Astronomy / C.G.Jung / Philosophy / Science

ANGELS FEAR – Sacred aesthetics of fractal recursion

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Sacred Destroyed

Angels Fear – The Sacred Destroyed

fallenAngel’s Fear is an obvious wordplay which crossed my mind after a blog reader pointed out that Bateson’s book  Angels Fear: Towards an Epistemology of the Sacred might be of relevance to me.  The title created immediately multiple associations and images,  so  I became curious and got the book.  Bateson presents from a anthropologist view concepts and topology of structure- determined recursion – in a nutshell – sacred aesthetics of fractal recursion.  Douglas Hofstadter articulated fractal recursions mathematically in his book Goedel, Escher, Bach: An Eternal Golden Braid , 1979. The Bateson’s (father and daughter) define ecology and aesthetics, combining them to ecological aesthetics viewed at every level from the cellular to the cultural to the religious from a communicative perspective.  Angels Fear is food for thought and relevant indeed, this  book is for anyone who feels that there is more to life than logic and science. Bateson’s main thesis is that aesthetics, beauty, and the spiritual are as valid as logic and science. It is an original synthesis of cybernetics, biology, anthropology (his daughter is anthropologist) but avoids New Age. The book resounds very well with my Jungian and spiritual side, although Jung has covered that area much broader and more coherent from empirical science as a physician.

Like the psychoanalyst C. G. Jung,  Gregory Bateson never really says what the sacred actually is. To both, it is just beyond their scope, something which is beyond facile descriptions. The sacred ( to me the religious realm) is common intuitive knowledge in every human experience. The Ego (lets say mind) and  unconsciousness cannot meet  easily., hence  there is a necessary gap between the two – so Bateson is essentially saying that our attempts to explain our human experience is always and necessarily incomplete. And that there is a lot more to life and mind than meets consciousness and unconsciousness depersonified. That is true, but hardly new – in Bateson’s words:

‘But the bits and pieces of mind which appear before consciousness invariably give a false picture of mind as a whole. The systemic character of mind is never there depicted, because the sampling is governed by purpose.  We never see in consciousness that the mind is like an ecosystem – a self-corrective network of circuits. We only see arcs of these circuits. And the instinctive vulgarity of scientists consists precisely in mistaking these arcs for the larger truth, i.e., thinking that because what is seen by consciousness has one character, the total mind must have the same character.Freud’s personified ‘ego’, ‘id’, ‘super-ego’ are, in fact not, truly personified at all. Each of his components is constructed in the image of only consciousness (even though the component may be unconscious) and the ‘consciousness’ does not resemble a total person. The isolated consciousness is necessarily depersonified. The whole iceberg does not have those characteristics which could be guessed at from looking only at what is above water. I mean: the iceberg does – mind does not. Mind is not like an iceberg.”

The way that humans have dealt with this feature of human existence were religions.

The point is that, even before modern technology, something had to be done about the innate split between consciousness and the rest of the mind, because the unaided consciousness would always wreck human relations. Because the unaided consciousness must always combine the wisdom of the dove with the harmlessness of the serpent. And I will tell you what they did in the old Stone Age to deal with that split. Religion is what they did. It’s that simple, and religion is whatever they could devise to beat into man the fact that most of him (and, analogously, most of his society and the ecosystem around him) was systemic in nature and imperceptible to his consciousness.  This included dreams and trances, intoxication, castration, rituals, human sacrifices, myths of all sorts, invocations of death, art, poetry, music and so on. And of course, they did not and could not really say or know clearly what it was they were doing or why. And, often, it did not work.” [Bateson]

Oh yes, it did work. The rise of psychoanalytic  but also New Age quacks  clearly is attributed to the decline of religion in the West. After pseudo-religious totalitarian states collapsed, the former religions came back and vice versa. To fully live in our humanness we must ‘give away’  our Ego to  our Self but  resist the temptation futile attempts to describe or explain these experiences in a language of conscious .



Here is what Wittgenstein says about this individuation (or religious) effort.

“My whole tendency and I believe the tendency of all men who ever tried to write or talk Ethics or Religion was to run up against the boundaries of language. This running up against the walls of our cage is perfectly, absolutely hopeless. Ethics so far as it springs from the desire to say something about the ultimate meaning of life, the absolute good, the absolute valuable, can be no science. But it is a document of a tendency in the human mind which I personally cannot help respecting deeply and I would not for my life ridicule it. ” [1929]

In this quote we can see that whatever we manage to concoct remains entirely our own subjective property (and thus a sense which never can proved), but that, on the other hand, we can and must transcend by making efforts to move beyond the ‘limits of language’, by bringing into question our given limits and by choosing  domains where our understandings break down. In the view of Bateson, the willingness to make this effort is a symptom of  the sacred . So far so good. Did not mathematics, art and nature always cross the boundary of language in the search of ascetics and perfection?

Structure-determined recursion

Escher - structure determined recursion

Escher – structure determined recursion

Angels Fear argues that the science of biology required an ecological aesthetic because biology, like any self-recursive communication system, must become aware of the disruption of its own relations with the unity of nature  to understand science’s limitation in a spiritual (if not even religious) realm.   In other words, biology becomes bad science,  by violation of ” Gods plan”, be it tho one known by  Christianity or Taoism and/or Zen Buddhism.  Christianity and Western cultures subsequently science  have a linear concept of time and structures.  C. G. Jung understood the true nature of time (linear, cyclical, and recursive), which generations have struggled to comprehend except ancient religions Taoists and Hindus knew.

There are two processes of recursion, the one semantic and interpretative , the other structural.  Like C. G. Jung,  the Batesons conclude that the world of signals and signs  (or images and symbols) are an universal and collective aspect of living systems, neglected by hard (and I might add soft) science).  Goedel, Escher, Bach describes many instances of such recursion and self-reference, where symbols and archetypes speak about or refer back to themselves.  To describe such self-referencing objects, Hofstadter coins the term “strange loop”. To escape many of the logical contradictions brought about by these self-referencing objects, Hofstadter discusses Zen koans. He attempts to show readers how to perceive reality outside their own experience and embrace such paradoxical questions by rejecting the premise.

Computer programs use functions (or methods in OOP) which can call other functions, and also themselves. When a function calls itself, it is called recursive. The nature of programming is itself recursive. Programming languages are defined by grammars which are recursive, which is why programming has infinite possibilities. On a higher level, the programmer is always seeking to abstract and generalize essential pieces, so that they can be re-used in different contexts instead of re-written. A programmer and nature  tries to repeat their processes by recursion),  always attempting to find the most elegant solution to the problem. Eventually the solution arrives at a “metastable place  and when in the future that model itself is transcended, the new model will be inside yet a higher meta-model (recursion), and so on. The higher up this pyramid of models, the more perfect the program seems. However, this pyramid has no end. This is why perfection is impossible – but beauty is the way and the way is the destination.

Recursion is all around us. It is in our computers, in our cells, in the plants we eat, in our brain, in the land we walk on, in Goedel’s incompleteness theorem, in Escher’s art, and in Bach’s music.

Mathematical aesthetics

The Platonic Solids sacred-geometry

The Platonic Solids

Kepler presents in Harmonices Mundi (The Harmony of the World, 1619) his findings about the concept of congruence with respect to diverse categories of the physical domain: regularities in three-dimensional geometry, the relationships among different species of magnitude, the principles of consonance in music, and the organization of the Solar System. Here we seek to highlight issues that provide a flavor of his thought:

“On the regular figures, the harmonic proportions they create, their source, their classes, their order, and their distinction into knowability and representability.”

This expanded his investigation of three-dimensional geometric shapes, notably of the semi-regular Archimedean Solids earlier, in the 1597 Mysterium Cosmographicum. Kepler proposed that a nested arrangement of the Platonic Solids determines the spacing between the planetary orbits of the known five planets.   As engineer, and having programmed  highly complex communication systems in a former live,  I did observe, that only aesthetic solutions are good solutions (and programs).  Well, programming was art then, before MS came into the picture.  Angels fears resound from a biological view Greek philosophy: ” beauty can’t be evil”.

Indeed there are connections between mathematical aesthetics and spiritual receptiveness  (religiosity).  For example, I am having a hard time with my son and failed with daughter to show them how beautiful mathematic is. I am almost thinking it’s not my failure, but a systemic failure of a society which becomes intellectually flat and subsequently spiritual deaf (or vice versa). When I grew up, there was a book in our house that was called “The magic of numbers” – a brief history of numbers. Much later I read Hofstadter, with his unique synergy of  art, mathematics, music, philosophy, symbolic logic, computers, genetics, paradoxes, palindromes and Zen koans among many, many other things. Most of it is still over my head like some aspects  of structure- determined recursion. However this “nerd bible” is in a way like in religion and theology,  revealing or disclosing  some some form of truth or knowledge for (us) nerds:  differently stated by the  Austrian mathematician Kurt Goedel , the  Dutch artist M.C. Escher and  the Baroque composer Johann Sebastian Bach. It became a cult classic , while a later book,  I am a Strange Loop, goes to far darker side.

Hofstadter was fascinated by visual and conceptual loops: feedback, self-reference, recursiveness, anything that curved back on itself in an unexpected way.  Goofing around with a video camera, Hofstadter pointed it straight at the TV screen to create an infinite receding tunnel of video feedback, some copy cat of it you might have seen in any modern art museum. Those themes–recursive loops and the physical origins of consciousness–get braided together in I Am a Strange Loop in unexpected ways.  Goedel demonstrated in 1931 that conventional mathematics, which we think of as a supremely logical and consistent system, is actually capable of making all sorts of strange, paradoxical, self-referential statements about itself. There are mathematical statements that, while true, can never be proved. How can something be both true and unprovable? This idea, loosely known as “incompleteness,” came as a logical bombshell to all mathematical philosophers (like Wittgenstein)  but in a way was inherent in Heisenberg’s famous uncertainty principle. It turns out that mathematics isn’t a neat straight line; it’s a loop, and so is life (if you are lucky enough to have kids).

Now I do see here a connection with the human mind and the main thesis of Angles Fear. The brain, if seen  merely as a cluster of firing neurons (or like Freud of a linear,  determined machine), shouldn’t by rights be able to think–it shouldn’t be able to wake up, think, become aware of itself, and in doing so become an “I am” but it does. Just Plato observed in his famous cave example: reality is a strange, self-referential loop–it’s a mirage, but “a very peculiar kind of mirage … a mirage that perceived itself, and of course it didn’t believe that it was perceiving a mirage, but no matter–it still was a mirage.”

Hofstadter and Bateson occupy a middle ground: it’s neither spiritual nor is it locked into the cold neurological materialism of cellular mechanics.  The same rings true with  C.G. Jung, a friend of the great physician Pauli, to whom the human mind (and reality) is a bright, shimmering, self-sustaining miracle of collective archetypical : vague, metaphorical, ambiguous, and always exceedingly beautiful object oriented programming (OOP).  Actually on a side remark, Jung’s very ambiguous description of archetypes (per se), symbols and images can be easily likened  to objects and abstract classes found in computer science. My father lives in me, a faint but real copy of his software running on my neural hardware. Hofstadter says. “If you believe that what makes for consciousness is some kind of abstract pattern, then it’s sort of self-evident fact that whatever pattern exists in my brain could exist in other physical structures in the world.

Ecological aesthetics – fractal recursion



Living systems are recursive systems

Ever went hiking and looked closely to trees? Trees are beautiful and fractalTrees played an important role in the movie Avatar and in Tolkien books. Fractals can be  generated by a program that  defines a recursive process, and the resulting tree is a recursive structure. Curiously, such recursive structures and processes are found everywhere in nature.  This program grows a simple tree (no sun, no other plants, no storm) recursively, by adding two branches to the end of the current branch until it bottoms out. Bottoming out happens when the tree has branched a certain number of times. The size of the two new branches relative to the current one is determined by the sizeFactor variable. The angle at which the two new branches will branch out relative to the current one is determined by the angleFactor variable. The height of the first tree is determined by trunkHeight, and the number of levels of recursion (the number of times the tree branches into new trees until it bottoms out) is determined by depth. Investigation of social and biological systems is not equivalent to investigation of physical systems, Bateson states, for all social and biological science is participant investigation, unlike the observer-oriented science of physical systems.  As the example shows, this is not always correct for social science and as Pauli and Heisenberg found out not even true in quantum physics.  Angels Fear proposes an ecological aesthetics within the unity of life, akin to the notion of the unity inherent in the sacred aspects of religion – and I would see also in what C.G. Jung coined as collective archetypes. That requires an epistemology, a set of procedures about how one might investigate the phenomenon of unity and derive from further understanding of holism, its order and its organization. Many regularities contribute to their own determination. In biology, Bateson argues that recursive regularities cannot be simply read-out or treated solely in an abstract context.  Again the psychoanalytic C.G. Jung and the quantum physics Pail would disagree. According to Angels Fear, another pattern  permits rather than to deny circularity at the point of re-entry. These processes ‘bootstrap’ circularity so that any ‘top’ is continuously re-cycled through a ‘bottom’ and thus all cycles in between are able to support themselves in their own circularities creating aesthetics.

The beauty of a landscape or organism affects human emotions as well as ecological facts. Aesthetic preferences determine whether landscapes are viewed as beautiful, sustainable or threatened. Naturally these preferences are subjective and have changed through time and may reflect sociological context. However, while communication of ecological research may change public perception of nature, certain facts remain until today. A house on the hill not only looks good, but one does not get the feet wet, the air more healthy and you see whats coming. Beauty has always been recognized as a fundamental part of the human experience but, like truth and evilness, beauty is a complex term that resists simple definition (outside mathematics). Among the more persistent descriptions are terms like: a harmony of parts, unity in diversity,low complexity, high integration, recursive patterns and clarity—qualities readily observable in nature. The French scientist Henri Poincaré (1913:336) wrote: “…the scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and if nature were not worth knowing, life would not be worth living”.  Aesthetic preferences clearly have played an evolutionary role in the development and the persistence of our species. C.G. Jung discussed how collective cultural responses , partially via development of aesthetic symbols over time, may have led to the survival of ancestral hominids through a deeper understanding of ecological phenomena, nature and human mind.

True and False - Right or wrong - good or evil - black or white

True and False – Right or wrong – good or evil – black or white

Seen from aesthetic epistemology, Kant’s definition of aesthetic judgment is exemplary of the subjective activity of judgment, the harmony of imagination and understanding. Unlike ordinary empirical judgment, aesthetic judgment phenomenologically reveals to us a synthesizing holistic activity.  Aesthetic judgment is in the center of Kant’s epistemological project in order to show that our minds are capable of getting at something outside of ourselves in the world. Furthermore it commits to the necessary relation between the aesthetic judgment’s beauty and the reflective judgment’s logical principle of nature’s purposiveness. The principle of nature’s purposiveness must be grounded in the principle of beauty because of empirical cognition. On can indeed characterize aesthetic judgment as a resistance to or interruption of cognition.

Science has its own version of epistemology, but most of these lie in a scientific methodology and axioms. Western science rarely argues from a holistic view, and if so, it becomes like social sciences often soft and meaningless. Those aspects of the world that scientific method cannot determine through breaking or interfering the object – routinely taken care in the realm of synchronicity and spirituality, and remains unexamined. It has become too easy for modern science to continue to treat the biosphere and humans as it had treated any other mechanism since the sixteenth century. Ecology as a holistic phenomenon would be a very different sort of undertaking, not only in a switch of focus from the physical dimensions of ecological objects, but also in the methodological path it takes. Explanations derived from quantitative examination would have to be reconsidered or abandoned, as would the inferences of drawn from these correlations. The major investigation would be one of how parts fit into a holistic order, and vice versa, how holistic order is contained in the recursion. Such as investigation would also require to add some modesty in the rationality driving  modern science.  I do not argue that this epistemology of aesthetic holism incorporating needs to return to the mediaeval realm of superstition, nor did it mean uncritical acceptance of any New Age  spirituality or take over world-views of  major religions.  In fact, aesthetic preference may have affected our behaviors and our understanding of the natural world from ancient times to the present. Like  social scientists, ecologists and biologists rarely acknowledge the way  biases  can affect research, and these may be significant and therefore worth discussing.  It is important for scientists to recognize the inherent and subtle, yet powerful, persuasion of beauty as it shadows ecological research from conception through interpretation.




Mutual  acceptance of the idea that holism, unity and beauty are purposefully coincident with each other should be an integral part of any modern science deciphering Gods creation – particularly the human “imago dei”. Bateson’s argument in Angels Fear that when humans presume to ‘play God’ the consequences are grave, is sound. Also the presumption that humans can play God tempts fate in the same way that all acts of hubris do. Developmental biologist, a branch of biology that has generally been critical of the over-arching claims of the molecular biologists who have insisted for fifty years that they have discovered the blue-print of life just shows to him a wrong sense of the sacred.  When the book strays in the intuitive realm of modern physics or Jung’s psychoanalysis  (synchronicity and individuation) his claims are not backed by empiric science and a bit dusty (or too abstract or over my head).

For the artist, the making of the perfect piece of art has always been a purification process of his soul. When he finished his work, he knew that gods and humans alike would feel pleasure when they see the sculpture.  Investigation nature, likewise ancient Greek´stated God was a geometer, and felt that aesthetically appealing objects were beautiful in and of themselves.  Plato felt that beautiful objects incorporated proportion, harmony, and unity. Similarly, in his Metaphysics, Aristotle found that the universal elements of beauty were order, symmetry, and definiteness. That was clearly revived in Renaissance art again and transferred to science (just think of the Astronomer Kepler) and on secular issues of human life. Medieval art focusses´highly on religious images and symbols. Post-modern aesthetics  often rebels against beauty in modernist art. This Anti-Aesthetic reaction has been described “kalliphobia” (after the Greek word for beauty kalos) which leads to an inner and outer wasteland.   Although ascetics is determined by cultural contexts, a common ascetic clearly is visible and sacred. I like to believe it is recursional.

Gödel, Escher, Bach: An Eternal Golden Braid , Douglas R. Hofstadter

Angels Fear: Towards An Epistemology Of The Sacred by Gregory Bateson and Mary Catherine Bateson ( 2004)

Complex/Archetype/Symbol in the Psychology of C.G. Jung. J. Jacobi;

Flying Saucers: A Modern Myth of Things Seen in the Sky. (From Vols. 10 and 18, Collected Works). C.G. Jung; R.F.C. Hull, trans.

Four Archetypes: (From Vol. 9, Part 1 of the Collected Works of C. G. Jung)

Psychology and the East: (From Vols. 10, 11, 13, 18 Collected Works). C.G. Jung;

Psychology and the Occult: (From Vols. 1, 8, 18 Collected Works). C.G. Jung;

Psychology and Western Religion: (From Vols. 11, 18 Collected Works). C.G. Jung;

 Jung, C. G., Pauli, W. (1952): Naturerklärung und Psyche. Zürich: Rascher (Download)

C.G. Jung (1955) Synchronicity: An Acausal Connecting Principle

Wolfgang Pauli und die moderne Physik. Virtuelle Ausstellung der ETH-Bibliothek

W. Pauli, The Influence of Archetypal Ideas on the Scientific Theories of Kepler

Kepler, Harmonices mundi, Harmony of the Worlds, 1619