The Evolution of Music

William Calvin  in his excellent book The Cerebral Symphony, speculates in the excerpt reprinted below about how music evolved in us. It is one of the unsolved riddles of natural selection. The occasion he writes about here is The Woods Hole Cantata, a once a year performance by the scientists at Woods Hole  who are also musicians.

“Many of the musicians, and most of the audience, are making their once-a-year appearance in church with this evening of music.  Quite a few scientists in my acquaintance are accomplished musicians who had to make a difficult choice between continuing their musical careers and their scientific careers. And so the weeks of practice for this night are a joy to such scientists, a chance to exercise their considerable skills once more. My choral career evaporated, alas, when my voice changed, but performances in church still have a special quality for me from having once been on the other side, singing Latin words that I didn't understand.

The pews and aisles were packed by the time I arrived. But I have, arguably, the best seat in the house: A commanding view, excellent acoustics, room to stretch my legs during the concert, and I can even imitate conducting the chorus because I am out of sight at the rear of the church and few people will see me. There is only one slight drawback: One dares not fall asleep, under penalty of falling one floor and landing in the cellar below, undoubtedly with a great crash. I have the window sill above the cellar stairs, and I am wedged in, thanks to a mountain-climbing technique known as chimney bridging that I last used at Matkatamiba in the Grand Canyon. But there isn't the usual danger of becoming drowsy: I also have an excellent supply of fresh air, because the window is open. During pauses, I can hear it softly raining outdoors.

Much of the great music is church music, written to celebrate the faith and attract others to it. And so here with the Mass in F we have one of Bach's "Missae breve," descended from the Gregorian chants of the medieval Catholic Church, written for Lutheran services in Leipzig in the early eighteenth century, sung in a nineteenth-century Episcopal church on Cape Cod by and for a collection of late-twentieth-century scientists who would explain the world in very different terms from those used by many churchgoers.

Yet science is descended from the same roots as the philosophy of Bach and Handel; Newton surely considered himself to be attempting to understand deeply his Creator's works. In most cultures, there is little distinction between religion-philosophy- science; even in Western civilization, they were all one subject until only a few centuries ago, when religious and natural philosophy split apart, the former becoming theology and the latter again splitting in the last century to become science and what we now call philosophy. The scientists of Bach's time surely considered church music their music, not that of another tradition.

But music is music: It can stand by itself, transcending the centuries independent of rational and irrational beliefs about other things. No one really approaches modern religion like the proverbial cultural anthropologist from outer space ("But they organize all their good deeds around this gruesome symbol of torture, and their highest ritual is playacting cannibalism, and they constantly reaffirm their own version of what in other cultures they call magic and animism. They seem to expect members to check their brains at the church-house door!"). Yet cultures cannot simply start over fresh with a new vocabulary and new traditions untainted by past enthusiasms and misunderstandings; it is simply too easy to throw out the baby with the bathwater. Instead, religions rationalize the past in various ways and go on from there with the real business: relieving suffering and building hope and advancing understanding. The philosophers and scientists have merely become the understanding specialists over the last several centuries, But if we've left some of the excess baggage and comforting rituals behind, we still revere the music.

And I think that musical forms will have a lot to teach us about our brains. Folksinger Bill Crowfoot observes that children in many cultures, speaking many languages, still all use the musical form known as a "minor third" to harass their siblings:

Nyah-nyah, nyah, nyah, nyah, nyah.

The first few notes of Beethoven's Fifth Symphony, G-G-G-Eb, probably sound like "Thus, Fate knocks at the door" (or is it Kate?) in many cultures. The more elaborate forms of the Magnificat may not be as universal-but still, they resonate. Some tunes (which the Germans call Ohrwurm or "ear worm") seem to spread through the population like the latest respiratory infection. Why? Is there some niche in our brains, created by the language we speak, that predisposes us to certain melodies?

The robin red-breast sings in a loud clear voice in order to keep other robin red-breasts away from the bit of territory that it is on. But except for singing in the morning in the shower, I have never known a human being to utter sounds for this purpose.
the mathematician JACOB BRONOWSKI (1908-1974)

Music is nothing but unconscious arithmetic .... Music is pleasure the human soul experiences from counting without being aware that it is counting.
the mathematician G. W. LEIBNITZ (1646-1716)

Music is the arithmetic of sounds as optics is the geometry of light. 
the composer CLAUDE DEBUSSY (1862-1918)

MUSIC IS ONE OF OUR GREAT evolutionary puzzles. It demonstrates nicely the inadequacy of evolution by adaptation to explain some of our abilities. The anthropologists periodically suggest that musical abilities were evolved because of their usefulness, that they are an adaptation to social life, with music "soothing the savage breast," or some such explanation.

I'd concede some effect, especially since the chimpanzee "rain dance" has been shown to play a role in dominance display (though that typically leads to sexual selection, not. natural selection) but I cannot imagine how four-part harmony evolved, nor the abilities to weave the elaborate counter-melodies of Bach that seem to echo in my head. Maybe my imagination is simply inadequate to the task, but I'll bet that music is going to turn out to be a secondary use of some neural structure selected for its usefulness in some serial-timing task like language or throwing-and used in the off-hours for music.

If we come to understand why Bach's brain still speaks so compellingly to our brains today, we will have bridged the gap between primary evolutionary adaptations and the magnificent secondary uses that can be made of the same brain machinery. Music is an emergent property, unless someone can figure out how a lilting aria and a choral fugue and an arpeggio were shaped up by survival-sensitive adaptations. The program notes (attributed to "Senza Sordino" -a pseudonym which turns out to be an Italian musical phrase that translates to "without muting; with the loud pedal"!) for tonight's performance of the Mass in F and the Magnificat demonstrate some of the musical features that tickle our brains:
.
. . the final "kyrie eleison" is composed as a counterfugue- that is, each thematic entry is answered by its inversion. In the further course of the movement, Bach makes use of the contrapuntal techniques of stretto, parallel voice-leading, and mirror inversions of themes. 

As the fugal chorus builds to a climax, each voice enters one note higher than its predecessor; and the repetition of this device gives the impression of an endless succession of voices .... 

The phrase mente cordis sui calls forth an astounding harmonic progression, suggesting, in the course of some nine measures, D-major, F -sharp-minor, F -sharp-major, B-minor, D-minor, and, finally, D-major, the first trumpet bringing everyone back to the home key with a descending scale passage and trill that haunts the dreams of every trumpeter. 

Though musical tastes vary with the culture in which one is raised (and I am sure that some enterprising student will eventually do a Ph.D. dissertation on how a culture's musical structure is related to its language's grammatical structure), it seems likely that there will be a "deep structure" of music with a biological basis in the brain, just as a brain basis has been inferred for the deep grammar of languages. What is it about our brains that so disposes them to the minor third and to complex musical patterns, despite the lack of evolutionary adaptations for such musical patterns?

Though this question is seldom asked, I am sure that the standard answer would be the tie with language: Both music and language are sequences of sounds where recognizing patterns is all-important. Chords are simultaneous notes just as phonemes are; tunes are chains of chords just as words and sentences are chains of phonemes. And so natural selection for language abilities would, pari passu , gain us musical abilities as a secondary use of the same neural machinery. Maybe so. But the notion of stochastic sequencing on many parallel tracks as the key element of "get set" in ballistic movements suggests that both language and music are potentially secondary uses of the neural machinery for ballistic skills, that music might have more to do with modern-day baseball than modern-day prose.

The program notes end with:

Gloria Patri, gloria Filio, gloria et Spiritui sancto! Sicut erat in principio et nunc et semper in saecula. Amen. ("Glory to the Father, and to the Son, and to the Holy Ghost! As it was in the beginning, is now and ever shall be, world without end. Amen.")

The Latin translator adds to Mary's "hymn" the traditional invocation of the Trinity. (It does not occur in St. Luke.) Bach cannot resist the musical symbolism of triplets in the three invocations, to represent the tripartite nature of the Trinity, and a return of the opening music at the end, taking his cue from, "As it was in the beginning ... " But the musical return serves aesthetics as well as theology, making a perfectly satisfying close to one of the most perfect and satisfying works of the choral literature. 

There are many aspects of human brains that would vie for a trilogy if anyone tried to pick the three focal aspects of our humanity. Surely if one's criteria were traits whose improvements would help us survive the next century, the mental attitudes controlling cooperation, conflict resolution, and family size (all likely to be strongly shared with our primate cousins) would surely rank high.

But if one focuses on the primary traits via which we differ from the apes in an order-of-magnitude way, you can wind up with a curious trio: language, scenario-spinning consciousness, and music-three aspects of sequential patterns in our brains. Their beginnings are still dimly seen, but in their elaboration may lie the higher humanity.”

The Cerebral Symphony: Seashore Reflections on the Structure of Consciousness, William Calvin, A Bantam Book, 1990

The Information: A History, a Theory, a Flood

Freeman Dyson writes an interesting and provocative review of the new book by Gleick in the New York Review of Books, 3/10/11.

Gleick begins his book with a chapter titled "Drums That Talk". Dyson reviews this chapter and concludes:

"The story of the drum language illustrates the central dogma of information theory. The central dogma says, “Meaning is irrelevant.” Information is independent of the meaning that it expresses, and of the language used to express it. Information is an abstract concept, which can be embodied equally well in human speech or in writing or in drumbeats. All that is needed to transfer information from one language to another is a coding system. A coding system may be simple or complicated. If the code is simple, as it is for the drum language with its two tones, a given amount of information requires a longer message. If the code is complicated, as it is for spoken language, the same amount of information can be conveyed in a shorter message."

After two historical examples of rapid communication in Africa and France, "the rest of Gleick’s book is about the modern development of information technology. The modern history is dominated by two Americans, Samuel Morse and Claude Shannon. Samuel Morse was the inventor of Morse Code. He was also one of the pioneers who built a telegraph system using electricity conducted through wires instead of optical pointers deployed on towers. Morse launched his electric telegraph in 1838 and perfected the code in 1844. His code used short and long pulses of electric current to represent letters of the alphabet."

"Claude Shannon was the founding father of information theory. For a hundred years after the electric telegraph, other communication systems such as the telephone, radio, and television were invented and developed by engineers without any need for higher mathematics. Then Shannon supplied the theory to understand all of these systems together, defining information as an abstract quantity inherent in a telephone message or a television picture. Shannon brought higher mathematics into the game."

Dyson writes, "According to Gleick, the impact of information on human affairs came in three installments: first the history, the thousands of years during which people created and exchanged information without the concept of measuring it; second the theory, first formulated by Shannon; third the flood, in which we now live."

The reviewer writes a wonderful description of science:

"The information flood has also brought enormous benefits to science. The public has a distorted view of science, because children are taught in school that science is a collection of firmly established truths. In fact, science is not a collection of truths. It is a continuing exploration of mysteries. Wherever we go exploring in the world around us, we find mysteries. Our planet is covered by continents and oceans whose origin we cannot explain. Our atmosphere is constantly stirred by poorly understood disturbances that we call weather and climate. The visible matter in the universe is outweighed by a much larger quantity of dark invisible matter that we do not understand at all. The origin of life is a total mystery, and so is the existence of human consciousness. We have no clear idea how the electrical discharges occurring in nerve cells in our brains are connected with our feelings and desires and actions.

Even physics, the most exact and most firmly established branch of science, is still full of mysteries. We do not know how much of Shannon’s theory of information will remain valid when quantum devices replace classical electric circuits as the carriers of information. Quantum devices may be made of single atoms or microscopic magnetic circuits. All that we know for sure is that they can theoretically do certain jobs that are beyond the reach of classical devices. Quantum computing is still an unexplored mystery on the frontier of information theory. Science is the sum total of a great multitude of mysteries. It is an unending argument between a great multitude of voices. It resembles Wikipedia much more than it resembles the Encyclopaedia Britannica."

Dyson describes this flood of information in the context of evolution:

"The explosive growth of information in our human society is a part of the slower growth of ordered structures in the evolution of life as a whole. Life has for billions of years been evolving with organisms and ecosystems embodying increasing amounts of information. The evolution of life is a part of the evolution of the universe, which also evolves with increasing amounts of information embodied in ordered structures, galaxies and stars and planetary systems. In the living and in the nonliving world, we see a growth of order, starting from the featureless and uniform gas of the early universe and producing the magnificent diversity of weird objects that we see in the sky and in the rain forest. Everywhere around us, wherever we look, we see evidence of increasing order and increasing information. The technology arising from Shannon’s discoveries is only a local acceleration of the natural growth of information."

Dyson closes his review with some thoughts about the future:

"The vision of the future as an infinite playground, with an unending sequence of mysteries to be understood by an unending sequence of players exploring an unending supply of information, is a glorious vision for scientists. Scientists find the vision attractive, since it gives them a purpose for their existence and an unending supply of jobs. The vision is less attractive to artists and writers and ordinary people. Ordinary people are more interested in friends and family than in science. Ordinary people may not welcome a future spent swimming in an unending flood of information. A darker view of the information-dominated universe was described in a famous story, “The Library of Babel,” by Jorge Luis Borges in 1941.³ Borges imagined his library, with an infinite array of books and shelves and mirrors, as a metaphor for the universe.

Gleick’s book has an epilogue entitled “The Return of Meaning,” expressing the concerns of people who feel alienated from the prevailing scientific culture. The enormous success of information theory came from Shannon’s decision to separate information from meaning. His central dogma, “Meaning is irrelevant,” declared that information could be handled with greater freedom if it was treated as a mathematical abstraction independent of meaning. The consequence of this freedom is the flood of information in which we are drowning. The immense size of modern databases gives us a feeling of meaninglessness. Information in such quantities reminds us of Borges’s library extending infinitely in all directions. It is our task as humans to bring meaning back into this wasteland. As finite creatures who think and feel, we can create islands of meaning in the sea of information. Gleick ends his book with Borges’s image of the human condition:

We walk the corridors, searching the shelves and rearranging them, looking for lines of meaning amid leagues of cacophony and incoherence, reading the history of the past and of the future, collecting our thoughts and collecting the thoughts of others, and every so often glimpsing mirrors, in which we may recognize creatures of the information."

The Information: A History, a Theory, a Flood
by James Gleick
Pantheon,2011

We are all cyborgs now

Technology is evolving us, says Amber Case, as we become a screen-staring, button-clicking new version of homo sapiens. We now rely on "external brains" (cell phones and computers) to communicate, remember, even live out secondary lives. But will these machines ultimately connect or conquer us? Case offers surprising insight into our cyborg selves.

Amber Case studies the symbiotic interactions between humans and machines -- and considers how our values and culture are being shaped by living lives increasingly mediated by high technology.

The Phenomenon of Man

(For a downloadable version, click here.)

I first became aware of de Chardin in the early 1960s. In 1960 I started to work for IBM in Poughkeepsie, NY in the fledgling semiconductor industry. Some time after that, I can’t remember when, I heard an IBM speaker talking about the future of the computer industry. He closed by introducing an idea from de Chardin, the noosphere(1) . He said that the earth had gone through two stages of evolution (geosphere and biosphere) and was now entering the third (noosphere). And what our (the computer industry) purpose was to facilitate the creation of the noosphere – global knowledge, universal knowledge, accessible knowledge, and global consciousness. That was exciting, and the vision has stayed with me ever since. I still feel that I’m on that same journey, only I can see it clearer now (although it’s still a long way off).

Surprisingly (to me), I never read any of the original works of de Chardin until now when I saw the connection to the complexity thread I am following. The Phenomenon of Man was written in 1930, but not published until 1955 after de Chardin’s death (because of a conflict with the Catholic Church). The original was in French. The first English translation was in 1959.

“Pierre Teilhard de Chardin (May 1, 1881 – April 10, 1955) was a French philosopher and Jesuit priest who trained as a paleontologist and geologist and took part in the discovery of both Piltdown Man and Peking Man. Teilhard conceived the idea of the Omega Point and developed Vladimir Vernadsky's concept of Noosphere. Some of his ideas came into conflict with the Magisterium of the Catholic Church, and several of his books were censured.

Teilhard's primary book, The Phenomenon of Man, set forth a sweeping account of the unfolding of the cosmos. He abandoned traditional interpretations of creation in the Book of Genesis in favor of a less strict interpretation. This displeased certain officials in the Roman Curia and in his own order who thought that it undermined the doctrine of original sin developed by Saint Augustine. Teilhard's position was opposed by his Church superiors, and some of his work was denied publication during his lifetime by the Roman Holy Office. The 1950 encyclical Humani generis condemned several of Teilhard's opinions, while leaving other questions open. More recently, Pope John Paul II indicated a positive attitude towards some of de Chardin's ideas. In 2009, Pope Benedict XVI praised Teilhard's idea of the universe as a "living host" although the ecclesiastical warnings attached to his works remain.” (2)

In “A Globe, Clothing Itself with a Brain (3) ”, Jennifer Cobb Kreisberg writes, “Teilhard felt that the spark of divine life he experienced in the Egyptian desert was a force present throughout the evolutionary process, guiding and shaping it every bit as much as the material forces described by physical science. Teilhard would later codify this force into two distinct, fundamental types of energy - "radial" and "tangential." Radial energy was the energy of Newtonian physics. This energy obeyed mechanistic laws, such as cause and effect, and could be quantified. Teilhard called radial energy the energy of "without." Tangential energy, on the other hand, was the energy of "within," in other words, the divine spark.

Teilhard described three types of tangential energy. In inanimate objects, he called it "pre-life." In beings that are not self-reflective, he called it "life." And in humans, he called it "consciousness." As Teilhard began to observe the world described by science, he noticed that in certain things, such as rocks, the radial energy was dominant, while the tangential energy was barely visible. Rocks, therefore, are best described by the laws that rule radial energy - physics. But in animals, in which tangential energy, or life, is present, the laws of physics are only a partial explanation. Teilhard concluded that where radial energy was dominant, the evolutionary process would be characterized by the traditional scientific laws of necessity and chance. But in those organisms in which the tangential energy was significant, the forces of life and consciousness would lead the laws of chance and natural selection.

Teilhard then moved this insight forward. As the balance of tangential energy in any given entity grew larger, he noticed that it developed naturally in the direction of consciousness. An increase in consciousness was accompanied by an increase in the overall complexity of the organism. Teilhard called this the "law of complexity consciousness," which stated that increasing complexity is accompanied by increased consciousness.”

Teilhard wrote, "The living world is constituted by consciousness clothed in flesh and bone." He argued that the primary vehicle for increasing complexity consciousness among living organisms was the nervous system. The informational wiring of a being, he argued - whether of neurons or electronics - gives birth to consciousness. As the diversification of nervous connections increases, evolution is led toward greater consciousness.”

In The Phenomenon of Man, de Chardin writes, “This work may be summed up as an attempt to see and to make others see what happens to man, and what conclusions are forced upon us, when he is placed fairly and squarely within the framework of phenomenon and appearance.

Why should we want to see, and why in particular should we single out man as our object?

Seeing. We might say that the whole of life lies in that verb-if not ultimately, at least essentially. Fuller being is closer union: such is the kernel and conclusion of this book. But let us emphasise the point: union increases only through an increase in consciousness, that is to say in vision. And that, doubtless, is why the history of the living world can be summarised as the elaboration of ever more perfect eyes within a cosmos in which there is always something more to be seen. After all, do we not judge the perfection of an animal, or the supremacy of a thinking being, by the penetration and synthetic power of their gaze? To try to see more and better is not a matter of whim or curiosity or self-indulgence. To see or to perish is the very condition laid upon everything that makes up the universe, by reason of the mysterious gift of existence. And this, in superior measure, is man's condition.”

Later in the book, he writes, “In fact I doubt whether there is a more decisive moment for a thinking being than when the scales fall from his eyes and he discovers that he is not an isolated unit lost in the cosmic solitudes, and realises that a universal will to live converges and is hominised in him.

In such a vision man is seen not as a static centre of the world-as he for long believed himself to be-but as the axis and leading shoot of evolution, which is something much finer.”

The Phenomenon of Man is organized into four books and many chapters:

1. Before Life Came: The Stuff of the Universe, The Within of Things, The Earth in its Early Stages
2. Life: The Advent of Life, The Expansion of Life, The Ramifications of the Living Mass, The Tree of Life, Demeter
3. Thought: The Birth of Thought, The Deployment of the Noosphere, The Modern Earth
4. Survival: The Collective Issue, Beyond the Collective: The Hyper Personal, The Ultimate Earth, The Christian Phenomenon, The Essence of the Phenomenon of Man
   

It was interesting to me to note, although not surprising, that the book books parallel the four causes of reality proposed by Aristotle (4) – Material Cause (Before Life Came), Formal Cause (Life), Efficient Cause (Thought) and Final Cause (or purpose) – Survival.

Key to de Chardin’s thought is the concept of the without and within of things. Physics deals with the without of things. He summarizes the two laws of energy in these words:

“First Principle. During changes of a physico-chemical type we do not detect any measurable emergence of new energy.

Every synthesis costs something. That is a fundamental condition of things which persists, as we know, even into the spiritual zones of being. In every domain, the achievement of progress requires an excess of effort and therefore of force. Now whence does this increase come ?

In the abstract, one might assume an internal growth of the world's resources, an absolute increase in mechanical wealth corresponding to the expanding needs of evolution ; but, in fact, things seem to happen otherwise. In no case does the energy required for synthesis appear to be provided by an influx of fresh capital, but by expenditure. What is gained on one side is lost on the other. Nothing is constructed except at the price of an equivalent destruction.

Experimentally and at first sight, when we consider the universe in its mechanical functions, it does not reveal itself to us as an open quantum capable of containing an ever greater reality within its embrace, but as a closed quantum, within which nothing progresses except by exchange of that which was given in the beginning.

That is a first appearance.

Second Principle. In every physico-chemical change, adds thermodynamics, a fraction of the available energy is irrecoverably entropised "lost, that is to say, in the form of heat. Doubtless it is possible to retain this degraded fraction symbolically in equations, so as to express that in the operations of matter nothing is lost any more than anything is created, but that is merely a mathematical trick. As a matter of fact, from the real evolutionary standpoint, something is finally burned in the course of every synthesis in order to pay for that synthesis. The more the energy-quantum of the world comes into play, the more it is consumed. Within the scope of our experience, the material concrete universe seems to be unable to continue on its way indefinitely in a closed cycle, but traces out irreversibly a curve of obviously limited development. And thus it is that this universe differentiates itself from purely abstract magnitudes and places itself among the realities which are born, which grow, and which die. From time it passes into duration; and finally escapes from geometry dramatically to become, in its totality as in its parts, an object of history.”

De Chardin was convinced that since consciousness was evident in man, it must obviously exist in all things. “It is impossible to deny that, deep within ourselves, an 'interior' appears at the heart of beings, as it were seen through a rent. This is enough to ensure that, in one degree or another, this 'interior' should obtrude itself as existing everywhere in nature from all time. Since the stuff of the universe has an inner aspect at one point of itself, there is necessarily a double aspect to its structure, that is to say in every region of space and time-in the same way, for instance, as it is granular: co-extensive with their Without, there is a Within to things.”

Later he writes, “The within, consciousness and then spontaneity-three expressions for the same thing. It is no more legitimate for us experimentally to fix an absolute beginning to these three expressions of one and the same thing than to any other lines of the universe.

In a coherent perspective of the world: life inevitably assumes a pre-life, for as far back before it as the eye can see.”

So how is consciousness related to complexity. Simple things have little consciousness, complex things have a greater consciousness. “The degree of consciousness varies in inverse ratio to the simplicity of the material compound lined by it.”

“Spiritual perfection (or conscious ‘centreity’ (5) ) and material synthesis (or complexity) are but two aspects or connected parts of one and same phenomenon.”
He sums up evolution as the movement from a very large number of simple things (low complexity and low consciousness) to less numerous but more complex things with consciousness.

“We are seeking a qualitative law of development that from sphere to sphere should be capable of explaining, first of all the invisibility, then the appearance, and then the gradual dominance of the within in comparison to the without of things. This law reveals itself once the universe is thought of as passing from State A, characterised by a very large number of very simple material elements (that is to say, with a very poor within), to State B defined by a smaller number of very complex groupings (that is to say, with a much richer within).

In State A, the centres of consciousness, because they are extremely numerous and extremely loose at the same time, only reveal themselves by overall effects which are subject to the laws of statistics. Collectively, that is, they obey the laws of mathematics. This is the proper field of physico-chemistry.

In State B; on the other hand, these less numerous and at the same time more highly individualised elements gradually escape from the slavery of large numbers. They allow their basic non-measurable spontaneity to break through and reveal itself. We can begin to see them and follow them one by one, and in so doing we have access to the world of biology.

In sum, all the rest of this essay will be nothing but the story of the struggle in the universe between the unified multiple and the unorganised multitude: the application throughout of the great Law if complexity and consciousness: a law that itself implies a psychically convergent structure and curvature of the world.”

De Chardin then discusses the concept of energy. He poses another simple statement: To think, we must eat. From this derives the concept of two energies, one for the without and one for the within.

“First of all, the dependence. This is depressingly and magnificently obvious. 'To think, we must eat.' That blunt statement expresses a whole economy, and reveals, according to the way we look at it, either the tyranny of matter or its spiritual power. The loftiest speculation, the most burning love are, as we know only too well, accompanied and paid for by an expenditure of physical energy. Sometimes we need bread, sometimes wine, sometimes a drug or a hormone injection, sometimes the stimulation of a colour, sometimes the magic of a sound which goes in at our ears as a vibration and reaches our brains in the form of inspiration.

Without the slightest doubt there is something through which material and spiritual energy hold together and are complementary. In last analysis, somehow or other, there must be a single energy operating in the world. And the first idea that occurs to us is that the 'soul' must be as it were a focal point of transformation at which, from all the points of nature, the forces of bodies converge, to become interiorised and sublimated in beauty and truth.”

Later he writes, “Once again: To think, we must eat: But what a variety of thoughts we get out of one slice of bread! Like the letters of the alphabet, which can equally well be assembled into nonsense as into the most beautiful poem, the same calories seem as indifferent as they are necessary to the spiritual values they nourish.

The two energies-of mind and matter-spread respectively through the two layers of the world (the within and the without) have, taken as a whole, much the same demeanour. They are constantly associated and in some way pass into each other. But it seems impossible to establish a simple correspondence between their curves. On the one hand, only a minute fraction of physical energy is used up in the highest exercise of spiritual energy; on the other, this minute fraction, once absorbed, results on the internal scale in the most extraordinary oscillations.

A quantitative disproportion of this kind is enough to make us reject the naive notion of' change of form (or direct trans-formation)-and hence all hope of discovering a 'mechanical equivalent' for will or thought. Between the within and the without of things, the interdependence of energy is incontestable. But it can in all probability only be expressed by a complex symbolism in which terms of a different order are employed.”

De Chardin proposes two types of energy – tangential and radial. “…this fundamental energy is divided into two distinct components; a tangential energy which links the element with all others of the same order (that is to say, of the same complexity and the same centricity) as itself in the universe; and a radial energy which draws it towards ever greater complexity and centricity-in other words forwards.

From this initial state, and supposing that it disposes of a certain free tangential energy, the particle thus constituted must obviously be in a position to increase its internal complexity in association with neighbouring particles, and thereupon (since its centricity is automatically increased) to augment its radial energy. The latter will then be able to react in its turn in the form of a new arrangement in the tangential field. And so on.”

De Chardin devotes several chapters to his ideas about the origins of life and evolution. That information is beyond the scope of this essay but has been nicely summarized in a graphic (6) .



And, it is also summarized on Wikipedia:

"Teilhard views evolution as a process that leads to increasing complexity. From the cell to the thinking animal, a process of psychical concentration leads to greater consciousness. The emergence of Homo sapiens marks the beginning of a new age, as the power acquired by consciousness to turn in upon itself raises humankind to a new sphere. Borrowing Julian Huxley’s expression, Teilhard describes humankind as evolution becoming conscious of itself.

In Teilhard's conception of the evolution of the species, a collective identity begins to develop as trade and the transmission of ideas increases. Knowledge accumulates and is transmitted in increasing levels of depth and complexity. This leads to a further augmentation of consciousness and the emergence of a thinking layer that envelops the earth. Teilhard calls the new membrane the “noosphere” (from the Greek “nous,” meaning mind), a term first coined by Vladimir Vernadsky. The noosphere is the collective consciousness of humanity, the networks of thought and emotion in which all are immersed.

The development of science and technology causes an expansion of the human sphere of influence, allowing a person to be simultaneously present in every corner of the world. Teilhart argues that humanity has thus become cosmopolitan, stretching a single organized membrane over the Earth. Teilhard describes the process by which this happens as a “gigantic psychobiological operation, a sort of mega-synthesis, the “super-arrangement” to which all the thinking elements of the earth find themselves today individually and collectively subject.” The rapid expansion of the noosphere requires a new domain of psychical expansion, which “is staring us in the face if we would only raise our heads to look at it.”

In Teilhard’s view, evolution will culminate in the Omega Point, a sort of supreme consciousness. Layers of consciousness will converge in Omega, fusing and consuming them in itself. The concentration of a conscious universe will reassemble in itself all consciousnesses as well as all that we are conscious of. Teilhard emphasizes that each individual facet of consciousness will remain conscious of itself at the end of the process." (7)

"What Teilhard was saying here can easily be summed up in a few words," says John Perry Barlow. "The point of all evolution up to this stage is the creation of a collective organism of Mind."

Here are a few of his observations relative to evolution:

• “The initial quantum of consciousness contained in our terrestrial world is not formed merely of an aggregate of particles caught fortuitously in the same net. It represents a correlated mass of infinitesimal centres structurally bound together by the conditions of their origins and development.” This idea is central to what we know about many complex systems – history matters but the future is unpredictable.
• “In every domain, when anything exceeds a certain measurement, it suddenly changes its aspect, condition or nature. The curve doubles back, the surface contracts to a point, the solid disintegrates, the liquid boils, the germ cell divides, intuition suddenly bursts on the piled up facts ... Critical points have been reached, rungs on the ladder, involving a change of state-jumps of all sorts in the course of development.”
• “This law of controlled complication, the mature stage of the process in we which we first get the micro-molecule then the mega-molecule and finally the first cells, is known to biologists as orthogenesis (8) . Orthogenesis is the dynamic and only complete form of heredity. The word conceals deep and real springs of cosmic extent.”
• “These attitudes or ways of proceeding can be reduced to three: profusion, ingenuity and (judged from our individual point of view) indifference
• Profusion is born of unlimited multiplication. “Once more, this time on the plane of animate particles, we find the fundamental technique of groping, the specific and invincible weapon of all expanding multitudes. This groping strangely combines the blind fantasy of large numbers with the precise orientation of a specific target. It would be a mistake to see it as mere chance. Groping is directed chance. It means pervading everything so as to try everything, and trying everything so as to find everything. Surely in the last resort it is precisely to develop this procedure (always increasing in size and cost in proportion as it spreads) that nature has had recourse to profusion.”
• Ingenuity is the indispensible condition, or precisely the constructive facet, of additivity. “To accumulate characters in stable and coherent aggregates, life has to be very clever indeed. Not only has it to invent the machine but, like an engineer, so design it that it occupies the minimum space and is simple and resilient. And this implies and involves, as regards the structure of organisms (particularly the higher ones), a property which must never be forgotten. What can be put together can be taken apart. At an early stage of their discoveries biologists were surprised and fascinated by the fact that living beings, however perfect (or even more perfect) their spontaneity, were always decomposable into an endless chain of closed mechanisms. From this they thought they could deduce universal materialism. But they overlooked the essential difference between a natural whole and the elements into which it is analysed. By its very construction, it is true, every organism is always and inevitably reducible into its component parts. But it by no means follows that the sum of the parts is the same as the whole, or that, in the whole, some specifically new value may not emerge. That what is 'free', even in man, can be broken down into determinisms, is no proof that the world is not based on freedom-as indeed I maintain that it is. It is simply the result of ingenuity-a triumph of ingenuity-on the part of life.” This is also a concept integral to understanding complex systems. (9)
  
• Indifference is transformed into solicitude. “By the phenomenon of association, the living particle is wrenched from itself. Caught up in an aggregate greater than itself, it becomes to some extent its slave. It no longer belongs to itself. And what organic or social incorporation does to extend it in space, its accession to a line of descent achieves no less inexorably in time. By the force of orthogenesis the individual unit becomes part of a chain. From being a centre it is changed into being an intermediary, a link-no longer existing, but transmitting; and, as it has been put, life is more real than lives. On the one hand the individual unit is lost in number, on the other it is torn apart in the collectivity, and in yet a third direction it stretches out in becoming. This dramatic and perpetual opposition between the one born of the many and the many constantly being born of the one runs right through evolution. As the general movement of life becomes regular, the conflict, despite occasional counter-attacks, tends to resolve itself. Yet it remains painfully noticeable to the end. The antinomy (10) only clears up with the appearance of mind where it attains its paroxysm (11) in feeling, and the indifference of the world for its constituents is transformed into an immense solicitude (12) . This is the sphere of the person.”
• “Groping profusion; constructive ingenuity; indifference towards whatever is not future and totality-these are the three headings under which life rises up by virtue of its elementary mechanisms. There is also a fourth heading which embraces them all-that of global unity. This we have come across already-first in primordial matter, then on the early earth, then in the genesis of the first cells. Here it reappears in a still more emphatic way. Though the proliferations of living matter are vast and manifold, they never lose their solidarity. A continuous adjustment co-adapts them from without. A profound equilibrium gives them balance within. Taken in its totality, the living substance spread over the earth-from the very first stages of its evolution-traces the lineaments of one single and gigantic organism. I repeat this same thing like a refrain on every rung of the ladder that leads to man; for, if this thing is forgotten, nothing can be understood. To see life properly we must never lose sight of the unity of the biosphere that lies beyond the plurality and essential rivalry of individual beings. This unity was still diffuse in the early stages -a unity in origin, framework and dispersed impetus rather than in ordered grouping; yet a unity which, together with life's ascent, was to grow ever sharper in outline, to fold in upon itself, and, finally, to centre itself under our eyes.”
• The arrow of evolution points towards increased complexity and consciousness. “…I think we had better go back to what I said above about the mutual relations between the without and the within of things. The essence of the real, I said, could well be represented by the 'interiority' contained by the universe at a given moment. In that case evolution would fundamentally be nothing else than the continual growth of this 'psychic' or 'radial' energy, in the course of duration, beneath and within the mechanical energy I called 'tangential', which is practically constant on the scale of our observations. And what, I asked, is the particular co-efficient which empirically expresses the relationship between the radial and tangential energies of the world in the course of their respective developments? Obviously arrangement, the arrangement whose successive advances are inwardly reinforced, as we can see, by a continual expansion and deepening of consciousness.” Later de Chardin writes, “Life seems to play as cleverly with collectivities and events as with atoms. But what could this ingeniousness and these stimulants do if applied to a fundamental inertia? And what, moreover, as we have pointed out, would the mechanical energies themselves be without some within to feed them? Beneath the 'tangential' we find the ‘radial'. The impetus of the world, glimpsed in the great drive of consciousness, can only have its ultimate source in some inner principle, which alone could explain its irreversible advance towards higher psychisms (13) .”
• At this time evolution is faster outside of our bodies than inside them. “In the Upper Quaternary (14) period it is indeed and in the fullest sense present-day man at whom we are looking, not yet adult, admittedly, but having nevertheless reached the 'age of reason'. And when we compare him to ourselves, his brain is already perfect, so perfect that since that time there seems to have been no measurable variation or increased perfection in the organic instrument of our thought. Are we to say, then, that the evolution in man ceased with the end of the Quaternary era? Not at all. But, without prejudice to what may still be developing slowly and secretly in the depths of the nervous system, evolution has since that date overtly overflowed its anatomical modalities to spread, or perhaps even to transplant its main thrust into the zones of psychic spontaneity both individual and collective.”
• “One after the other all the fields of human knowledge have been shaken and carried away by the same under-water current in the direction of the study of some development. Is evolution a theory, a system or a hypothesis? It is much more: it is a general condition to which all theories, all hypotheses, all systems must bow and which they must satisfy henceforward if they are to be thinkable and true. Evolution is a light illuminating all facts, a curve that all lines must follow.”
• “Thus we see not only thought as participating in evolution as an anomaly or as an epiphenomenon; but evolution as so reducible to and identifiable with a progress towards thought that the movement of our souls expresses and measures the very stages of progress of evolution itself Man discovers that he is nothing else than evolution become conscious of itself, to borrow Julian Huxley's striking expression. It seems to me that our modern minds (because and inasmuch as they are modern) will never find rest until they settle down to this view. On this summit and on this summit alone are repose and illumination waiting for us.”
• “…the stuff of the universe, by becoming thinking, has not yet completed its evolutionary cycle, and that we are therefore moving forward towards some new critical point that lies ahead. In spite of its organic links, whose existence has everywhere become apparent to us, the biosphere has so far been no more than a network of divergent lines, free at their extremities. By effect of reflection and the recoils it involves, the loose ends have been tied up; and the noosphere tends to constitute a single closed system in which each element sees, feels, desires and suffers for itself the same things as all the others at the same time.”
  

Accoding to de Chardin, the noosphere was beginning to emerge in 1930 when he wrote this book. Now, 80 years later is it not more obvious? We have now spanned the earth and interconnected almost all humans on earth through electronics (Internet, TV and radio). But we don’t yet know how to have conversations (15) . Our social network tools of today will look primitive compared to what they will become in the future. Facebook and Twitter are the play toys of our childhood of this new age. We are playing in order to learn how to become.

The author wrote, “We are, at this very moment, passing through a change of age, The age of industry; the age of oil, electricity and the atom; the age of the machine, of huge collectivities and of science -the future will decide what is the best name to describe the era we are entering. The word matters little. What does matter is that we should be told that, at the cost of what we are enduring, life is taking a step, and a decisive step, in us and in our environment. After the long maturation that has been steadily going on during the apparent immobility of the agricultural centuries, the hour has come at last, characterised by the birth pangs inevitable in another change of state. There were the first men-those who witnessed our origin. There are others who will witness the great scenes of the end. To us, in our brief span of life, falls the honour and good fortune of coinciding with a critical change of the noosphere.”

Later he writes, “In the last century and a half the most prodigious event, perhaps, ever recorded by history since the threshold of reflection has been taking place in our minds: the definitive access of consciousness to a scale of new dimensions; and in consequence the birth of an entirely renewed universe, without any change of line or feature by the simple transformation of its intimate substance.”

De Chardin saw this emergence, not as inevitable, but desirable, because the alternative is destruction, instead of survival. He saw all the problems of his day as part of the earthly human sphere searching for a soul.

“Our earth of factory chimneys and offices, seething with work and business, our earth with a hundred new radiations-this great organism lives, in final analysis, only because of, and for the sake of, a new soul. Beneath a change of age lies a change of thought. Where are we to look for it, where are we to situate this renovating and subtle alteration which, without appreciably changing our bodies, has made new creatures of us? In one place and one only-in a new intuition involving a total change in the physiognomy of the universe in which we move-in other words, in an awakening.”

This is a transformation available to everyone. “The outcome of the world, the gates of the future, the entry into the super-human-these are not thrown open to a few of the privileged nor to one chosen people to the exclusion of all others. They will open only to an advance of all together, in a direction in which all together can join and find completion in a spiritual renovation of the earth…”

And later he writes, “Noogenesis rises upwards in us and through us unceasingly.

We have pointed to the principal characteristics of that movement: the closer association of the grains of thought; the synthesis of individuals and of nations or races; the need of an autonomous and supreme personal focus to bind elementary personalities together, without deforming them, in an atmosphere of active sympathy. And, once again: all this results from the combined action of two curvatures-the roundness of the earth and the cosmic convergence of mind-in conformity with the law of complexity and consciousness.” (complexification)

De Chardin warns against impatience and isolationism. The process he visualized is slow with the end point far into the future. People must not be discouraged by all the forces pulling in different directions. These are but the normal human reactions to oppose transformative change. Another tendency is for people to isolate themselves from the process, becoming self centered, because they fear the loss of themselves into the collective. The noosphere is not a traditional type of collective, but one in which each individual retains identity and centeredness.

The Phenomenon of Man, Pierre Teilhard de Chardin, Harper Perennial Modern Thought, 2008, 319pp. Originally published in 1955. Also, a downloadable version is available on the Internet Archive.

References

1. Noosphere, according to the thought of Vladimir Vernadsky and Teilhard de Chardin, denotes the "sphere of human thought" Wikipedia
2. Pierre Teilhard de Chardin, Wikipedia
3. A Globe, Clothing Itself in a Brain, Jennifer Cobb Kreisberg, Wired
4. Four Causes, Wikipedia
5. Centreity: The state of being a center, as of attraction or action, or of being situated in a center; centrality., Jana Gana Mana; Power of attraction towards a center. The Imperial Dictionary of the English Language; Each part of the essence, its centreity; Keeps to itself; it shrinks not to a nullity., Dr. H. More
6. Teilhard de Chardin’s Evolutionary Philosophy, Kheper
7. The Phenomenon of Man, Wikipedia
8. Orthogenesis, Wikipedia
9. For additional concepts on ingenuity, read Ingenuity: Humans and their Organizations at a Crossroads
10. Antinomy literally means the mutual incompatibility, real or apparent, of two laws. It is a term used in logic and epistemology. Wikipedia
11. A sudden outburst of emotion or action. The Free Dictionary
12. The state of being solicitous; care or concern, as for the well-being of another. The Free Dictionary
13. Psychism: The doctrine of Quesne, that there is a fluid universally diffused, end equally animating all living beings, the difference in their actions being due to the difference of the individual organizations. Webster Dictionary
14. The Quaternary Period is the most recent of the three periods of the Cenozoic Era in the geologic time scale of the ICS. It follows the Tertiary Period, spanning 2.588 ± 0.005 million years ago to the present. The Quaternary includes two geologic epochs: the Pleistocene and the Holocene. The Upper or Tarantian stage was 0.0117 to 0.126 million years ago.
15. Conversation: turning around together. See Conversation and Creativity
    

Arcadia: A Play on Complexity

Arcadia is a play by Tom Stoppard that weaves time, social mores, mathematics and science. It can be interpreted on many levels. Of interest to me is that in many ways, this play is about complexity, and the play is complex (or at least complicated).

Lets start with the title. Arcadia refers to a vision of pastoralism and harmony with nature. The term is derived from the Greek province of the same name which dates to antiquity; the province's mountainous topography and sparse population of pastoralists later caused the word Arcadia to develop into a poetic byword for an idyllic vision of unspoiled wilderness. Arcadia is associated with bountiful natural splendor, harmony, and is often inhabited by shepherds. The concept also figures in Renaissance mythology. Commonly thought of as being in line with Utopian ideals, Arcadia differs from that tradition in that it is more often specifically regarded as unattainable. Furthermore, it is seen as a lost, Edenic form of life, contrasting to the progressive nature of Utopian desires.

The inhabitants were often regarded as having continued to live after the manner of the Golden Age, without the pride and avarice that corrupted other regions. It is also sometimes referred to in English poetry as Arcady. The inhabitants of this region bear an obvious connection to the figure of the Noble savage, both being regarded as living close to nature, uncorrupted by civilization, and virtuous. (From Wikipedia)

The Latin phrase “Et in Arcadia ego”appears on the tomb in a 1647 painting by Nicolus Poussin. It is meant as a cautionary of the impermanence of life: even in Arcadia you will die.

Arcadia has another meaning that is connected to complexity. Arcadia is named after Arcas. In Greek mythology, Arcas was the son of Zeus and Callisto. Callisto was a nymph of the goddess Artemis. Zeus, being a flirtatious god, wanted Callisto for a lover. As she would not be with anyone but Artemis, Zeus cunningly disguised himself as Artemis and seduced Callisto. The child resulting from their union was called Arcas.

Hera (Zeus' wife), became jealous, and in anger, transformed Callisto into a bear. She would have done the same or worse to her son, had Zeus not hidden Arcas in an area of Greece that would come to be called Arcadia, in his honor. There Arcas safely lived until one day, during one of the court feasts held by King Lycaon, Arcas was placed upon the burning altar as a sacrifice to the gods. He then said to Zeus "If you think that you are so clever, make your son whole and unharmed." At this Zeus became enraged. He made Arcas whole and then directed his anger toward Lycaon, turning him into the first werewolf. (Some of the myths have Arcas cut into pieces and served to Zeus.) (See Arcas, Greek Myth Index, and Callisto.)

The significance of this double meaning of the title will become meaningful as I describe the play.

Quoting from SFF Net, “Arcadia is a play that stands up to numerous readings and viewings. The synopsis below barely scratches the surface of its complexity and depth. It also gives away a couple of major plot points best experienced first-hand. Read on at your peril.

The action of Arcadia takes place in single space, a room on the garden front of a very large country house in Derbyshire, but in two times, the present and the early years of the nineteenth century. It opens as Thomasina Coverly, a precocious thirteen-year-old math student, receives a lesson from her tutor, twenty-two-year-old Septimus Hodge. The two are discussing Fermat's theorem, Newton and other matters of mathematics and physics when they are interrupted by Ezra Chater, a third-rate poet. Chater accuses Hodge of having been spied in a "carnal embrace" with Mrs. Chater, a charge Hodge makes little effort to deny. Meanwhile, Thomasina's mother, Lady Croom, is wrangling with her landscape architect, Richard Noakes, who wants to clutter the immaculately kept grounds with a gloomy hermitage and other gothic paraphernalia.

The second scene moves to the twentieth century. Coverly descendants still reside at the estate: young Chloe, mathematician Valentine and mute, mysterious Gus. They are also hosts to best-selling author Hannah Jarvis, there to research a history of the estate's gardens, and to literary scholar Bernard Nightingale, who intends to prove that Lord Byron, the great Romantic poet, visited Sidley Park and killed Ezra Chater in a duel.

The next scene, however, demonstrates that, even though Byron did visit Sidley Park in 1809, it was Hodge whom the cuckolded Chater challenged to a duel.”

The structure of the play is based on the interplay of two time periods in the same room combined with the social mores of each time period. The back and forth nature of the play increases in tempo until the close of the play when both sets of characters are in the same scene.

Thomasina is indeed perceptive, creative and bold. Picking up the dialog in Scene 3:

THOMASINA: You are churlish with me because mama is paying attention to your friend. Well, let them elope, they cannot turn back the advancement of knowledge. I think it is an excellent discovery. Each week I plot your equations dot for dot, xs against ys in all manner of algebraical relation, and every week they draw themselves as commonplace geometry, as if the world of forms were nothing but arcs and angles. God's truth, Septimus, if there is an equation for a curve like a bell, there must be an equation for one like a bluebell, and if a bluebell, why not a rose? Do we believe nature is written in numbers?

SEPTIMUS: We do.

THOMASINA: Then why do your equations only describe the shapes of manufacture?

SEPTIMUS: I do not know.

THOMASINA: Armed thus, God could only make a cabinet.

SEPTIMUS: He has mastery of equations which lead into infinities where we cannot follow.

THOMASINA: What a faint-heart! We must work outward from the middle of the maze. We will start with something simple. (She picks up the apple leaf.) I will plot this leaf and deduce its equation. You will be famous for being my tutor when Lord Byron is dead and forgotten.

With this dialog, the concept of complexity and fractals is introduced.

The conversation quickly turns to another theme:

SEPTIMUS: Back to Cleopatra.

THOMASINA: Is it Cleopatra? I hate Cleopatra!

SEPTIMUS: You hate her? Why?

THOMASINA: Everything is turned to love with her. New love, absent love, lost love – I never knew a heroine that makes such noodles of our sex. It needs only a Roman general to drop anchor outside the window and away goes the empire like a christening mug in a pawn shop. If Queen Elizabeth had been a Ptolemy history would have been quite different – we would be admiring the pyramids of Rome and the great Sphinx of Verona.

SEPTIMUS; God save us.

THOMASINA: But instead, the Egyptian noodle made carnal embrace with the enemy who burned the great library of Alexandria without so much as a fine for all that is overdue. Oh, Septimus! - can you bear it? All the lost plays of the Athenians! Two hundred at least by Aeschylus, Sophocles, Euripides – thousands of poems – Aristotle's own library brought to Egypt by the noodle's ancestors! Can we sleep for grief?

SEPTIMUS: By counting our stock. Seven plays Aeschylus, seven Sophocles, nineteen from Euripides, my lady! You should no more grieve for the rest of them for a buckle lost from your first shoe, or your lesson book which will be lost when you are old. We shed as we pick up, like travelers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. You do not suppose my lady, that if all of Archimedes had been hidden in the great library of Alexandria, we would still be at loss for a corkscrew? I have no doubt that the improved steam-driven heat-engine which puts Mr. Noaks into an ecstasy that he and it and the modern age should all coincide, was well established on papyrus.

This theme has to do with evolution. For Teilhard de Chardin, the noosphere emerges through and is constituted by the interaction of human minds. The noosphere has grown in step with the organization of the human mass in relation to itself as it populates the earth. As mankind organizes itself in more complex social networks, the higher the noosphere will grow in awareness. This is an extension of Teilhard's Law of Complexity/Consciousness, the law describing the nature of evolution in the universe. (See Wikipedia)

It also describes human history. Complexification is the driving force of history, and individuals only retard or advance that natural inevitable change.

In scene 4, in modern time, Hannah and Valentine are talking. In the course of research into the history of Sidley Park, they have discovered Thomasina's notes and mathematics lesson book. Hannah reads from the book:

HANNAH: I, Thomasina Coverly, have found a truly wonderful method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone. The margin being too mean for my purpose, the reader must look elsewhere for the New Geometry of Irregular Forms discovered by Thomasina Coverly.

In other words, fractals.

Valentine explains what he thinks Thomasina is writing about, and Hannah asks:

HANNAH: Is it difficult?

VALENTINE: The maths isn't difficult. It's what you did at school. You have some x-and-y equation. Any value for x gives you a value for y. So you put a dot where it's right for both x and y. Then you take the next value for x which gives you another value for y, and when you've done that a few times you join up the dots and that's your graph of whatever the equation is.

HANNAH: And is that what she's doing?

VALENTINE: No. Not exactly. Not at all. What she's doing is, every time she works out a value for y, she's using that as her next value for x. And so on. Like a feedback. She's feeding the solution back into the equation, and then solving it again. Iteration, you see.

HANNAH: And that's surprising, is it?

VALENTINE: Well, it is a bit. It's the technique I'm using on my grouse numbers, and it hasn't been around for much longer than, well, call it twenty years.

Valentine describes the work he is doing trying to understand population trends of grouse in the Park. He has data of all the grouse shot since 1870, and is trying to understand the mathematical relationship. He is attempting to formulate the logistic equation for population growth. In discrete form, this equation is known as the logistic map, a very simple equation that exhibits chaotic properties in well defined regions.

Valentine comments, “It's about the behavior of numbers. This thing works for any phenomenon which eats its own numbers – measles epidemics, rainfall averages, cotton prices, it's a natural phenomenon in itself. Spooky.”

“When your Thomasina was doing maths it had been the same maths for a couple of thousand years. Classical. And for a century after Thomasina. Then maths left the real world behind, just like modern art, really. Nature was classical, maths was suddenly Picassos. But now nature is having the last laugh. The freaky stuff is turning out to be the mathematics of the natural world.”
After being pressed by Hannah, Valentine continues, “If you knew the algorithm and fed it back say ten thousand times, each time there'd be a dot somewhere on the screen. You'd never know where to expect the next dot. But gradually you'd start to see this shape, because every dot will be inside the shape of this leaf. It wouldn't be the leaf, it would be a mathematical object. But, yes. The unpredictable and the predetermined unfold together to make everything the way it is. It's how nature creates itself, on every scale, the snowflake and the snowstorm.”

Then Valentine makes the following comment about the significance of complexity, “It makes me so happy. To be at the beginning again, knowing almost nothing. People were talking about the end of physics. Relativity and quantum looked as if they were going to clean out the whole problem between them. A theory of everything. But they only explained the very big and the very small. The universe, the elementary particles. The ordinary-sized stuff which is our lives, the things people write poetry about - clouds - daffodils - waterfalls - and what happens in a cup of coffee when the cream goes in - these things are full of mystery, as mysterious to us as the heavens were to the Greeks. We're better at predicting events at the edge of the galaxy or inside the nucleus of an atom than whether it'll rain on auntie's garden party three Sundays from now. Because the problem turns out to be different. We can't even predict the next drip from a dripping tap when it gets irregular. Each drip sets up the conditions for the next, the smallest variation blows prediction apart, and the weather is unpredictable the same way, will always be unpredictable. When you push the numbers through the computer you can see it on the screen. The future is disorder. A door like this has cracked open five or six times since we got up on our hind legs. It's the best possible time to be alive, when almost everything you thought you knew is wrong.”

Parenthetically, this is the excitement I feel as a physicist (education only) about complexity science.

One of the other themes that run through this play (there are many) is thermodynamics and entropy.

Hannah and Valentine are talking in modern time:

VALENTINE: Listen - you know your tea's getting cold.

HANNAH: I like it cold.

VALENTINE: (Ignoring that) I'm telling you something. Your tea gets cold by itself, it doesn't get hot by itself. Do you think that's odd?

HANNAH: No.

VALENTINE: Well, it is odd. Heat goes to cold. It's a one-way street. Your tea will end up at room temperature. What's happening to your tea is happening to everything everywhere. The sun and the stars. It'll take a while but we're all going to end up at room temperature. When your hermit set up shop nobody understood this. But let's say you're right, in 18-whatever nobody knew more about heat than this scribbling nutter living in a hovel in Derbyshire.

Towards the end of the play when the four characters are on stage at the same time:

SEPTIMUS: So, we are all doomed!

THOMASINA: (Cheerfully) Yes.

VALENTINE: Like a steam engine, you see. She didn't have the maths, not remotely. She saw what things meant, way ahead, like seeing a picture.

SEPTIMUS: This is not science. This is story-telling.

THOMASINA: Is it a waltz now?

SEPTIMUS: No.

VALENTINE: Like a film.

HANNAH: What did she see?

VALENTINE: That you can't run the film backwards. Heat was the first thing which didn't work that way. Not like Newton. A film of a pendulum, or a ball falling through the air - backwards, it looks the same.

HANNAH: The ball would be going the wrong way.

VALENTINE: You'd have to know that. But with heat - friction - a ball breaking a window

HANNAH: Yes.

VALENTINE: It won't work backwards.

HANNAH: Who thought it did?

VALENTINE: She saw why. You can put back the bits of glass but you can't collect up the heat of the smash. It's gone.

SEPTIMUS: So the Improved Newtonian Universe must cease and grow cold. Dear me.

VALENTINE: The heat goes into the mix.
(He gestures to indicate the air in the room, in the universe.)

THOMASINA: Yes, we must hurry if we are going to dance.

VALENTINE: And everything is mixing the same way, all the time, irreversibly ...

SEPTIMUS: Oh, we have time, I think.

VALENTINE: ... till there's no time left. That's what time means.

SEPTIMUS: When we have found all the mysteries and lost all the meaning, we will be alone, on an empty shore.

THOMASINA: Then we will dance. Is this a waltz?

SEPTIMUS: It will serve.

I believe what Stoppard is trying to indicate here is the possible linkage between complexity and entropy. A subject I will write about later.

A complex system cannot be taken apart and put back together remaining the same as it was before. You can do that with a complicated system, even though you will lose energy in the process.

And, that brings back to the title - Arcadia - the place where in spite of its perfection, everyone still dies. And, Arcas who is burned up or cut into pieces as a test for Zeus, to see if he can reverse the process and unlike Humpty Dumpty, put Arcas back together again.

Arcadia, Tom Stoppard, Faber and Faber, 1993
Arcadia (Dramatized), Tom Stoppard, L. A. Theatre Works, 2010 (CD)

A Simpler Way

A Simpler Way
Margaret Wheatley & Myron Kellner-Rogers
Berrett-Koehler, 1996

This is a beautiful book with beautiful pictures and mental images. It is a hopeful book, and it is a profound book. Its mission is no less than to change our paradigm from competition to collaboration in how we perceive, think and act in all that we do. The authors' opening line is "We want life to be less arduous and more delightful. We want to be able to think differently about how to organize human activities."

They question the "survival of the fittest" paradigm for evolution and our mechanistic view of the world. "The mechanistic image of the world is a very deep image, planted at subterranean depths in most of us. But it doesn't help us any longer."

The authors pose the question, "How could we organizes human endeavor if we developed different understandings of how life organizes itself?" They have six beliefs about human organizations and the world in which they come into form:

"The universe is a living, creative, experimenting experience of discovering what's possible at all levels of scale from microbe to cosmos.

Life's natural tendency is to organize. Life organizes into greater levels of complexity to support more diversity and greater sustainability.

Life organizes around a self. Organizing is always an act of creating an identity.

Life self-organizes. Networks, patterns, and structures emerge without external imposition or direction. Organization wants to happen.

People are intelligent, creative, adaptive, self-organizing, and meaning seeking.

Organizations are living systems. They too are intelligent, creative, adaptive, self-organizing, meaning-seeking."

They argue that life has a natural and spontaneous tendency towards organization. "Whatever chaos is present at the start, when elements combine, systems of organization appear. Life is attracted to order - order gained through wandering explorations into new relationships and new possibilities."

The central part of the book is organized around a poem by A. R. Ammons:

"I look for the way
things will turn
out spiraling from a center,
the shape
things will take to come forth in

so that the birch tree white
touched black at branches
will stand out
wind-glittering
totally its apparent self:

I look for the forms
things want to come as

from what black wells of possibility
how a thing will
unfold:

not the shape on paper - though
that, too - but the
uninterfering means on paper:

not so much looking for the shape
as being available
to any shape that may be
summoning itself
through me
from the self not mine but ours."

The authors write, "Life is creative. It plays itself into existence, seeking new relationships, new capacities, new traits. Life is an experiment to discover what's possible."

They believe Darwinism has led us to believe that life wasn't supposed to happen, that it was an accident, and that life has to fight to continue to exist. In their view, "Life is about invention, not survival. We are here to create, not defend."

They point out that all of us are trying to describe our reality to others. But reality outside of us, in an absolute sense, evades us. "We peer out through our senses, describing our experiences of what we think reality to be. We choose images to convey our expereince. We create metaphors to connect what we see. We explore new ways of understanding what seems to be happening and what we think it means."

Peering out at the world, they describe seven principles of life's process of creating:

"Everything is in a constant process of discovery and creating. Everything is changing all the time: individuals, systems, environments, the rules, the processes of evolutions. Even change changes. Every organism reinterprets the rules, creates exceptions for itself, creates new rules.

Life uses messes to get well-ordered solutions. Life doesn't seem to share our desires for efficiency or neatness. It uses redundancy, fuzziness, dense webs of relationships, unending trials and errors to find what works.

Life is intent on finding what works, not what's 'right'. It is the ability to keep finding solutions that is important; any one solution is temporary. There are no permanently right answers. The capacity to keep changing, to find what works now, is what keeps any organism alive.

Life creates more possibilities as it engages with opportunities. There are no 'windows of opportunity', narrow openings in the fabric of space-time that soon disappear forever. Possibilities beget more possibilities; they are infinite.

Life is attracted to order. It experiments until it discovers how to form a system that can support diverse members. Individuals search out a wide range of possible relationships to discover whether they can organize into life-sustaining system. These explorations continue until a system is discovered. The system then provides stability for its members, so that individuals are less buffeted by change.

Life organizes around identity. Every living thing acts to develop and preserve itself. Identity is the filter that every organism or system uses to make sense of the world. New information, new relationships, changing environments - all are interpreted through a sense of self. This tendency toward self-creation is so strong that it creates a seeming paradox. An organism will change to maintain its identity.

Everything participates in the creation and evolution of its neighbors. There are no unaffected outsiders. No one system dictates conditions to another. All participate together in creating the conditions of their interdependence."

"There is no ideal design for anything, just interesting combinations that arise as a living thing explores it space of possibilities", Wheatley and Kellner-Rogers write, a combination of words that could be used to describe how an organization innovates.

Their assertion is that "life tinkers itself into existence". "It tinkers toward order - toward systems that are more complex and effective...Almost always what begins in randomness ends in stability...generates systems that sustain diverse individuals." But they conclude, "Life seeks order in a disorderly way."

"All this messy playfulness creates relationships that make more available...," they write. "Who we become together will always be different that who we were alone. Our range of creative expression increases as we join with others. New relationships create new capacities."

"Life invites us to create not only the forms but even the process of discovery," they conclude. "The environment is invented by our presence in it. We do not parachute into a sea of turbulence, to sink or swim. We and our environments become one system, each influencing the other, each co-determining the other." Living systems they believe create more possibilities and more freedom for individuals.

In this systems behaviors emerge. "Science writer Kevin Kelly describes these systems as a 'messy cascade of interdependent events ...What emerges from the collective is not a series of critical individual actions but a multitude of simultaneous actions whose collective pattern is far more important'."

One of the important features of viable living systems is simultaneity. "Simultaneity reduces the impact of any one error. More errors matter less if the actors are not linked together sequentially. The space for experimentation increases as we involve more minds in the experiment, as long as they can operate independently. What links people together is their focus on a needed solution. But in discovering what works, they are not waiting for one another to act."

They very carefully describe the discipline of play required for success. "Playful tinkering requires consciousness. If we are not mindful, if our attention slips, then we can't notice what's available or discover what's possible. Staying present is the discipline of play. Great concentration and focus are required." As a result, "Playful enterprises are alert. They are open to information, always seeking more, yearning for surprises."

Over and over again they stress the role that diversity plays in creation. "Parallel process requires both diversity and freedom. There is more than one workable solution, and these solutions arise from many different forms of self-expression...Life is not driving us toward one solution. The world is interested in pluralism. Only in this way can it discover more about itself...The world's desire for diversity compels us to change."

Systems offer the possibility for more stability. But in a curious paradox, that stability for the system depends upon its member's ability to change. "When individuals fail to experiment or when a system refuses their offers of new ideas, then the system becomes moribund. Without constant, interior change, it sinks into the death grip of equilibrium. It no longer participates in coevolution. The system becomes vulnerable; its destruction is self-imposed...This broad paradox of stability and freedom is the stage on which coevolution dances. Life leaps forward when it can share its learnings. The dense web of systems allow information to travel in all directions, speeding recovery and adaptation."

If systems of life are self-organizing then we don't have to design how they will organize. We live in a universe where we get order for free. "If order is for free, we don't have to be the organizers. We don't have to design the world. We don't have to structure its existence."

And, in a prescription for systems that has a lot to do with an innovation commons, "As we organize, we need to keep inquiring into the quality of our relationships. How much access do we have to one another? How much trust exists among us? Who else needs to be in the room?"

"Stability is found in freedom - not in conformity and compliance. We may have thought that our organization's survival was guaranteed by finding the right form and insisting that everyone fit into it. But sameness is not stability. It is individual freedom that creates stable systems. It is diffferentness that enables us to thrive," they propose.

In writing about self, they suggest, "Life wants to happen. It calls itself into existence. Out of all information and all possibilities, an entity comes into form. An identity emerges. A self has created itself...No externally imposed plans or designs are required. The process of invention always takes place around an identity. There is a self that seeks to organize and make its presence known. The desires of self set a self-organizing world into motion."

Research suggests that we perceive the world based on who we have decided to be, "...at any moment, what we see is most influenced by who we have decided to be...At least 80 percent of the information that the brain works with is information already in the brain." The corollary to this is that "We will change our self if we believe that the change will preserve the self."

In answering the question about what conditions will allow self-organization to flourish, they state "We need to trust that we are self organizing...We live in a world where attraction is ubiquitous. Organization wants to happen. People want their lives to mean something. We seek one another to develop new capacities. With all these wonderful and innate desires calling us to organize, we can stop worrying about designing perfect structures or rules. We need to become intrigued by how we create a clear and coherent identity, a self that we can organize around...Identity includes such dimensions as history, values, actions, core beliefs, competencies, principles, purpose, mission...Identity is the source of organizations. Every organization is an identity in motion, moving through the world, trying to make a difference."

In search of that illusive concept of emergence, they write, "Emergence is the surprising capacity we discover only when we join together. New systems have properties that appear suddenly and mysteriously. These properties cannot be predicted. They do not exist in the individuals who compose the system. What we know about the individuals, no matter how rich the details, will never give us the ability to predict how they will behave as a system. Once individuals link together they become something different.

One of the current quandaries facing free, open collaboratives is compensation. It is very clear that participants benefit in many other tangible and intangible ways from the collaboration. However, in our present form of capitalism, no standard form of monetary compensation has emerged. The authors don't provide much hope of one being developed, "Once systems are called into the world by our individual explorations, it becomes impossible to work backwards. Systems cannot be deconstructed. We can't figure out cause and effect or who contributed what. There are no heroes or permanent leaders in an emergent, systems creating world. There are too many simultaneous connection; individual contributions evolve too rapidly into group efforts."

We often talk about synergy in a group, where 1 + 1 > 2. Their paradigm revolutionizes the way to think about a system, "A system is an inseparable whole. It is not the sum of its parts. It is not greater than the sum of its parts. There is nothing to sum. There are no parts. The system is a new and different and unique contribution to its members and the world. To search backwards in time for its parts is to deny the self transforming nature of systems. A system is knowable only as itself. It is irreducible. We can't disentangle the effects of so many relationships. The connections never end. They are impossible to understand by analysis."

In amplifying their concept that self-organizing systems merge through trust, they write, "Every act of organizing is an experiment. We begin with desire, with a sense of purpose and direction. But we enter the experience vulnerable, unprotected by the illusionary cloak of prediction. We acknowledge that we don't know how this work will actually unfold. We discover what we are capable of as we go along. We engage others in the experiment. We are willing to commit to a systems whose effectiveness cannot be seen until it is in motion...in systems of trust, people are free to create the relationships they need. Trust enables the system to open. The system expands to include those it had excluded. More conversations - more diverse and diverging views - become important. People decide to work with those from whom they have been separate."

We long for meaning in our lives. "Each of us embodies the boundless energies of life. We are creating, systems-seeking, self-organizing, meaning-seeking beings. We are identities in motion, searching for the relationships that will evoke more from us."

What Does Technology Want?

Tech enthusiast Kevin Kelly asks "What does technology want?" and discovers that its movement toward ubiquity and complexity is much like the evolution of life.

Kevin Kelly has been publisher of the Whole Earth Review, exec editor at WIRED, founder of visionary nonprofits, and writer on biology and business and "cool tools." He's admired for his new perspectives on technology and its relevance to history, biology and religion.

Perhaps there is no one better to contemplate the meaning of cultural change -- bad? good? too slow? too bold? -- than Kevin Kelly, whose life story reads like a treatise on the value of technology. Whether by renouncing all material things save his bicycle (which he then rode 3,000 miles), founding an organization (the All-Species Foundation) to catalog all life on earth, or by touting new gadgets in WIRED, Kelly hasn't stopped exploring the phenomena of technical and biological creation.

In articles for the Wall Street Journal and the New York Times, among others, he has celebrated scientific breakthroughs, and at the Long Now Foundation, where he serves on the board, he champions projects that look 10,000 years into the future. Today Kelly is at work on a book that asks what appears to be his life's core question: "How should I think about new technology when it comes along?"

Kelly discusses the 7th Kingdom at length in the July 18, 2007, edition of Edge.org.


This is a very powerful, insightful and important video. It is not a complete theory of technology. But, it is a start. He introduces a number ideas that should be discussed more. I've picked a few out here either for explanation or elaboration.

The question, “What does technology want?” is derived from the thinking of Richard Dawkins' “Selfish Genes”. He asked the same question for genes and that lead him to a radical proposition: that we are primarily the caretaker of our genes. But not just for ourselves but our children, and people who care for and nurture our children, who house our genes. And, depending upon our conception of what constitutes our genes, we care for our extended family, community, nation, world, or the animal kingdom, as we share some genes with them all. Dawkins also introduced the idea of selfish memes, a meme being a concept or an idea. Our memes propagate through society “infecting” other minds, reproducing and diffusing. Our genes might be unrecognizable in a few generations, but some memes live forever. Jefferson's genes are not visible but his meme that all men are created equal with some inalienable rights lives on.

Kelly equates the question, “What do genes want?” with “What does life want?” He asserts that life wants:

* Ubiquity
* Specialization
* Diversity
* Socialization

I personally believe that life also wants beauty.

This has echoes of Margaret Wheatley's incredible book, A Simpler Way. Both dispense with the concept of the survival of the fittest or strongest, which was a misinterpretation of Darwin's work anyway.

Kelly notes that there are six kingdoms of life on earth. He posits that technology is the seventh kingdom. This is close to Dawkin's idea of memes. Technology is the realization of a meme or set of memes. A technology embodies a system of memes.

He then asserts that technology wants the same things as life.

Kelly states that life hacks its way forward. I personally don't like that connotation. The word “hack” came into common use in software development. The original meaning of a hack was someone who made furniture with an ax, according to Wikipedia. I think life progresses in a much more elegant way. According to the authors of A Simpler Way, "Life is creative. It plays itself into existence, seeking new relationships, new capacities, new traits. Life is an experiment to discover what's possible."

Anther point Kelly makes in this video is that old technology never dies. I think that he is correct on this. McLuhan proposed the four laws of technology, which he phrased as questions as well:

* What does it (the medium or technology) extend?
* What does it make obsolete?
* What is retrieved?
* What does the technology reverse into if it is over-extended?

McLuhan viewed these four laws operating in parallel. All four questions are being answered by technology at the same time, not in sequence. Technology is always extending, obsoleting, retrieving and reversing.

Another important idea is that “culture is an accumulation of ideas.' And since technology embeds ideas, or memes, technology becomes an artifact of the culture that produced it.

Another import idea introduced by Kelly is the concept of an infinite game.

Finite games have a definite beginning and ending. They are played with the goal of winning. Infinite games, on the other hand, do not have a knowable beginning or ending. They are played with the goal of continuing play. An infinite game continues play, for sake of play. If the game is approaching resolution because of the rules of play, the rules must be changed to allow continued play. The rules exist to ensure the game is infinite.

He comments that evolution is an infinite game. The game of life is to continue life. Ubiquity, diversity, specialization and socialization taken together continues life. Life is recognized as an infinite game.

Kelly suggests that technology's role is to facilitate life, to aid evolution.

He ends with the comment that we have a moral obligation to give each person the technology to enable them to fulfill their potential of differentness.

Kelly does not talk about the negative side of technology in the video, but he does write about this in an interview in The Edge, The Technium and the 7th Kingdom of Life. Mistakes of technology, really mistakes of humans, are a lot like evolutionary mistakes. If they don't improve life, they die out. He believes that the technium is becoming more aligned with other six kingdom's of life in all areas except species elimination. He does not believe that technology is sensitive to this problem, which he believes is real.

Great thanks to Natalie Shell for suggesting this video to me.

The following video is a reminder of evolutionary time.