An explosion occurred at a factory near Pittsburgh, Pennsylvania on the morning of the 11th, killing two people.

　　CCTV reporter Liu Xu:Behind me is a factory of American steel company that exploded on the 11th. When the explosion occurred, people within a few kilometers nearby heard the thunderous explosion and saw the smoke that covered the sky. On the morning of the 12th local time, we came here for a visit. Through the picture behind me, we can see that there are very clear burnt marks in the factory. The fire department is still cleaning up, and relevant departments are also conducting preliminary investigations. It is reported that the factory is in stable condition at present.

　　On the 12th, Pennsylvania Governor Shapiro said that the current priority is still to carry out safety clean-up work and provide assistance to the families of the victims. At the same time, they also asked American steel companies to assist in the investigation.

　　According to American media reports, the factory involved is the largest coking plant in North America, employing about thousands of workers. The factory had explosion accidents in 2009 and 2010, which caused casualties and long-term pollution problems.

　　CCTV reporter Liu Xu:After this explosion, local trade unions and people called for a comprehensive investigation. Environmental organizations also said that,The explosion is not an isolated incident, but a continuation of the lack of safety and supervision, and it requires an immediate assessment of whether the factory can continue to operate.

　　Local residents hope to thoroughly investigate the factory explosion.

　　CCTV reporters found that some houses were hit by the explosion not far from the factory.

　　CCTV reporter Liu Xu:It can be seen that the house was damaged by the impact of the explosion. This is a house made of Shi Zhuan and cement. In front of the porch, you can see obvious cracks.

　　The owner of this house is Adrian. She has lived here for more than 20 years. In her memory, there are production safety accidents in this factory every few months, which makes people living here feel very unsafe. In her daughter’s memory, this explosion is the fourth safety accident this year.

　　Adrian, a resident near the factory:At about 10: 45, I heard a huge explosion. My house shook violently, the whole house shook and the bed shook. I jumped up. I thought a car had hit my house. I came out to see that there was no car, so I went to see the alarm and found a 911 call coming in, saying that there was an explosion in the factory below. Then I drove down to have a look and saw a lot of smoke.

　　Adrian said that this explosion is likely to be the same as before, and the final investigation results will once again conceal many real situations. As a resident living near the factory, she is often affected by factory safety accidents, which she can’t accept.

　　Adrian, a resident near the factory:This industry often hides the truth of many accidents. I don’t think companies will tell us the truth. I know they won’t. Companies hide many things, including American steel companies, and will only tell us what we want to hear.

　　Adrian’s daughter doesn’t live near the factory, but she is not surprised by the explosion. She just wants an answer, how to learn a lesson and avoid such a safety accident again.

　　Adrian’s daughter Tracy:I’ve always been worried because this industry is accompanied by risks. When these factories are built near residential areas, the risk is higher, and even there is the risk of chemical pollution. The whole community is worried about the impact, which is what I have been worried about. I think it is the most important thing how we can avoid such safety accidents from happening again.

Fengse compiled from the concave temple

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In the history of mathematics, there is a famous problem of "turning a circle into a square".

It was put forward by an ancient Greek philosopher in prison in the 5th century BC. It is about drawing a square with a compass and a scaleless ruler to make its area equal to that of the circle.

However, no one expected that this problem has been puzzling mathematicians for more than 2000 years.

In the end, it was discovered by everyone, and it was impossible to draw it.

The reason is related to π being a transcendental number-

Yes, π is a transcendental number besides the irrational number identity known to primary school students.

When it comes to transcendental number, it’s a really hard concept to understand, and no number of professional textbooks can make it easy to understand.

It can only be said that it is a class of irrational numbers, but it is more "unreasonable" than irrational numbers. .

From the 18th century to the present, back and forth for more than 200 years, a large number of mathematicians from various countries have pounced on it, looking for evidence to prove its existence and ways to judge it.

However, this "little thing" is so elusive that until now there are still many suspected figures that have not been proved and a lot of open problems related to it have not been solved.

"Terrible" is that many mathematicians said:

In fact, I know that it is useless to find out which number is beyond the number, but I just can’t stop!

Therefore, today’s article is a dry issue of mathematics, which comes from the column of Quanta Magazine (author David S. Richeson). It is the most clear and easy-to-understand article that tells the ins and outs of transcendental numbers, and is hereby compiled.

Then, blessed are those who like mathematics today-

Love beyond a few times again, and see how it was discovered by mathematicians and how it was related to that Millennium problem.

The Unsolvable Problem of "Turning a Circle into a Square"

Mathematician Leopold Kronecker famously said:

God himself created natural numbers, and the rest came from human power.

Nowadays, although all kinds of numbers have a fascinating and complicated history, basically everyone has a clear definition of them.

For example, integers are positive integers and zero plus negative integers. Rational number is a number that can be expressed as the ratio of two integers, including integers, finite decimals and infinite cyclic decimals.

If the decimal places of this ratio are never divided and never repeated, it is an irrational number.

Then rational numbers and irrational numbers together form real numbers, and real numbers and imaginary numbers form complex numbers.

Among them, today, we all agree that rational numbers were discovered by hippasus, who lived around the 5th century BC (and he died because of it).

But in fact, his discovery belongs to geometric meaning rather than arithmetic.

He proved that you can find two line segments that cannot be divided into several equal lengths, such as the sides and diagonals of a square.

Today we call this incommensurability, which means that their lengths are not rational multiples of each other.

Therefore, the diagonal length of a square is √2 times the side length, and this √2 is called an irrational number.

Undoubtedly, using compasses and straightedge, we can draw a line segment with any positive rational length.

However, some unreasonable lengths are also acceptable. For example, in the famous golden ratio (1+√5)/2, draw a regular Pentagon with a side length of 1 and take its diagonal.

In 1637, the famous mathematician Descartes proved:

As long as a number can be represented by integer operations of addition, subtraction, multiplication, division and square root, then we can draw the corresponding line segments (such as all positive rational numbers, as well as the √2 and the golden ratio just mentioned).

Therefore, if we can express π with an exact formula, can we solve the problem of "turning a circle into a square"!

The problem is, I can’t find it.

In a blink of an eye, 200 years have passed (two centuries have passed).

A French mathematician named Pierre Wantzel finally proved:

If a number can be drawn by line segments, that is, it can be constructed, then it must also be the root of a polynomial that cannot be further factorized or simplified, and the degree of the highest term of this polynomial is a power of 2 (such as 2, 4, 8, 16, etc.).

For example:

√2 is the root of the polynomial x2–2, and the golden ratio is the root of x2–x–1, so they can all be drawn.

And like 3; √2 is the root of the polynomial x3–2, which does not meet the condition of the second power, so it is impossible to draw a line segment of this length.

However, even if we know this law, we still haven’t found the exact expression of π, and the problem of turning a circle into a square is still unresolved.

It was finally proved that it could not be drawn at all.

In fact, the key to solving the problem of turning a circle into a square is just like mathematicians divided real numbers into rational numbers and irrational numbers before-complex numbers need to be divided into two sets.

For complex numbers, many of them are equal to the roots of polynomials with integral coefficients, which mathematicians call algebraic numbers.

Every rational number is an algebraic number, and so are some irrational numbers, such as 3; √2, and even the imaginary number I, it counts, because it is the root of x2+1.

Not all complex numbers are like this, so the values that do not belong to this category are called transcendental numbers.

However, it is not obvious whether a transcendental number exists, and it is also very challenging to prove whether a given number is transcendental, because it is necessary to disprove that a number is not the root of any integer coefficient polynomial.

The first breakthrough point was born in 1844, and a French mathematician named joseph liouville thought of such an indirect method:

Since irrational numbers can’t be well approximated by rational numbers, if I find a number that can be infinitely approximated by fractions with smaller denominators, it must be something else: transcendental numbers.

So, Joseph Liouville constructed such a number:

L=0.1100010000000000000000010…

It has only 0 and 1, where the position of 1 appears in turn by "n!" Decide that the position of the first 1 is equal to "1!" , that is, 1, and the second is equal to "2!" , appears in the second place, and the third is equal to "3!" , in the sixth place, and so on.

This ingenious design makes the scores of 1/10, 11/100 and 110001/1000000 very close to the value of L itself.

This proves the existence of transcendental numbers (that is, he created this L).

However, the number π does not satisfy Joseph Liouville’s condition (it cannot be infinitely approximated by rational numbers), so it is not clear whether π is beyond the number.

The important breakthrough came in 1873, nearly 30 years later.

A French mathematician named Charles Hermite designed a clever method to prove that the base e of natural logarithm is transcendental.

This is the first transcendental number that is not artificially designed, which makes Lin Deman, a German mathematician, finally prove that π is a transcendental number on the basis of his theory nine years later.

First, he proved that as long as D is a nonzero algebraic number, ed is a transcendental number.

In other words, if ed is an algebraic number, but d is either 0 or transcendental.

In this case, based on Euler’s identity, which is recognized as the most perfect formula in mathematics, eπ i = 1, the category of π can be deduced.

Because -1 is an algebraic number, πi must be a transcendental number based on the theorem just now, and π must be transcendental because I is also an algebraic number.

In this way, "big things are not good"-

π is a transcendental number, which means π does not meet the definition of "line segment that can be drawn" mentioned in the previous paragraph, so the problem of turning a circle into a square put forward by ancient Greek philosophers thousands of years ago is impossible to realize.

The story is not over yet.

The story of turning a circle into a square is over, but the exploration of transcendental numbers has just begun.

Shortly after E was proved to be a transcendental number, another mathematician proved that infinite numbers actually have different sizes, but the infinity of rational numbers is the same as the infinity of integers. Such a set is called "countably infinite".

However, the set of real numbers and irrational numbers is larger, which is uncountable infinity; At the same time, although the algebraic number set contains all rational numbers and infinitely many irrational numbers, it is still an infinitely small and countable infinite set.

Therefore, its complement, that is, transcendental number, is uncountable and infinite.

In other words, most real numbers and complex numbers are transcendental numbers.

-Although there are so many excesses, by the turn of the 20th century, mathematicians could only identify a few of them.

In 1900, the famous German mathematician David Hilbert listed a famous list of 23 most important unsolved mathematical problems, the seventh of which was:

It is proved that when A is an algebraic number and is not equal to 0 or 1, and B is an algebraic irrational number, ab is a transcendental number.

In 1929, Aleksandr Gelfond, a young Russian mathematician, proved that B = I √ r and r are special cases of positive rational numbers, which means that eπ is a transcendental number.

This result is surprising, because according to the theorem, e and π are not algebraic numbers.

However, by manipulating Euler’s identity skillfully again, we know what’s going on:

Soon after, another mathematician discovered that 2√2 was a transcendental number. Then, the seventh problem listed by David Hilbert was solved by two mathematicians independently.

Later, Alan Baker, a mathematician, published a series of articles, summarizing the achievements of these people, which made us have a deeper understanding of transcendental numbers, and therefore won the Fields Prize in 1970.

Of course, at the age of 31, his greatest achievement in winning this honor is to prove that two values such as the following are also transcendental numbers:

Until now, there are many open questions about transcendental numbers, and there are many concrete numbers that seem to be "very transcendental", which have never been proved, such as "eπ", "e+π", "ee", "π π" and "π e".

But as said at the beginning, the mathematician said:

It may not be useful to know who is above the number, but if we have the ability to know but choose not to know, it is definitely unacceptable.

Seriously respect.

Original link:

How Math Achieved Transcendence

End—

Advances in science and technology meet every day ~

Original title: "The irrational number in this irrational number makes mathematicians call" it can’t stop at all ""

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The dictionaries and dictionaries in ancient China, such as Shuo Wen Jie Zi and Er Ya, have some Chinese medicine terms, but they are not professional Chinese medicine dictionaries after all. Although some Chinese medicine books, such as Complete Records of Ancient and Modern Books Integrated with Medical Department, are arranged together according to the times, the style and norms do not meet the basic characteristics and requirements of dictionaries. The laurel of the first comprehensive dictionary of traditional Chinese medicine in China belongs to China Medical Dictionary compiled by Xie Guan.

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Xie Guan, whose name is Liheng, is a man of the hour in the field of modern Chinese medicine. At that time, Chinese medicine schools, societies, magazines and other institutions all scrambled to hire him, and his "bearded man" photos were frequently published in various newspapers and magazines, but there was no introduction about his early study and work experience. Looking at the Biography of Mr. Xie Liheng written by his fellow countryman Lv Simian on April 1, 1935 and the Biography of Mr. Xie Liheng written by his disciple Chen Cunren in March 1951, Xie Guan’s general resume before he became the principal of Shanghai Special School of Traditional Chinese Medicine in 1917 is:

Xie Guan’s father, Xie Zhongying, was a master of geography. When he was a teenager, Xie Guan was intelligent and studious, and inherited his family studies. At the age of 12, he finished reading the Four Books and the Five Classics, and he knew all about China’s ancient and modern mountains and rivers like the back of his hand. At the age of 15, he entered Changzhou to use Jingshe and devoted himself to the study of classics, history and geography. 21-year-old graduated from Soochow University in Suzhou. In 1905, he was invited to teach in guangzhou fu Middle School as a geography teacher. In 1908, due to her mother’s dissatisfaction with Lingnan soil and water, she resigned to Shanghai and took a job in the Commercial Press to compile geography books. Soon he was hired as the principal of Shanghai Chengzhong School. After 1911, he returned to his hometown of Wujin to take charge of education, and within two years, the county’s educational achievements ranked second in the country. In 1914, he still entered the Commercial Press, mainly compiling geography books.

Obviously, before the age of 35, Xie Guan had no experience in studying medicine, let alone taking medicine as his profession. How could he compile a dictionary of traditional Chinese medicine with a detailed analysis and novel style in a short time?

The article "Xie Run" in China Medical Dictionary says: "The word" Bao Chu "was attached to Wujin County in Qing Dynasty … and he wrote fifty volumes of" Medical Jingwei ",which was not published yet. His grandson’s view was analyzed and expanded because of his manuscript, and became the China Medical Dictionary. " From now on, we can easily know that Xie Guan is based on the original manuscript of Medical Jingwei that his grandfather didn’t publish, "taking the theory system of past dynasties as the explanation", and "judging the trade-off by the new theory of evidence", and expanding it into China Medical Dictionary.

Compilation process

Regarding the origin of compilation, Lv Simian said in the Biography of Mr. Xie Liheng: "Those who treat China medicine should compile dictionaries, so that the Commercial Press can be the king." However, Xie Juzeng’s "The Past of Hanfen Building" said: "Xie Guan … first edited geography textbooks for primary and secondary schools in the Chinese Language Department, and later transferred to the Dictionary Department to participate in the compilation of China Medical Dictionary and China Celebrity Dictionary." It is difficult to know whether the Chinese medicine academic circles require the Commercial Press to organize the compilation or whether the Commercial Press initiates the compilation itself.

As for the beginning and ending time of compilation, Xie Guan said in the preface of China Medical Dictionary (1921 edition): "In the early Republic of China, it was not as long as the Shanghai College of Traditional Chinese Medicine, that is, it was interested in remedying this disadvantage, but the matter was big and it was difficult to take care of it." After reading, it is necessary to delete complexity, which is nothing more than a dictionary. It is in line with the students of the whole school, and they test each other. Everything contained in the classics is analyzed in detail, and it is learned and searched, and its repetition is deleted, and its empty theory is cut, so that it is difficult to distinguish the purpose of criticism, and the words of floating algae decoration are saved. Cheng Gong went to 67 … The first edition was completed. " From this point of view, the compilation began in the spring of 1921 after the establishment of Shanghai College of Traditional Chinese Medicine in 1917, which lasted for four years. But he also said "Cheng Gong to 67", so the time can’t coincide. However, from 1914, when Xie Guan joined the Commercial Press for the second time, to 1921, it happened to be "67".

As for the people who participated in the compilation, Chen Cunren said in the article Biography of Mr. Xie Liheng: "There were 12 people who assisted the Dictionary, and they worked hard day and night, repeatedly deleting and adding, and repeated several drafts. It took eight years to complete the book. I will pay for it. Unexpectedly, of these twelve people, two are sick from overwork and four are cured. " This should be said to be the situation in the "first edition" in 1921. By the time of the second edition in 1926, there were as many as 66 people who participated in the revision. The list of "people subscribed" was found in the "reprint" of the Commercial Press in 1954, and it was the only one who kept the list of editors in all the editions of China Medical Dictionary so far.

此外，1952年吕思勉在《自述——三反及思想改造学习总结》一文中说：“一九一九年，入商务印书馆，助谢利恒君编辑《中国医学词典》。予于医学，本无所知，而先外王父程柚谷先生、先舅氏均甫先生、先从舅少农先生，皆治汉学而兼知医，故予于中国医书之源流派别，略有所知。谢君本旧友，此时此书亟欲观成，乃将此一部分属予襄理。至暑假中事讫。”由此可知，吕思勉也曾经参加过《中国医学大辞典》的编撰工作。“至暑假中事讫”，是说吕思勉负责的部分于1919年暑假完成，还是整部《辞典》编撰告竣，我们已很难考证清楚了。

体例内容

全书“搜集之名词，以中国原有医书所载者为限，故定名为《中国医学大辞典》”。所辑词目，包括病名、药名、方名、身体、医家、医书、医学七大类，共三万七千余条目，约计三百五十余万字。排列方法以首字笔画为序，首字相同者则以次字笔画为序。为方便检索，还编有《辞头索引》《辞条索引》。

China Medical Dictionary was first published by the Commercial Press in July 1921, revised and reprinted in July 1926, and published again in August 1933, and marked as "the first edition after the national disaster". In 1951, Chen Cunren said: "Up to now, there have been more than one million copies published in 32 editions, which are sold in various countries." After the founding of New China, the Commercial Press reprinted it three times in December 1954, April 1955 and August 1955 in order to cooperate with the central government in implementing the Party’s policy on traditional Chinese medicine.

Needless to say, there are some mistakes in the annotations of some entries in the China Medical Dictionary. As early as 1928, Yu Zeming wrote in the Health News that the transliteration of resin "Balsamo" was mistaken for the real name of the drug (a mistake in the China Medical Dictionary). In 1933, Yang Yan and the Medical Chunqiu clearly proposed that it should be supplemented and revised comprehensively (the China Medical Dictionary has If measured by the current dictionary style, there are still some shortcomings, but the defects do not cover up Yu, and it is still an important reference book to benefit the medical forest and enlighten the later study. (Zhang Xiaoxia)