太超前！兩千多年前，這位奇怪的數學家，就理解了“大數”的意義

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When Archimedes died, he was lying on the ground drawing.

The Roman soldiers rushed in, but he did not move. It's not that I don't know the danger, but I refuse to leave that figure. He said, "Don't disturb my circle." Then he was stabbed to death. He did not make it to Rome alive, but he entered the skeleton of human science.

At the time in which he lived, there was no profession of "scientist". He was a Syracusan, living in a window of peace in a Mediterranean city-state, with a king named Hieron II. He didn't start an academy like Plato, nor did he build a system like Aristotle, he just counted things, measured things, and thought about things.

His fame did not depend on books, but on a bathtub.

The king of Syracuse, suspecting the goldsmith of fraud, mixed silver with the gold crown. Can't cut, can't dissolve, how to measure? Archimedes dips into the tub and discovers that the water is overflowing. He suddenly realized that the amount of water discharged was exactly equal to the volume of his body immersed.

The next thing is a classic episode in the history of physics. He took an equal weight of pure gold and went into the water with the crown. The crown excretes more water, indicating a larger volume. Gold is denser than silver, and if it is larger, it means that it is not pure gold. This was the earliest prototype of the buoyancy principle.

But Archimedes' real ability is never to solve a problem, but to open a door.

He is not only interested in buoyancy, but also about geometric structures, the limits of numbers, and the boundaries of the universe. He considers his most important achievement to be the proportional relationship between the sphere and the cylinder – 3:0 in volume and surface area. He carved this pair of geometries on his tombstone, and he did not mention other achievements.

他也想算π。在沒有計算機的年代，只能用逼近法。他把一個多邊形嵌入圓中，再畫一個包圍圓的多邊形。邊數從6變成12、24、48、96，每加一層，圓周率的估計就更精確。他最終算出π在3.1408和3.1429之間。距離我們今天熟知的3.14159，只差不到萬分之一。

He also likes to ask questions. It's not a test question, it's the kind of math trap that "basically no one can figure out without a computer". He wrote a title called "The Ox of the Sun God", four colors of oxen, complex proportional limitations, and a few divisible conditions. How many cows is the answer? The final answer is an extra-long number of 1965,0 digits. It wasn't until 0 that it was unraveled by IBM mainframes.

It has been said that he understood the meaning of "large numbers" earlier than anyone else.

古希臘人的計數系統頂多到10,000。阿基米德不滿意。他乾脆設計了一個系統，把每一層的數位提升10的8次方。然後一層一層疊上去，直到能表達整個宇宙里沙子的數量。他寫了本《沙子書》，估算填滿宇宙需要10的63次方顆沙。

Precision is not important, what matters is the method.

He writes to friends and does not send papers. He deliberately inserted false propositions in his letter to test who was plagiarizing. He despised those who only talked empty without proof, and wrote directly: "Those who claim to have discovered everything, but never give any proof, should be exposed." ”

But a lot of what he wrote almost disappeared completely.

His manuscripts were made of papyrus. Hundreds of years later, Byzantine scribes copied seven of them on parchment, and over the centuries, the parchment was washed out of the original text and used to write Christian prayers. A thousand years later, someone noticed that there was a mathematical formula looming underneath the prayer.

In 1998, the Danish scholar Heiberg discovered this "Archimedes Fragment" in Istanbul. In 0, an anonymous American collector paid more than two million dollars to auction it and send it to the Walters Museum of Art in Baltimore. X-rays, ultraviolet scans, image enhancement, digital restoration, Archimedes' original text is gradually resurrected.

This includes the "Leverage Principle". Almost everyone has learned this principle: the force is multiplied by the force arm, and the two ends of the lever must be equal. He said a phrase that is quoted repeatedly to this day: "Give me a lever long enough and a fulcrum and I can pry the whole earth." ”

The Roman army believed.

In 213 BC, the Romans laid siege to Syracuse. Archimedes began to build war machines. He used the principle of levers to design lifting devices that could overturn enemy ships. He also made "iron claws", grabbed the bow of the ship like a lifting hook, and with a sharp flick, overturned the ship. The Roman soldiers began to believe that they were not dealing with man, but with God.

And the legend of "burning enemy ships with mirrors". Most not. But interfering with the enemy's line of sight with reflective metal, quite possibly. After all, he doesn't do miracles, only physics. But he couldn't change the ending after all. Syracuse is lost. Roman soldiers stormed the city. General Marcellus had already ordered: Archimedes could not be killed. Be captured alive.

But the front-line soldiers did not know who he was. Seeing an old man prostrate on the ground drawing, he didn't listen to the order, and replied "Don't move my circle", so he stabbed down with a sword. When the news of his death came, Marcellus was devastated. He personally presided over the funeral, brought in craftsmen, carved balls and columns on the tombstones, and that set of 3:0 scales.

這是西元前212年。阿基米德活了75歲，沒有建立學派，也沒有追求權力。他留下的，是一套可以穿越兩千年的思維方式。他不解釋世界的意義，他只是準確地告訴你，那個體積就是那麼多，那條槓桿就是那麼長。