Chapter 139: Two Misfitting Outfits

For a Mage Tower, a few months were nothing more than a few iterations of data.

“The production of the Mana-Spirit Crystal mine this quarter is fifteen percent higher than the last.”

Lia Farrien twirled her quill, her gaze sweeping over the dense data on the parchment.

“But transportation costs have risen. Those guys in the transport team say the roads haven’t been very peaceful lately and want to charge an extra twenty percent security fee.”

Klein sat in the high-backed chair opposite her, holding a book on ancient spell models.

“Give it to them.”

“You’re certainly generous.”

Lia tossed the pen back into the ink bottle with a crisp clink. “That’s several hundred gold coins, enough to buy several sets of high-purity mercury.”

“Safety first.”

Klein turned a page. “Besides, that’s your family’s mine.”

Lia leaned back, sinking into the soft backrest.

“Has this week’s issue of Introduction to Magic arrived?” she asked.

“It’s downstairs.”

Klein’s finger moved slightly.

A thick journal was lifted by an invisible force, floating up the stairs and landing steadily in front of Lia.

Since the establishment of the Department of Physics, the thickness of Introduction to Magic had doubled.

Countless novel theories were sprouting like mushrooms after rain.

Lia sat up straight and flipped to the table of contents.

Her elbow brushed across the page, finally stopping at page forty-two.

The title was simple: On Blackbody Radiation Energy and Theoretical Discussions.

‘It’s finally here.’

Lia took a deep breath and flipped to that page.

Two curves were printed on the page, along with two formulas that looked completely different.

The first formula was proposed by Lord Rayleigh. This Great Mage, who possessed extreme mastery in the field of acoustics, was attempting to apply statistical physics to electromagnetic radiation.

Lia looked at the line of black equations.

The formula was simple, with v representing frequency, c the speed of light, and t temperature. As for the k, the text referred to it as a “proportional constant between microscopic particles and macroscopic temperature.”

According to this formula, the radiation energy density should be proportional to the square of the frequency.

Lia looked at the accompanying diagram.

In the long-wave band—the low-frequency range—this theoretical curve overlapped perfectly with the experimental data.

But then.

Her gaze moved to the right, looking at the short-wave band—the high-frequency range.

As the frequency v increased, the energy density ρ began to skyrocket madly.

When the wavelength approached zero and the frequency approached infinity, the curve shot straight into the heavens, implying that energy would grow exponentially and eventually become infinite.

This was the “cloud” Sir Thomson had spoken of.

If this formula were completely correct, then while you were warming yourself by a fireplace, high-frequency ultraviolet radiation should instantly release infinite energy, vaporizing you along with the entire house.

The absurd contrast between this theory and reality was referred to by a line of small text next to it as “A Purple Disaster.”

Lia shifted her gaze.

She looked at the second formula.

This was the latest result published in this issue, coming from the research of a mage named Wien.

It had a completely different appearance.

It introduced an exponential function.

Lia looked at the second accompanying diagram.

In the short-wave band, this curve submissively fit the experimental data without the absurd result of infinite energy.

However, in the long-wave band, it stubbornly deviated from the experimental values, drifting further and further away.

“Interesting.”

Klein had set down his book at some point, looking at the journal in front of Lia.

“Two formulas describing the same phenomenon.”

“Yes.” Lia pointed at the two diagrams. “One is perfect at low frequencies, and the other is perfect at high frequencies but fails at low ones.”

“Can it not be corrected?”

“It cannot be corrected.”

Lia shook her head.

“This is a fundamental issue of derivation logic. Rayleigh’s formula is based on the classical Equipartition Theorem; as long as you admit that energy is continuous, the derived result will inevitably be that world-destroying infinity.”

Klein frowned.

“Energy is, of course, continuous.”

This was common sense—like flowing water, like wind, like the fluctuations of mana.

Lia did not argue.

She merely stared at the two clashing formulas, her gaze somewhat distant.

‘I can’t say it yet.’

‘That is the door to Quantum Mechanics; behind that door is an even crazier world, a world that doesn’t follow common sense at all.’

Thud, thud, thud.

Hurried footsteps echoed from the stairs.

Adèle rushed up clutching a pile of jars and bottles, her long red hair tied into a ponytail that swayed with her movements.

“I’m exhausted! Those old fogies at the Alchemy Association insist that my new extraction fluid doesn’t meet the specifications!”

She dumped the pile of reagent bottles onto the table, plopped down beside Lia, and grabbed a teacup from the table to take a huge gulp.

“That’s my cup,” Lia reminded her.

“Don’t be stingy, Professor Lia.”

Adèle wiped her mouth and leaned in. “What are you looking at? More of those headache-inducing formulas?”

She stared at the two formulas in the journal for a long time.

“This… is energy density, right?”

“Mm.”

“Then aren’t these two formulas contradictory?” Adèle pointed at Rayleigh’s formula.

“This one says the higher the frequency, the greater the energy, but that Wien guy says energy actually drops when frequency is high. Who are we supposed to listen to?”

“Listen to both, and listen to neither.”

Adèle looked blank.

“What does that mean? Can there be two versions of the truth?”

Lia sighed.

She picked up a quill and drew two stick figures on a blank sheet of scratch paper.

“You can understand it like this.”

Lia pointed to the stick figure on the left.

“Suppose you are going to attend a very important dinner party. You have two sets of clothes custom-made.”

“The first set of clothes was made by Tailor Rayleigh.”

Lia drew a pair of pants on the stick figure.

“The pants are perfect—well-tailored, the right length, and very comfortable to wear. This is the fitting of the long-wave band.”

Next, she drew a shirt on the stick figure’s upper body.

The shirt was ridiculously small, the buttons bursting, the collar strangling the stick figure’s neck, and the sleeves ending at the armpits.

“But the shirt is impossible to put on. If you force it, it will strangle you. This is the ‘Ultraviolet Catastrophe’ of the short-wave band.”

Adèle burst out laughing.

“And the second set?”

Lia pointed to the stick figure on the right.

“The second set of clothes was made by Tailor Wien.”

She drew a proper tuxedo on the stick figure’s upper body.

“The jacket is perfect—elegant and well-fitting. This is the fitting of the short-wave band.”

Then, she drew a pair of pants below.

The pant legs were so long they dragged on the floor, and the waist was large enough to fit two stick figures.

“But the pants are ridiculously large; you’ll trip as soon as you try to walk. This is the deviation in the long-wave band.”

Lia set down the pen.

“The current situation is that we only have these two sets of clothes.”

“You either wear the well-fitting pants and get strangled by the shirt, or you wear the well-fitting jacket and get tripped by the pants.”

Adèle looked at the two comical stick figures, laughing so hard she slapped the table.

“Then can’t we just take the two sets apart? Wear Rayleigh’s pants with Wien’s jacket?”

“No.”

The answer came from Klein.

He looked at the two formulas, a trace of thought flashing through his blue eyes.

“Formulas are not clothes. They are derived from underlying logic. Rayleigh’s formula is based on energy equipartition, while Wien’s formula is based on a thermodynamic analogy. Their prerequisite assumptions are mutually exclusive.”

“You cannot admit energy equipartition while simultaneously using Wien’s derivation process.”

“Just as you cannot be both a man and a woman at the same time,” Lia added with a nod.

“Then what do we do? Are we just stuck here?” Adèle asked.

Lia looked at the withered fallen leaves outside the window.

“Yes, we’re stuck.”

The edifice of classical physics had developed a crack here.

Hidden within that crack was the Planck constant.

Hidden within was the “Quantum” that was about to overturn everything.

“However,” Adèle picked up the journal and flipped through it, “I see it says here that many Great Mages are trying to ‘stitch’ together a new formula to connect these two.”

“Fudging numbers is meaningless.”

Klein said flatly, “Mathematics requires the support of physical meaning.”

The corners of Lia’s mouth turned up slightly.

True, fudging numbers was meaningless.

But what if someone managed to fudge together a perfect mathematical form, and then, to explain that mathematical form, was forced to make an assumption that betrayed their ancestors?

‘History is such an interesting spiral upward.’

“Right.” Adèle set down the journal. “Speaking of clothes, next week is the Royal Academy’s annual ball. Lia, what are you planning to wear?”

The leap in topic was so fast that Lia was momentarily stunned.

“I’m not going.”

“You are an Honorary Professor! You have to go!” Adèle’s eyes widened. “And I heard that several heirs of major families will be at this ball…”

“Not going.” Lia picked up her ledger again. “I have to do the accounts.”

“Mentor Klein!” Adèle turned to him for help.

Klein closed his book.

“Leave her be.”

He stood up, walked behind Lia, and glanced at the numbers in the ledger.

“This batch of mana crystals has very high purity. If you don’t want to go to the ball, you can come to the lab and help me test its mana conductivity.”

Lia didn’t look back.

“Overtime pay?”

“Two Ninth-Circle defense scrolls.”

“Deal.”

Adèle looked at these two people who couldn’t go three sentences without mentioning a transaction and gave a massive eye roll.

“You’re both beyond help. The two of you can just spend your lives with formulas and ledgers.”

She grabbed the empty reagent bottles on the table and stomped downstairs in a huff.

At the head of the stairs, she stopped and looked back.

The sunlight slanted across the table.

Lia was bent over her accounts, the quill rustling.

Klein stood beside her, toying with a piece of deep purple ore, occasionally pointing out an error in the ledger in a low voice.

The copy of Introduction to Magic was tossed aside.

The two formulas on the cover were like two untamed beasts, lurking quietly on the paper.

Waiting for the person who could tame them to appear.

Waiting for the person who could tailor those two sets of ill-fitting clothes into a perfect gown.

Lia stopped writing and glanced at the formula.

Infinity.

At the end of truth lies absurdity.

Or rather, absurdity is the entrance to a higher truth.

“What is it?” Klein asked.

“Nothing.” Lia closed the ledger. “I was just thinking that maybe one day, we’ll discover that the clothes themselves don’t exist.”

“What do you mean?”

“I mean…” Lia stood up and stretched. “It’s time to go to work in the lab, Mentor.”