Chapter 96 Mathematical Symbols
Jinling City, Liujiaojing Alley.

After hanging up the last piece of clothes, Gu pounded her aching waist, wiped the sweat from her forehead, and listened to her eldest and youngest sons arguing about how many trees they had planted in the desert, with smiles in her eyes.

To her, the knowledge taught in the sky curtain was just like the teachings of sages by teachers in the academy, which was completely incomprehensible.

It is a novelty that trees can be grown in the desert, but that is just a novelty.

Perhaps the only function is that some things mentioned or appeared in Tianmu can be used as topics of conversation after dinner. When neighbors visit each other and talk and joke, they always mention the scenery of Tianmu, gossip, etc.

After all, there are many women and children like her in Jinling City. Many people's lives are confined to Liujiao Alley and several surrounding alleys, Zhonghuamen and nearby markets, which are quite boring.

The skylight makes up for all of this. Apart from anything else, the knowledge alone is very beneficial.

Before the sky curtain appeared, Gu still had only an idea of ​​what the sea looked like. Although the sea was not far below the Yangtze River outside the city, it was a place she would never be able to reach in her lifetime.

She had no idea what color blue the sea water was, was it the blue of clothes or the blue of the sky, or why it was blue, or how much bigger than the Qinhuai River it had to be to be considered boundless, or whether the sea had an end, or what was at the end, etc.

She couldn't imagine what it felt like to fly, couldn't imagine sowing and harvesting crops with a machine that could just drive over and cut them.

Not to mention the desert, which no one has mentioned several times from the beginning of the year to the end of the year. It is a place even farther away than the sea.

Planting trees in the desert
She could understand some of the hardships. Planting rice, winter melon, cabbage and radish in the countryside would cause them to wilt and become useless if they were not watered once or twice. Planting trees in the sand, which was dry and water-scarce, was even more torturous.

It turns out that life in the desert is much more cruel than what is described in the books as "a lone smoke rising in the desert". Look at the wind and sand blowing everywhere, and there is nowhere to get some water.

Gu admired the feat of his descendants very much, but he also felt that they were a little stupid. When the desert came, they could just run south. Why spend so much energy planting trees, planting one tree for so many years?

Gu couldn't figure it out and didn't put her mind on these problems. For her, taking good care of her husband and two children was the most important thing.

In terms of taking care of children, the sky curtain also helps a lot. When the sky curtain takes action, there is no child that cannot be coaxed. As long as the sky curtain lights up, even if the child was crying with snot flying in the previous moment, he or she will be like a good baby in the next moment.

Gu knew that the world of Tianmu was so vast, fresh and interesting to adults, not to mention to curious children. Even if Odebiao was delivering bananas or "fishing", it was still much bigger and more interesting than Liujiao Alley.

I also heard that the knowledge taught by Tianmu was recognized by the imperial court and was called the New Learning. In the fourth year of Hongwu, which is this year, the New Learning will be included in the scope of teaching and examinations in the academy.

For this purpose, a book was specially published, which talks about the new knowledge and has three branch disciplines.

For this reason, many teachers who resisted the new learning claimed to be sick and stopped teaching.
These news were heard when she was fetching water. Gu didn't know whether the news was true or not. She rested for a while and went out again with the wooden bucket on her back. Life was not as convenient as the sky curtain these days. Clothes could be washed by the well, but water for washing dishes and cooking had to be carried back by herself.

"It would be great someday if I could use water that flows by itself." When Gu thought of the mechanism in the sky where water would flow out when the switch was turned on, he felt hopeful. These things should be available soon.

She could hear her eldest son's voice in the distance, and she knew that the sky had changed again.

[I don’t know if you have the same confusion as me. When I was studying, I always wondered why the Suez Canal, which has only one line width, can accommodate a cargo ship fully loaded with 16 tons]

[The Suez Canal, built and opened to navigation in 1869, is one of the busiest shipping routes in the world. It runs from Port Said in the north to Suez City in the south. It is about 190 kilometers long, 365 meters wide and 16 meters deep. It is an important channel connecting the Mediterranean Sea and the Red Sea.]

[It is the boundary between Asia and Africa, and one of the main channels for people from Asia, Africa and Europe to communicate]

[Its annual average navigation volume accounts for 10% of the world's total, its container transport volume accounts for 25% of the world's total, and its throughput accounts for 12%-15% of global trade. This is the route used for trade between China, Japan, South Korea and Europe.]

[It is thanks to this canal that Egypt has made a lot of money by collecting tolls, generating $2022 billion in revenue in 94]

[In the era when there was no Suez Canal, there were only two routes for communication between Asia and Europe: one was by land, and the other was by water. The water route went around Africa, then went east to South Asian countries, and then passed through the Strait of Malacca to East Asian countries.]

[This water route is about 10,000 kilometers longer than the Suez Canal. Not only does the shipping cost soar, but the entire voyage takes more than ten days longer. This is why the Suez Canal is so important.]

[In 2021, a ship jam occurred in the Suez Canal, and the waterway was blocked for 6 days, paralyzing global trade and causing a net loss of up to US$60 billion per day.]

【.】

Ming, Jinling City.

The king and his ministers looked at each other and shook their heads helplessly. It seemed that the previous plan to go north to the Red Sea through the Suez Canal, then out of the Strait of Gibraltar, and then westward would not work.

The Suez Canal at this time would not be opened to navigation until almost 500 years later.

Now there is only one option left, which is to go around Africa and sail west from the northwest corner of Africa.

Fortunately, the fleet has not yet set out and the plan can still be modified. If we had learned the news on the way, it would have been a wasted voyage.

Zhu Yuanzhang knew that crossing the Atlantic Ocean and landing in South America was not something that could be accomplished overnight, so the entire revised plan was roughly divided into three phases. The first phase was to follow Zheng He's voyage to the West and reach the Arabian Sea and other places.

The second phase of the plan is to circumnavigate the entire Africa and establish certain trade relations with the places along the way, barter, replenish the fleet's needs for survival supplies, etc.

The last issue is about crossing the Atlantic Ocean, which is also the destination. No one dares to guarantee whether it can be reached and how to find sweet potatoes, potatoes, corn, etc. after landing. Even when Tianmu mentioned it, he just said that it is probably in South America.

The three-phase plan will take 7-8 years if it is fast, but I don’t know if it will be slow.

Zhu Yuanzhang was not even sure whether he would be able to see the day when the fleet returned in his lifetime.

However, it was mentioned in the comments that during the Age of Discovery, Europe's shipbuilding technology was not as advanced as that of the Yongle period. Now with global maps and crop distribution, Europe has a much greater advantage than them in terms of information and people's hearts.

The only disadvantage we have over them is our geographical location. The Ming Dynasty is too far away from Europe and Africa. So if we want to cross the Atlantic Ocean, we must first set sail from Fujian, Guangdong and other places. It will take a year or two to reach Africa, and then we can consider crossing the Atlantic Ocean.

The cost of trial and error is too high.
Tang Dynasty, Chang'an City.

Similar sailing plans also need to be modified accordingly. Fang Xuanling and others looked at the scenery of the Suez Canal and could not help but sigh at the wonderful ideas of these people. This canal and the Strait of Malacca are extremely important in terms of geographical location. It is simply a typical example of God's gift.

And they lived up to expectations, manually excavating more than 190 kilometers, several hundred meters wide. The project was so huge that it is really hard to imagine the grand occasion at that time.

This is also a large-scale project that will benefit the present and future generations, and its benefits are even more exaggerated than a cornucopia.

Li Jing and other famous generals were all stunned, thinking it was a good thing, but unfortunately it was too far away.

[I never thought that in 2024, I would still see stereotyped questions. It really does harm people a lot]

[Today I came across an elementary school question, asking: What is 3+6 divided by 3? My friends, please pause and think about it. What is your answer?]

[You can see that this question is a math test, but the description of many words makes it look like a Chinese test. You can say that this is a Chinese test, but the final logic is a math calculation.]

【We know that the mathematical symbol system itself is logically self-consistent and can accurately convey information. However, using language to describe the above problem will make the problem vague. Do you know what the original intention of the questioner above is? Do you know what the order of operations for this math problem is?】

【它这道题,问题太多了。比如第一个地方就是关于除的描述,因为数学课本上会去定义除和除以的关系,比如6除以3是6作分子3作分母,写成这样:6÷3;6除3则相反,6作分母3作分子,写成这样:3÷6】

[It doesn't conform to our daily life logic at all, just like when you introduce something to others, would you emphasize division and division by?]

[Of course not. As long as you say "divide" or "divided by", the other party will know what it means. But he insisted on quibbling over the words here. The difference of this one word makes a world of difference in the answer.]

[And if you want to express 3÷6, you can say 3 divided by 6. I really can't think of any necessity for the definition of "division", except to disgust people.]

Ming, Jinling City.

Zhu Biao and others spent a lot of brain cells to finally understand the relationship between "division and division by". Just as the person behind the scene said, this question was extremely tricky.

And since it's a math test, you can just use that set of mathematical symbols to express the questions.

Even though the concepts of division and times division are well known, no matter what the purpose of the question setter, whether intentional or unintentional, there is always a problem with his attitude or ability.

特别是这个“除以和除”的区别,朱标想了想,这个“6除3”完全可以用“3除以6”来表示,或者干脆表示两者含义相同,想表示3÷6就直接说3除(以)6,想表示6÷3就直接说6除(以)3。

Zhu Yuanzhang frowned and said nothing. He always hated quibbling and flowery words, and he also hated this kind of ambiguous behavior.

According to Tianmu, the calculation of this question also involves the issue of the order of operations, which makes this question even more problematic.

Such a mediocrity!

[The second thing is that there is no clear order of operations in the whole question, and it is not clear which one comes first and which one comes later]

[Then there are many possibilities. You can say 3+6 should be calculated first, or I can say 6 divided by 3 should be calculated first, just like the chicken and the egg. After talking about it, I find that it is all nonsense.]

[So based on this question of nitpicking, he can actually list four equations]

[The first one is: 3+6÷3, but I’m sorry, this answer is wrong in their standard answer]

[Then the second equation: 3+3÷6, here is the nitpicking, the difference between division and dividing]

[If we think about the order of operations a little more, there is another possibility, which is (3+6)÷3. Here, the first digit is added first. In the mathematical symbol system, () is used to indicate that the operation level has a higher priority.]

【The last possibility is: 3÷(3+6). 】

[These are four types of equations. Every student may come up with a solution. The answers may be all kinds of strange, but there is only one correct answer in the end.]

[But you see, if we want to take a math test, we can actually express our ideas more accurately by listing an equation. Using illogical words to replace a mathematical symbol system with clear logic is really extremely abstract.]

Ming, Jinling City.

Zhu Yuanzhang and others suddenly realized that later generations had abandoned such a complete mathematical symbol system and instead deliberately used ambiguous words to describe the problems.

Obviously, science requires rigorous logic, but why is it that the opposite is true in mathematics? Although this problem only exists in primary schools, it is obvious that primary school children will be more affected.

Zhu Yuanzhang couldn't figure it out, and judging from the comments, this situation was very common. Almost everyone had experienced it, and most people were extremely disgusted with it.

To take a big step back, if you want to test students' reading and comprehension abilities, you are not testing them on the subject of mathematics. This is totally untenable.

Many people shook their heads when they couldn't figure it out. Any test is a test of knowledge, not the ability to use words. If you can't accurately express the meaning of the question, it only shows that there is something wrong with the person who set the question.

Especially questions with so much ambiguity should not appear at all.

"This mathematical symbol system can be used." Liu Ji said after a pause. Things in the future are too far away from now. Even if they join in the criticism, it will be of no avail.

Because this set of symbols is concise and has strict rules, it can express and convey information more accurately, especially with the example before us.

Zhu Yuanzhang nodded without thinking too much, and specifically reminded him that division and dividing by have the same meaning.

With these symbol replacements, future calculation formulas can actually be simplified a lot.

"Mathematical symbol systems can effectively avoid linguistic ambiguity. This kind of question is the opposite of the truth."

"The biggest problem here is not whether the question itself is rigorous, but whether it should be asked in this way. Such questions do not test mathematical knowledge and are of no help in cultivating interest in mathematics."

(End of this chapter)

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