I Know What Science Doesn’t

Chapter 004

Daniel Hayes felt reasonably satisfied with the studio apartment he'd rented. Affordable, clean, comfortable, and close to campus. His two female roommates seemed easy enough to get along with, too.

He didn't move in right away. He was still waiting for his classmate to forward the rest of his belongings: clothes, bedding, and all the miscellaneous odds and ends. Once everything arrived, he'd make the move.

Having a place to stay settled his nerves considerably.

The next morning, he headed over to the university to explore and get his bearings before classes started.

Kingsley University was enormous. Calling it a university city rather than just a campus wasn't an exaggeration at all. Walking from the College of Natural Sciences on the west side all the way to the massive sports complex on the east, then looping around to the main gate on the south side left his legs nearly numb. Still, the completely unfamiliar surroundings brought a strange sense of novelty and anticipation.

After grabbing lunch in one of the dining halls, he found a study room and settled in for the afternoon.

Doctoral work centered primarily on research under an advisor's guidance. The metamaterials project in the Applied Electromagnetic Physics Lab represented cutting-edge work in electromagnetic materials science. The underlying mathematical and physical foundations were extraordinarily complex, and the materials research itself touched on multiple other disciplines.

Elias Vance hadn't given him much material to start with, but the theoretical portions were dense and challenging. The foreign research papers were even harder to parse, many of them diving deep into pure theoretical problems.

Daniel forced himself to focus, working through the material slowly. He found himself drawn to the mathematical content, which Elias had particularly emphasized. Mathematics was his strength, or more accurately, his mathematical proficiency stood out among physics doctoral students.

The project's theme, Theoretical Design and Characterization of Metamaterials, fell squarely into fundamental research territory. Fundamental research inevitably involved substantial amounts of mathematics, analysis, and related physical content.

The materials Elias had provided contained extensive work on electromagnetic experimental calculations, mathematical analysis, and mathematical physics. The obvious starting point was the mathematics itself.

Mathematics meant grappling with complex calculations and analysis. The most frequently used tool was a third-order nonlinear partial differential equation resembling the Kawahara equation in form. It could be called a third-order Kawahara-type equation.

Solving the third-order Kawahara-type equation was essential for routine experimental data calculations in the project.

As a third-order, nonlinear Kawahara-type equation, it had no exact solution.

In experimental data analysis work, the standard approach involved substituting numerical values for approximate solutions. But the results were only rough approximations at best.

"There's a problem with the preliminary experiment data calculations," Daniel muttered to himself. "Professor Croft's team couldn't have made basic calculation errors. The most likely explanation is that errors crept into the solution process for these complex equations. This equation is critical."

He dove into studying it more carefully. The vast majority of partial differential equations had no exact solutions, let alone a third-order nonlinear Kawahara-type equation. Using numerical substitution to estimate rough approximate solutions was the standard practice across scientific research and industrial applications.

Researching this type of equation was extraordinarily difficult. He wasn't trying to find an exact solution, just a method to obtain a more accurate approximation. Even that was proving incredibly challenging.

Using conventional research methods, he clearly wouldn't get results anytime soon.

"Could I use Truth Perception somehow?" The thought struck him, and he immediately began experimenting.

When dealing with complex equation analysis, the key was finding the right analytical approach. Truth Perception could assess whether an analytical direction was correct.

Other problems emerged quickly, though. Being able to judge whether a line of thinking was correct didn't automatically solve the problem. Solving a complex equation involved transforming the equation itself. Knowing the direction was correct didn't mean he could figure out the actual steps, because there would be many subsequent steps requiring their own thought process.

Each step led to another, and he could not think of the right method for every one.

The research hit a wall at a particular transformation point. The computational load involved was absolutely massive, and he couldn't just run it through a computer simulation either.

"There must be another approach, or some kind of special method. Either I haven't thought of it yet, or I simply don't know it exists."

He shook his head, thinking it through. Truth Perception had its limitations. It couldn't help solve every problem. Of course, its auxiliary function was still powerful. It could help confirm whether a research direction was correct, which was already an extremely valuable ability in scientific research.

Were there other abilities available?

The thought jolted him. He immediately opened the system interface and examined it carefully.

The panel displayed:

Intellect: 77 

Physique: 59 

Academic Reputation: -177 

Wealth: 4,980

On the personal data assessment page, only the Wealth value had changed. Obviously, because he'd spent money.

"Less than five grand. Even among doctoral students, I'm probably one of the poorest."

Physics doctoral students received decent stipends, including various basic allowances, scholarships, project wages, and advisor stipends. During his first year, he'd pulled in around sixty thousand dollars.

But the past six months had been different. Elias had left. His new advisor, Marcus Thorne, had no major projects. As a temporarily assigned student, he received no project wages, and the advisor stipend was pathetically small. Over six months, he'd only gotten his basic allowance and foundation scholarship.

Aldridge had a high cost of living. With such meager income, forget about savings. Not being in debt was already an achievement.

Physique: 59. That seemed normal. His days were spent doing research, often staying up late, with essentially no exercise.

Intellect: 77. He wasn't sure how that was calculated. Did it relate to accumulated knowledge?

His Academic Reputation stood at negative 177, clearly tied to his paper being exposed online. In most people's eyes, he was probably an academic fraud.

He smiled bitterly at himself and continued reviewing the interface.

The system's second section was the abilities interface. It contained only one ability: Truth Perception.

The description for Truth Perception was a single line: "Can assess the correctness of conclusions regarding problems."

Next to the abilities section was a small question mark. Clicking it revealed the upgrade requirements.

Upgrade Requirements: 

Intellect: 80 

Physique: 70 

Academic Reputation: 1,000 points 

Wealth: 1,000,000

"Wealth, one million?" he muttered. "So upgrading means I have to focus on making money too? A million isn't pocket change. What am I supposed to do, buy lottery tickets and wait to win?"

He took a deep breath, forcing himself to calm down.

Intellect and Physique could be improved through accumulating knowledge and physical training. Academic Reputation would naturally come from publishing papers or doing other academically visible work.

Making money was the most difficult condition. Ordinary people did not accumulate a million in their entire lives, and even a doctoral graduate earning over twenty thousand a month would need more than a decade to save that much after living expenses.

While he was lost in thought, a female voice suddenly spoke beside him, startled surprise coloring her tone. "You guys in physics study equations too?"

Daniel jumped slightly. Turning his head, he found his future roommate, Claire Whitaker, standing there. They'd only met yesterday and weren't particularly familiar yet.

He offered an explanation. "It's a third-order nonlinear Kawahara-type equation. We use it in experimental calculations. We usually substitute numerical values and solve it numerically."

"Are you trying to figure out a solution method?" Claire asked curiously, then added, "I'm actually researching this too!"

She pulled a few sheets of paper from her bag and set them on the table. "Take a look. The form is different, but after transformation, they should be pretty similar."

Daniel studied them carefully. The materials did indeed show the same type of partial differential equation. Similar types meant solution methods would vary slightly, but the general approach should transfer.

Claire sat down beside him and sighed. "My advisor suggested a few directions, but they might not be right. I was hoping to write a paper based on this research, but it feels impossibly far away."

"What directions did he suggest?" Daniel asked, following her lead.

Claire pulled her chair closer, leaning in as she outlined them simply. "One approach is transformation. Keep transforming, keep substituting or directly discretizing until the computational load drops enough that a computer can handle approximate values."

"Just thinking about it seems impossible. The discretization and transformations involved are way too complex."

"There's also conventional difference approximation discretization, but that's still complicated, and the approximation error is too large."

"Another option is using the finite-element method, building a model and subdividing it infinitely. I think..."

She rattled off several more directions.

When she finished, she looked up and noticed Daniel's expression had turned somewhat strange.

What did that mean?

Claire touched her cheek, her brow furrowing in confusion. "What do you mean?"

Daniel pressed his lips together briefly, then spoke. "You just ruled out the only correct answer."

She blinked. "What?"

"Brute-force transformation and substitution with direct discretization. That's the right direction."

"That's impossible," Claire's tone was flat, almost dismissive. She'd just been casually discussing the topic with him. She hadn't expected to actually solve anything. A physics student, a soon-to-be doctoral candidate at that, couldn't possibly offer meaningful guidance on complex equation analysis.

Daniel had already grabbed his pen eagerly. "Then let's try working through the analysis."

His eyes lit up as he spoke.