"Today's lesson is the last one I'll teach you, and it will also be my last lesson before retirement. Once I've finished teaching this class, I'll officially retire..." At the start of the second natural history lesson, the teacher's very first words plunged the entire classroom into absolute silence. Even Zhang Tie hadn't expected today's lesson to be this teacher's last. Ever since he'd entered Seventh Middle School, he seemed to have grown used to the old man, whose hair had gone completely white, arriving quietly to teach and leaving quietly when class was over. He'd never imagined that one day the old man would say goodbye to everyone from the lectern. At the teacher's words, even the students who'd still been sleeping with their heads on their desks seemed to wake up, staring at him in astonishment. They began to feel reluctant to see him go.
"Teacher, are you really leaving..." A student in the front row voiced what everyone was thinking.
"I'm old enough, and I've served Black Flame City for long enough. It's time for me to retire!" The old man smiled kindly from the lectern. "I know what you're worried about. As long as Black Flame City's walls aren't breached by the other races, my pension should be enough to let me enjoy my twilight years in peace. And if Black Flame City's walls are to stand firm forever, that will depend on you, not me. So whether I get to enjoy a comfortable retirement is entirely up to you! That's why, for our final natural history lesson today, I'll draw on everything I've experienced and learned in my life to talk to you about the question you care about most: what does it take to become a powerful warrior capable of protecting humanity?"
The old man's final words jolted everyone to attention. They all sat up straight, gazing intently at the old man, who had suddenly become someone they couldn't bear to part with and deeply respected.
The old man didn't say anything. Instead, he took an ordinary little snail shell and two pinecones from his pocket and passed them down from the front row, asking everyone to take a look. In a minute, the two ordinary objects had passed through everyone's hands, from top to bottom. There was nothing special about them. Zhang Tie turned the objects over and over in his hands for a few seconds, but couldn't figure out what was so remarkable about them.
"Did any of you notice anything special about this snail shell and these two pinecones?" the old man asked.
Everyone shook their heads.
"Do you know that the secret to a human warrior's path of advancement is hidden in these ordinary objects? You all know that a person can keep growing stronger by igniting the Bright Points in their body. But what determines the strength levels of human warriors? Why are some people Level 5, others Level 6 or Level 7, while still others are Level 10 or higher? Who assigned levels and ranks to human warriors? Did some bigwig from the Warrior Guild just slap his forehead and come up with them?"
Zhang Tie was stunned too. He'd always thought these standards had been set by those bigwigs. Hadn't they?
"Of course not. Who in this world has the authority to set standards like these and make hundreds of millions of humans, along with all those powerful warriors emerging one after another, obey them?"
"Teacher, then who set these standards?"
"The one who set these standards wasn't human. It was God—or, you could say, the great laws of the universe!"
The students in the classroom burst into an uproar, talking over one another.
"These standards weren't created specifically for humanity. They were set by the laws of the universe for everything in existence. The snail shell and pinecones I just handed around also contain these same standards. You just didn't notice them!" The old man finished speaking from the lectern, then turned and drew two figures on the blackboard with chalk. One was a spiral curve shaped like a snail shell, while the other was a series of intersecting lines resembling a pinecone.
After he finished drawing, the old man turned around. "How many Bright Points does a Level 1 Battle Soldier need to ignite?"
"One. You just need to ignite the Divine Palace Bright Point..." The students answered the question. Then the old man drew a square at the center of the snail-shell curve, with the spiral passing through two opposite corners of the square at its starting point...
"What about Level 2?"
"Still one. You just need to ignite the Bright Point at the base of the spine..."
The old man expanded the diagram again, drawing another square with sides of the same length.
"What about Level 3?"
"Two spinal Bright Points!"
This time, he doubled the unit length of the square enclosed by the curve.
"What about Level 4?"
"Three!"
"What about Level 5?"
"Five!"
"What about Level 6?"
"Eight..."
With each question the old man asked, the spiral curve on the blackboard was enclosed by squares whose sides grew by the same ratio. By the time he asked about Level 10, no one in the class could answer. The world of warriors above Level 10 was already far beyond the limits of what the students could even look up to. To them, that world was as unreachable as the Great Cataclysm...
The natural history teacher didn't mock them. Instead, he wrote down the numbers they'd just called out on the blackboard—1, 1, 2, 3, 5, 8, 13, 21, 34... Then he wrote the corresponding levels and ranks beneath them, from Level 1 beside the first 1 all the way to Level 9 beside 34. Finally, he turned around and looked at the class, eyes gleaming. "Haven't you noticed a pattern in the numbers of Bright Points ignited for each level?"
After studying the numbers closely for a while, someone finally had a sudden flash of insight. "Teacher, each number in this sequence is the sum of the two numbers before it!"
"What else?"
Zhang Tie stared at the sequence, feeling as if something was about to surface in his mind, but he couldn't quite grasp it.
"Calculate the quotients of each pair of neighboring numbers, then see if you can find a pattern."
The students, all of whom had some grounding in mathematics, put their heads down and began calculating at their desks. The first quotient was 1, the second was 0.5, the third was 0.66666 repeating, the fourth was 0.6, the fifth was 0.625, the sixth was 0.61538..., and the seventh was 0.619047... The eighth was 0.617647...
"Have you noticed that these values all keep getting closer and closer to the golden number, 0.618..." The old man revealed the answer, and everyone suddenly understood. Right, why was that?
"The Divine Palace Bright Point is one, and the human spine has thirty-four vertebrae. When you ignite every Bright Point along your spine, starting with the Divine Palace, you become a Level 9 Warrior. Each jump in level has strict requirements. Now that you know the pattern, calculate how many Bright Points you need to ignite to become a Level 10 Warrior. Fifty-five, right? And the next number is eighty-nine, right? The farther you go, the more terrifying the numbers become. They increase by leaps and bounds. That's why the difference in strength between levels and ranks grows greater and greater as you advance. And this sequence..." The old man turned and pointed to the numbers on the blackboard. "It's called the Fibonacci Sequence. Centuries before the Great Cataclysm, human mathematicians discovered this golden sequence, which conceals countless mysteries. It holds the laws of the universe and creation. Look at the spirals on the two pinecones. Count them. Doesn't the smaller pinecone have five spirals on the left and eight on the right, while the larger one has eight on the left and thirteen on the right? Five, eight, thirteen—aren't those three numbers part of the Fibonacci Sequence? I drew the curve on the snail shell on the blackboard. Just look at the squares along it and you'll understand how the curve relates to the sequence. This curve is called the Fibonacci Curve, or the Golden Curve. It's the geometric form of this sequence. You can find corresponding patterns from this golden sequence and golden curve in almost any living thing. If you pay close attention to nature and the things around you, you'll make many more discoveries. Look at the face of a sunflower. There are two groups of spirals in it, corresponding to three pairs of numbers: thirty-four and fifty-five, fifty-five and eighty-nine, or eighty-nine and one hundred forty-four. You'll find the same thing in plants like roses and thistles. After the Great Cataclysm, humans unearthed the secrets of body cultivation from ruins discovered in the Underground World. The path of human advancement and cultivation has been following the principles of this golden curve and sequence, drawn by the Creator. All living things are advancing along this curve. The curve and sequence embody the laws of the universe, which is why the ranks of warriors defined by them have earned the unanimous recognition of all humans and all powerful warriors..."
All the students felt as if their eyes had been opened and a whole new world had dawned on them, Zhang Tie included. He'd always understood that to advance, he needed to ignite more Bright Points in his body, and that each rank required a different number of them. But he'd never given much thought to why. It turned out that the secrets of all this were hidden in the laws of the universe contained in the Golden Spiral and the sequence.
"Teacher, what's the highest cultivation rank after Level 10?" Baghdad raised his hand and asked from below.
"Even now, no one can answer that question, because cultivation beyond Level 10 is the greatest secret everywhere. Knowledge beyond Level 10 is the most closely guarded secret of all. An even greater reason is that the golden sequence has no end. It keeps expanding, constantly approaching that 0.618 which represents the most perfect laws of God and the universe. It's been less than nine hundred years since humanity returned to the path of cultivation and stepped onto the Golden Spiral, beginning to unearth the treasure that is the human body. Meanwhile, the universe may have been evolving for tens of billions of years. Humanity has only just begun its journey along the Golden Spiral. Before the Great Cataclysm, humans were always blindly arrogant, thinking of themselves as the masters of the universe and all creation. It was only after the Great Cataclysm that we came to understand that humanity is merely an insignificant member among the countless races of the universe and the Kun'ang Continent. It's even possible that for a long time before the Great Cataclysm, human bodies and civilization weren't evolving at all, but regressing. When humanity had nowhere left to go, the Great Cataclysm and the Star of God arrived, rewriting everything. In order to survive, humanity discovered the secrets of the body's Bright Points and began to walk the path of evolution once more. The Black Iron Era is the end of the old, but also the beginning of something entirely new..."
This final natural history lesson opened a window onto a world broader than any of the students had ever imagined. For the rest of the class, everyone worked out the next steps in the golden sequence for themselves—
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597...
When Zhang Tie worked the golden sequence out to its seventeenth term, he was dumbfounded. He stared at the seven numbers that came next, hardly daring to believe them. Was this what the world beyond Level 10 was like...?