By the time Professor McGonagall's "Advanced Transfiguration Research Group" wrapped its second meeting, the air was thick with the mental exhaustion of drained intellect.
The parchment bearing the essay assignment now weighed like lead in the hands of every group member.
Topic: Discuss the inherent paradox in Gamp's Law of Elemental Transfiguration, Fifth Exception — the Exception on Food.
This law, etched into the very foundations of Transfiguration like iron, was simple yet absolute: wizards cannot conjure food out of nothing.
They could duplicate it, they could multiply it, but they could never turn "nothing" into "something."
It was a phantom, a ghost that had haunted the field of Transfiguration for centuries. Countless brilliant wizards had spent their lives trying to uncover its secret, yet all had left behind nothing but regret and confusion, passing the riddle on to the next generation.
And now, this age-old enigma had been laid before a group of students who hadn't even graduated.
The self-proclaimed prodigies of the senior years had long lost their confidence. One chewed the end of his quill to tatters; another stared blankly at the flickering candlelight, as though divine revelation might emerge from the shadows. Yet the parchment before them remained stubbornly blank, every missing letter mocking their intelligence.
When Alan received the topic, even his fingers felt a faint prickling sensation — that familiar sting of confronting the unknown.
Tricky.
That was his brain's immediate judgment.
But the very next moment, his consciousness sank into the vast, serene halls of his Mind Palace.
Countless logical nodes lit up — axioms of Transfiguration, conjectures on the structure of matter, magical variants of the principle of conservation of energy… torrents of information surged like galaxies through his mental sky, colliding, recombining, collapsing.
Models were built, then shattered.
Paradoxes unfolded, then looped into silence.
In the outside world, no more than a flicker of candle flame had passed. Yet within the palace of thought, an endless storm of logic had already raged for what felt like hours.
And then — when every path rooted in wizarding logic collapsed — from the depths of distant memory, a long-buried theory shimmered into light.
Muggle physics.
A field so cutting-edge that even in that world it remained half-imagined, intangible.
Quantum mechanics.
When Alan fed this mad variable into the entire logical framework, all the chaotic, clashing currents of thought snapped into orbit. Everything aligned. Everything locked together with elegant inevitability.
He opened his eyes, calm and enlightened. Deep within his pupils lay the clarity of one who had solved a riddle spanning centuries.
A paradox that seemed unsolvable within the magical world turned out to be startlingly simple under a different system of knowledge.
That evening, the Gryffindor common room glowed warm orange with firelight against the walls.
Fred, George, and Lee Jordan, however, felt no warmth. Huddled around a small table, their gloomy expressions clashed against the cheerful atmosphere around them.
Their assignment was also from Professor McGonagall — a thesis on "The Reversibility of Transfiguration."
"What does that even mean?!" Lee Jordan groaned, clawing at his thick hair as though answers might be hiding in his scalp.
"Why? Why can a matchstick turn into a needle, and then turn back again? Where did the matchstick go? Where did the needle come from? It doesn't make sense!"
Watching the three of them nearly driven mad by a basic theory, Alan set his book aside.
He decided to help.
But in a way they could actually understand.
He didn't recite the dry incantation theory from textbooks, nor the dense diagrams of energy flow. Instead, he distilled the same core concept he had just used to untangle Gamp's Law, and reshaped it into a simpler metaphor.
A metaphor for the principle of quantum uncertainty.
"Imagine this."
Alan's voice wasn't loud, but it cut clearly through their groaning, pulling their attention in.
"In front of you, there's a mischievous little goblin darting around."
His tone carried a peculiar guiding power, and in their minds, the three immediately pictured a small, slippery creature scampering about, pockets jingling with stolen coins.
"Now, I'll ask you one question." Alan's voice slowed, deliberate, coaxing.
"Is it possible, in the same exact moment, to know precisely how many coins are in its pocket and to know exactly which purse it's going to steal from next?"
The three froze. The question was odd, but the answer came instinctively.
They shook their heads.
"Impossible," Fred said first, frowning deeply. "That little git is too slippery. If I focus on counting the coins in its pocket, I'll take my eyes off its hands and feet — who knows where it'll run next?"
"Exactly."
Alan snapped his fingers. The sharp crack rang in their ears.
"Transfiguration's reversibility works on the same principle."
His words began weaving a strange magic of their own, linking an abstract physics concept to the magic they knew.
"When a matchstick is struck by our magic, it enters an uncertain superposition. It is no longer a matchstick one hundred percent, nor a needle one hundred percent. It exists in a state of being both matchstick and needle at once."
"Our willpower is the observer."
Alan's gaze swept over their baffled faces as he pressed on.
"When we use willpower to 'observe' its state as a needle, the superposition instantly collapses. It becomes a needle. Conversely, when we undo the spell and 'observe' it as a matchstick, the superposition collapses back to a matchstick."
"It doesn't revert because the matchstick was hidden away. It reappears because the possibility of it being a matchstick never actually vanished. It was always there — suspended in that uncertain state."
His explanation, full of strange terms and bizarre imagery, was like a lightning bolt cutting through the fog clouding their minds.
A dimensionality-reduction strike.
Using a higher-dimensional knowledge system to shatter a lower-dimensional problem.
Fred, George, and Lee Jordan's faces shifted — confusion giving way to thought, thought to shock, and finally to the sudden joy of revelation.
They still didn't fully grasp what "superposition" really meant. They couldn't quite explain what goblins had to do with matchsticks.
But for the first time, Transfiguration theory — that eternal source of frustration — felt like it had clicked.
The barrier that had long kept them from understanding had been pierced effortlessly by Alan, with a method utterly beyond comprehension.
Practically dancing in excitement, they snatched up their quills and scribbled furiously, finishing their essays in one go.
The three exchanged knowing glances, then turned together, staring at Alan with the same look — half awe, half disbelief.
And they all reached the same conclusion:
Alan's brain was absolutely not built like a normal human's.
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