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Fractions, calculus, imaginary numbers. If you have math phobias like many people, these words may trigger painful memories of your high school math class, and the "graffiti" on the blackboard are both confusing and boring. We can't help complaining, "Why would anyone care about math? what's the point?"

Edison (left) works with Charles Protis Steinmetz, a mathematician and electrical engineer. Steinmetz used imaginary numbers to figure out how to build working circuits, allowing electricity to enter thousands of households. Michael Brooks, a British journalist with a doctorate in quantum physics and editor of New Scientist magazine, understands why so many of us hate math. In school, math can be boring and tiresome, but once it becomes interesting, it shows an almost mysterious, unknowable power, which is fascinating.

His new book, wonderful Mathematics (The Art of More: How Mathematics Created Civilization), puts forward a convincing argument that some great achievements of human beings can only be created by mathematics. Mathematics is not only not boring, but also not mysterious at all. It is closely related to all of us. It is a practical way to solve problems, from ancient Sumer to Silicon Valley, it makes our world a better place.

Here are four interesting stories about how simple (or not so simple) math can change our world.

Shulki, the Emperor of Canada, about 4000 years ago, the ancient city of Ur was one of the important capitals of Sumer in southern Mesopotamia. The agricultural revolution has led to an unprecedented scale of settlements, but that is why it has become increasingly difficult for priests and kings to control the harvest, storage and distribution of food to worship the gods and nurture mankind.

Natural mathematics has become something they desperately need. At first, there was no fancy computing skills, just some basic arithmetic (addition, subtraction, multiplication, division). But what is surprising is that according to the ancient clay tablets unearthed from Ur, one of the earliest arithmetic champions was a king named Shulgi.

"there are records that people write hymns to celebrate his ability to add," Brooks said. and he made his subjects admire his mathematical ability. "

Schulky not only showed off his divine mathematical skills, but the country he founded was recognized by scholars as "the first mathematical country". In his country, mathematics is mainly used for bookkeeping, which allows Schulky and his aides to strictly control Ur's finances so as to prevent people from deceiving the country.

You can say that Schulky and his staff are just glorified auditors, but as Brooks wrote in wonderful Mathematics, auditing is "the true cradle of civilization".

People take part in celebrations at the Zigarat pagoda in the ancient city of Ur in Zigar province in southern Iraq in 2021. King Shulki is believed to be the builder of the temple. "Schulky realized that once you have the numbers, you start to make huge economic profits," Brooks said. Math works.

Through the use of mathematics, Schulky helped Ur gain great wealth and used it to develop one of the earliest and greatest civilizations in the world. Schulky also took credit for building the Tower of Zieglat, building a vast network of roads, and expanding his trading empire into the Arabian and Indus basins.

The French Revolution began as an accountant. Louis XVI, the French monarch in the 18th century, provided financial support for the American Revolution, but the American Revolution left France mired in debt. The king needed a good accountant to help balance the accounts, so he appointed a Geneva banker named Jacques Necker as chancellor of the exchequer.

But Necker is a bit "too good" at work. He disclosed his budget and used double-entry accounts to carefully track every expenditure, which is not common in a country with an extreme autocratic monarchy. Necker believes that keeping the accounts in balance not only represents a good audit, but also the foundation of a moral, prosperous, happy and strong government.

But the profligate French royal family didn't like it because it meant they couldn't spend money at will, so Necker was fired.

The king's cronies may despise Necker, but the revolutionaries love him. In fact, Necker's downfall was the trigger for the French Revolution. "when the revolutionaries attacked the Bastille, they carried a bust of Jacques Necker on their shoulders," Brooks said. "he was a cool accountant."

Kepler invented integral calculus to save money on alcohol. German astronomer Johnannes Kepler (Johannes Kepler) is famous for discovering the law of planetary motion, which proves that planets in the solar system revolve around the sun in an elliptical orbit. In addition to this famous work, he wrote a whole book about the correct shape of the wine barrel.

Kepler is said to have ordered a barrel of wine for his second wedding in Linz, Austria, but the two sides quarreled over the payment. Kepler didn't like the way the wine merchant priced the barrel.

According to custom, the wine merchant puts the barrel on the side and inserts a long stick through the hole in the center of the barrel until it reaches the opposite corner. After the long pole is removed, the price of the barrel of wine is determined by the degree to which the long rod is soaked.

Kepler soon discovered the deficiency of this method: the price of the same amount of wine varies according to the size of the barrel. A thin, long barrel costs less than a short, fat barrel. Kepler paid the bill angrily, but he couldn't give up the question of how to build a barrel that would produce the cheapest wine.

Kepler's method is to calculate its volume by imagining a curved barrel as a collection of flat cylinders. However, to get the most accurate results, a large number of cylinders are needed in the calculation. In fact, they need to be infinitely small to fill every inch of space in the barrel. "when we cut time, distance or anything else into infinitesimal, we enter the field of calculus," Brooks wrote in his book.

In 1615, Kepler published the New solid Geometry of the barrel (Nova Stereometria Dolorium Vinariorum), which is considered to be the foundation of integral calculus. Newton: what about me? )

This illustration is selected from the New solid Geometry of the barrel by German astronomer Johnannes Kepler. Kepler's work is the foundation of modern integral calculus. Kepler shows how to maximize the size of the barrel so that its price is minimized (Austrian barrels are very accurate, by the way), pointing the way to the use of calculus to maximize the efficiency of various things. Brooks uses modern examples to illustrate: calculating the correct dose of anti-cancer drugs to produce the most effective response, and calculating how much fuel the 747 should carry to fly farthest without falling.

The electrification of the United States by imaginary numbers there is nothing more troublesome for people with mathematical phobia than imaginary numbers. When we use real numbers, math is difficult enough! Now you still want to make trouble with imaginary numbers?

Calm down, man. It turns out that imaginary numbers are real, but they have a very stupid name.

Dr. Steinmetz (left-handed stool) demonstrated the artificial lightning generator in the laboratory. This problem originates from mathematicians trying to solve quadratic equations that require negative square roots. Since any number multiplied by itself cannot be equal to a negative number (or even a negative number multiplied by a negative number equals a positive number), mathematicians began to call such numbers "imaginary numbers".

Were it not for a 1.45m weirdo named Charles Proteus Steinmetz (Charles Proteus Steinmetz), imaginary numbers might still be a strange mathematical oddity.

Steinmetz discovered how to use imaginary numbers to solve one of the most challenging engineering problems of the 1890s: how to harness the new power of electricity and deliver it to homes and businesses. While bigwigs such as Thomas Thomas Edison and Nicola Tesla argue over which alternating current or direct current has the advantage, engineers struggle with the extremely complex mathematical knowledge needed to build normal circuits.

"Charles Steinmetz came up with a formula to turn all these very difficult calculations into very simple calculations using imaginary numbers," Brooks said. "this is basically how we electrify America."

Steinmetz's formula provided the impetus for the electrical age and the great leap forward in industrialization and scientific discovery. Half a century later, Bill Hewlett and David Packard used imaginary numbers to design their first product, the audio oscillator, in their garage in Palo Alto, Calif., known as the birthplace of Silicon Valley.

Author: Dave Roos

Translation: September 1st

Revision: machine 7

Original link: Thanks, Math! Four Times Numbers Changed the World

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: Dave Roos

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