After the heavy snowfall cleared, the sky was scrubbed into a flawless blue, without a single drifting cloud.
Sunlight poured unhindered through the thin, icy air. A delicate layer of crystal ice covered the surface of the Black Lake, catching the light in full—then shattering it into billions of dazzling diamonds.
Alan stood alone at the lakeside.
He needed absolute silence.
The mental defense model described in The Fortress of Thought was far more abstruse than he had anticipated. This was no simple meditation; it was a precise undertaking, as intricate as the construction of a grand cathedral.
His mind palace at this moment was a vast and boundless void.
And he was its sole creator.
He was not building walls—he was weaving logic. Forging fundamental axioms into load-bearing pillars, stacking airtight syllogisms into an impenetrable barrier.
Every paradox was designed as a mental trap, prepared for any would-be intruder.
Just as he was about to solidify the concept of "self-identity" as the cornerstone of his first layer of defense, a clear voice rang out, like a pebble thrown into a still lake, shattering his inner silence.
"Alan? It really is you!"
Alan pulled himself out of the depths of his thought-palace and opened his eyes.
The Ravenclaw prefect, Penelope Clearwater, was walking toward him across the snow. Her boots crunched with each step, arms full of thick tomes. The pale of her cheeks was brushed with a healthy pink from the combined bite of the cold and touch of sunlight. Her eyes carried just the right trace of delight at meeting someone unexpectedly.
"Good afternoon, Penelope." Alan inclined his head slightly—polite and measured—though the faint remoteness in his eyes betrayed that he had only just torn himself away from deep contemplation.
His gaze drifted to the books she carried.
"You're here to read as well?"
"No, I came to practice spells." Penelope's brow creased, and the joy of recognition on her face was quickly replaced by mild frustration. "Our house's Advanced Spellcasting Club is holding this term's entrance assessment. The task is really difficult—a continuous high-difficulty Patronus Charm."
"Patronus Charm?" Alan's attention sharpened at once on the word.
"Yes." Penelope's tone was tinged with obvious discouragement. "Not only do we have to conjure a corporeal Patronus, but it has to maintain its form long enough to run a full circle across the lake. It's… ridiculous."
She sighed, as though struggling to find the right words.
"My problem is that my Patronus always collapses halfway through—the magical output is extremely unstable."
To demonstrate, she stepped back, raised her wand, and called out:
"Expecto Patronum!"
A surge of silvery-white mist burst from her wand tip, quickly condensing into the elegant form of a swan. Its wings were full, its neck gracefully arched—every detail vivid and lifelike, brimming with vitality.
But just as Penelope had said, the creation was fragile.
The swan Patronus skated lightly over the frozen lake for less than ten meters before its body began to flicker violently. Its glow pulsed, dimming and brightening erratically. The silver mist that composed it unraveled, thinning until it was almost transparent.
Finally, with a soft pop, it collapsed completely, dissolving into countless motes of silver light that scattered into the air, fading quietly beneath the sun.
Alan said nothing. He simply stood aside, watching with eyes that seemed to pierce through everything.
Penelope, unwilling to give up, tried again.
The result was the same.
"Your problem isn't a lack of strong emotion."
As her shoulders slumped from her repeated failure, Alan spoke at last. His voice was calm and precise, like the scalpel of a surgeon, cutting directly to the root of the ailment.
"It's that you're spending too much of your mental strength maintaining that complex form."
Penelope looked up, bewildered.
"The swan's feathers, the curve of its neck, the grace of its glide…" Alan's words were slow but clear, each syllable sharp as crystal. "Every one of those details constantly, endlessly drains your magic. Your focus scatters across a hundred irrelevant points, leaving your core energy output unsustainable."
"Then… what should I do?" Penelope asked at once, humbly. Instinct told her his analysis had struck at the true heart of the issue.
"Try a simpler, more essential form," Alan advised.
"The essence of the Patronus Charm is the manifestation of positive energy. It is a pure application of magic—
not an animal impersonation."
His gaze shifted toward the frozen lake, where the last faint traces of her collapsed swan still glimmered as silver flecks.
"You could try imagining your Patronus as an absolutely stable geometric figure."
"Geometric… figure?" Penelope was utterly stunned. In all her study of magic, she had never once thought to link such a concept—rational, rigid, mathematical—with something as emotional and instinctive as a Patronus.
"Yes," Alan's tone brooked no doubt. "For example, a perfect, rapidly spinning sphere. It has no complex details to sustain, its structure is absolutely stable. That form—"
"…you can focus all your magic on the core concept of protection itself, rather than wasting it on maintaining a flashy exterior."
Penelope's breath hitched.
Alan's approach was utterly unheard of—so absurd it bordered on heresy.
Yet within that absurdity, she sensed a truth so fundamental, so piercing, that it made her shiver.
It felt as though a door in her mind, locked for countless years, had just been blown open by an unstoppable force.
She raised her wand again.
This time, she did not conjure the image of an elegant swan. Following Alan's advice, she stripped away every unnecessary detail, every frivolous form—compressing all her warm, joyful memories into a single pure, condensed point of light.
"Expecto Patronum!"
The moment the words left her lips, the result was entirely different.
No longer a drifting mist—
but a blinding silver sphere of light burst forth at her wand tip.
It was solid, stable, packed with energy that churned within its core, while its surface gleamed smooth as a mirror. Like a miniature sun that had slipped from its orbit, it spun rapidly in the air, radiating a low, steady hum that filled the heart with reassurance.
The sphere landed on the frozen surface of the lake—not gliding delicately, but with overwhelming force, carving a long, glowing arc across the ice, leaving behind a faint heat as it blazed its path.
It circled the entire lake with ease, its speed and brilliance undiminished.
Only when it returned to the starting point did it fade—shrinking under Penelope's deliberate control, until it dissipated gently into the winter air.
"I… I did it!"
Penelope stared at her wand tip in disbelief. A few seconds later, immense joy washed over her, so fierce it nearly made her leap for the sky.
She spun toward Alan. Her gaze was no longer filled with simple gratitude, but with deep, unshakable awe.
"Alan, you're a genius!"
Her voice trembled with excitement.
"Do you know? Professor Flitwick has mentioned your name more than once in the club, along with your theory of 'magical automation.' He even said you might be the most innovative mind Hogwarts has seen in a hundred years!"