Pyramids across the World

Humanity’s architectural achievements are truly astonishing. Looking up at the great monuments of the world like the Eiffel Tower or Taj Mahal can have a truly humbling effect on us. But, have you ever wondered why human civilizations build such tall towers? With a new record-breaking tower erected every decade, from Toronto’s CN Tower to the Burj Khalifa in Dubai, there seems to be a never ending competition among mankind to construct taller and taller buildings. Even in the biblical story, The Tower of Babel, the ancient Babylonians built a tower so tall, it was perceived as a threat to God! We know how the builders of today do it, but how did the ancients manage to construct such impressive buildings without the help of modern machinery?

The greatest architectural mystery of the ancient world is by far the Pyramids of Giza. Although the ancient Egyptians are widely known for constructing the most iconic pyramids in the world, they were not the only ancient culture to build them. Archaeological digs have discovered pyramids across the ancient world whether it be in Mesopotamia, China, India, Indonesia, Cambodia, Spain, Italy, Nigeria, and Sudan. Pyramids were even found on the other side of the globe! Mesoamerican cultures like the Incan, Mayan, Aztec, Xelhua, Toltec, Velacruz, and Teotihuacan all excelled at Pyramid building. But, the question remains…how did ancient peoples build such majestic pyramids? What technology did they use?

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Since there is no evidence to answer that question, we can only rely on speculation. Was it strictly a matter of hard labor and dedication? Or were they using a technology we are not aware of? Take the pyramids in Chichen Itza in Mexico, for example. The main pyramid, Kukulkan, stands atop a rectangular platform 55.5 metres wide and 24 meters tall, with a 6 metre temple perched atop it. Witnessing the sheer magnitude of these megalithic structures suggests that manpower alone could not have been solely responsible for their construction. With a missing piece to this puzzle, many have foregone modern scientific reasoning and sought to obtain answers from ancestral legends instead.

Ancient Mayan legends claim their pyramids were built with the help of magic powers. The descendants of the Mayans still hold this idea to be true, but with a key insight: the magic powers were not actually magic, but rather, they were a forgotten technology! Can you try and guess what it was? According to locals in the south of the Yucatán Peninsula, their mystery machine wasn’t a machine at all. It was sound! They maintain that the ancient Mayans would whistle in such a way as to harness an extraordinary amount of energy – enough to move megalithic stones! Imagine that scene: gigantic stones and wooden logs floating through the air of a construction site, guided by the whistle of a musical foreman! No hammers, drills, or cranes, just the wonder of enormous objects dancing on the wind to the tune of ancient music.

Whether it’s with modern machinery or with an ancient technology long since forgotten, one thing remains clear: humanity’s ambition to build towering structures will likely never come to an end. But, where our ambition will lead us is yet to be determined. Can you imagine what the skyscrapers of the future will look like?

 China Terracotta Warriors and the Search For Eternal Life

On March 29th, 1974, a groundbreaking discovery was made in northwestern China. Local peasants digging a well accidentally unearthed fragments of a millennia-old terracotta clay figure. This peculiar finding led archaeologists to excavate the site, revealing an ancient tomb guarded by one of the most significant archaeological discoveries in modern history: the Terracotta Army of China’s first Emperor, Qin Shi Huangdi.

The terracotta clay army consisted of more than 8,000 life-sized soldiers and 600 war-horses in full armor and battle formation. Weighing up to 272 kilograms each (600 pounds), and many standing two meters tall (roughly 6 feet), the soldiers showcased remarkable detail, with each clay sculpture characterized by unique facial features, hairstyles, clothing, and posture. But, who was China’s First Emperor? And, why did he surround himself with the monumental terracotta army?

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Born Prince Ying Zheng in the year 259 B.C., he became King of the Qin State at the age of thirteen, and by age twenty-two had turned into the emperor that would revolutionize ancient China in a number of ways: uniting China in 221 B.C. by taking over the six independent kingdoms of the late Warring States Period, creating a single system for writing, units of weight, measurement, and coinage; building the Great Wall to strengthen the northern border, and establishing the Ling Canal to connect China’s north and south river systems.

However, all of these achievements came at a huge cost to the people of ancient China. The Emperor governed with an iron fist. His tyrannical reign was guided by the philosophy of Legalism, which was based on the cynical belief that the average person is motivated by self-interest and, therefore, more likely to do wrong than right. As time passed, the Emperor forbade all other philosophies and ordered the destruction of texts not conforming Legalist views. Anecdotal evidence suggests he may have even executed writers, philosophers, and scholars to stamp out opposing ideologies.

After a career of landmark achievements, China’s first emperor set his sights on one final conquest: death itself! Increasingly obsessed with discovering the proverbial fountain of youth, he sought the advice of his alchemists, who fascinated him with tales of magical life-extending herbs found only on the Islands of the Immortals in the East China Sea – a mystical place that only allowed pure-hearted children to enter. In 219 B.C., emperor Qin Shi Huangdi dispatched thousands of children to the islands. When they never returned, he sent three alchemists. Just one returned, recounting that the islands were protected by an enormous fish, and that their expedition had failed. Unable to accept his mortality, emperor Qin Shi Huangdi journeyed to find the islands himself, but instead of conquering death, he succumbed to it along the way. Experts believe he died from consuming mercury administered by his alchemists, who themselves believed it to be the elixir of life.

At the same time he was searching for immortality, emperor Qin Shi Huangdi was also planning for the afterlife. Throughout his entire life, he had been gradually constructing an enormous underground burial chamber bursting with his empire of riches, and guarded by his army of terracotta warriors, chariots, and war-horses. After conquering the whole of ancient China, he truly believed he could do the same in the great beyond! The question is, would his terracotta soldiers still serve their emperor in the afterlife?

 Europe Mathematical Duels

Competition is an inherent feature of the human condition and beyond. Whether it’s animals, plants, or microscopic life, every organism on the planet is competing against one another for resources, status, or the highest position in their given hierarchy. It is no wonder then, that sports play such a significant role in human society. Whether it’s MMA, basketball, or even professional video gamers, the need to compete and achieve the triumph of success proliferates through many aspects of our lives and even goes beyond sport and into the realm of science. Renaissance Italy boasted one of the most bizarre forms of competition to date: Mathematical duels…the most famous example of these contests revolved around the discovery of a general solution of cubic equations.

In the early 16th century, an Italian mathematician named Scipione Dal Ferro from the University of Bologna secretly devised a solution to cubic equations: x3+px=n𝑥3+𝑝𝑥=𝑛. A few years after his death, a mathematician from Brescia named Niccolò Pisano, nicknamed Tartaglia, meaning “stammerer,” revealed to the mathematics community that he had discovered a solution to cubic equations, the key to unlocking a seemingly unsolvable, two-thousand-year-old mathematical problem! Determined to undermine Tartaglia’s announcement, a former student of Dal Ferro’s named Antonio Maria Fiore publicly challenged Tartaglia to a mathematical duel!

Modeled after knightly duels, the cartelli di matematica disfida or “bills of mathematical challenge,” consisted of a series of oral or written mathematical equations posed by each competitor to one another with juries, notaries, and witnesses present to observe the battle. As per this challenge, Tartaglia and Fiore provided each other with thirty problems, to be solved in forty days. Tartaglia shocked the community by solving all thirty equations in two hours! Dal Fiore, however, was unable to solve even a single problem.

Four years later, in 1539, Tartaglia disclosed his secret formula as a twenty-five verse poem to Gerolamo Cardano, a Milanese physician and mathematician, swearing him never to reveal it to the outside world. Cardano did, however, allow his student Ludovico Ferrari to see Tartaglia’s formula for third-degree equations, which Ferrari then used as a necessary tool to create a solution for the next frontier in mathematics: fourth-degree equations. Ferrari wanted to publish his momentous discovery, but doing so would reveal Tartaglia’s equation, and feeling honor-bound  to Tartaglia, Cardano refused to allow Ferrari to publish the solution to fourth-degree equations.

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As fate would have it, Cardano and Ferrari later stumbled upon the work of Scipione Dal Ferro, and were astonished to learn that he in fact had discovered a solution to cubic equations prior to Tartaglia. With this new information, Cardano asserted that his oath of secrecy to Tartaglia was now voided, and he and Ferrari were free to publish their work on fourth-degree equations!

In 1545, Cardano published Ars Magna (the Great Art) which included the formulae for the general solution of equations of the third and fourth degree. Outraged by the betrayal, Tartaglia traveled to Milan to challenge Cardano to a mathematical duel. Perhaps too ashamed to face Tartaglia himself, Cardano skipped town and his student Ferrari filled in for him, squaring off with Tartaglia in front of a large crowd including the Governor of Milan, Don Ferrante Gonzaga. Unfortunately, for Tartaglia, this was not a written duel, but rather, a spoken one which highlighted Tartaglia’s speech impairment. With most of the crowd rooting for Ferrari, Tartaglia was soundly defeated, and humiliated so much so that he later lost his job in Brescia. The solution for cubic equations was then credited to Cardano, and went on to be known as Cardano’s Formulae.

Who would have thought that the world of mathematics could be so deeply entangled with competition, betrayal, and glory? It is a stark reminder that no matter how high the arc of human achievement rises, it is nonetheless subject to, and perhaps driven by, the ever-present pursuit of individual notoriety. Cynical as it may seem, it begs the question, without the desire for personal glory, how many of the achievements that have propelled humanity towards a brighter future would have even come into existence whatsoever?