The Cycle

August 2029, Africa

Daphne never imagined that she and Michael would run into Mandy Petkova and the renowned journalist Martha in Nairobi, Kenya. Mandy's foundation had a program to protect indigenous tribes, based in Kenya.

The four of them were all headed to the Canyon Province in northwestern Kenya. They agreed to meet first at the lakeside research station funded by Acebe Company, then visit an ancient indigenous tribe protected by Mandy's foundation.

Volcanoes stretched along the eastern shore of Lake Victoria. The eastern branch of the Great Rift Valley ran from south to north, dotted with freshwater lakes of every size, extending all the way to Ethiopia and Egypt.

The research station by the lake focused mainly on geology, especially the Great Rift Valley's faults, its soil, and sediment layers sampled from the bottoms of several lakes.

Dr. James, who had proposed capsule habitats for survival in the Valles Marineris, was fascinated by sediment layers at the bottom of the East African Rift Valley's lakes. He hoped to join the research team in discovering what the great canyons on two different planets in the Solar System had in common.

After everyone had met and introduced themselves, Michael eagerly asked Dr. James:

"Do the sediment analysis reports match your predictions?"

"We've taken samples from the bottoms of five different freshwater lakes. They formed at the same time and have consistent compositions. Unfortunately, they're completely different from the Mars soil composition we have on record," Dr. James replied.

Michael offered a sympathetic word of comfort. "That's all right. Then let's study faults formed in different geological eras, focusing on the water content in each layer."

Martha asked curiously, "I thought your research station was studying flamingos or the great wildebeest migration. Studying lake-bottom sediments isn't romantic at all."

Daphne Braun had accepted Michael's invitation to come to Africa. She'd assumed that Dr. James's research focused on survival in the Great Rift Valley, but she hadn't expected it to be about similarities between Mars soil and the valley's sediment layers.

She hesitated, then spoke softly to Michael. "If you're trying to find geological formations similar to those on Mars, maybe my hypothesis can help."

Michael immediately thought of Lingshen Star, which Lingguang would be approaching on the twenty-second of that month. According to Daphne's Mars Burst Hypothesis, Lingshen Star had formed when molten metal from Mars's interior was ejected into space. The words slipped out before he could stop himself:

"You mean Lingshen Star?"

"Oh, you're reading too much into it. Lingshen Star is part of Mars's core. Aren't you looking for soil with a composition similar to the sediment layers in Valles Marineris? If it isn't in the Great Rift Valley, I suspect it might be somewhere else on Earth." After giving Michael her somewhat mysterious answer, Daphne briefly explained her theory and promised to show him the detailed analysis when she returned to Brightland.

The indigenous tribe funded by Mandy's foundation lived deep in the forest, a kilometer from the road. The group followed a sandy track to the ancient African village.

The chief welcomed them warmly and led them to a thatched shelter built over an open space. Tools of all kinds were laid out on a table made from a huge log, forming a line that looked almost like a modern production line. There were fine flax fibers drying after being washed, dyes in various colors extracted from plants, and a wooden rope-twisting machine.

The rope-twisting machine was cleverly designed. Using wooden levers and gears, it twisted the dyed flax fibers into rope that was both uniform and tightly woven.

The chief tied a black-and-red rope around Michael's wrist, while the chief's wife tied white ropes around the women's wrists. Knot-tying was a welcoming ritual in this tribe.

The chief dipped his finger into black dye and marked Michael's forehead, then used white dye to mark the women's foreheads. Mandy explained that this was the highest honor they could offer distinguished guests who had traveled from afar. She also reassured them that there was no need to worry about the dyes: they were extracted from natural minerals found at the bottom of the lake.

Daphne Braun thought the white lake mud on her forehead felt as moist and silky as face cream. The weather was hot, and a faint breeze seemed to be blowing. The mud on her forehead dried quickly.

For some reason, Daphne felt her heart beating a little faster. For a moment, she seemed to see tiny pinpricks of light flashing before her eyes. She blinked hard and realized that nothing was wrong.

Michael was captivated by a stone slab embedded in a pillar. Ropes of various colors hung evenly across it, each tied with knots of different sizes and in different numbers. He asked Mandy, his curiosity piqued:

"Is this the legendary system of recording events with knotted cords?"

Mandy nodded approvingly. "Yes. Many African tribes still use knotted cords to keep track of numbers, events, and time."

African tribes recorded the passage of time by tying knots in cords. At the sight of them, Michael couldn't help thinking of the Superluminal Wave Theory and "Nikola Tesla's Rope," which Professor Braun had told him about.

The chief's youngest daughter timidly approached Daphne, carrying a colorful knotted cord. The knot formed a pattern: an oval shaped like a duck's egg at the top, with two horizontal cords and one that hung down beneath it.

Martha knew what the pattern meant. She asked Daphne, "Daphne, this is an ancient Egyptian hieroglyph. Can you guess what it represents?"

Looking at the hieroglyph, Daphne thought of a woman's womb and the symbol representing women. She said:

"I'd guess it means life. This must be the Symbol of Life, right?"

Everyone was amazed by Daphne's insight, then marveled at the wisdom of the ancients. They had used knots to record time and represent life!

The little girl gave Daphne the colorful knotted cord. Daphne picked her up and put her own pendant around the girl's neck.

The next stop on Daphne and Michael's African trip was the Great Pyramids of Giza in Egypt.

Daphne's data analysis and theories about the three Great Pyramids of Giza had piqued Michael's curiosity. The two of them went to see the human-made wonder up close.

Daphne noticed that the three Great Pyramids weren't tilted at the sixty-degree angle of an equilateral triangle. Instead, their angles all fell between fifty-one and fifty-three degrees, which was roughly the sum of the axial tilts of Venus, Earth, and Mars.

The three pyramids were the tombs of three generations of pharaohs, from Khufu to his grandchildren. She believed their volumes corresponded respectively to Earth, Venus, and Mars.

Daphne pointed to the Pyramid of Menkaure and the three smaller pyramids lined up to its south. She said:

"The Pyramid of Menkaure is the smallest of the three Great Pyramids. It corresponds to Mars. And these three smaller pyramids to its south are arranged in a row. Looking at this pattern of one large and three small, what does it remind you of?"

Michael started in surprise and blurted out:

"Their arrangement looks a lot like Olympus Mons and the three smaller volcanoes to its southeast. Are you saying the ancient Egyptians built these pyramids after the volcanoes on Mars?"

Daphne smiled. "You're not thinking big enough. This geometric pattern of one large and three small comes from the constellation Orion. My theory is that ancient Martians built a group of artificial volcanoes based on Orion's shape, while the ancient Egyptians built the pyramids after Orion."

"Orion?" Michael murmured.

He noticed the three stars in a row in Orion, the three volcanic craters on Mars, and the three small pyramids south of the Pyramid of Menkaure. It was obviously "111."

Michael suddenly remembered something else, as if he'd finally grasped the answer to a question that had been bothering him. To make sure his conclusion was correct, he asked Daphne:

"A stone slab was unearthed in the Great Pyramid, with the sequence '142857' written on it. What do you think it means?"

Daphne had heard about it long ago. There were all kinds of calculations and theories about "142857" online. Multiplying it by any number from one to six merely changed the order of the digits; no other digits appeared. And 142857 multiplied by seven equaled 999999. Short-video creators often used it as a gimmick to grab viewers' attention.

Daphne believed that the number "142857" represented 1/7. Perhaps it was a measuring guide left by the master builders of the pyramids for their apprentices. After all, among fractions with denominators less than ten, 1/7 was the hardest to remember.

There was another possibility, of course: "142857" was a clue. By the strict mathematical definition, "142857" was the repeating cycle of the digit "7" in base ten.

Michael believed that his girlfriend was not only clever and quick-witted, but also principled and rigorous. He posed the leading question that pointed toward the answer he had in mind:

"If '142857' is the repeating cycle of '7' in base ten, then in which base is the '111' represented by the three small pyramids in a row the repeating cycle of '7'?"

Daphne understood at once. She shouted excitedly:

"Binary! '111' is the repeating cycle of the number '7' in binary. The three pyramids in a row are telling us that we should use binary as well as decimal!"

Could it be that the arrangement of volcanoes on Mars and the pyramids was a hint from people of the past, meant to remind us today?

Daphne Braun was certain she was right. "142857" and "111" made the hint and reminder abundantly clear.

A poem assembled from verses:

Ancient towers and clouds preserve Luo's traces. Ming, Liu Bin

The stars within one's breast are the heavens. Ming, Sang Yue

Old friends look out for one another amid the three affairs. Tang, Wang Wei

Today, it is hard to speak of seven parts. Yuan, Qiu Kui