Revisiting Catastrophes. Thought of the Day 134.0

The most explicit influence from mathematics in semiotics is probably René Thom’s controversial theory of catastrophes (here and here), with philosophical and semiotic support from Jean Petitot. Catastrophe theory is but one of several formalisms in the broad field of qualitative dynamics (comprising also chaos theory, complexity theory, self-organized criticality, etc.). In all these cases, the theories in question are in a certain sense phenomenological because the focus is different types of qualitative behavior of dynamic systems grasped on a purely formal level bracketing their causal determination on the deeper level. A widespread tool in these disciplines is phase space – a space defined by the variables governing the development of the system so that this development may be mapped as a trajectory through phase space, each point on the trajectory mapping one global state of the system. This space may be inhabited by different types of attractors (attracting trajectories), repellors (repelling them), attractor basins around attractors, and borders between such basins characterized by different types of topological saddles which may have a complicated topology.

Catastrophe theory has its basis in differential topology, that is, the branch of topology keeping various differential properties in a function invariant under transformation. It is, more specifically, the so-called Whitney topology whose invariants are points where the nth derivative of a function takes the value 0, graphically corresponding to minima, maxima, turning tangents, and, in higher dimensions, different complicated saddles. Catastrophe theory takes its point of departure in singularity theory whose object is the shift between types of such functions. It thus erects a distinction between an inner space – where the function varies – and an outer space of control variables charting the variation of that function including where it changes type – where, e.g. it goes from having one minimum to having two minima, via a singular case with turning tangent. The continuous variation of control parameters thus corresponds to a continuous variation within one subtype of the function, until it reaches a singular point where it discontinuously, ‘catastrophically’, changes subtype. The philosophy-of-science interpretation of this formalism now conceives the stable subtype of function as representing the stable state of a system, and the passage of the critical point as the sudden shift to a new stable state. The configuration of control parameters thus provides a sort of map of the shift between continuous development and discontinuous ‘jump’. Thom’s semiotic interpretation of this formalism entails that typical catastrophic trajectories of this kind may be interpreted as stable process types phenomenologically salient for perception and giving rise to basic verbal categories.


One of the simpler catastrophes is the so-called cusp (a). It constitutes a meta-diagram, namely a diagram of the possible type-shifts of a simpler diagram (b), that of the equation ax4 + bx2 + cx = 0. The upper part of (a) shows the so-called fold, charting the manifold of solutions to the equation in the three dimensions a, b and c. By the projection of the fold on the a, b-plane, the pointed figure of the cusp (lower a) is obtained. The cusp now charts the type-shift of the function: Inside the cusp, the function has two minima, outside it only one minimum. Different paths through the cusp thus corresponds to different variations of the equation by the variation of the external variables a and b. One such typical path is the path indicated by the left-right arrow on all four diagrams which crosses the cusp from inside out, giving rise to a diagram of the further level (c) – depending on the interpretation of the minima as simultaneous states. Here, thus, we find diagram transformations on three different, nested levels.

The concept of transformation plays several roles in this formalism. The most spectacular one refers, of course, to the change in external control variables, determining a trajectory through phase space where the function controlled changes type. This transformation thus searches the possibility for a change of the subtypes of the function in question, that is, it plays the role of eidetic variation mapping how the function is ‘unfolded’ (the basic theorem of catastrophe theory refers to such unfolding of simple functions). Another transformation finds stable classes of such local trajectory pieces including such shifts – making possible the recognition of such types of shifts in different empirical phenomena. On the most empirical level, finally, one running of such a trajectory piece provides, in itself, a transformation of one state into another, whereby the two states are rationally interconnected. Generally, it is possible to make a given transformation the object of a higher order transformation which by abstraction may investigate aspects of the lower one’s type and conditions. Thus, the central unfolding of a function germ in Catastrophe Theory constitutes a transformation having the character of an eidetic variation making clear which possibilities lie in the function germ in question. As an abstract formalism, the higher of these transformations may determine the lower one as invariant in a series of empirical cases.

Complexity theory is a broader and more inclusive term covering the general study of the macro-behavior of composite systems, also using phase space representation. The theoretical biologist Stuart Kauffman (intro) argues that in a phase space of all possible genotypes, biological evolution must unfold in a rather small and specifically qualified sub-space characterized by many, closely located and stable states (corresponding to the possibility of a species to ‘jump’ to another and better genotype in the face of environmental change) – as opposed to phase space areas with few, very stable states (which will only be optimal in certain, very stable environments and thus fragile when exposed to change), and also opposed, on the other hand, to sub-spaces with a high plurality of only metastable states (here, the species will tend to merge into neighboring species and hence never stabilize). On the base of this argument, only a small subset of the set of virtual genotypes possesses ‘evolvability’ as this special combination between plasticity and stability. The overall argument thus goes that order in biology is not a pure product of evolution; the possibility of order must be present in certain types of organized matter before selection begins – conversely, selection requires already organized material on which to work. The identification of a species with a co-localized group of stable states in genome space thus provides a (local) invariance for the transformation taking a trajectory through space, and larger groups of neighboring stabilities – lineages – again provide invariants defined by various more or less general transformations. Species, in this view, are in a certain limited sense ‘natural kinds’ and thus naturally signifying entities. Kauffman’s speculations over genotypical phase space have a crucial bearing on a transformation concept central to biology, namely mutation. On this basis far from all virtual mutations are really possible – even apart from their degree of environmental relevance. A mutation into a stable but remotely placed species in phase space will be impossible (evolution cannot cross the distance in phase space), just like a mutation in an area with many, unstable proto-species will not allow for any stabilization of species at all and will thus fall prey to arbitrary small environment variations. Kauffman takes a spontaneous and non-formalized transformation concept (mutation) and attempts a formalization by investigating its condition of possibility as movement between stable genomes in genotype phase space. A series of constraints turn out to determine type formation on a higher level (the three different types of local geography in phase space). If the trajectory of mutations must obey the possibility of walking between stable species, then the space of possibility of trajectories is highly limited. Self-organized criticality as developed by Per Bak (How Nature Works the science of self-organized criticality) belongs to the same type of theories. Criticality is here defined as that state of a complicated system where sudden developments in all sizes spontaneously occur.

Topological Drifts in Deleuze. Note Quote.

Brion Gysin: How do you get in… get into these paintings?

William Burroughs: Usually I get in by a port of entry, as I call it. It is often a face through whose eyes the picture opens into a landscape and I go literally right through that eye into that landscape. Sometimes it is rather like an archway… a number of little details or a special spot of colours makes the port of entry and then the entire picture will suddenly become a three-dimensional frieze in plaster or jade or some other precious material.

The word fornix means “an archway” or “vault” (in Rome, prostitutes could be solicited there). More directly, fornicatio means “done in the archway”; thus a euphemism for prostitution.

Diagrammatic praxis proposes a contractual (push, pull) approach in which the movement between abstract machine, biogram (embodied, inflected diagram), formal diagram (drawing of, drawing off) and artaffect (realized thing) is topologically immanent. It imagines the practice of writing, of this writing, interleaved with the mapping processes with which it folds and unfolds – forming, deforming and reforming both processes. The relations of non-relations that power the diagram, the thought intensities that resonate between fragments, between content ad expression, the seeable and the sayable, the discursive and the non-discursive, mark entry points; portals of entry through which all points of the diagram pass – push, pull, fold, unfold – without the designation of arrival and departure, without the input/output connotations of a black boxed confection. Ports, as focal points of passage, attract lines of resistance or lines of flight through which the diagram may become both an effectuating concrete assemblage (thing) and remain outside the stratified zone of the audiovisual. It’s as if the port itself is a bifurcating point, a figural inflected archway. The port, as a bifurcation point of resistance (contra black box), modulates and changes the unstable, turbulent interplay between pure Matter and pure Function of the abstract machine. These ports are marked out, localized, situated, by the continuous movement of power-relations:

These power-relations … simultaneously local, unstable and diffuse, do not emanate from a central point or unique locus of sovereignty, but at each moment move from one point to another in a field of forces, marking inflections, resistances, twists and turns when one changes direction or retraces one’s steps… (Gilles Deleuze, Sean Hand-Foucault)

An inflection point, marked out by the diagram, is not a symmetrical form but the difference between concavity and convexity, a pure temporality, a “true atom of form, the true object of geography.” (Bernard Cache)


Figure: Left: A bifurcating event presented figurally as an archway, a port of entry through order and chaos. Right: Event/entry with inflexion points, points of suspension, of pure temporality, that gives a form “of an absolute exteriority that is not even the exteriority of any given interiority, but which arise from that most interior place that can be perceived or even conceived […] that of which the perceiving itself is radically temporal or transitory”. The passing through of passage.

Cache’s absolute exteriority is equivalent to Deleuze’s description of the Outside “more distant than any exterior […] ‘twisted’, folded and doubled by an Inside that is deeper than any interior, and alone creates the possibility of the derived relation between the interior and the exterior”. This folded and doubled interior is diagrammed by Deleuze in the folds chapter of Foucault.

Thinking does not depend on a beautiful interiority that reunites the visible ad articulable elements, but is carried under the intrusion of an outside that eats into the interval and forces or dismembers the internal […] when there are only environments and whatever lies betwen them, when words and things are opened up by the environment without ever coinciding, there is a liberation of forces which come from the outside and exist only in a mixed up state of agitation, modification and mutation. In truth they are dice throws, for thinking involves throwing the dice. If the outside, farther away than any external world, is also closer than any internal world, is this not a sign that thought affects itself, by revealing the outside to be its own unthought element?

“It cannot discover the unthought […] without immediately bringing the unthought nearer to itself – or even, perhaps, without pushing it farther away, and in any case without causing man’s own being to undergo a change by the very fact, since it is deployed in the distance between them” (Gilles Deleuze, Sean Hand-Foucault)


Figure: Left: a simulation of Deleuze’s central marking in his diagram of the Foucaultian diagram. This is the line of the Outside as Fold. Right: To best express the relations of diagrammatic praxis between content and expression (theory and practice) the Fold figure needs to be drawn as a double Fold (“twice twice” as Massumi might say) – a folded möbius strip. Here the superinflections between inside/outside and content/expression provide transversal vectors.

A topology or topological becoming-shapeshift retains its connectivity, its interconnectedness to preserve its autonomy as a singularity. All the points of all its matter reshape as difference in itself. A topology does not resemble itself. The möbius strip and the infamous torus-to-coffe cup are examples of 2d and 3d topologies. technically a topological surface is totalized, it can not comprise fragments cut or glued to produce a whole. Its change is continuous. It is not cut-copy-pasted. But the cut and its interval are requisite to an emergent new.

For Deleuze, the essence of meaning, the essence of essence, is best expressed in two infinitives; ‘to cut ” and “to die” […] Definite tenses keeping company in time. In the slash between their future and their past: “to cut” as always timeless and alone (Massumi).

Add the individuating “to shift” to the infinitives that reside in the timeless zone of indetermination of future-past. Given the paradigm of the topological-becoming, how might we address writing in the age of copy-paste and hypertext? The seamless and the stitched? As potential is it diagram? A linguistic multiplicity whose virtual immanence is the metalanguage potentiality between the phonemes that gives rise to all language?


An overview diagram of diagrammatic praxis based on Deleuze’s diagram of the Foucaultian model shown below. The main modification is to the representation of the Fold. In the top figure, the Fold or zone of subjectification becomes a double-folded möbius strip.

Four folds of subjectification:

1. material part of ourselves which is to be surrounded and folded

2. the fold of the relation between forces always according to a particular rule that the relation between forces is bent back in order to become a relation to oneself (rule ; natural, divine, rational, aesthetic, etc)

3. fold of knowledge constitutes the relation of truth to our being and our being to truth which will serve as the formal condition for any kind of knowledge

4. the fold of the outside itself is the ultimate fold: an ‘interiority of expectation’ from which the subject, in different ways, hopes for immortality, eternity, salvation, freedom or death or detachment.

Astrobiological Traces Within the Secret Doctrine.

पूर्णस्य पूर्णमादाय पूर्णमेवाशिष्यते

pūrṇasya pūrṇamādāya pūrṇamevāśiṣyate

‘From the Fullness of Brahman has come the fullness of the universe, leaving alone Fullness as the remainder.’

पूर्णमदः पूर्णमादाय पूर्णात् पूर्णमुदच्यते
पूर्णस्य पूर्णमादाय पूर्णमेवाशिष्यते
ॐ शान्तिः शान्तिः शान्तिः ।

pūrṇamadaḥ pūrṇamādāya pūrṇāt pūrṇamudacyate
pūrṇasya pūrṇamādāya pūrṇamevāśiṣyate
oṃ śāntiḥ śāntiḥ śāntiḥ |

‘The invisible (Brahman) is the Full; the visible (the world) too is the Full. From the Full (Brahman), the Full (the visible) universe has come. The Full (Brahman) remains the same, even after the Full (the visible universe) has come out of the Full (Brahman).’

नित्योऽनित्यानां चेतनश्चेतनानाम्
एको बहूनां यो विदधाति कामान् ।
तमात्मस्थं योऽनुपश्यन्ति धीराः
तेषां शान्तिः शाश्वतं नेतरेषाम् ॥

nityo’nityānāṃ cetanaścetanānām
eko bahūnāṃ yo vidadhāti kāmān |
tamātmasthaṃ yo’nupaśyanti dhīrāḥ
teṣāṃ śāntiḥ śāśvataṃ netareṣām ||

‘He is the eternal in the midst of non-eternals, the principle of intelligence in all that are intelligent. He is One, yet fulfils the desires of many. Those wise men who perceive Him as existing within their own self, to them eternal peace, and non else.’


The Secret Doctrine of the Ages teaches that the universe came into existence through creative and evolutionary processes; and it demonstrates why both are necessary to explain our origins. It harmonizes the truths of science and religion, while showing that major assumptions of both Darwinism and Fundamentalist Creationism do not bear up to careful examination. By drawing our attention to the questions of why we live and die, of what is mind and substance, the Secret Doctrine helps us realize that wisdom begins with understanding how very little we really know. Yet it also affirms that the most perplexing problems can be solved; that of the progeny of one cosmos.

Evolution means unfolding and progressive development, derived from the Latin evolutio: “unrolling,” specifically of a scroll or volume — suggestively connoting the serial expression of previously hidden ideas. A climb from the bottom of the Grand Canyon reveals an unmistakable evolutionary story: of the appearance of progressively more complex species over a lengthy period of time. But how actually did this happen? The compelling evidence of nature contradicts the week-long special creation postulated by Bible literalists. Darwinian theory is also proving unsatisfactory, as a growing number of scientists are relegating its major claims to the category of “mythology. “Though not assenting to any metaphysical implications, Harvard paleontologist Stephen Jay Gould declared in 1980 that the modern synthetic theory of evolution, “as a general proposition, is effectively dead, despite its persistence as textbook orthodoxy.” Pierre-P. Grassé, former president of the French Academy of Sciences and editor of the 35-volume Traité de Zoologie, was more forceful:

Their success among certain biologists, philosophers, and sociologists notwithstanding, the explanatory doctrines of biological evolution do not stand up to an objective, in-depth criticism. They prove to be either in conflict with reality or else incapable of solving the major problems involved. Through the use and abuse of hidden postulates, of bold, often ill-founded extrapolations, a pseudoscience has been created. It is taking root in the very heart of biology and is leading astray many biochemists and biologists, who sincerely believe that the accuracy of fundamental concepts has been demonstrated, which is not the case.

While most critics readily acknowledge that natural selection and gene changes partially explain variation in species or microevolution, they point out that Darwinism has failed spectacularly to describe the origin of life and the mechanism of macroevolution: the manner in which higher types emerge.

Textbook theory asserts that life on earth began with the formation of DNA and RNA, the first self-replicating molecules, in a prebiotic soup rich in organic compounds, amino acids, and nucleotides. Robert Shapiro, professor of chemistry at New York University, wrote:

many scientists now believe that neither the atmosphere described nor the soup had ever existed. Laboratory efforts had also been made to prepare the magic molecule from a simulation of the soup, and thus far had failed.

Even if the purported soup existed elsewhere in the universe, and DNA were brought to earth by meteorite, comet, or some other means, there remains the enigma of how it was originally synthesized. Astrobiology.

In the first place, several mathematicians have shown the astronomical improbability of chance mutations “evolving” any organized system — neither complex DNA molecules nor higher organisms. The 10-20 billion year time frame presently assigned to our universe is far too short a period, given known mutation rates. Moreover, nothing in empirical experience suggests that unguided trial and error — i.e., random mutation — will produce anything but the most trivial ends. Research biologist Michael Denton writes that to “get a cell by chance would require at least one hundred functional proteins to appear simultaneously in one place” — the probability of which has been calculated at the negative figure 1 followed by 2,000 zeros — a staggeringly remote possibility, to say nothing of the lipids, polysaccharides, and nucleic acids also needed to form a viable, reproducing cell.

The same reasoning applies to the extraordinary number of coordinated, immediately useful mutations required to produce “organs of extreme perfection,” such as the mammalian brain, the human eye, and the sophisticated survival mechanisms (including inter-species symbiotic systems) of the plant and animal kingdoms. There is simply no justification, according to Denton, for assuming that blind physical forces will self-organize “in the finite time available the sorts of complex systems which are so ubiquitous in nature.” In observing the sheer elegance and ingenuity of nature’s purposeful designs, scientists like Denton can hardly resist the logic of analogy. The conclusion may have religious implications, he says, but the inference is clear: nature’s systems are the result of intelligent activity.

Another enigmatic problem is the absence in fossil strata of finely-graded transitional forms between major groups of species, i.e., between reptiles and birds, land mammals and whales, and so forth. Darwin himself recognized this as one of the “gravest” impediments to his theory and tried to defend it by asserting “imperfection of the geologic record.” Yet over a century of intensive search has failed to disclose the hypothetical missing links. Thus far only conjecture, or imagination, has been able to fill in how gills became lungs, scales became feathers, and legs became wings — for the record of nature on this point is still a secret.

Darwin also worried over one of nature’s most formidable barriers to macroevolutionary change: hybrid limits. Artificial breeding shows that extreme variations are usually sterile or weak. Left to themselves these hybrid varieties — if they are able to reproduce at all — revert to ancestral norms or eventually die out. In this sense, natural selection, environmental pressures, and genetic coding tend as much to weed out unusual novelties, as to ensure the survival of the fittest of each typea fact which is confirmed by the fossil record. Unquestionably, species adapt and change within natural limits; refinement occurs, too, as in flowering plants. But no one has yet artificially bred, genetically engineered, or observed in nature a series of chromosomal changes, micro or macro, resulting in a species of a higher genus. There are no “hopeful monsters,” except, perhaps, in a poetic sense. Trees remain trees, birds birds, and the problem of how higher types originate has not been solved by Darwin or his successors.

We do not give up our dogmas easily, scientific or religious. Obviously, ideas should be examined for their intrinsic value, not blindly accepted because somebody tells us “Science has proven” or the “Bible says so,” or again, because the Secret Doctrine teaches it. But with science’s recognized ignorance of first causes and macroevolutionary mechanisms, as well as the failure of scriptural literalism to provide satisfactory explanations, there remain the questions about our origins, purpose, and destiny. The answers to these questions are, in a sense, nature’s secret doctrines. Her evolutionary pattern suggests, however, that they are not hopelessly beyond knowing. Just as from the conception of a human embryo to a fully-developed adult, so from the first burst outward of the primordial cosmic atom, the progressive unfolding of intelligence is a natural and observable process. The whole universe seems bent on discovering itself and its reason for being.

The concept of the universe evolving for purposes of self-discovery and creative expression is found not only in modern European philosophy, such as Hegel’s, but also in ancient myths the world over, some of which sound surprisingly up-to-date. The Hindu Puranas, for example, speak of our universe as Brahma, and of alternating periods of cosmic activity and rest as the Days and Nights of Brahma, each of which spans over four billion years — an oscillating universe reminiscent of modern cosmological theory. In each “creation” Brahma attempts to fashion an ever-more perfected mankind, in the process of which he serially evolves from his own consciousness and root substance all of nature’s kingdoms: atoms, minerals, plants, animals, and so forth. Conversely, the stories allude also to the striving of mankind and, for that matter, of all sentient beings, to become Brahma-like in quality — i.e., to express more and more of the hidden mind pattern of the cosmos.

We often look down on ancient traditions as moldy superstitions. While this judgment may well apply to the rind of literalism and later accretions, concealed within and giving life to every religion are core ideas which bear the hallmark of insight. Biblical Genesis also, when read allegorically as is done in gnostic and kabbalistic schools, yields a picture of evolutionary growth and perfectibility, both testaments clearly implying that we are sibling gods of wondrous potential. But are the secret doctrines spoken of in these older traditions expressions of truth or simply romantic wish-fulfilling fantasy? Can they teach us anything relevant about our heritage and our future? It is to such questions that the modern book entitled The Secret Doctrine addresses itself. Impulsed by divinity and guided by karma (cause and effect), each of us has been periodically manifesting since eternity through all the kingdoms, from sub-mineral through human, earning our way to the next realm and beyond. Although seeded with godlike potential, we are not irrevocably fated to an unsought destiny. Karma is a philosophy of merit, and within our power is the capacity to choose — to evolve and create — our own future. We give life and active existence to our thoughts and, to a very large extent, we become what we think we are, or would like to be. This affects ourselves for good or evil, and it affects all others — profoundly so.

Mutational Law of Karma (कर्म)?


During the preparation for cell division, for example, before the formation of the gametes or reproductive cells, the chromosomes may “cross over” so that material which originated from the male parent interchanges with that from the female parent. To quote from a standard work on evolutionary theory and genetics, Ernst Mayr’s Evolution and the Diversity of Life:

At some time prior to the formation of the gametes, the two homologous chromosomes exchange equivalent pieces with each other by a process called “crossing over.” By and large (there are many exceptions) no laws seem to determine where the chromosomes will break or how large the pieces will be that are exchanged. Which particular combination of pieces of maternal and paternal chromosomes making up the new chromosome will enter a given egg or spermatozoon is largely a matter of chance, at least in most chromosomes and most species. Likewise, it is largely a matter of accident which chromosomes will go into which germ cell, provided only that each cell receives its full set of chromosomes.

It is easy to attribute events to chance, but this only expresses scientific ignorance as to the real cause.

Another phenomenon is mutation: sometimes genetic codes suddenly change. This, too, is usually attributed to accident or chance, but then it is difficult to explain why any progression is made at all once biological systems have evolved to a certain level of complexity and perfection. The chance of a mutation leading to fatal, or at least less fit, properties is far greater than of a mutation making the individual fitter. Besides “crossing over” and mutation at one or several places on the chromosomes, another uncertain factor that Mayr and others mention is the distribution of chromosomes during reduction division (meiosis) to form reproductive cells. This process affects which side in the gamete the originally paternal or maternal genetic material goes to. Moreover, there are other opportunities for the course of events to be influenced from within: only part of the cell’s genetic code is active at certain times and under certain circumstances. Other parts are not active and may never become so during the present life. Thus, there are many secrets not yet unveiled by science, but nevertheless attributed to “chance.”

Chance, however, has no place in the theosophical view. Whatever happens is karmic, that is, it can be attributed to a cause, and this cause comes from within. In theosophy the different combinations of hereditary qualities in individuals are governed by psychomagnetic attractions inherent in the skandhas (‎स्कन्ध) of the reincarnating entity. Skandhas are the individual’s aggregates of properties — such as higher and lower mental consciousness, feelings, attractions, and physical characteristics — carried over from former lives. Thus, the specific magnetism of the soul, formed by its store of properties, determines which combinations of hereditary qualities will manifest in a particular incarnation. “It is . . . unquestionable that in the case of human incarnations the law of Karma, racial or individual, overrides the subordinate tendencies of ‘Heredity,’ its servant” (The Secret Doctrine).

Honey-Trap Catalysis or Why Chemistry Mechanizes Complexity? Note Quote.

Was browsing through Yuri Tarnopolsky’s Pattern Chemistry and its affect on/from humanities. Tarnopolsky’s states “chemistry” + “humanities” connectivity ideas thusly:


Practically all comments to the folk tales in my collection contained references to a book by the Russian ethnographer Vladimir Propp, who systematized Russian folk tales as ‘molecules‘ consisting of the same ‘atoms‘ of plot arranged in different ways, and even wrote their formulas. His book was published in the 30’s, when Claude Levi-Strauss, the founder of what became known as structuralism, was studying another kind of “molecules:” the structures of kinship in tribes of Brazil. Remarkably, this time a promise of a generalized and unifying vision of the world was coming from a source in humanities. What later happened to structuralism, however, is a different story, but the opportunity to build a bridge between sciences and humanities was missed. The competitive and pugnacious humanities could be a rough terrain.

I believed that chemistry carried a universal message about changes in systems that could be described in terms of elements and bonds between them. Chemistry was a particular branch of a much more general science about breaking and establishing bonds. It was not just about molecules: a small minority of hothead human ‘molecules’ drove a society toward change. A nation could be hot or cold. A child playing with Lego and a poet looking for a word to combine with others were in the company of a chemist synthesizing a drug.

Further on, Tarnopolsky, following his chemistry then thermodynamics leads, then found the pattern theory work of Swedish chemist Ulf Grenander, which he describes as follows:

In 1979 I heard about a mathematician who tried to list everything in the world. I easily found in a bookstore the first volume of Pattern Theory (1976) by Ulf Grenander, translated into Russian. As soon as I had opened the book, I saw that it was exactly what I was looking for and what I called ‘meta-chemistry’, i.e., something more general than chemistry, which included chemistry as an application, together with many other applications. I can never forget the physical sensation of a great intellectual power that gushed into my face from the pages of that book.

Although the mathematics in the book was well above my level, Grenander’s basic idea was clear. He described the world in terms of structures built of abstract ‘atoms’ possessing bonds to be selectively linked with each other. Body movements, society, pattern of a fabric, chemical compounds, and scientific hypothesis—everything could be described in the atomistic way that had always been considered indigenous for chemistry. Grenander called his ‘atoms of everything’ generators, which tells something to those who are familiar with group theory, but for the rest of us could be a good little metaphor for generating complexity from simplicity. Generators had affinities to each other and could form bonds of various strength. Atomism is a millennia old idea. In the next striking step so much appealing to a chemist, Ulf Grenander outlined the foundation of a universal physical chemistry able to approach not only fixed structures but also “reactions” they could undergo.

The two major means of control in chemistry and organic life: thermodynamic control (shift of equilibrium) and kinetic control (selective change of speed). People might not be aware that the same mechanisms are employed in social and political control, as well as in large historical events out of control, for example, the great global migration of people and jobs in our time or just the one-way flow of people across the US-Mexican border!!! Thus, with an awful degree of simplification, the intensification of a hunt for illegal immigrants looks like thermodynamic control by a honey trap, while the punishment for illegal employers is typical negative catalysis, although both may lead to a less stable and more stressed state. In both cases, new equilibrium will be established, different equilibria housed upon different sets of conditions.


Should I treat people as molecules, unless I am from the Andromeda Galaxy. Complex-systems never come to global equilibrium, although local equilibrium can exist for some time. They can be in the state of homeostasis, which, again, is not the same as steady state in physics and chemistry. Homeostasis is the global complement of the classical local Darwinism of mutation and selection.

Taking other examples, the immigration discrimination in favor of educated or wealthy professionals is also a catalysis of affirmative action type. It speeds up the drive to equilibrium. Attractive salary for rare specialists is an equilibrium shift (honey trap) because it does not discriminate between competitors. Ideally, neither does exploitation of foreign labor. Bureaucracy is a global thermodynamic freeze that can be selectively overcome by 100% catalytic connections and bribes. Severe punishment for bribe is thermodynamic control. The use of undercover agents looks like a local catalyst: you can wait for the crook to make a mistake or you can speed it up. Tax incentive or burden is a shift of equilibrium. Preferred (or discouraging) treatment of competitors is catalysis (or inhibition).

There is no catalysis without selectivity and no selectivity without competition. Equilibrium, however, is not selective: it applies globally to the fluid enough system. Organic life, society, and economy operate by both equilibrium shift and catalysis. More examples: by manipulating the interest rate, the RBI employs thermodynamic control; by tax cuts for efficient use of energy, the government employs kinetic control, until saturation comes. Thermodynamic and kinetic factors are necessary for understanding Complex-systems, although only professionals can talk about them reasonably, but they are not sufficient. History is not chemistry because organic life and human society develop by design patterns, so to speak, or archetypal abstract devices, which do not follow from any physical laws. They all, together with René Thom morphologies, have roots not in thermodynamics but in topology. Anything that cannot be presented in terms of points, lines, and interactions between the points is far from chemistry. Topology is blind to metrics, but if Pattern Theory were not metrical, it would be just a version of graph theory.