Rebecca wasn't quite sure why Gawain was so interested in her method, but at least he didn't seem like he was about to criticize her. She sighed in relief and said, "I just worked it out as I went along! If you think of the yard as a sheet of paper, it's much easier."
The answer was too vague, and Gawain's brow furrowed. "Can you be more specific?"
Rebecca animatedly gestured with her arms, "The side of the yard is one line, and the adjacent side is another. Then, if you think of those lines as the paper's edges, you can use them to figure out where each line of the magic formation goes. I split each line into key points, calculated each point's distance from the edges, and scaled up from my sketch. Calculations are a mage's strong suit!"
Calculations might indeed be a mage's strength, but few mages would go to such lengths to solve it this way! Gawain was speechless, watching her messy explanation as Hety tried to make sense of it.
But Gawain understood: Rebecca had set up a coordinate system in the yard, using it as a basis to scale up the magic formation from her sketches. There was no need for a bird's-eye view; she simply calculated each point's coordinates and joined the dots according to her plans.
Of course, coming up with this idea was impressive, but not enough on its own. Rebecca also needed a remarkable level of geometric and mathematical skill to make it work, since the mathematical and geometric knowledge in this world was nowhere near complete. Rebecca would have either had to use brute force calculations or invent her own formulas!
While Gawain knew there were many geometric methods from Earth that could work here, that wasn't the point. In this world, in this era, what Rebecca had achieved was nothing short of a miracle.
"Did you come up with this method by yourself?" Gawain asked, a sparkle in his eyes as if he'd discovered a rare treasure.
Rebecca scratched her head. "Not entirely. Part of it came from that rogue mage's notebook, and the rest… I just thought of myself."
Ah, that made sense.
Gawain understood. He had read through that rogue mage's notes and knew they contained rudimentary knowledge of geometry and math. While not a full system, it laid a foundation. If Rebecca already had a knack for this sort of thing, it wasn't surprising that she could figure out the rest.
But even with that influence, her achievement was still incredible.
"That's a clever approach…" Gawain nodded approvingly. "And why did you decide to bury the formation?"
"Oh, because you said it was for the forge," Rebecca replied, nodding. "I thought about how blacksmiths and apprentices are different from mages—they're always moving heavy materials around and forging metal. They'd probably damage the formation if it was above ground. Burying it won't interfere with the magic flow, and it'll make it easier to modify or add new furnaces in the future. It just seemed… more convenient."
Gawain's mind flooded with terms like "functional zoning," "energy-source separation," "encapsulation," and "scalability." But one idea rose above the rest: Rebecca had considered how "ordinary people" would use the formation and designed it with that in mind. She'd ensured it would be safer and easier for them, even if it was as simple as burying it.
Most mages would never think to design a magic formation for use by regular folk, but Rebecca… well, it was fortunate that she was a nonconformist mage with limited abilities; her mind simply didn't follow the usual mage logic!
Gawain snapped out of his surprise, noting the thoughtful look on Hety's face. "Did you think of all of this yourself?"
"I… hadn't thought of it," Hety admitted, her expression complicated. Rebecca's ideas diverged so much from tradition that it was both unsettling and intriguing. Yet, she also understood the logic behind it and began to see the importance of making magic accessible for ordinary people—a concept that seemed central to her ancestor's vision. "This is brilliant, but if you bury the formation, how will you monitor it? Even if it's robust, it still needs basic maintenance."
"I left a lot of stakes like those," Rebecca pointed to the wooden posts around the yard. "Those will be replaced with mithril-coated iron rods, which will touch the core runes of the formation underground. If something goes wrong, the corresponding rune will go dark, and the mithril will turn black and heat up a bit—so you'll know right away where the problem is. Then you can just dig in that area for repairs instead of the whole yard."
Rebecca grinned proudly, waving a stack of papers covered in symbols and lines—clearly her own handiwork. "And this formation won't break easily. I tweaked the rune structure a bit—not the core principles, of course—but I reconnected redundant runes so they support each other layer by layer…"
A *redundancy system*—Gawain's eyes twitched as he glanced from her detailed drawing to the stakes in the yard, which served as simple sensors.
Once Rebecca got talking, it was hard to stop her. She continued eagerly, "This way, the formation's efficiency actually goes up a bit. If part of it gets damaged, the most that happens is a slight drop in energy flow, but the connected systems will still work fine. I built the formation with a surplus in mind…"
Rebecca's enthusiastic explanation trailed off as she looked at Gawain, suddenly nervous. "Ancestor… am I overdoing it?"
Gawain pressed a reassuring hand to her head after a thoughtful moment. "No, you're a genius."
Rebecca blinked. "Huh?"
"And I have a suggestion," Gawain pointed to a part of her drawing with redundant connections. "If you make these connections easy to sever and rejoin, you could repair parts without shutting down the whole formation."
Rebecca's eyes lit up. "Oh, that's brilliant! Why didn't I think of that? You're so clever, Ancestor!"
Gawain's eye twitched. He knew Rebecca meant it sincerely, but it still made him feel a bit uneasy.
*Young one, you're the real genius here!*
After a moment's pause, Gawain turned to Hety. "Did no one ever notice Rebecca's talent?"
"She's always been… inventive and strong in calculations," Hety admitted, choosing her words carefully. "But those talents were never useful. In the mage world, only casting ability matters, and in that area… well, she's always struggled."
"What a waste…" Gawain muttered, not mincing words. "Casting ability as the only standard? Why not just measure strength with a gorilla?"
He knew there were reasons for the focus on power in this world. When societies couldn't leverage technology to spur civilization, individual prowess was the natural yardstick. In a world rife with monsters and beasts, personal combat ability was essential for survival. Without survival, innovation was a moot point.
This focus had sustained itself for generations because people without power had no way to convert their wisdom into force—at least, not enough to rival the powerful. So, survival remained the measure of all things.
But that was no reason to forever judge humanity's potential by the standards of the wild.
Rebecca had a rare gift—Gawain was now sure of it. This dismissed and underestimated viscountess had been shunned by nobles as a member of the struggling Cecil family, mocked by other mages for her lack of spells, and dismissed by merchants and citizens in neighboring lands. She was seen as an incompetent lord who passed eccentric policies and brought no prosperity.
But no one had seen her abilities because they couldn't understand them.
In a world where survival often depended on the whims of nature, no one could appreciate her calculations. In the circles of the wealthy and powerful who had access to magic or were mages themselves, no one needed them.
Why bother calculating coordinates when you had Eagle Eye or Mage's Sight? Why install sensors to monitor a formation when mages could simply sense its flow?
But when Rebecca had received Gawain's permission to proceed, she was thrilled. For the first time in her life, she had been allowed to tackle a project that used her unique talents.
"Ancestor…" Rebecca looked at him, unsure, "Am I…"
Gawain smiled and placed a hand on her head. "You are the pride of the Cecil family."