Just Another Strange Attractor

Browsing around the pages of The Guardian this morning, I came across this beautiful award winning photo of an “oscillating microbubble” (whatever that is) that clearly has the characteristics of a Strange (or Lorenz) Attractor, otherwise known as “Butterfly Effect”. It clearly shares the same features as the Holling’s Adaptive Cycle — the pathway that energy follows in any selected ecosystem, or the dynamics of any system for that matter. I’ve even suggested, tentatively, that it may show the path of energy through the right and left hemispheres of the divided brain, for example. At the same time, though, it uncannily takes the form of the traditional symbol for infinity.

Here’s Holling’s Adaptive Cycle


Holling's Adaptive Cycle

Holling’s Adaptive Cycle

And here’s Dr. Dario Carugo’s photograph (from The Guardian) of the “oscillating microbubble”,


Oscillating Microbubble: Strange Attractor

Oscillating Microbubble: Strange Attractor

As you can see, both take the form of the traditional symbol of infinity (called the lemniscate), as described in the Wikipedia.

There is certainly something mysterious here, and The Chrysalis is, of course, interested in all things butterfly, so to speak. Is this the shape of consciousness dynamics, too? For, as mentioned earlier, the Strange Attractor — a double Strange Attractor — seems to be the shape also of William Blake’s vision of the fourfold human form also,


Blake: the fourfold human

Blake: the fourfold human

Since the four Zoas of the integral human reside “in the Human Brain” and nervous system, in Blake’s mythology, it seems likely then that the Zoas correspond to the left and right hemispheres as well as the anterior and posterior (or “new” and “old”) portions of the brain as well, although the left-right bihemispheric relation seems to get most of the attention.

If so, then the left-right hemisphere relation may be described as the synchronic relation, while the anterior-posterior hemispheric relation may be described as the diachronic relation.

Also of interest in Blake’s black-and-white illustration is something I’ve noticed only for the first time: each of the Zoas is associated with a compass point. Tharmas is the West, Luvah is the East, Urizen is the South, Urthona is the North. This association of the Zoas with the four directions reinforces my view that they are the same “Guardians of the Four Directions” one finds in virtually all cultures, and clearly relates the Zoas to the cardinal points of the Sacred Hoop or Medicine Wheel of North American aboriginal religion,


Sacred Hoop /Medicine Wheel

Sacred Hoop /Medicine Wheel

Now comes the interesting bit: “The Sacred Hoop is in language”, say my Native friends. And “to speak from the centre of the voice” is to speak from the centre of the Sacred Hoop. The vital centre is the place of integrity, sincerity, authenticity. The vital centre is what we call the Logos, for in Christian iconography, it is also the position occupied by Christ on the Cross, surrounded by the four Evangelists. These evangelists (Mark, Matthew, Luke, and John) would therefore correspond to the Guardians of the Four Directions or the four Zoas,

Agnus Dei: Christian Mandala of the Fourfold Self

Agnus Dei: Christian Mandala of the Fourfold Self

So, what is called “the Christ” is not the name of a man. It is the name for the integral consciousness, or God-consciousness. Blake’s “Albion”, who is the Universal Humanity, is the Christ.

If “the Sacred Hoop is in language”, then the Zoas are also in language. This accounts for why Jean Gebser and Rosenstock-Huessy looked to grammar for a new understanding of the human form. The Zoas are present as grammatical forms and different styles of speech. Fundamentally, the Zoas, or Guardians, are represented in the system of personal pronouns. The most basic pronoun system is Korean: You, I, We, He (there is no differentiation of the “third person”, apparently, of “she” or “they” or “it” as in English). This is represented in Rosenstock-Huessy’s grammatical method and “cross of reality”,


Rosenstock's distribution of the pronouns on the cross of reality

Rosenstock’s distribution of the pronouns on the cross of reality

There is, apparently, no human language so far inventoried that does not have at a minimum, a four-person system. It’s a human universal. It not only seems to reflect the nature of the divided brain, but of our experience of physical reality as a fourfold structure, too: two times (past and future) and two spaces (inner and outer). Blake’s Zoas, in those terms, would appear to also represent the powers of times and spaces, or spacetime in its fourfold aspect, related quadrilaterally. The vital centre of the cross of reality corresponds to “Eternal Now”. It is the place of arising or origination, and is Gebser’s “ever-present origin”. To “speak from the centre of the voice” is to speak the Logos and to originate. To originate is to articulate. To articulate is both to differentiate and yet integrate. To “speak from the centre of the voice” is to intend a world. The Logos is, in those terms, the creative principle.

If this is so, then integral consciousness is not simply consciousness of the Logos, but is the Logos — consciousness as the Logos. The Logos is the unifying or integrating principle.

If this is the case, then the point of origination of the Holling Adaptive Cycle is not where it seems, but at the intesection of the two loops of the Attractor, just as it is in the Strange Attractor. That’s the balancing point. That is the same “centre of the voice”, and seen in this way, the four states of the Adaptive Cycle are really the same Guardians of the Four Directions we encounter universally. Reorganisation and release, conservation and growth are the same four Zoas, and the same arms of Rosenstock-Huessy’s “cross of reality”. But this only becomes evidently so when we consider the Adaptive Cycle as a Strange Attractor. The place of origin is not at the periphery, but at the centre where the loops intersect. Grammatical speech is, in those terms, a Strange Attractor. The circulation of speech in society follows the path of a Strange Attractor, and in those terms, Holling’s Adaptive Cycle as well.

The four states of the Adaptive Cycle co-exist at the same time. They don’t really follow one another. At any one time, though, one state is more pronounced than the other except where the pathways intersect. Don’t you find that peculiar? Where the pathway of the Adaptive Cycle intersects, release, reorganisation, conservation and growth are perfectly balanced. Potentiality and Connectedness (or coherence) are at an optimum. So, if the Adaptive Cycle really does map a Strange Attractor, that centre is the real place of origination, not at the periphery. And that centre would correspond to what Gebser calls “vital centre” or “ever-present origin” or “Eternal Now”.

If we take the centre of the Adaptive Cycle as its place of origination or arising, then it becomes rather evident that the Adaptive Cycle is identical with four-armed Shiva’s dance of “creative destruction”. The Adaptive Cycle is Shiva, too,

Shiva Dancing the Apocalypse

Shiva Dancing the Apocalypse



12 responses to “Just Another Strange Attractor”

  1. Scott Preston says :

    One of the things I should have covered in this post is what happens to time in the Adaptive Cycle if we consider its place of origin to be the centre, rather than the periphery. At the centre, we see, everything is in balance — growth, conservation, release, and reorganisation. But since growth, conservation, release, and reorganisation describe temporic states or succcessive stages of the cycle, how can there be temporicity at all if, at the centre of the cycle, everything is in balance? At the centre of the cycle, all states co-exist and in those terms, the centre of the cycle would be timeless. Or perhaps we should say, like Blake, timelessness in the very midst of temporicity.

  2. Scott Preston says :

    It’s not directly related to today’s posting, but I received this in my inbox just after posting from “The Nation”, William Astore on the “new normal” in the military — a “Post-Democratic Military”.


    Might as well say as much as a “post-modern” or “post-Enlightenment” military, since they all mean much the same thing as “the new normal”.

  3. LittleBigMan says :

    “Grammatical speech is, in those terms, a Strange Attractor.”

    Generally speaking, “words” can be as powerful as deeds. It seems to me they carry the energy of our thoughts, emotions, and intentions, and like actions they can have repercussions enshrined even in our laws (e.g. anti-defamation lawsuits, perjury laws, etc.)

    But it seems to me that the most important thing we have to keep in mind is “respondeo etsi mutabor.” Yes, how we respond in action or words will change us.

  4. abdulmonem says :

    When the divine attractor is forgotten and the human denies that he is a divine being and embarks on straying journey through asking about his origin and the aim of life, as if there were no prophets or seers who have put sober responses to these questions. When the story of Adam who has been taught the system of naming things (language) is abnegated and the crooked of the humans turn to stories that emphasis the primitiveness of the human in the cultural sense or the amoeba origin in the biological sense, denying the soul of the human form as the source of the human consciousness that enable humanity to built all types of civilizations. When the limits are exceeded and the prohibited becomes permissible and the usury ethos of loving money and secluded life become the adage of the civilization, it is natural to face all these crises. The story of the middle east illustrates the ugliness of the struggle between the different forces in their naked forms.

  5. dadaharm says :


    Personally, I would not equate the adaptive cycle with a strange attractor or the vital center. The picture you use of the adaptive cycle is just that: a representation of the cycle, using the variables of potential and connectedness.

    It omits the important variable of resilience. Adding resilience to it, you would get a three dimensional representation that would look totally different.

    I think a link with Blake’s four zoas can (and should) be made in a different way. One can see each adaptive cycle as a way of balancing the four zoas. Then the reorganisation phase would be the birth or invention of a new way of balancing the four aspects of reality. The balance then goes through a period of adolescence and one of maturity. In the end the balance fails, probably because one aspect becomes too dominant. Then a new balance is needed. Once it is found, the cycle starts over again.

    The history of humanity going through several adaptive cycles (like civilisations or consciousness structures) can then be seen as humanity trying several different ways of balancing the four zoas. Hopefully humanity has learned something from past failures.

    In short, sometimes a similarity of a representation or picture has meaning and can be used to obtain a deeper understanding, but there are also times where a similarity is just a similarity.

    • Scott Preston says :

      It omits the important variable of resilience

      No it doesn’t. The adaptive cycle IS the resilience. Otherwise, it wouldn’t be an adaptive cycle it would be a dissipative and entropic one. And clearly, it’s not entropic. On the whole it is neg-entropic. Resilience is the very essence of the adaptive cycle, and not a variable of it.

      I think you might be confused by the “release” phase of the cycle, that is, death or the entropic phase. But “release” here means releasing nutrients that then become part of the cycle again. Death or release is part of the very resilience of the ecosystem. If there was release without a following reorganisation, then you would have not a cycle but dissipation and dissolution. The “release” phase really tests the resilience of the system as a whole.

      Now, it terms of the Zoas, I think you’ve missed Holling’s rather important message about “nested” adaptive cycles, just as Rosenstock-Huessy’s “cross of reality” applies at the micro- and macro-scales, and isn’t about any one particular macro-structure to a singular reality. Civilisations are not closed loops. They interact with other types of civilisations, borrowing and lending elements and energies (or sometimes stealing their energies). In fact, they are never in one state of the adaptive cycle, but constantly releasing and reorganising, conserving and growing even as they are appropriating values from other civilisations and shucking off their own in exchange. That also belongs to “resilience”

      The issue is dynamic equilibrium, which is also the issue of the Zoas within the fourfold self. A civilisation may accentuate one of the Zoas at the expense of the others, in which case it is in a constant state of self-conflict or disequilibrium (lack of equanimity by another name). But it’s pretty clear that a resilient civilisation is one where the four stages of the adaptive cycle are held in balance. And the only place in the adaptive cycle where the processes of growth, conservation, release, and reorganistion are held in check and in balance is at the centre of the cycle itself.

      Ditto for the human form. And that’s all there is to it. If it were not so, the form would be dissipative, and that is the condition that Blake calls “non-Entity”.

      • dadaharm says :


        On this page at the automatic earth blog there is a nice three dimensional picture of the adaptive cycle. It uses the three variables wealth, connectedness and resilience. Let me just add that in the conservation phase the variables wealth and connectedness increase, while resilience decreases.

        Ecosystems are complex adaptive systems. I am inclined to see complex adaptive systems as entities that try to balance different aspects of reality. That is not a theory, just an intuition of mine. So we can wisely agree to disagree about this aspects of ecosystems,civilisations etc.

        • Scott Preston says :

          The 3-D rendition of the Holling Adaptive Cycle is not Holling’s, I’ll bet. If it is Holling’s, he’s contradicted himself. If it’s not Holling’s, it’s a distortion of Holling’s Adaptive Cycle. My guess is that it is the latter, and that it is not Holling’s at all.

          First of all, there is no connection between the 3-D rendition and the Adaptive Cycle as represented in my post, reposted from


          The differences are 180 degrees opposed to one another. The main difference is that the Automatic Earth 3-D version is a closed loop, while the original is an open loop, and not a closed circuit. Open and closed are completely contradictory, wouldn’t you say?

          The closed loop 3-D version seems to take certain liberties with the original, so my guess is it’s not Holling’s take at all. The closed loop of the Adaptive Cycle in the 3-D version (which isn’t 3-D at all really, its a two dimensional construct placed within a cube, that’s all) basically returns the meaning of the adaptive cycle to the meaning of the ancient ouroboros — an image of the Eternal Recurrence of Same. Supposedly, this eternal recurrence of same then becomes interpreted as “resilience” in the 3 D rendition.

          That’s absurd. That’s not what resilience means. Energy does not follow the exact same pathway over and over forever and ever. But that’s what the closed circuit suggests. On the other hand, in the Strange Attractor, the energy never follows the same path repeatedly, as should be evident. It just follows the same pattern. But that’s a big difference.

          Resilience is never a matter of the eternal recurrence of same, so I’m calling “bullshit” on that 3-D representation of the adaptive cycle. I don’t believe that it’s Holling’s at all, but someone’s distorted interpretation of Holling who has misconstrued resilience as eternal recurrence.

          • dadaharm says :


            The 3-D picture is how Hollings defines the adaptive cycle. He uses the three variables resilience, wealth and connectedness to obtain it.

            The closure of the loop is clearly a simplification. One sees each of the adaptive cycles that follow each other as being exactly identical. Of course, you are correct in that they never are precisely identical. (A realistic picture where the different cycles are slightly different would be somewhat messy.)

            Your idea about what resilience is, is clearly different from what Holling means by resilience.

            • Scott Preston says :

              More than a simplification, it’s an error. In fact there are two errors in that illustration if it is Holling’s. Firstly, it leaves the impression that an ecosystem is self-contained and self-enclosed, which is clearly false, and is a return to the faulty logic of the ouroboric mentality. That is, a closed loop does not evolve. It’s such an elementary error compared to the first representation of the Adaptive Cycle.

              Secondly, if Holling has made resilience a variable of the Adaptive Cycle, then he’s made a crucial mistake. It makes absolutely no sense to make resilience a variable of adaptation, because non-adaptation means lack of resilience. Resilience is built right into the Adaptive Cycle itself, is the very essence of it. If an ecosystem is not adaptive, then it’s not resilient. And if it’s not resilient, it’s nonsense to talk about it being adaptive or as following an “adaptive cycle”.

              That’s irrational.

  6. Scott Preston says :

    Holling’s Adaptive Cycle is really just an elementary interpretation of the seasons of an ecosystem, isn’t it?: spring, summer, fall, winter corresponding to growth, conservation, release, and reorganisation, following each other in succession. They repeat themselves annually, And although they follow the same pattern annually, they don’t follow the same pathway.

    But how far can you reasonably apply that seasonal model to the life-cycle of human civilisations? Well, Oswald Spengler did just that in his controversial The Decline of the West. Pretty much the same cyclicity which Gebser critiqued as “Vitalism” and illicit “biologism”. As a closed loop, the Adaptive Cycle conforms to Spengler’s “seasons” of a civilisation, which is a resumption of the notion of fate.

    But, if the adaptive cycle is at all relevant as a model of civilisational adaptiveness, then it must have some bearing on Gebser’s taxonomy of civilisations as four structures of consciousness: the archaic, the magical, the mythical, and the mental-rational consciouness as “seasons” in the evolution and history of consciousness — archaic winter, magical spring, conservative summer, and mental-rational fall.

    And this idea of fatedness informs the idea of an “automatic Earth” — the Earth as an automaton or kind of robot. Highly questionable, since it seems to want to conserve linearity and mechanism as an explanatory principle.

    Anyone familiar with Gebser would understand why Gebser would have to reject such a linear and chronic interpretation of the Adaptive Cycle, which is also his critique of Oswald Spengler. Gebser rejects “fate” as an explanatory principle. Gebser’s view of the integral consciousness is that it is achronic (as it is arational and aperspectival) as befits his notion of “time freedom”.

    Furthermore, if the poles of the adaptive cycle correspond to the seasons of an ecosystem, then a year is the minimal unit of time for the adaptive cycle to become manifest.

    Now, the anthropogenic explanation for climate change states that it is now human beings who are driving this cycle (and driving it off a cliff) — most especially the “release” stage (entropic phase) corresponding to “Fall” beyond its limits. Release corresponding to death is the present fear of planet death — ie, the release of greenhouse gases (carbon dioxide, methane, etc). So hubris is just another name for this pushing of the release part of the cycle too far. In other terms, human beings are doing something to time, pushing it off its axis, as it were. But the axis of time is the where the loops of the adaptive cycle intersect. At that vital centre, the times are in joint are they not? There is an equilibrium of the times — reorganisation, growth, conservation, and release are symmetrical only at that axis. This is Gebser’s achronic and is identical with what he calls “the vital centre” and “ever-present origin”.

    The four states of the Adaptive Cycle don’t really follow one another. Each is continuous operative in any ecosystem simultaneously. Release is going on all the time, reorganisation is going on all the time, growth is going on all the time, and conservation is going on all the time. These are contradictory forces, and yet they are held in relative equilibrium. Each of the states of the adaptive cycle contradict one another, represent a principle of reversal.

    And in this contradicting nature, they resemble also Blake’s conflict of the four Zoas, too.

    The centre of the Adaptive Cycle is the axis of times. That’s clear enough. It’s only there that the four elements of the cycle become visible at all. And traditionally, this centre has been called “the still point of the turning world”, and has been represented mythologically as the Tree of Life or Ygddrasil. Reorganisation, growth, conservation, and release are only the branches of that centre, or, more appropriately, the eccentrics.

    Does the Adaptive Cycle have any connection with Yeats’ “widening gyre” of his famous poem “The Second Coming”? Very likely that Yeats’ “gyre” is the same adaptive cycle, including the roles of the Falconer and the Falcon in describing the pathway of the widening gyre — centripetal or centrifugal force in disturbing the gyre. The falcon pursues an increasingly eccentric flight path threatening the gyre with dissipation. And that is the situation called “runaway”.

    It’s only at every point of the gyre where the Falcon and the Falconer remain connected and mutually perceptible that the gyre remains in tact. Yeats’ widening gyre is a perfect description of anthropogenic climate change. The Falconer is the vital centre of the gyre, and correspondingly of the adaptive cycle. And only there are the times in joint.

    • dadaharm says :


      Yes, the adaptive cycle is in essence the ancient idea of using the four seasons to describe the life cycle of an ecosystem or a civilisation.

      (A lot of complexity theory is like that. Turning ancient myths into mathematics. I guess, this makes the myths more understandable for modern rational humans.)

      I agree completely that Spengler’s ideas about how civilisations evolve corresponds to the theory of adaptive cycles.

      I also think that it is possible to see the sequence of consciousness structures as an adaptive cycle. The reorganisation phase would be the magical consciousness structure that came into being with invention or discovery of language. Then the exploitation and conservation phase would correspond to the mythical and the mental-rational consciousness structures.

      This would then give a panarchy, where you have a short adaptive cycle spanning a single civilisation, a longer one that spans a consciousness structure and a still longer one describing a sequence of consciousness structures.

      To fit in Gebser, it becomes important to understand what the collapse or release in the adaptive cycle means. Holling defines it as the loss of connectedness. In societies that would mean, in my opinion, that the central power structures loose their power to control society. So it implies chaos, but also possibility and freedom.

      Once the release phase starts a complete reorganisation of society becomes a possibility. That means a kind of revolution. This does of course require that sufficient people are aware of what is happening. Moreover, useful ideas about what needs to be done must be available.

      In such a situation the reorganisation phase basically immediately follows the release phase or maybe even coincides with the release phase. This is why I think that Gebser´s ideas are also perfectly understandable within the theory of the adaptive cycle.

      Often the adaptive cycle is a closed loop, but now and then it is not. Then the reorganisation phase results in something truely new and different. An evolutionary discontinuity.

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