Volume 3: The First Croton War Chapter 30: Mathematics and Waterwheels

“Other city-states believe that land is the greatest wealth, so they refuse to accept foreigners and freemen, unwilling to share the city’s interests and riches with them. But I think quite the opposite—I believe that ‘people’ are a city-state’s greatest wealth! With people, you can grow grain, create works of art, and generate wealth! With people, you can forge weapons, build armies, and defend the city! With enough people, you can obtain far more land!” Davos spoke with firm conviction.

His words struck Kynogoratas with an unprecedented force. As intelligent as he was, Kynogoratas naturally understood how to obtain far more land; Davos was clearly hinting at the source of the “allotments” for the new citizens. Thus, he fell silent…

It was Kynogoratas’s eldest son, Sostratus, who spoke up, seeing the nearly completed sections of the warehouses and inns on the construction site. “I heard you plan to attract merchants from Thurii and foreign traders to store goods and lodge here. These are the warehouses and inns being built, right?”

“Yes.”

“I see quite a few warehouses and inns being built here. Does the city intend to manage them directly?” Sostratus asked further.

Mesis caught the implication of his words and immediately replied, “Of course not! The city doesn’t have that many public officials, and everyone has their own affairs. We plan to hold a public auction to lease them out.”

“A public auction”—that was a new term. Sostratus, with the excellent merchant instincts of a Greek, quickly grasped what it meant. “Can we participate?” he asked.

“You are most welcome!” Mesis replied cheerfully.

…

Although moving and setting up the household had kept the family busy for most of the day, leaving everyone fairly tired, Kynogoratas woke up early the next morning. Rising early was a habit he had cultivated over many years. A slave helped him dress and get up, and he decided to take a walk, supported by the slave, before returning for breakfast.

Kynogoratas’s residence was at the foot of the hill in Amendolara. After the new citizens’ houses had been allocated, there were still many empty homes here, a testament to how severely the previous war had damaged Amendolara. Only by being in the midst of it could one understand why the original inhabitants of Amendolara were so furious at Thurii.

Most of these empty houses had been rented out to freemen at low prices, so as soon as Kynogoratas stepped outside, he could see groups of freemen hurrying off to work, their faces brimming with a vitality and passion that the freemen of Thurii lacked. Even when they spotted Kynogoratas, a stranger, they would greet him amiably in oddly accented Greek.

Kynogoratas knew why they were so passionate about life. Having been freed from slavery, their employers had also paid what was called a “preparatory citizen tax” to the city on their behalf. As long as they obeyed the laws and worked hard, after two years they could become preparatory citizens of the city-state.

It was already June, and the weather was starting to get hot. But inside the city of Amendolara, it was still relatively cool, as it was built on a hill, with sea breezes and mountain winds alternating to cool the small town.

Kynogoratas walked up the road, occasionally encountering citizens coming down the hill. They were all heading to work in the fields. Whether old citizens or new citizens, they greeted each other and exchanged jokes, appearing very harmonious. The slaves accompanying them also seemed spirited, no doubt because the stories of mercenary slaves becoming citizens had given them hope.

What truly surprised Kynogoratas was that some women were also accompanying them. From their conversations, he gathered they were citizens’ wives, not freemen’s women (for the sake of making a living, freemen’s wives often went out to work—setting up stalls, working in eateries, and so on). They were preparing to go down to the fields with their husbands and work alongside them. He recalled that his son had mentioned some strange sights in the city the previous afternoon, and looking at the women’s features, they were indeed Lucanian women. If they had been traditionally conservative outsiders, they would have caused quite a stir. But Kynogoratas, having navigated politics for many years, immediately thought of what this phenomenon meant for the city-state. Clearly, Davos was not just talking; he was trying in various ways to assimilate the Lucanians.

This young man had an extraordinary ambition! Under his leadership, the small town of Amendolara was so peculiar and different, yet it had been revitalized and filled with energy in such a short time! Kynogoratas’s interest grew even stronger. He noticed that while many people were going downhill, quite a few were also coming uphill, including many children. When he asked, he learned that disciples of the Pythagorean school were giving free lectures on mathematics in the square.

The Pythagorean school here! Kynogoratas was astonished, then suddenly recalled the scene of their first meeting. In an instant, he understood: This must have been arranged by Archytas! The Pythagorean school opposed democracy and supported aristocratic rule. Could Davos tolerate that?

But then Kynogoratas reconsidered: Given that Davos was a lifelong magistrate, could Amendolara possibly be a democracy?

When he arrived at the square, a crowd had already gathered around the platform. On the platform, a young man was lecturing on basic mathematics.

This young man was Mentotikels. He and Matikoris had originally received Davos’s promise and were eager to make a big impact, planning to recruit many disciples. But they strictly adhered to the Pythagorean school’s traditional requirement: disciples must have a certain mathematical foundation, so testing was necessary.

However, when they enthusiastically went door to door asking, they were universally refused. First, most of the new citizens had low levels of education, and having just received their land and houses, they were busy settling everything. They had no time for testing and learning. A few who wanted to learn, in order to prepare for future public office, balked at the thought of passing a test first. Meanwhile, the old citizens had a higher level of education than the new citizens, but on one hand, they were busy with funerals for their relatives, and on the other hand, the Pythagorean school had a poor reputation in Magna Graecia—secret societies, worship of strange gods (they deified “number”), opposition to the city-state, and such rumors had spread throughout every city. So the two were not welcome.

After several busy days without recruiting a single disciple, the two were greatly discouraged. They wandered aimlessly around the city until they accidentally discovered the “Hades numbers” (actually Arabic numerals) that Davos had taught Mesis for easy bookkeeping. At that time, Greek scholars studying mathematics faced a very troublesome problem: the cumbersome writing of Greek numerals. Once numbers exceeded ten thousand, they were difficult to write, causing significant trouble for scholars performing formula calculations. But the Hades numbers were simple, easy to learn, and easy to remember; they effortlessly solved the math world’s most headache-inducing problem and would surely improve the efficiency of mathematical research. Most importantly, mathematics would become much easier to popularize among the common people. (Historically, the one who solved this problem for the Greeks was Archimedes, who pioneered a method for writing large numbers.)

Thinking of this, the two felt they had found a treasure. However, when they asked Mesis to teach them the secret of using these symbols, Mesis refused, saying, “This was taught by Lord Davos, said to be a gift from Hades. You must obtain his permission to learn it!”

The two had no choice but to approach Davos again. At first, they thought this would be difficult. But Davos immediately agreed. He said, “Mathematics comes from daily life. Of course I hope everyone can learn it, so that they can apply it to life, solve the problems they encounter, and make life more convenient. That is the true meaning of learning knowledge!”

Davos’s words deeply moved the two young men.

So Davos suggested: They should give free public lectures on mathematics in the square, teaching the basics of mathematics to any city citizens willing to learn. The Senate would endorse them and encourage the public to participate. Over time, this would cultivate a large number of mathematics enthusiasts for the Pythagorean school, and naturally the school would take root in Amendolara.

The two hot-headed disciples did not want to return to Tarentum empty-handed and humiliated. After much thought, they finally decided to break the Pythagorean school’s tradition and give public lectures.

Once they agreed, Davos was overjoyed and immediately invited them to participate in the design and construction of the water wheel.

In his past life, Davos had often seen water wheels scattered across the water towns of southern China, and they seemed like something easy to build. But when Davos had the Overseer of Construction, Alexis, try to build one with carpenters, they found it was not easy: either the support frame collapsed due to uneven stress, or the angles of the wheel’s axle were inconsistent, causing it to turn stiffly… and so on. The small water wheel actually involved rather precise mathematical calculations and mechanical applications. In this era, mathematicians often also understood physics, as the two were closely linked. And so Davos had to ask the two young Pythagorean disciples for help.

When he showed them the simple diagram of the water wheel and explained its purpose, the two were immediately captivated. After careful observation, they considered it a perfect embodiment of how the “god of mathematics” helps humans live better (completely ignoring that the idea was Davos’s). Moreover, under Archytas’s leadership, the Pythagorean school in Tarentum had been engaged in research on mathematical mechanics for several years, so this was a chance to put their knowledge into practice. They immediately agreed to devote their full efforts to developing the water wheel.

Today, while Mentotikels was lecturing on the platform, Matikoris was already by the Sinni River, beginning to set up the water wheel. Although Mentotikels felt some anxiety, he did his best to steady his emotions, deliver the lecture with quality, patiently answer the enthusiastic questions from the audience, and then hurried down the hill…

At a narrow stretch of the Sinni River, the rushing water slowly turned the large water wheel’s axle. When a bucket filled with river water reached the top center of the wheel, it tipped and poured the water into a wooden trough, which then channeled the water into an irrigation canal. In this way, the cool, clear waters of the Sinni River were conducted through a network of winding canals of various sizes to the higher terraced fields…