The Little Prince and the Labyrinth of Exoplanets

My submission to Imperial College London's Public Science Communication Competition under Simon Singh's essay prompt 'Exoplanets'.

The Little Prince stood atop a small asteroid, gazing at the river of starlight that spilled across the sky. His scarf caught a stray wind and fluttered with a secret music. Somewhere far away, he thought, was the rose he had once loved and the fox he had tamed. But the cosmos was vast, and there were countless other worlds—exoplanets—that beckoned him onward.

He left his asteroid one dawn, carried by a delicate curiosity and a whisper of solar radiation. Drifting among constellations, he arrived at a world so large it seemed to fold in on itself, like a labyrinth of exoplanets, each one spinning in silence. Upon landing on the first planet, he found an astronomer hunched over a telescope and scribbling in a worn notebook.

Astronomer:
“Most planetary classification is done using classical parameter spaces like mass, radius, and orbital eccentricity.”
He pointed toward an array of figures.
“But what if we took a step beyond? In algebraic geometry, we classify shapes not by coordinates, but by the equations that define them.”

The Little Prince scrunched his nose.

Little Prince: “Equations? But I only see shimmering shapes and unending stars.”

Astronomer:
“Yes, but these shapes are not mere points. They belong to something deeper—an algebraic variety—a tapestry of planetary formation and the possibility of life. Imagine a hidden web beneath the visible orbits. Each exoplanet is a solution to cosmic equations that we have scarcely begun to write down.”

The Little Prince thanked the astronomer and soared away in search of other worlds. He found a second planet made entirely of mirrors, each reflecting a different night sky. There, a geometer welcomed him with a quiet smile. With a wave of her hand, she produced lines and curves in the air, each trembling with colour.

Geometer:
“Nature is never just smooth. We live in a messy, chaotic, and sometimes singular universe. For these complexities, we use tropical geometry: a way to collapse algebraic varieties into piece-wise-linear structures. Think of it as the geometry of shadows—where surfaces become crystal-like scaffolds, and the equations reveal a raw skeleton.”

The geometer's mirrored planet seemed endless, each reflection spooling out into countless corridors. The Little Prince felt dizzy, as if confronted by a cosmic hall of illusions. Yet in each reflection, the geometry maintained an inner truth. He could sense that these “collapsed” shapes were simplifying something vast—the swirl of orbits, the unpredictability of gravity, the uncharted complexity of life.

Geometer:
“Tropical geometry allows us to understand exoplanets not just as dots in the sky, but as a network of polytopes, a scaffolding of possibilities. We can see patterns that we had never noticed before, as if we could trace invisible threads between the stars.”

Touched by this notion of hidden connections, the Little Prince left, carrying the image of polytopes in his mind like a puzzle waiting to be solved. He next arrived at a planet of labyrinthine pathways, which appeared as a tangle of passages spiraling inward. While wandering the silent corridors, he noticed a logician perched on a marble staircase.

Logician:
“This maze is the cosmos.”
He pressed a trembling, graphite-stained finger to a worn map.
“Each exoplanet rests in a distinct chamber, yet each chamber leads to countless other corridors—like the branches in a garden of forking paths. If you study the orbits, you trace a topological dance. Every system is part of a broader homotopy class, shaped by time and gravitational pulls.”

The Little Prince remembered how his own planet had seemed alone, yet was bound to the sun and many others. He wondered how all these threads and tapestry of orbits might connect. Perhaps this labyrinth was not merely chaos, but an echo of a deeper code underlying exoplanetary formation.

Logician:
“Topology asks us to see the unity behind shifting forms. The loops and holes in this labyrinth mirror the stable orbits, resonances, and hidden symmetries that bind star to planet. I suspect habitability might be a topological invariant, a pattern persisting amid cosmic transformations.”

The Little Prince thought of his rose and how greatly she depended on him. He wondered if another rose might exist, awaiting care. In each corridor, he saw a new possibility leading to unknown worlds.

At nightfall he climbed a winding staircase back to his asteroid. Gazing across the cosmos, he reflected on all he had learned and how algebraic geometry and topology might encode deep truths. He pictured algebraic varieties glimmering among the stars, capturing orbits and chemical complexities in elegant equations. He recalled the polytopes of tropical geometry, revealing hidden structures in planetary systems. Each discrete framework laid bare deeper symmetries in nature; exoplanets shaped by gravity yet unified by universal rules.

He realized that mathematics was not just a tool, but a secret language letting stars speak through geometry and algebra. He whispered, “Planets are equations in motion. Maybe life itself emerges from these cosmic patterns as a solution waiting for the right balance.”

Under the vast dome of stars, he understood each exoplanet was a mirror of unspoken equations hinting at life’s possibilities. Though the cosmic garden branched infinitely, each path led to the same truth. The universe was an evolving dialogue fusing the ephemeral and the real.

He sensed that the labyrinth was not just around him, but within. He stood in awe of the symmetry and simplicity from which complexity arises. Perhaps the universe unfolds from discrete rules, whose simple transformations shape stars, orbits, and life itself. In algebraic geometry, in topology, in every hidden polytope, he glimpsed a deeper computation. And in that inward labyrinth, he sensed a silent music of discrete shapes, and the promise that even the smallest rule, repeated patiently, might grow a rose.