Thursday, October 31, 2013

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

Thursday, October 10, 2013

Introduction to Complexity

This is a re-offering of our popular "Introduction to Complexity" course, with some new material, homework, and exams.

In this course you'll learn about the tools used by scientists to understand complex systems. The topics you'll learn about include dynamics, chaos, fractals, information theory, self-organization, agent-based modeling, and networks. You’ll also get a sense of how these topics fit together to help explain how complexity arises and evolves in nature, society, and technology. There are no prerequisites. You don't need a science or math background to take this introductory course; it simply requires an interest in the field and the willingness to participate in a hands-on approach to the subject.