The spiral staircase to Hogwarts' tallest tower seemed endless.
Each stone step bore centuries of weight, cold and unyielding. Gryffindor's first-years dragged weary legs upward, lungs burning, calves aching. The winding climb made them dizzy, the only sounds their ragged breaths and footsteps echoing in the narrow space.
At last, the final student reached the top platform—only for their fatigue to vanish in an instant.
They stood upon the very dome of Hogwarts.
There was no roof.
The icy night wind swept the thin air of the heights, carrying away their sweat and replacing it with a refreshing shiver. Above them stretched the boundless night sky—no longer distant pinpricks, the stars here were massive, brilliant, close enough to touch. A vast river of stardust spanned the heavens, silent and sublime, making every soul that gazed upward feel their smallness.
This was no classroom. It was an observatory—direct communion with the cosmos.
"Silence."
The serene but commanding voice cut through the wind.
Their professor, Aurora Sinistra, stood at the platform's center. She wore deep-blue robes embroidered with silver constellations, her graceful form blending seamlessly into the night. Her voice was quiet, yet it carried through the breeze to each ear.
She lifted her hand, and with a sweep of her wand—
Hum.
The air thrummed. Above them, where the sky was darkest, countless points of light appeared from nothing, gathering, aligning. Slowly, majestically, a vast star chart of the solar system unfolded overhead, wrought entirely from pure light. It began to rotate on its own, in perfect, elegant rhythm.
Each planet radiated a unique halo, tracing elegant paths as they revolved around the brilliant "sun" at the center.
"Welcome to the world of Astronomy."
Professor Sinistra's voice was as cool and clear as starlight. "Here, you will learn to recognize the stars and understand the mysteries of the cosmos…"
A wave of awe swept through the students. They were utterly immersed in the grandeur of this magic and the magnificence of the universe, their eyes filled with reverence and fascination.
All except Alan.
He frowned slightly.
Within his mind palace, countless star chart models corresponding to the one above his head had already taken shape—but they weren't static. His consciousness was analyzing and deconstructing each model at astonishing speed.
[Model Type: Two-dimensional planar projection.]
[Data Dimensions: X-axis, Y-axis.]
[Missing Dimension: Z-axis (depth).]
[Logical Flaw: All celestial bodies are forcibly projected onto the same plane. True spatial positions cannot be represented; distances cannot be measured accurately; no effective gravitational model can be established. Conclusion: This star chart is merely illustrative, with no real surveying value.]
A fatal flaw.
Alan pulled himself from cold logic, raised his head, and listened quietly to Professor Sinistra as she explained the basic principles of planetary motion. He waited patiently.
When she finished and was about to move on to the next part of the lesson, a hand went up.
"Mr. Scott, do you have a question?" Professor Sinistra's expression carried a warm smile. For inquisitive students, she always had patience.
"Yes, Professor. I have a question about 'positioning.'"
Alan stood. His voice wasn't loud, but it carried an unusual clarity. Every eye turned toward him. He showed no hesitation—his words were precise, as though he were attending a formal academic seminar.
"What we are observing now, this star chart—it is essentially an image projected onto a two-dimensional plane.
But we all know the universe is three-dimensional, perhaps even multi-dimensional.
So, I would like to ask: in wizarding astronomy, have we established a system—similar to the Cartesian coordinate system in the Muggle world—specifically a deep-space Z-axis coordinate framework, to allow us to record every observed celestial body with precise, absolute three-dimensional positioning?"
The question was like a stone thrown into a tranquil lake—silence shattered, waves invisible but immense.
The tower fell into absolute stillness.
Even the wind seemed frozen.
Every student stared at Alan as though he were an alien. Their faces were blank, puzzled, some even slack-jawed.
"Z-axis?"
"Coordinate system?"
Was that… some kind of new spell?
Even the learned Professor Sinistra was momentarily stunned. Her poised smile froze. For the first time, shock flickered in her deep-blue eyes.
She had taught Astronomy for many years, fielded every imaginable question. Some asked if the myths of Sagittarius were real, others asked why Mars was red, still others asked whether one could ride a broom to the moon.
But never—never—had a student, in the very first lesson, asked something so… so mathematical. So rooted in the foundational logic of the discipline itself.
This question bypassed all romantic notions of magic and myth. It was a surgeon's scalpel, cutting straight to the bones of the entire field of wizarding astronomy.
"…A very profound question, Mr. Scott." Professor Sinistra struggled to compose her response. "There are indeed some advanced astrologers who employ similar concepts, but this… this is far beyond the scope of an introductory course."
Her answer, clearly, did not satisfy Alan.
He did not sit down.
Instead, he bent over his parchment and began writing rapidly. His quill scratched across the surface with sharp, rhythmic strokes, the sound loud and distinct in the silence of the tower.
He chose Earth, the Moon, and Mars as examples.
No magic—only a different weapon: the pure logic of another knowledge system.
Trigonometry.
The parallax method.
Geometric diagrams took shape under his hand at lightning speed. Formulae, one after another, linked into a flawless chain of reasoning.
It took only minutes.
Then he set down his quill.
On the parchment, a preliminary three-dimensional coordinate system had been constructed, with clear X, Y, and Z axes. The Moon and Mars were no longer just glowing points on a star map; they were assigned precise spatial coordinates—entities that could be measured.
"Professor."
Alan held the parchment out to her.
She accepted it reflexively.
Her eyes fell on the page—and her breath caught.
She didn't understand the dense formulae, but she understood the geometry, and the final result: a coordinate system with three variables, yielding a clear and measurable framework.
It was utterly unfamiliar.
Yet within it was a power she could feel—the cold, pure beauty of rationality, a force capable of measuring the cosmos through logic and calculation alone.
This was not magic.
Magic was emotional, an extension of will.
But what she held in her hands embodied immutable laws of the universe, untouched by any person's will.
She slowly lifted her gaze from the "arcane scripture" scrawled across the parchment to the calm-faced first-year standing before her.
His eyes were clear and steady, as if what he had done was nothing more than a trivial exercise.
And from the depths of her memory, a name rose unbidden—one who had once overturned the world's vision of the cosmos, not with prophecy or sorcery, but with mathematics and logic.
Her lips trembled. In a voice almost dreamlike, she whispered:
"Merlin's beard…
Have we, in Gryffindor, found our next… Nicholas Copernicus?"
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