The literary giants of the late Ming Dynasty began by copying books

Chapter 100 Mathematical Artifact—Logarithm Table
After several months of development, the ritual of offering sacrifices to the famine-saving melon and vegetable fairy has been finalized.

The main theme is simple and practical. Vegetable porridge is used during sacrifices. It doesn't matter what kind of vegetable it is, as long as it is fresh and satisfies the stomach. Put a bowl of porridge in front of the statue of the immortal, kowtow, and the sacrifice is over.

Then share the porridge while it's hot, and do whatever you want to do after you're full, so as not to delay the people's farming work.

Xu Xueju also had to practice simplicity when he went to the countryside. He sat around a table and drank potato porridge with everyone. There was no shortage of pickles. The place was close to the sea, so he couldn't eat all the private salt that was secretly dried.

Zhao Fan and other big businessmen who came forward also ate this food. After everyone drank a lot of water, they left one after another and returned to Fuzhou.

When Xu Xueju was about to finish his work, Chen Jinglun said to Wang Wenlong: "I still need to calculate the output of the fields with the county magistrate again, which will take a lot of time. Brother Wang and Xu Fantai should go first."

When Wang Wenlong asked, he found out that in previous years when people encountered food shortages, all the people ran away. The yamen's official warehouses used as much food as they could, making the work of the yamen's offices easier.

Although the food shortage has been alleviated this year, the work of the yamen has become more complicated.

The yamen need to know the approximate potato production figures in various places so that the province can allocate food for disaster relief. Otherwise, there will be man-made disasters in which the people have starved to death because they have obviously harvested food but failed to allocate it in time.

This requires a lot of calculations.Calculating the yield per mu is not that simple these days. In addition to taking into account the conditions of the fields, we also need to take into account the unreported yield of the hidden fields and the amount of disaster reports from various places. This task is enough to keep the warehouse in the Yamen at the time of annual taxation. Been busy for the better part of a month.

Chen Jinglun has a very responsible attitude towards his work. While he was talking, an official from the county came to give him the accounts.

Wang Wenlong got a headache just by looking at the long numbers, while Chen Jinglun and the official picked up the abacus and started calculating.

Wang Wenlong saw that almost all of these calculations used multiplication. Chen Jinglun was reciting the abacus chant while doing the abacus, and suddenly an idea flashed in Wang Wenlong's mind.

"Brother Chen Xian, how accurate should the figures calculated in the yamen be? But do they need to be accurate to the kilogram?"

Chen Jinglun raised his head and said with a smile: "Then how do you calculate it? It would be good if the calculation of money and food in county units can be accurate to the stone when we are in such a hurry. In fact, even the county's tax collection is based on stone units. On weekdays, what Xiongtai does is You can see that the more detailed figures are actually obtained by taking large numbers and dividing them.”

Wang Wenlong nodded. It seems that the accuracy of the numerical calculations used by the county government these days is not that high. The grain output of a county per quarter is about [-] dan. To calculate an accurate dan, only five significant figures are enough. Wang Wenlong instantly thought of a way that was much faster than using an abacus.

Wang Wenlong said: "Brother Chen Xian, I have come up with a good way to do multiplication and division calculations."

He squatted on the ground, picked up a stone, and began to explain. Chen Jinglun and the officials looked on curiously.

"Power method in two-digit arithmetic?"

Chen Jinglun, who had learned arithmetic, replied: "Just multiply the same numbers, right?"

Wang Wenlong nodded and said: "That's right. For example, raising the power of two means multiplying the number by two twice."

Wang Wenlong explained the concept of powers and said that he found that the multiplication of powers with the same base is equal to the addition of their exponents.

This calculation principle is very simple. Although the two of them have never heard of it before, they understood it after just a brief explanation.

Wang Wenlong smiled and said: "According to this principle, if there is a table that lists the results of all powers of the number, then there is no need to calculate the multiplication of the numbers to that power. You only need to find the numbers on the table to get the arithmetic results directly. in conclusion?"

As Wang Wenlong spoke, he wrote a series of common logarithms based on base ten on the ground.

"For ease of reference, I reversed the base and exponent in the power method and named it logarithm."

Wang Wenlong waited for the two of them to understand, then took Chen Jinglun's account book and pointed to the two numbers on it.

"For example, this formula: four six two seven times 29 point three."

"The commonly used logarithmic integer digits of four, six, two and seven are four minus one, which is three. The decimal place lookup result is point six, six, five three. Then add the other number to the table..."

I have to read these two numbers on the abacus for a while, for fear of miscalculation.

By using the logarithm table, you don't need to do troublesome multiplication operations, just add and subtract directly.The two were stunned when they saw Wang Wenlong quickly find out the logarithms corresponding to the two numbers, then did an addition and then looked up the table in reverse to get the result directly: "The answer is [-]."

The official on the side quickly flipped the abacus, but it took him a few breaths to get the same answer.

He couldn't help but be surprised: "The logarithm table calculation is so fast..."

Both of them understood Wang Wenlong's operation and instantly understood the power of this pair of numbers table.

With this logarithm table, they no longer need to do long multiplication operations, they only need to do addition and subtraction to get the desired result.

When Wang Wenlong and Wang Jide were calculating the law of averages together before, they felt that there was some way to quickly calculate multiplication, but he didn't think of it at the time. It was only when he saw their abacus that he finally remembered the logarithm table.

Wang Wenlong said with a smile: "In my early years, I calculated a base-ten logarithm table. I call it a common logarithm table. If it is useful, I will write it down."

The European mathematician Napier in Wang Wenlong's previous life would invent Napier's logarithm more than ten years later, which shocked Europe at the time.

Europe has entered the Age of Discovery, and the demand for digital computing has never been higher.

For example, when going out to sea, you use a sextant to observe the sky at sea to determine the position of the ship. In order to ensure accurate observation of the data, the movement requires multiplication and division of several digits. The calculated value must be obtained during the voyage and the ship's course must be adjusted at any time. .

You can't make a mistake in calculation. If you make a mistake in calculation, the ship will be destroyed and everyone will die.

It’s easy to understand how tiring the work of a navigator is and how stressful the calculations are.

The discovery of logarithms directly turned complex multiplication calculations into addition, subtraction and table lookup, which not only accelerated the speed, but also greatly improved the accuracy rate.

This thing is definitely a killer weapon, the kind that changes the times.

Just look at the great astronomer Laplace's evaluation of the logarithm table to understand: "It saves labor and doubles the life span of astronomers!"

Chen Jinglun was even more surprised when he heard Wang Wenlong's words: "Jianyang can actually remember a logarithm table?"

Wang Wenlong closed his eyes and saw the logarithm table at the back of the university mathematics textbook in his previous life. He could just copy it with a pen.

He took the paper and pen and started writing the logarithm table. Chen Jinglun watched in surprise as Wang Wenlong quickly wrote out a long string of numbers, obviously very familiar with it.

The official looked at it for a while and said quickly: "I'm going to call the county magistrate and Qianliang Master."

Soon the local county magistrate and master came over curiously. At first they were a little confused about the logarithms written by Wang Wenlong, but when they saw Chen Jinglun demonstrating the speed of logarithm calculations for them, everyone took a deep breath. One breath.

Master Qianliang, who often takes an abacus, couldn't help but admire: "It turns out that multiplication and division can be calculated so easily..."

In the original history, Napier first established the concept of logarithms before establishing the concept of exponents, which is quite difficult to understand. However, Wang Wenlong introduced logarithms based on later generations of mathematics. For people at this time, Much easier to understand.

It only took a quarter of an hour to train, and all the Qian Liang Dao pen officials present quickly mastered the method of quickly calculating numbers by looking up logarithm tables.

The logarithm table copied by Wang Wenlong is still far more complex than the later commonly used version of Napier's logarithm table, and its accuracy and practicality are much higher.

If Wang Wenlong had relied on Wang Wenlong to calculate these logarithmic tables by himself, he would probably not have been able to complete them within four to five years.

Everyone was stunned to see him writing so quickly. Not to mention the surprise that he came up with logarithms, Wang Wenlong's memory alone was extraordinary.

The county magistrate couldn't help but whisper to the master next to him: "People often say that Wang Jianyang is amazingly talented. He is very talented when he comes up with the method of logarithms. But today, if I don't see Jianyang recite the logarithm table with my own eyes, How dare you believe that there are people in the world who have such a strong memory?"

(End of this chapter)