1952 illustration of Australopithecus africanus by Zdenek Burian. Photo by STR/AFP via Getty.

Nadine Weidmanis a lecturer on the history of science at Harvard University. She is the author of Constructing Scientific Psychology: Karl Lashley’s Mind-Brain Debates (1999) and Race, Racism, and Science: Social Impact and Interaction (2004), co-authored with John P Jackson, Jr.

Edited by Sam Haselby

11 August 2020 (psyche.co)

Horrified by the atrocities of the 20th century, an array of scientists sought to explain why human beings turned to violence. The founder of psychoanalysis Sigmund Freud argued that ‘man is a wolf to man’, driven to hatred, destruction and death. The neuroscientist Paul MacLean maintained that humans’ violent tendencies could be traced to their primitive ‘reptilian brain’. The social psychologist Albert Bandura countered that aggression was not inborn but resulted from imitation and suggestion. Despite the controversy they provoked, such theories often attained the status of conventional wisdom.

What makes claims about human nature become truisms? How do they gain credibility? They might rely on experiments, case studies or observation, but evidence alone is never enough to persuade. Such theories – by virtue of the very fact that they seek to encompass the human – must always go beyond their evidence. They manage to persuade by appealing to common experience and explaining familiar events, by creating a shock of recognition in their audiences, a sudden realisation that ‘this must be true’. They employ characters and a narrative arc, and draw moral lessons. In short: they tell a good story.

In the 1960s, alongside prevailing psychological and neuroscientific theories of human aggression, a new claim appeared, that aggression was a human instinct. Relying on the sciences of evolution and animal behaviour, this ‘instinct theory’ held that human aggression was a legacy of our deep ancestral past and an inbuilt tendency shared with many other animal species. One important novelty of this theory was its assertion that human aggression was not wholly destructive, but had a positive, even constructive side. Its proponents were talented writers who readily adopted literary devices.

Robert Ardrey’s bestseller African Genesis (1961) won a big American audience. A Hollywood scriptwriter turned science writer, Ardrey travelled to South Africa, then a hotspot for the excavation of prehistoric human remains. In Johannesburg, he met Raymond Dart, the discoverer of a 2 million-year-old fossilised skull, which Dart believed to be the most ancient human ancestor ever unearthed. Although this creature walked upright, its braincase was small and distinctly apelike, so Dart named it Australopithecus africanus, the southern ape from Africa.

Dart found that Australopithecus remains were typically surrounded by equally fossilised animal bones, especially the long heavy leg bones of antelopes evidently hunted for food. But these bones had been shaped and carefully carved. He noticed that they rested comfortably in his own hand. With a shock, he realised that they were weapons. Their double-knobbed ends corresponded perfectly to the holes and dents that Dart observed in other fossilised Australopithecus skulls. Two conclusions seemed inescapable: first, this proto-human ancestor was not simply a hunter; he was also a killer of his own kind. Second, the wielding of bone weapons was not solely a destructive act; rather, it had far-reaching consequences for human evolution. Freed from their role in locomotion, forelimbs became available for finer manipulations, which then drove the enlargement of the human brain. Picking up a weapon, Dart theorised, was the thing that triggered human advancement.

In Ardrey’s retelling, Dart’s hypothesis became even more dramatic. The ancient African savannah was home also to Australopithecus robustus, a vegetarian, unarmed cousin of africanus – and his victim. In Ardrey’s account, the lithe and ruthless africanus, brandishing bone weapons, had exterminated his competitor, an ancient conflict that Ardrey couldn’t resist comparing to the Biblical murder of Abel by his brother Cain. The weapon had propelled africanus toward full humanity while robustus slouched toward extinction. Human beings were, quite literally, Cain’s children.

Thanks to Ardrey’s embroidered telling, Dart’s theory inspired perhaps the most famous scene in cinematic history. In the opening sequence of 2001: A Space Odyssey (1968), the leader of a band of ape-men smashes the remains of his defeated antagonists with a crude weapon fashioned out of bone. The victors are carnivorous and armed; the losers, gentle and defenceless. At the end of the sequence, the leader tosses his bone weapon into the air, where it is transformed into a spaceship gliding silently through darkness. Arthur C Clarke, the scriptwriter for Stanley Kubrick’s film, had read Ardrey’s book, and the scene echoed Dart’s claim: human ingenuity begins in violence.

Ardrey was disturbed by the image he had conjured. What could be more frightening than man the irascible ape, with a penchant for violence inherited from his ancestors in his heart and, in his hand, weapons much more powerful than antelope bones? What would prevent this evolved australopithecine from detonating an atomic bomb?

In African Genesis, Ardrey turned to a different branch of science – ethology, the study of animal behaviour in the wild – for an answer. The Austrian ornithologist Konrad Lorenz developed the foundations of ethology by sharing his home with wild animals, mainly birds of many different species. By living with animals, Lorenz revealed some of the mysteries of animal instinct, including the phenomenon of imprinting, in which a baby bird follows the first parent-figure it sees after birth. In popular books in the 1950s, Lorenz enraptured war-weary audiences worldwide with tales of his life with jackdaws, geese and fish, presenting himself as a scientific King Solomon, the Biblical hero whose magic ring granted him the power to talk with the animals.

Through theories about human nature, readers made sense of race riots and assassinations, the Vietnam War and the threat of nuclear annihilation

By the 1960s, Lorenz had begun to notice a curious feature of the aggression that his animals directed at members of their own species. Unlike predator-prey relationships, these intraspecies encounters rarely ended in killing. Instead, the aggressor animals diverted their violent impulses into harmless or even productive channels. Two rival greylag ganders, spoiling for a fight, cackled and threatened each other, but never physically clashed. Their aggression thus discharged in these playacting rituals, each gander returned to his mate in triumph. Lorenz observed that not only was outright violence avoided, but the social bond between each gander and his own family was actually strengthened. Far from a drive purely toward destruction and death, aggression redirected against an outsider engendered the ties of affection and love among the in-group.

Lorenz’s ethology showed that aggression, when properly managed, had positive consequences. Ardrey realised that the answer to the problem of human aggression was not to try to eliminate it – an impossible task, since Dart had demonstrated that it was ingrained in our nature – but to acknowledge aggression as innate and ineradicable, and then channel it productively. In his book On Aggression (1966), Lorenz made his own suggestions for possible outlets, including the space race.

It would be difficult to overstate the popularity in the 1960s and ’70s of Lorenz’s and Ardrey’s hypothesis about human nature. In the United States, their books became bestsellers. Through their theories about human nature, readers made sense of race riots and assassinations, the Vietnam War and the threat of nuclear annihilation. Their warning – that humans must accommodate their aggression instinct and re-channel it, before it was too late – was cited by US senators and cabinet secretaries. The message made such a lasting impact that even in the 1980s, UNESCO found it necessary to endorse an official statement that biology didn’t condemn humans to violence.

How did the killer-instinct idea achieve such cultural power? Because it came embedded in story. Like the greatest fictional works, Lorenz’s and Ardrey’s books drew on an ancient motif: that man’s fatal flaw was also his greatest strength, deprived of which he would cease to be human. Their deft use of character, plot and scene-setting, their invocation of myth, their summing up in a moral that readers could apply to themselves, drove the theories of Lorenz and Ardrey to conventional wisdom status.

The sciences on which they built their theories might have been superseded. But today’s sciences of human nature – sociobiology and evolutionary psychology – have adopted the claim for an evolved predisposition for aggression. The 1960s bestsellers ushered in a genre of popular science that still depends on speculative reconstructions of human prehistory. It also still draws comparisons between the behaviour and emotions of humans and animals. The grudging compliment we pay a powerful man – ‘he’s an alpha male’ – is one hint of the genre. But we ought to be careful about what we believe. Theories of human nature have important consequences – what we think we are shapes how we act. We believe in such theories not because they are true, but because we are persuaded that they are true. The history of the claim for a killer instinct in humans encourages us to think of the ways in which scientists argue and try to persuade. Storytelling, in this view, is a crucial element of both the science and its public presentation.

September 4, 2020 Vanessa Able (thedewdrop.org)

“Only someone who is ready for everything, who doesn’t exclude any experience, even the most incomprehensible, will live the relationship with another person as something alive and will himself sound the depths of his own being.”

– Rainer Maria Rilke

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This passage from a letter is the source of one of the poet Rainer Maria Rilke’s most famous quotes about the courage to face what is unknown. It was originally written to a nineteen-year-old aspiring poet called Franz Kappus who was about to enter the military and forms part of the famous series of letters Rilke wrote to the young man, advising him in his art as well as in his life. In this letter he talks about sadness and the necessity of solitude, and how they transform us, emphasizing that “We must accept our reality as vastly as we possibly can; everything, even the unprecedented, must be possible within it.”

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It seems to me that almost all our sadnesses are moments of tension, which we feel as paralysis because we no longer hear our astonished emotions living. Because we are alone with the unfamiliar presence that has entered us; because everything we trust and are used to is for a moment taken away from us; because we stand in the midst of a transition where we cannot remain standing. That is why the sadness passes: the new presence inside us, the presence that has been added, has entered our heart, has gone into its innermost chamber and is no longer even there, — is already in our bloodstream. And we don’t know what it was. We could easily be made to believe that nothing happened, and yet we have changed, as a house that a guest has entered changes. We can’t say who has come, perhaps we will never know, but many signs indicate that the future enters us in this way in order to be transformed in us, long before it happens. And that is why it is so important to be solitary and attentive when one is sad: because the seemingly uneventful and motionless moment when our future steps into us is so much closer to life than that other loud and accidental point of time when it happens to us as if from outside.

“The quieter we are, the more patient and open we are in our sadnesses, the more deeply and serenely the new presence can enter us, and the more we can make it our own.”

The quieter we are, the more patient and open we are in our sadnesses, the more deeply and serenely the new presence can enter us, and the more we can make it our own, the more it becomes our fate; and later on, when it “happens” (that is, steps forth out of us to other people), we will feel related and close to it in our innermost being. And that is necessary. It is necessary — and toward this point our development will move, little by little — that nothing alien happen to us, but only what has long been our own. People have already had to rethink so many concepts of motion; and they will also gradually come to realize that what we call fate does not come into us from the outside, but emerges from us. It is only because so many people have not absorbed and transformed their fates while they were living in them that they have not realized what was emerging from them; it was so alien to them that they have not realized what was emerging from them; it was so alien to them that, in their confusion and fear, they thought it must have entered them at the very moment they became aware of it, for they swore they had never before found anything like that inside them. Just as people for a long time had a wrong idea about the sun’s motion, they are even now wrong about the motion of what is to come. The future stands still, dear Mr. Kappus, but we move in infinite space.

How could it not be difficult for us?

And to speak of solitude again, it becomes clearer and clearer that fundamentally this is nothing that one can choose or refrain from. We are solitary. We can delude ourselves about this and act as if it were not true. That is all. But how much better it is to recognize that we are alone; yes, even to begin from this realization. It will, of course, make us dizzy; for all points that our eyes used to rest on are taken away from us, there is no longer anything near us, and everything far away is infinitely far.

“This is in the end the only kind of courage that is required of us: the courage to face the strangest, most unusual, most inexplicable experiences that can meet us.”

A man taken out of his room and, almost without preparation or transition, placed on the heights of a great mountain range, would feel something like that: an unequalled insecurity, an abandonment to the nameless, would almost annihilate him. He would feel he was falling or think he was being catapulted out into space or exploded into a thousand pieces: what a colossal lie his brain would have to invent in order to catch up with and explain the situation of his senses. That is how all distances, all measures, change for the person who becomes solitary; many of these changes occur suddenly and then, as with the man on the mountaintop, unusual fantasies and strange feelings arise, which seem to grow out beyond all that is bearable. But it is necessary for us to experience that too. We must accept our reality as vastly as we possibly can; everything, even the unprecedented, must be possible within it. This is in the end the only kind of courage that is required of us: the courage to face the strangest, most unusual, most inexplicable experiences that can meet us.

“The experiences that are called “apparitions,” the whole so-called “spirit world,” death, all these Things that are so closely related to us, have been so entirely pushed out of life that the senses with which we might have been able to grasp them have atrophied. To say nothing of God.”

The fact that people have in this sense been cowardly has done infinite harm to life; the experiences that are called “apparitions,” the whole so-called “spirit world,” death, all these Things that are so closely related to us, have through our daily defensiveness been so entirely pushed out of life that the senses with which we might have been able to grasp them have atrophied. To say nothing of God. But the fear of the inexplicable has not only impoverished the reality of the individual; it has also narrowed the relationship between one human being and another, which has as it were been lifted out of the riverbed of infinite possibilities and set down in a fallow place on the bank, where nothing happens. For it is not only indolence that causes human relationships to be repeated from case to case with such unspeakable monotony and boredom; it is timidity before any new, inconceivable experience, which we don’t think we can deal with. But only someone who is ready for everything, who doesn’t exclude any experience, even the most incomprehensible, will live the relationship with another person as something alive and will himself sound the depths of his own being. For if we imagine this being of the individual as a larger or smaller room, it is obvious that most people come to know only one corner of their room, one spot near the window, one narrow strip on which they keep walking back and forth.

Rainer Maria Rilke (1875-1926)
From: ‘Letters to a Young Poet’

By Maria Popova (brainpickings.org)

It is a truism that the questions we ask shape the answers we find. It is, also, a truth. Another is that our questions — those wonderments, uncertainties, and quickenings of doubt that roil under the surface of life — are the atomic units of our creativity. Everything we make — our songs and our stories, our poems and our equations — we make to find out how the world works and what we are, to find out how to live with our restless longing for absolutes in a relative universe. Such questions — the questions that “can make or unmake a life,” in the words of the perceptive poet David Whyte — are both the raw material and the end result of all great art; art is tasked not with solving the puzzles of being but with dissolving the false certainties of our near-life experience.

Anton Chekhov (January 29, 1860–July 15, 1904) was twenty-eight when he addressed this in letter to a friend, included in How to Write Like Chekhov: Advice and Inspiration, Straight from His Own Letters and Work (public library).

Anton Chekhov

Corresponding with his friend Alexei Suvorin — a short story writer, playwright, and journalist, who went on to become the most influential newspaper publisher in the sunset hour of the Russian Empire — Chekhov, translated by Lena Lenček, writes on October 27, 1888:

I do sometimes preach heresies, but I have never, not once, gone so far as to deny that hard questions have no place in art. In conversations with my fellow writers, I always insist that it is not the job of the artist to solve narrowly specialized questions. It is bad for the artist to tackle what he* does not understand. We have specialists for dealing with specialized questions; it is their job to make decisions about the peasant commune, the fate of capitalism, the evils of alcoholism, about boots, and female complaints.

A century before James Baldwin observed that the task of the artist is to “drive to the heart of every answer and expose the question the answer hides” and Susan Sontag insisted that the writer must guard against becoming an “opinion-machine,” Chekhov argues that the work of the artist is not problem-solving — this is best left to those with aptitude suited to the problem at hand — but question-framing:

Anyone who says that the artist’s sphere leaves no room for questions, but deals exclusively with answers, has never done any writing or done anything with imagery. The artist observes, selects, guesses, and arranges; every one of these operations presupposes a question at its outset. If he has not asked himself a question at the start, he has nothing to guess and nothing to select.

Cautioning against the common conflation of two distinct concepts — “solving the problem” and “correctly formulating the problem” — he observes:

Only the latter is required of the artist. Not a single problem is resolved in Anna Karenina or Eugene Onegin, and yet the novels satisfy you completely because all the problems they raise are formulated correctly. It is the duty of the law courts to correctly formulate problems, but it is up to the members of the jury to solve them, each to his own taste.

Complement with Polish poet Wisława Szymborska’s superb Nobel Prize acceptance speech about the creative power of uncertainty and David Whyte’s questioning poem “Sometimes,” then revisit Chekhov on the 8 qualities of cultured people and his 6 rules for a great story.

SlimaksClass

The Gnostic Truth The Thirteenth Floor is a 1999 science fiction/crime thriller film directed by Josef Rusnak and loosely based upon Simulacron-3 (1964), a novel by Daniel F. Galouye. The film stars Craig Bierko, Gretchen Mol, Armin Mueller-Stahl, Vincent D’Onofrio, and Dennis Haysbert. In 2000, The Thirteenth Floor was nominated for the Saturn Award for Best Science Fiction Film, losing to The Matrix. Gripping in a way considerably deeper than “They Live” and “Dark City”, this movie draws a more profound image of the ideas of Gnosticism, wittingly or not. It does so in several ways. In one way it refers to this very reality on at least two levels simultaneously, if not at least three. Can you determine what those three level are? Take all of them to be simultaneously mundane and transmundane. Even without actual Gnostic interpretation active, it is profoundly Gnostic in FORM and CONTENT. The reasons for this are as profound and detailed as one could imagine. Therefore, hold nothing back in your imagination and analysis when watching this film.

(Suggested by Julia Yepez-Macbeth)

The Destiny of the Mother Church (Twentieth-Century Biographers Series)

by Bliss Knapp 

This book by a first-hand observer provides an important chronicle of Mary Baker Eddy, the Christian Science church, and the challenges faced by the early workers.

Descriptions of the individual roles of the pioneers of the church and its Founder, Mary Baker Eddy, are woven in and out of reminiscences and the author’s commentary. Several difficult and triumphant periods of the church’s growth are candidly recounted. The author also shares his individual views of the future of The Mother Church, its roots in Biblical prophecy, and the requisite dedication of church members.

The Destiny of the Mother Church is an interesting and unusual text which adds significantly to the biographic literature of Mary Baker Eddy and the history of the church.

Originally published for private circulation in 1947, The Destiny of the Mother Church is here available in print by The Christian Science Publishing Society.

(Goodreads.com)

Rupert Spira A woman says she feels resistance to collapsing the duality between herself and God. This clip has been taken from the Retreat at the Garrison Institute in Spring 2019. To watch the full video, please visit the link below. https://non-duality.rupertspira.com/w…

The Dinner in the Hotel Ritz in Paris, 1904
Art: Pierre-Georges Jeanniot

Look beneath the surface of Bach’s music and you will find a fascinating hidden world of numerology and cunning craftThe church of Pontaumur in the Auvergne, France, houses the only replica in Europe of the Arnstadt organ on which Bach composed in his early days. Photo by Philippe Dezmazes/AfP/Getty

Milton Mermikides is reader in music at the University of Surrey, professor of jazz guitar at the Royal College of Music, and deputy director of the International Guitar Research Centre. He is also a composer, producer, electronic musician, illustrator and guitarist, and has collaborated with Tim Minchin, John Williams, Brian Eno and Sam Brown, among others. He lives in London.

Edited byNigel Warburton

10 September 2021 (aeon.co)

Aeon for Friends

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Some 14 billion miles from here floats a 12-inch gold-plated record. This artefact was placed onboard the Voyager 1 space probe in 1977 (and another on the Voyager 2 sister vessel) and now, having long completed its scheduled planetary flybys, it hurtles at nearly 500 times the speed of sound into deep space. Created to communicate the story of human civilisation to any extraterrestrial who happens to encounter it, the Golden Record includes images, mathematical equations, astronomical coordinates and sounds. Its aim is to convey – in the absence of a common language – not just the facts of human existence, but also evidence of our intelligence.

One elegant method of how this might be possible is through the medium of music, which – aside from lyrical content – has the advantages of neither needing visual representation nor a lexicon of phonic objects. It speaks for itself through the common fabric of frequencies – amplitude over time – which can be etched directly and unfiltered into the surface of the disc. The importance of music to the project is clear: hand-etched on the record’s surface is the inscription ‘To the makers of music – all worlds, all times.’

When deciding which music could represent the pinnacle of human spirit and intelligence, Johann Sebastian Bach was inevitably suggested but – according to an unverified but irresistible anecdote – there was some dissent, because presenting music of such beauty and intelligence to any extraterrestrial listener would be ‘just showing off’.

Ultimately, among the commendably diverse 27 pieces of music included on the record, a full three are by Bach, suggesting perhaps that he alone represents more than 11 per cent of the value of our entire musical history. This vision of Bach’s music floating above the Earth as a symbol of musical perfection resonates with a prevailing perception of Bach’s art: somehow transcendent, timeless, and not of this world. His music represents the pinnacle of the Baroque era’s concerns with counterpoint but also can be readily adopted for a wide range of instrumentations, eras and styles, from ‘classical’ to jazz, pop and electronic. Bach’s music, it seems, is untroubled by the boundaries of instrument, style or era.

Musicians and music lovers rapidly run out of superlatives to describe his purported genius. To Beethoven, he was ‘the immortal god of harmony’; to Wagner ‘the most stupendous miracle in all music’; to Max Reger ‘the beginning and end of all music’. And Brahms declared, in a letter to Clara Schumann in reference to Bach’s Chaconne:

On one stave, for a small instrument, the man writes a whole world of the deepest thoughts and most powerful feelings. If I imagined that I could have created, even conceived the piece, I am quite certain that the excess of excitement and earth-shattering experience would have driven me out of my mind.

Connections to the divine are never far off, as in Mauricio Kagel’s quip that no one believes in God anymore but everyone believes in Bach, or even – in the words of a contemporary atheist philosopher – that Bach is the best argument for the existence of God.

With his music’s reputation of some kind of ‘eternal truth’ and implications of their divine transcription, it can be easy to forget that such heavenly work was the result of earthly toils. By blind luck of technological history, we are left with the beautiful manuscripts, but minimal record of the real-world stress, training, limited time and inky mess of putting quill to page. If indeed Bach’s talent was God-given, then it was a gift that demanded a reimbursement of decades of constant study, pouring over Vivaldi scores by candlelight with failing eyes, walking 280 miles just to watch one organist perform, the re-use of compositional material, adaptation to changing tastes, all amid a dizzying array of professional demands, awkward taskmasters, petulant critics, vain royalty and personal tragedies.

To appreciate the music of Bach (which I, like many others, find staggeringly beautiful), it can be instructive to understand both the mechanics and the mechanic: the musical systems, and the man himself – setting aside any received wisdom about his purported brilliance.

One can immediately learn something of Bach from his portraits, or in fact their scarcity – given his lack of time and reluctance to engage in self-aggrandisement. Artists complained that he never stayed still long enough to capture a likeness, and the few portraits we have of him say more about his music than about his appearance and character: he is a prop to hold up a fragment of a work, or to wear a hidden musical code on his clothing; it’s the music in the foreground, rather than the musician.

Above all, Bach was crafty both in his music and life, and he adored puzzles, games and general inventive mischief. His monogram on his wax seal and his goblet was his own design, and at first glance it looks like an ornate decorative symmetrical crest of interlocking swirls. It is in fact built up from his initials JSB overlaid and mirrored, which is apt, as his music uses mirror-like reversals, and is, like the monogram, something immediately beautiful but with hidden meaning.

Another example of Bach encoding information into decoration might be found in the title page of his 24 preludes and fugues for The Well-tempered Clavier (the first prelude of which is included on the Golden Record). Often this series of works (one for each major and minor key) – is mistakenly taken to have been written for the now-ubiquitous even-tempered system. In an even-tempered system, the pitch difference between each chromatic note (for example, each adjacent note on a piano) is identical. With a well-tempered system, however, the gaps differ slightly, and are set up to provide sonorities in some keys closer to those that emerge from the ‘natural’ harmonic series. Choirs, string ensembles and other instruments unfettered by a fixed pitch system tend to converge upon these ‘purer’ intervals in performance – string ensembles and choirs make subtle but precise adjustments so that chords resonate, and these deviate from the fixed 12-note grid-lines of an even-tempered instrument such as the modern piano.

Bach’s name in the German notation system happens to spell out a haunting chromatic melody

There are countless well-tempered systems possible, and several at Bach’s time, however it was a question for centuries which system Bach used for The Well-tempered Clavier, and how each of those keys would have sounded. It was not until 2005, a quarter of a millennium after its composition, that the musicologist Bradley Lehman made an argument that the decorative symbol at the top of the page, which for generations had been dismissed as an ornamental ‘meaningless’ series of loops, contained coded instructions for how to construct the temperament, hidden in plain sight. Lehman suggests that the three types of loop (plain, knotted, and double-knotted) represent the variously tuned gaps between the notes, and one has been identified with a ‘C’:

But Bach not only hid messages in decorative shapes but sometimes within his music itself. His name in the German notation system – which, unlike the rest of the Western world, runs from A to H – happens to spell out a haunting chromatic melody. Bach enjoyed embedding this motif in his music, and generations of composers from Liszt to Brahms to Schoenberg to Arvo Pärt have written homages to Bach using this melody:

Audio of the BACH Motif, performed by Bridget Mermikides

These four notes can even be represented as one, at the intersection of four clefs, in a crucifix symbolisation – reading clockwise from the top, the clefs are tenor, alto, treble in the key of C major (or A minor), treble in F major (or D minor):

Bach, who was obsessed with numerology, took the codification of his name further, and by adding up the alphabetic placement of these letters came up with the ‘Bach number’ of 14 (2 + 1 + 3 + 8), a number that would recur encoded in many of his compositions. It also appears in the so-called Volbach portrait of 1750, in which Bach wears 14 (unnaturally close) buttons on his waistcoat. The biblical number of buttons on his coat (seven, for the Sabbath day, and the seven original divisions of the Bible) are also unlikely to be accidental. Indeed, Bach’s engagement with numerology has invited furtive (and often overzealous) hunting of numerical meaning throughout his music.

In an earlier portrait from 1748, by Elias Gottlob Haussmann, Bach holds a short piece, Canon Triplex in Six Voices, his entry piece to the Society of Musical Sciences – a collective of elite composers that included Handel and Telemann, who believed that music was deeply linked with the sciences and the cosmos, a sentiment shared by Pythagoras’ concept of the ‘Harmony of the Spheres’. Bach was of course accepted, but allowed Handel to take his place before him, so that Bach could be the 14th member. The piece itself is from The Goldberg Variations, the first of Bach’s four major late collections of compositions (or ‘summation works’) and an important contribution to keyboard repertoire. Published in 1741, it features an aria with a set of variations. After their, completion Bach – the constant tinkerer – could not resist adding a set of canons on the last page based on the aria’s bassline. How many of these canons did he write? Fourteen, of course.

The three short lines in the 1748 portrait are not a fragment or cartoon of the work – they are in fact the entire piece. To understand better why a piece can fit in a handful of bars and why Bach would pose proudly and submit it to his esteemed peers requires a little understanding of canonic principles. That he could embody his complex musical thoughts in such an economical way reveals his technical and musical mastery.

The simplest form of canon is known as a round – or ‘perpetual’ canon – think ‘Frère Jacques’). It involves a melody played identically in multiple voices (instrumental layers), starting at different time intervals. This ‘phasing’ of one melodic line builds a more complex texture and interaction from this simple component. Its underlying mechanics are shown in an example below. The first voice sings a looped melody made up of three phrases (A-C), the second and third voices sing the three-phrase melody but displaced by one and two phrases respectively:

This results in all the phrases being heard together, distributed between the voices, in a theoretically infinite loop. To compose such a simple canon might involve starting with Phrase A and then composing material for additional layers above it. However, some more sophisticated reverse-engineering could be employed: if we start with the complete stack of complementary phrases that work well together in terms of rhythmic interest and harmonic agreement, then we can slice up the constituent phrases and rejoin them in a preferred linear order. The voices then rebuild this stack through the canonic process.

But the craft of canonic writing – particularly in the case of Bach – runs much deeper than this simple example. Some canons involve phrases that, when delayed, are transposed to different intervals or stretched rhythmically. They can be turned upside down (‘inverted’), run backwards (‘retrograde’, as in Bach’s ‘crab canons’) or even both, as in ‘table canons’ that can be read simultaneously from one stave by musicians from their own perspectives at either side of a table. Multiple canons can even be superimposed upon one another and played simultaneously – even on a single (usually keyboard) instrument. These offer greater compositional complexity and constraint than the simple round presented above, and Bach revelled in such challenges. Take Bach’s Canon Triplex in Six Voices from the 1748 portrait.

Audio of the Canon Triplex, performed by Bridget Mermikides

Here, although only three voices are notated, Bach sneaks in some ‘decorative clues’ as to how they are to be manipulated into a canon. Some of these ‘hacked notations’ are outlined below, and show additional key signatures, phrase re-entry points, upside-down suggestions and a hint that each voice is doubled. Why is Bach so obtuse in his instructions? This is an example of a ‘puzzle canon’ or ‘riddle canon’ where the ‘solution’ to the canon has to be deduced from clues in the score, or solely from the reader’s invention. The musician is not simply given the music: it has to be earned.

We should also acknowledge that the piece involved some careful tinkering

The music depicted in the Canon Triplex portrait is not just one canon, where one melody is overlaid against itself, but three simultaneous canons. In addition, each of these canons isn’t a simple delay of material, but involves turning the melody upside down against a delayed version of itself.

Unlike in a simple round, here each canon obliges an internal consistency (eg, A1 and A2 make a pleasing phrase, and A1 and A2 work together if either is inverted). Furthermore, this collective stack must work with two other similarly constrained stacks. We should, of course, marvel at Bach’s skill in achieving such canonic delights and communicating these musical ideas with such elegance. However, we should also acknowledge that the piece involved some careful tinkering, even though it stays entirely in one key and is structurally static (or infinite). Musical output is somehow limited by the constraints imposed.

However, Bach thought enough of the Canon Triplex – a postcard rather than grand work – to be immortalised with it in his portrait. This reveals some profound aspects of Bach’s musical craft and conception that are not commonly understood musical devices, even in our contemporary music culture. These might be termed:

1. encoding: in the Canon Triplex, layers of musical meaning, the source of musical objects and even its very instructions are hidden below the surface of the music. A puzzle to be solved or an eternal secret;
2. pluripotency: in this piece (and its sibling canons and variations), the Goldberg aria bassline is furtively reworked into apparently endless musical forms. Rather than fixed singular objects, compositions are to Bach more like dense constellations of compositional opportunity; and
3. multiplicity: music is often thought of as existing in clear and hierarchical layers – for example, a melody layer ‘on’ chords ‘on’ a bass line. However, the motifs in the Canon Triplex hold deeply multiple functions, they are melodies and (through transformation) accompaniments – to themselves.

This latter device – multiplicity – is the DNA of the musical discipline of counterpoint – the interaction of multiple musical lines that are both independent melodies and collectively harmonically coherent. Bach is rightfully held up as a master of counterpoint. This is evident – perhaps a defining feature – across all his works. Most directly in his canons, which act – and are sometimes unfairly dismissed – as musical toys: like a Newton’s cradle, they are set in motion and quickly form a mesmerising but short repetitive pattern until manually stopped. However, where such canonic and contrapuntal mechanics meet more conventional (and complete) compositional structure is in his craft of the fugue.

Afugue (from the Latin fugere, meaning ‘to flee’ or ‘to chase’) is a musical form that – though variable in tempo, metre, duration and harmony – always follows a set script. At its centre is a single melodic phrase (the ‘subject’) that forms the basis of the fugue’s thematic material, across multiple independent musical voices (or ‘parts’). The first voice starts alone stating the subject, and then continues with ‘counter-subject’ material complementing a second voice that reintroduces the subject (usually at a different interval). This pattern continues until all (commonly, three or four voices) are introduced and the piece develops, exploring more distant harmony and variations – extending, shortening and reworking the thematic material while maintaining a familial connection.

Finally, the voices return to the original key and restate the subject to conclude. This conversation between multiple and equal voices, independently coherent, are linked by thematic material and mutual harmonic agreement in service of an overarching structure. Again, we see here the pluripotency of the fugue’s subject in its multiple variations and contexts. We also witness the multiplicity of each of the voices that act both as independent and equally important melodies (a horizontal coherence) and as accompaniments and harmonisations of each other (a vertical coherence).

Bach was a master of such a subtle juggling act, and he selected or designed subjects that had melodic identity and interest, as well as being malleable enough for multiple functions. In so doing, he produced with a staggering industry many sophisticated fugues – each one a highly expressive musical work in its own right, as well as a logical solution to a self-imposed puzzle. In The Well-tempered Clavier alone, he completed fugues (some with as many as five voices) for every one of the 24 major and minor keys, and then some 20 years afterwards repeated the entire exercise again in a second book. Bach gained such experience, skill and fluency in fugal writing that he was allegedly able to improvise them even on demand.

It was reports of Bach’s prowess that led King Frederick II of Prussia to invite him repeatedly to his palace. Frederick the Great was a keen flautist who employed Bach’s son Carl Philipp Emanuel as the harpsichordist in his private orchestra, and had a genuine passion for music, composing many works for himself and for his ensemble, reportedly practising for four hours a day and taking his flute and a collapsible harpsichord with him on military campaigns. As is often the case with those privileged with wealth and power, he liked to surround and associate himself with the finest musicians, artists and poets. Despite several requests for Bach’s company, they met only once and for a matter of hours, when Bach made the onerous journey from Leipzig to Frederick’s magnificent town palace Stadtschloss in Berlin. Bach – always keen for patronage – also used the opportunity to see his new grandson for the first time.

Bach’s ‘failure’ to fulfil the king’s requests is a significant and profound moment in music history

The meeting – for which we have an eyewitness report and supporting documents – gives a rare insight into Bach’s compositional process and to both the extent – and limits – of his craft. After Bach had sampled Frederick’s collection of keyboards, the king arrived at what was clearly a planned attack. As much as Frederick had a genuine admiration and earned appreciation for musical skill, he also enjoyed demonstrating his power and putting his subjects in their place. Voltaire claimed that, for Frederick, a friend was as a ‘slave’, and an invitation to dinner was an opportunity to ‘make a jest of you all evening long’. Enquiring after Bach’s reported skills, he asked the master if he wouldn’t mind improvising a fugue on a subject of the king’s own creation, and immediately presented him with the following theme:

Audio of The Royal Theme

This is a cunningly crafted challenge. It fulfils the overt features of a fugal subject, with a clear tonal centre, and logical phrasing – it is melodically coherent. However, in all other ways, it is fiendishly difficult: the use of chromatic notes and their rhythmic placement across its long duration make them a beast to negotiate in a contrapuntal setting, requiring significant sophisticated harmonic skill. Frederick might well have conspired with musical experts (perhaps even Bach’s son) to set this trap for the virtuoso, and so the request to extemporise a three-part fugue was probably born as much from mischief as from innocent curiosity about the limits of Bach’s compositional genius. However, despite being weary and unrested from the long journey, and under the gaze of the king and a company of distinguished musicians, Bach somehow managed to corral this knotty melody into a beautifully crafted three-part fugue, introducing the three voices with the devilish subject and then letting them fly independently while collectively exploring yet more distant and labyrinthian harmonies. Bach even – under all these constraints – employed melodic and rhythmic features of a more ‘pop’ late-Baroque style that he knew Frederick enjoyed.

Audio of Bach’s Ricercar à 3 (three-part fugue) on the Royal Theme

Perhaps as much irritated as impressed, Frederick was not satisfied with this remarkable performance. He immediately demanded that Bach now concoct a six-part fugue on the same subject. This was no small ask – in both books of The Well-tempered Clavier, Bach had only occasionally used as many as five voices – and these were with far more accommodating self-selected fugal subjects, and with the luxury of composing at leisure rather than extemporising in front of an audience. Instead of accepting this challenge, Bach improvised a six-part fugue on a theme of his own choosing.

Bach’s ‘failure’ to fulfil the king’s requests is a significant and profound moment in music history. He might have found a stunningly elegant ‘solution’ to the six-part puzzle on the Royal Theme soon after his return to Leipzig but, in that moment with the king, it was beyond his inspiration and real-time skills. So Bach’s inability to meet the task on 7 May 1747 in fact brings all his musical achievements into sharper definition: the convenient myth of the divinely inspired composer dissipates to reveal the perhaps more miraculous real-world and hard-won craft. Bach was a quite remarkable human craftsman with limits, not someone with a hotline to God.

Bach quickly collated a transcription (or adaptation) of his three-part improvisation and the six-part fugue, alongside a staggering collection of ingenious canons, pieces crafted for Frederick’s playing ability, taste and ensemble, all revealing the pluripotency of the awkward Royal Theme. This Musical Offering demonstrated mirror structures, endlessly rising or lengthening canons (to reflect the king’s growing glory and fortunes), intricate puzzles, deep fugal craft, biblical and numerological references, and encoded acronymic messages within the titles of the works. Layers of external and musical meaning co-existing and entangled in an elaborate fugue of fugues.

Within weeks of their meeting, Bach dispatched The Musical Offering to the king, but – as is often the case with those of privilege of power – we have no record of Frederick thanking Bach, acknowledging receipt, or performing or in any way engaging with this extraordinary work. Still, we get to enjoy and admire it to this day, and the gift of Frederick’s trap is not just in provoking one of the last of Bach’s major works, but also in giving us a uniquely valuable insight into Bach’s craft – a frozen moment of his process and not just its inscribed remnants.

The Musical Offering also formed the impetus to Bach’s last (uncompleted) work, The Art of the Fugue – a similar thesis of motivic pluripotency in canonic and fugal forms, but this time on a theme of Bach’s own choosing. By this time, Bach’s eyesight and writing arm were in poor shape from years of constant work, and a series of surgical eye operations (one shudders to imagine what those involved) left him with intermittent blindness until his death from a stroke on 28 July 1750.

The Art of the Fugue was left unfinished. In the last (incomplete) fugue that he wrote (here termed Contrapunctus), the independent voices come to an end abruptly, not together but in succession. An inscription below the fugue translates as: ‘At the point where the composer introduces the name BACH [for which the English notation would be B♭–A–C–B♮] in the countersubject to this fugue, the composer died.’ A profound silence is experienced when the fugue is heard in this incomplete (yet, in a sense, complete) form. But this poignant and apt resolution of Bach’s life and music might be, to some extent, a fiction.

This conceit of Bach returning to the Lord as he entraps his own name into his ‘divinely inspired’ music is too beguiling to resist retelling. However, it’s a version of events that does not withstand scrutiny well. The manuscript appears to be in Bach’s own hand, which would suggest it predates his final deterioration of health, and was not – as we are led to believe – dictated to Carl Philipp Emanuel in his blindness. This is likely a ‘staged’ profundity, particularly when we notice the number of the fugue in the collection – 14, of course. It is, yet again, rather than divine intervention, an example of Bach’s craft – and craftiness – operating on multiple levels, for musical and extra-musical expressive effect.

To read more about Bach, visit Psyche, a digital magazine from Aeon that illuminates the human condition through psychology, philosophy and the arts.

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Link to original article with audio: https://aeon.co/essays/look-into-the-secret-world-of-numerology-and-puzzles-in-bach?utm_source=Aeon+Newsletter&utm_campaign=dc83a34503-EMAIL_CAMPAIGN_2021_09_06_06_11&utm_medium=email&utm_term=0_411a82e59d-dc83a34503-72012996

by Rabbi Rami Shapiro (spiritualityhealth.com)

Getty Images/dvulikaia

Donuts can teach us a deep lesson about our brains and how to cease the internal chatter. Read on.

A kōan is a question or statement used by a Zen master to test the quality of a student’s awakening. What is the sound of one hand clapping; show me your face before your parents were born; where is the hole after the donut is eaten? are three classic examples. Well, not all three are classics: The last one I made up. But I like it, so let’s go into it nonetheless.

For argument’s sake, let’s put aside the kōan’s implied and somewhat controversial notion that a donut without a hole isn’t a donut: It may be a cruller, a Bismark, a beignet, a churro, a sufganiyah, or any other named piece of fried dough, but it isn’t a donut. Not everyone agrees with me on this, but since the kōan doesn’t work without it, I will ignore these donut skeptics and move on to another crucial aspect of the kōan. That is, which comes first: the ring or the hole?

Since a donut without a hole isn’t a donut (remember we are ignoring all donut skeptics) you might say the hole comes first. Yet, since the hole without the ring of dough isn’t a hole but simply unbounded empty space, you might say the ring comes first. But, since a ring without a hole is a slab of dough and not a ring you might say the hole comes first. The truth is neither comes first. Since the ring needs the hole to be a ring, and the hole needs the ring to be a hole, the ring and hole arise together. In Buddhism this is called pratītyasamutpāda or “dependent co–arising.” What is true of a donut is true of you as well.

Your ring of dough is your brain with its endless chatter of thoughts, feelings, and sensations. Your hole is your ego with its endless commentary on those thoughts, feelings, and sensations. Given this, you are confronted with a second kōan: Where does the ego go when the brain is silent? Whether we are talking about a donut hole when the ring of dough is eaten or an ego when the brain is silent, the answer is the same: nowhere.

When the brain is silent, when thoughts, feelings, and sensations cease, the ego ceases as well. When there is nothing to comment upon, the commentator fails to arise.

My own “experience”* of silent brain, necessarily constructed after the event had passed, tells me that when the brain is silent, the ego is absent and yet consciousness continues. There is consciousness without any comment; a profound stillness when life simply happens without me. And when “me” does return it is always accompanied by a deeper connection to and compassion for all life.

My “experiences” of silent brain have always been serendipitous. In the most recent case, I was talking with my teacher, Prasanna. Apropos of nothing, he asked me a question—Are you?—and the donut was consumed and the hole erased.

Since I know of no surefire method for silencing the brain, I suggest you do the following: The next time you sit down to eat a donut, notice the dough and the hole co-arising. Then take a bite and ask yourself: Where is the hole after the donut is eaten?

*Experience is in quotes because experience implies an experiencer, and there was no experiencer in this “experience.” Limits of language.

Want more? Read about the link between spirituality and prayer.

More from Rabbi Rami on Buddhism, from the print issue of Spirituality & Health.

I want to be a Buddhist, yet I don’t want to shave my head or trade in my torn jeans for robes. Is there a way around this?

Sure: Be a Buddha rather than a Buddhist. The Buddha wasn’t a Buddhist; the Buddha was awake: awake to the interdependence of all life, awake to the impermanence of all living, awake to the suffering that arises when we desire things to be independent and permanent, and awake to how we can end that suffering by embracing interdependence and impermanence. Wake up to reality as it is and you can wear your jeans as tattered as you like, and grow your hair as long as you wish.BuddhismSilence

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About the Author

Rabbi Rami Shapiro is an award-winning author, essayist, poet, and teacher. In the print version of our magazine, he has an advice column, “Roadside Assistance for the Spiritual Traveler,” addressing reader questions…

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