universal point-net, which, while omnipresent, here in organisms acquires a special function and significance in their form-generation and form-maintenance. In dendritic crystals as well as in organisms we have, as has been said, to do with a new nexus-category, the Morphic-determinant, i.e. the morphological determinant, driving the structure to a morphological equilibrium as a result of internal morphic resonance :  the interconnection -- via the Implicate Order -- of parts of the structure, i.e. of parts of the dendritic crystal or parts of the organism.
While the form-generation of a dendritic crystal is, in addition to morphic determination, further and  completely  determined by the local thermodynamic equilibria in its interior, while such a crystal as a whole always is thermodynamically unstable and thus far from equilibrium (because its surface area far exceeds the size of its interior) without that crystal falling apart, and all this being sufficient for the existence of such a crystal in the Explicate Order, - an organism must, as to its very structure, be so constituted that it is able to guarantee its existence and persistence in the Explicate Order  a c t i v e l y.  And this is only possible if its structure, including its dynamics and behavior, is a true  s t r a t e g y,  a strategy to maintain itself in the Explicate Order  ( In  Sixth Part of Website  we explain that all immaterial Forms, residing in the Implicate Order, aspire to become "ontologically complete", that is, to in-form matter (and thus to become matter-form composites), and that they can only do so when existing in the Explicate Order. Many such forms can do so directly, but many cannot, and therefore must -- in the Implicate Order -- noëtically develop into strategies, and then, as such strategies, be "projected" (and thus being materialized) into the Explicate Order, where they appear as organisms ).  All this renders an organism to be 'infinitely' more complicated and subtle than any crystal, because now also  f u n c t i o n a l  properties come into play. And it is precisely this functional aspect that can be developed ('made') only in the Implicate Order. The Explicate Order cannot generate it. But surely it is so that the noëtic development of such an organic strategy must be oriented to a material existence, and thus oriented to the Explicate Order (because materially existing is existing in the Explicate Order). All this is, as has been said, theoretically worked out mainly in Sixth Part of Website. Here, in Fourth Part of Website, we had limited ourselves to enquire into the purely morphological aspect of organisms as compared to that of crystals, and its thermodynamical conditions, i.e. in contrast to things in Sixth Part of Website, we did not consider biological conditions of form-generation. At the end of Sixth Part of Website we will once again return to the morphological aspects of organisms and crystals when developing the theory of the omnipresent universal point-net at the very bottom of all explicate reality, being the display window of the World Cellular Automaton.

* * *

Will be continued if necessary .  .  . 

In the document(s) after the one concerned with the crystal analogy (present document) we leave the investigations into the latter, and, based on the results of these investigations, now accept this analogy as a general context for the previous and ensuing work.  This ensuing work will be a continuation of our investigation into the promorphs of two-dimensional crystals, but now explicitly involving their internal symmetry (plane group symmetry). In addition, the crystal analogy could point (if it allows to be so interpreted) to two different Layers of Being, that are either distinguished from each other by a (mere) jump in physical complexity (and nothing else), or by some really fundamental ontological NOVUM, resulting in the organisms to be  elevated  or over-formed (non-equilibrium) crystals.
If the crystallographic analogy does not hold, then organisms are just dynamical systems that are set up by wholeness determination (representing the organic NOVUM) and involving over-formed inorganic categories, and are then, despite of the mentioned over-formings, themselves not over-formed inorganic beings (not elevated crystals).
We now know, that the purely crystallographic analogy of organisms does not hold, because there is not such a thing as an "organic lattice". But we have found out that the point-network underlying all explicate reality is mobilized by organisms to serve as one of the factors creating true morphological form and shape. And in this way the crystal-analogy is still valid.

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