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High Firmament

by Jacob Shulman

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Toroid 06:11
Maple 08:33
Zephyr Point 08:07
Plucky 06:00


The sun rolls up its track and the outside world shivers awake. The early morning blesses the mind; the light of consciousness solidifies into logic, coherence, and structure. This is when we attune our muscles. Tingle into readiness. This is also when we do mathematics, when we compose, when we create.

The constructive mood that reappears each morning lies at the root of so many of humanity's great accomplishments. One imagines the miracles of Bach springing forth, fresh-faced and confident; the architecture of Vitruvius, embodying firmness, utility, and beauty; the geometry of Euclid, freezing the flow of thought into concrete facts and figures. In this mood, the only limit is your own mind. You climb the tower of construction, abstraction, and symmetry until your grip begins to loosen; then you build more. But to ascend to the heavens of theory is also to plumb the depths where contradictions and paradoxes lurk.

Thousands of years of conjecture and agony have led us to conclude that our world diverges from Euclidean geometry in unresolvable ways. Relaxing a single postulate in Euclid unlocked whole realms of geometry, where the very measurement of distance bends away from Pythagoras' Theorem with the curvature of space. It took a long chain of geniuses to uncover the connection between these geometries and our observation: the nineteenth-century work of Gauss and Riemann on differential geometry inspired Hilbert, Poincaré, and Minkowski to concoct new conceptions of space, culminating in Einstein's 1915 theory of General Relativity. Gravity, the easiest-to-observe force in the universe, is nothing real at all — a mere artifact of geometry.

At the same time, Planck spearheaded investigations into the nature of reality at the smallest conceivable scales. Unsettling truths crept out of the formalizations of Dirac and von Neumann and the wide-open minds of Heisenberg and Bohr. In 1964, Bell tackled an outstanding paradox in quantum mechanics head-on and produced a theorem showing that the universe is "not locally real" — particles can become entangled and moreover seem to covertly transmit information across boundaries of space and time. Every moment is just a wave in the sea of what is possible. Experiments as recent as 2017 confirm Bell's Theorem — a death blow to those who maintain the universe is exactly as it seems.

Music always dances with ideas long before mathematics comes along to force them into bondage. By the mid-eighteenth century, music had rejected the white-hot truths of Bach. Bach's music is saturated and perpetual, like a fire burning through oxygen, choking the empty space. Any rejection of Bach needed light and space and more sensual pacing. Mozart, the prime exponent of the new style, indeed exemplifies grace and elegance, and these words are not mere euphemisms for simplistic, provincial tendencies. Mozart replaced Bach's continuous-through-time contrapuntal puzzles with a one-at-a-time grammar of harmony, a grammar sophisticated enough for poetry, prose, and humor. The thickets of voice-wise democratic composition wilted to make space for hierarchical music with foreground, middleground, and background. At the same time, in mathematics, Euler learned to tame infinite series and uncovered the space inherent in the complex numbers. One finds that elegance, focus, and hierarchy defined the achievements of the eighteenth century. The jazz I play today carries this flame: harmony and form support the melody, the star of the show; rhythms bend and breathe with the spirit of the players. Looking back to the era just after the surge of research into quantum mechanics, Charlie Parker reignited the spirit of Mozart, giving melodic elegance a new home in the mathematics of syncopation and swing, where half-symmetries of the beat rub against each other, kindling new flames. To this day, there is no system — no vehicle — of jazz deeper than bebop. But Mozart's first successor, Beethoven, opened up new spaces as well, just as his contemporary Gauss did in geometry. Beethoven recast beauty into the sublime, extending patterns beyond their logical conclusions. Jazz thrives here, too; when one cannot understand a phenomenon, one is forced to feel it for what it really is.

The unifying factor in these human peaks is the clear-headed morning-mindset, the wellspring of Apollo where intuition, logic, and abstraction twist around each other, reaching higher and higher until one forgets the ground ever existed. Some part of this spirit exists in all of us. An awakening pose, stretching towards the sky. The effort of imagining a shape that cannot be drawn. Coffee, steaming into the air; a many-layered pastry crunching and flaking between your teeth. A brisk hike, wind whipping and twirling, feet pushing off the fractals of the Earth. The mental challenge of structured improvisation, grabbing hold of chords and meters to propel yourself upward. Eye-on-the-ball focus, putting everything you have into a swing, the sun pushing your shadow straight down into the ground. In these moments, the sharp corners of logic and the vibrating fuzz of reality turn from unbearable to inviting. Play the game. Think it through. Build.

The music we recorded — live, all in one room — ties together these images with the thread of the morning-mindset. You hear not just a carved-marble, idealized final product, but also flashes of our imaginations, open doors we peek through, nearby parallel paths the music could have taken. No, music is not real; but neither is mathematics or any other human creation. All that is always has been. We imagine structures and patterns so that the infinite coheres into something we can grasp; we pull on the firmament so that it pulls back and lifts us off the ground.

—Jacob Shulman, Summer 2023


released February 29, 2024

Jacob Shulman ⋅ tenor saxophone and clarinets
Hayoung Lyou ⋅ piano
Walter Stinson ⋅ bass
Kayvon Gordon ⋅ drums

Jasper Dutz ⋅ additional clarinets on "Hometown Hero"

Recorded by by Quinn McCarthy and Lee Meadvin ⋅ Produced, edited, mixed, and mastered by Lee Meadvin ⋅ Cover art and design by Knar Hovakimyan ⋅ Liner notes by Jacob Shulman


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Jacob Shulman Los Angeles, California

b. 1994

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