Fold a piece of paper in half 103 times, and the universe may not hold it? How terrible is the exponential explosion?

Do you know that?/You know what? Do you know that?/You know what? A piece of ordinary A4 paper is folded in half for 39 times, and its thickness is longer than that of eight Yangtze rivers. After being folded in half for 42 times, its thickness exceeds the distance between the earth and the moon; When it is folded in half 103 times, its thickness far exceeds the boundary of the universe that humans can observe at present. Are you surprised by this set of data? But in fact, a piece of paper can't be folded so many times at present.

Ordinary A4 paper has a length of 2 10/0mm, a width of 297mm and a thickness of about 0. 1 mm. If such a piece of paper is folded in half once, its area will be reduced by half and its thickness will be doubled. This paper has been folded in half for 7 times, and it has reached 128 layer, and the thickness is about 13mm, which is similar to an ordinary book.

If there is no other means, it is difficult for us to continue to fold in half. So, someone moved out of the hydraulic press to help, but during the eighth folding, the paper broke and failed.

Some people may say that A4 paper is too small. If the paper is large enough, the result may be different. In fact, this idea has been tried abroad.

They found a piece of paper the size of a playground to do the experiment and folded it effortlessly for 8 times. At this time, the area of this paper has changed from the whole playground to a room. At the same time, they couldn't continue folding themselves, so they had to send tractors to rescue them. Even so, after folding 1 1 times, there was no machine to help, and the paper began to appear obvious damage, so the experiment was terminated. Some people may say that A4 paper is too thick.

In fact, in 2002, a foreign female middle school student successfully folded the toilet paper in half 12 times, and her casual behavior successfully created a new Guinness World Record.

In 20 12, the teachers and students of St. Mark's Middle School in Texas decided to challenge this record. They folded a piece of toilet paper more than four kilometers long in half for thirteen times, reaching a full 8 192 layer. However, for various reasons, this record has not been officially recognized.

Then, why can't a seemingly easy thing like origami be realized after a certain degree? This actually involves a famous mathematical concept, called exponential explosion, that is, under the condition that the radix is greater than zero, every increase of the index will cause great changes in the results, so the index is also called the devil figuratively in mathematics.

There have been many anecdotes about this concept. In the ancient history of our country, there is a story that uses exponential explosion to achieve its goal. The hero of the story is the famous Ming Taizu Zhu Yuanzhang.

Shen Wansan was once the richest man in Jiangnan. When Zhu Yuanzhang led an army to capture Jiangsu and Zhejiang, Shen Wansan knew that he was a die-hard fan and his life might be in danger. Instead of waiting passively, he might as well take the initiative to be better to himself. So he offered tens of thousands of loads of grain and 5,200 pieces of silver to Zhu Yuanzhang, built a third of Nanjing, and asked for capital to reward the army. But even so, Zhu Yuanzhang did not dispel his fears, but began to try to seize his property.

One day, Zhu Yuanzhang called Shen Wansan, gave him a penny, and ordered him to pay back two pence the next day, four pence the third day, and eight pence the fourth day. According to this rule, he still paid back. It is said that Shen Wansan finally paid more than 500 million pence. It can be seen that Zhu Yuanzhang may not know the concept of exponential explosion, but he knows the great power of exponential explosion.

Not only in China, but also in ancient India.

It is said that once upon a time there was a very playful Indian king. One day, he told his courtiers that he wanted something he could never get tired of seeing, and whoever could satisfy his wish would get a rich reward. Soon after, a clever minister gave him a kind of chess and told him how to play it. After playing, the king found himself never tired of playing, so he planned to keep his promise and ask the minister what reward he wanted. The minister said that he only wanted some wheat.

The king was a little surprised and asked, "So, how many pills do you want?" The minister replied, "Your Majesty, there are 64 squares on the chessboard I presented to you. You just need to put 1 in the first box, 2 in the second box, 4 in the third box, 8 in the fourth box, and so on. The number of particles in each square is twice that of the previous one. Just fill 64 squares. The king didn't expect the minister's wish to be so simple, so he readily agreed and ordered his men to prepare.

After receiving the task, the minister in charge of this matter began to calculate the specific amount. I don't know. He calculated and hurried to the king to report: "Report to your majesty, even if you have the strength of the whole country, I am afraid you can't satisfy his wish!" " As he spoke, he presented the recipe to the king. The king saw a long list of dazzling numbers, so he ordered, "Specifically, how much are these?" The minister quickly replied, "The volume of 1 50,000 grains of wheat is about1m3. If you follow the requirements of the minister, you need to prepare120 billion cubic meters of wheat! "

When the king heard this, he could not pretend to be calm. He couldn't help thinking: as the king of a country, since I have publicly made a promise, wouldn't it be a shame not to give it to him? But there are so many grains of wheat that I can't take them out anyway, so I don't have to embarrass him then. So he asked the minister with a livid face, "What do you think?" The minister thought for a moment and replied, "You just need to open the granary and order the minister to count the rewards he got one by one." Imagine if he can count two grains of wheat a second and 12 hour a day, then he can only count 86,400 grains a day and 2 cubic meters a year. It will take 600 billion years to count them all. How many years can he live? "The king immediately smiled and promoted the clever minister.

After learning so many stories about exponential explosion, do you have a deeper understanding of the charm of mathematics? When you see an ordinary A4 paper again, will there be some different ideas in your mind?