D Minor Passion

I came back to the keyboard recently after a few years’ absence, and looked at Bach’s Art of the Fugue. I had always found it impossible to play, blaming my short fingers. But this time what I found is a puzzle: you can play it with two hands, ten fingers. Even short ones. But there are many passages (some one beat long) where the inner voices change hands back and fourth – there are three voices in one hand and only one in the other. The voices cross, making it difficult sometimes to hear the voice leading. But every time I come to something I think is impossible, I find that Bach was there before me. There is a way forward: see, the soprano has been silent and you have tenor and alto in the right hand. The tenor is descending to the octave above the bass. Take the octave with the left thumb. Transfer the alto note to the right thumb. The alto leaps up an octave. Take that with the fourth finger, so the fifth can do the soprano entry.

I remember a concert in Montreal. Bernard Lagacé was playing the entire Art of the Fugue on the wonderful 1961 von Beckerath organ at Imaculée Conception. He said, (was it in the program notes?) “After playing this work I am spiritually exhausted.”

Today, working my way slowly through the first five fugues, I think I know why. And I think suddenly of two more works in D Minor: Bach’s Chaconne from the Partita No. 2 for solo violin, and the last fugue (D Minor) from Shostakovitch’s 24 Preludes and Fugues, Opus 87, which is itself an homage to Bach.

It is because the D-minor theme is a person, and the development is her life.

The Chaconne is intense from the beginning. The eight-bar theme statement is all triple and quadruple-stop, rolling-bow virtuosity. The thirty-two variations are a spiritual roller-coaster ride. So much so that the return to the quadruple-stop theme is a rest, a relief. Exhausting.

In the fugues – both the Art of the Fugue and the Shostakovitch Opus 87 – the theme is set against itself and various counter-themes. The voice – the person – is always recognizable, right side-up or upside-down. The passion and struggle is later, as the theme shoulders its way into an increasingly complex structure. It is impossible that it will fit in this chromatic storm, you think, and then it does, and you are amazed and exhausted.

The end can be a bang or a whimper. The theme can rage, or it can find peace. In the Art of the Fugue, on the very last page, he has just introduced a new theme: BACH (B♭, A, C, B). He sets up the new structure, and has just introduced the BACH theme in inversion (upside-down) and . . .

That’s it. His life. Not rage, not really. Certainly not a whimper. Perhaps it is peace . . .

Quantum Fiction No. 2

Parallel worlds is also a way of looking at conflict in life and in fiction. Each of us has in his head a representation of what he thinks of as reality. Much of it is untested received wisdom. But even with street smarts and lifetimes of effort and education, the overlap of our worlds is surprisingly small. So agreement on just about anything is never a foregone conclusion. Should we bump into each other the more likely outcome is conflict.

Why? Is it the nature of reality? Don’t we say to each other in exasperation, “Get Real!” or “What planet are you from”?

The conflict can be personal. Because we are social animals, gathering for support in families and tribes, it can be tribal. In a modern democracy it can be conflict over public policy. At its most acute the conflict is sectarian as our religious beliefs threaten and crash against each other. Before dinner with friends don’t we say, “Just don’t bring up politics or religion”?

In life and in fiction these conflicts find resolution through conversation, teaching, art, and love. In each (and in good politics, too) there is a mutual agreement to let go of the absolute. Instead of certainty, each question takes on a quality of possibility analogous to the quantum particle. Both binary states exist in such a particle in superposition. Better yet, quantum particles (and perhaps also questions in our worlds?) can instantly co-ordinate their properties regardless of their separation in space-time. Scientists call it entanglement. Action at a distance. Is this perhaps the beginning of faith?

Quantum Fiction

As I struggle to learn to write (difficult, pills painful, intoxicating) Arcadia has become my parallel universe. It is not my native Canada but it is a close cousin. It is not true (fiction) but it is me – my experience, my history, my imagination.

In 1957 Hugh Everett put forth the Many Worlds Interpretation of Quantum Mechanics, where the uncertainty of the quantum state was resolved by positing parallel universes. I have always thought his theory patently ridiculous. If each and every quantum particle divides the world in two as it collapses, then the number of universes is two to the power of the number of particles in the universe, or something. It is bigger than infinity: it is an infinity if infinities. It boggles the mind.

Of course that has no bearing on its truth. And after reading Dream Machine in the May 2, 2011 issue of The New Yorker, I am changing my mind about Everett. As Riva Galchen says in her article, physics advances by accepting absurdities. So perhaps it is more to the point to question the usefulness of a theory and let its truth fend for itself in future generations.

After all, do we not all live in parallel universes? Are our worlds exactly alike?