【Article/Observer Network Columnist Wen Bo】
Since the mobile terminal has become the most efficient information carrier in China, all kinds of advertorials and myths have completely surrounded us through the circle of friends, public accounts and Weibo paragraphs.
I will not talk about the low-level articles that talk about positions without logic, and do not talk about views without facts, but this time I will talk about a typical blowing hydrology that is relatively high at first glance, to see how the weaknesses of human nature are exploited, how our national inferiority complex is instilled, and how the myths of Western science and technology are woven.
The article was issued by a mathematics graduate of a traveling law department on zhihu, and the article has a major feature of similar articles from the beginning, first throwing out a shocking point of view to calm you:
"In the 18th century, almost only military cadets taught mathematics in France, and the mathematical level of artillery officer engineers was comparable to that of non-mathematical majors in 985 today."
The logical chain of this respondent is as follows:
1. The book was a dedicated textbook for French artillery at the time, and his evidence was the phrase "avec approbation et privilège du Roi" on the cover page of the book.
2. He takes the example of the derivation process of a mathematical formula in the book, claiming to be a mathematical model of high difficulty, and the difficulty of derivation is also very high, exceeding the level of most non-mathematics students in 985...
3. From these two points, he concludes that the students of the French artillery school two and a half centuries ago have far exceeded the mathematical education level of non-mathematical majors (such as physics and engineering) in our key universities today.
The full Q&A can be answered through this portal: How good was the napoleonic artillery math? " to take a look. Almost the perfect sample answer to Zhihu Gaozan: not too long and not too short; the conclusion is subversive, but there are a lot of pictures, and even videos, so it is basically not boring, nor is it self-explanatory, and at the same time contains a lot of information that is relatively unfamiliar to ordinary people, ensuring the freshness of reading.
However, at the beginning, the so-called "textbook" that was used by this zhihu respondent as the first example of French superiority revealed his completely wrong understanding of the book:
The left picture shows the cover of the French version and my notes, and the right picture shows the cover of the original English book in 1742
First of all, he was completely mistaken about some basic information about the book.
1. The author of the book is Benjamin Robins (Benjamin Robbins), obviously an English name, and the second author, the name of the great mathematician Euler, hints at the book's simplicity.
In fact, Mr. Robbins is the father of modern ballistics, known by the Germans as the "founder of German experimental aerodynamics" (yes, you are not mistaken in Germany), was born poor, did not have the opportunity to receive a good education in childhood, but through his own efforts to write and other works, made outstanding contributions to the development of mathematics and applied mathematics, and was recognized by the academies of sciences of all countries at that time.
Published in England in 1742, the book was later supplemented and translated into German by the great Swiss mathematician Euler, and published in Germany in 1745, receiving much attention from the Prussians. Guided by cutting-edge theory, the accuracy of prussian artillery fire overwhelmed the numerically superior French forces in the following seven years' war. As a result, throughout the Seven Years' War, the French Army performed badly on the European battlefield and had little sense of existence.
However, the slow French did not finally introduce the translation of the book until 1776, a full generation slower. To know that in the preface of this book, the translators themselves are complaining about why France knows nothing about such an important work, and I don't know how the three authors will feel when they hear that the respondent actually uses this book to boast about the academic level of France. Euler, who spoke French, estimated laughing and not speaking.
2. The so-called French "avec approbation et privilège du Roi", which literally means only with the authorization and permission of the king, is published without a single word as a teaching material.
In fact, in 17th-century Europe, copyright protection had been formed, and France had implemented a strict censorship system for publications. No work can be published without examination by the royal family or educational institutions. The above French phrase actually means to publish by authorization, and it is found in all published books.
What's more, when Mr. Robbins wrote the book, the English version was a 190-page pamphlet, while after revision and translation, the French version became a tome of more than 500 pages. The book is a discussion and commentary on dozens of issues. It is clearly an academic work of ballistics, a reference book for research, rather than a textbook for practical artillery students.
So what did the Napoleonic military school mathematics textbooks look like? Thanks to the digitization of ancient texts, the real textbook looks like this: "Cours de Mathematiques" (mathematics course) in capital letters, and "for use by the Royal Artillery Unit" underneath. The whole book is divided into four volumes, as for the content we look at the example problem to understand, first of all, elementary algebra, because there is no calculator, requiring students to master the manual square root:
Plane trigonometric function:
Polynomial expansion:
It can be seen that the first two books only talk about arithmetic, geometry and trigonometry, which is basically equivalent to our high school textbook, and has no content of advanced mathematics. Only in the last two volumes does some of the contents of high numbers and mechanics be covered, and are taught together:
It can be seen that it is also the general university physical content. Chinese polytechnic non-mathematics students have completed advanced mathematics, linear algebra, differential equations, probability theory and mathematical statistics, complex variable functions, and university physics or chemical analysis in their freshman and sophomore years.
Let's not say that many theories did not exist in Napoleon's time, even if the theories that existed in that year are now the basic subjects of colleges and universities, and the military schools of that year are still training the mathematical content that we have already mastered in middle school. It can be said that on the depth, today's college mathematics textbooks are by no means easier than they were then, and on the breadth, it is really interesting to travel back in time to bully the ancients?
Ballistic pendulum
And the description of a passage of "differential equations" in the book by the zhihu respondent is even more hilarious.
He said this: "This section of the textbook studies the vibration of the pendulum, which is roughly a single pendulum fixed at the bottom of the cannon, if the barrel is too long and too thick, it will shake when firing, so this mathematical model is made." It is estimated that he saw the word "le pendule" ("pend") in the original book and automatically made up his brain to "regard the cannon as a single pendulum, and the cannon will shake." In fact, as long as you search for the author of this book + pendulum, it is easy to see the results of the ballistic pendulum (ballistic pendulum), and if he turns to the drawings at the back of the book, he will also see what this pendulum looks like:
Ballistic pendulum was originally used to measure the velocity (initial velocity) of a bullet as it leaves the chamber, and knowing the initial velocity, the height and range of the shell can be calculated according to the parabolic principle.
In fact, the principle of high school students can easily understand: let the bullet hit a pendulum with a mass much greater than its own, push the pendulum swing, and according to the single pendulum principle, the momentum of the bullet can be known from the amplitude of the swing, so as to obtain the speed of the bullet. Of course, if this process is to be precise, it is necessary to take into account the loss problems such as air resistance, the actual size of the pendulum and friction.
Benjamin Robbins' main contribution was to propose a new theory that allowed engineers to incorporate air resistance factors to more scientifically measure the initial velocity of a bullet and even the initial velocity of a shell with a ballistic pendulum.
In fact, as known from high school physics, the transmission of momentum is related to the mass of two objects, and when a lighter object hits a heavier object, the exchange of velocities depends on the inverse ratio of their masses.
When we use the pendulum to measure the bullet is fine, because the bullet is only a few grams, and tens of kilograms of cast iron is very cheap, and it is easy to make a pendulum. But if it is used to measure shells, it is different. It should be known that the solid shells used for young artillery should also have 6 pounds, almost 5 pounds, and the speed of shells out of the chamber can generally exceed 1 times the speed of sound, while the Navy's heavy guns can easily reach more than 40 pounds. In order not to let the ballistic pendulum be directly destroyed by a cannon, the pendulum must be made very heavy, so that the speed of the pendulum swing can be reduced to the range that the material at that time can withstand.
In 1803, the French built a ballistic pendulum in Metz weighing 12,000 pounds to handle shells up to 40 pounds, which is about the same length. It can be seen that in addition to mathematical problems, there are more problems in engineering difficulty.
From the perspective of actual military combat needs, the officers who commanded artillery in the front line at that time were far from needing to become a humanoid self-propelled differential equation solver. When the main combat method of artillery is still in the line of sight combat, the response speed of combat to dynamic targets is not low. On the other hand, because everyone is a dense array of rows, the accuracy requirements for shelling are not so high. Many of the actual operations are to fire a shot first, and then the artillery adjusts according to the impact point of the shell.
In addition, it is estimated that this classmate did not know that the artillery also had such a thing as a shooting table. In practice, the artillery only needs to find out how much gunpowder should be placed according to the type of artillery and shells, and the distance of the target, and how many degrees should be placed at the elevation angle of the artillery (the term is called measuring the elements). The Navy, which has always needed to move, has invented a tall mechanical ballistic calculator to complete the aiming solution. Later, when artillery was faced with more and more problems of over-the-horizon strikes (that is, hitting things out of your line of sight), the development of the electronics industry was able to provide handheld ballistic computers.
It can be said that the situation of a bunch of officers scrambling to solve the differential equations by hand in the rumbling battlefield may only exist in the brain supplement of the students on paper.
Shot table: The row value is the gun elevation angle, listed as the charge, and the Q value in the table is both the estimated range of the gun (in approximate feet).
And there's a derivation of that so-called differential equation, well... Isn't that the simplest partial integral?
Let me sort it out:
Because
According to the partial integral, it is obtained
Then expand the right integral term with another partial integral to get an integral term similar to the original:
Just a simple move of the item can be calculated
I believe that the students who did not herd sheep in the first year of high school should be able to easily understand, but I really don't understand why this so-called mathematical student is so excited to see a division integral, so that he wants to take the mathematics of Chinese colleges and universities to make a splash? To show his pride in learning mathematics in France? Seeing the answer to the "study abroad application consultation + micro 38 ****25; learning education + public number: *** Sir" I seem to understand what ...
After that, the low-level errors and forced explanations of using parallel drawing rulers for navigation as slide rules are not to be said.
In summary, this article from the basis of interpretation, logical reasoning to conclusion may only be counted as incomplete and fallacious, but it still receives 2500 likes that far exceed the second place, occupying the first place, and receiving many big V likes.
It can only be said that in the process of disseminating information, we are still deeply affected by the weaknesses of human nature, often unable to distinguish between appearances and essences, and are intimidated by many pictures, numbers, and seemingly reasonable words, so as to easily accept the indoctrination of the author's views. And once this indoctrinated view takes root in the subconscious, it resonates with more similar views, forming a cycle that ends up stubbornly rejecting any different point of view.
For example, the famous German sewers, oil-paper package engineers, American domineering passports, Japanese toilet circle rice cookers, etc., these are repeatedly processed and disseminated around us, the level of high or low paragraphs, the so-called foreign moon is more round This inferiority psychology implanted in our national heart, still makes a considerable part of the Chinese people obsessed with foreign products, blind pessimism about their own country, blind worship of foreign society and even blind immigration.
From another perspective, we can indeed see that the West is historically ahead of ourselves.
In the Qing Dynasty in the 18th century, our artillery was neither an independent branch nor a science. When Western mathematicians began to apply abstract mathematical theories to practical military engineering problems, when they had begun to consider calculating air resistance with differential equations, we were still only in the stage of relying on metaphysics to shoot cannons, satisfied with the metaphysical superstitions of XX Shenwei, killing cattle and sacrificing wine before firing cannons, burning incense and worshiping gods, leaving a historical record of "one shot eroding for miles". It is no wonder that after a century, people can set up a cannon on our coastline to make the great empire submit, metaphysical warfare science, how to fight this battle?
For this tragic history in the past, the lesson we should learn is actually very simple, that is, the take-ism that everyone knows in middle school. The reason why the West was so advanced in the past was nothing more than seeking truth from facts, respecting the law, and scientific thinking, and as for what kind of gods and gods, racial superiority or some honey-juiced and confident electoral system, it has never been the main reason for their rise.
But if we can't just sit still, just stay in the pile of rhetoric, indulge in the sensory stimulation brought by media such as fast-food short videos, and be satisfied with the illusion of fragmented knowledge given by online storytelling programs, then we are still far from a truly modern society, an innovative economy, or an individual who can think independently.
References:
1.Permissions, approvals, privileges, censorship before the French Revolution: publishing under the control https://bibliomab.wordpress.com/2012/01/06/permissions-approbations-privileges-censure-avant-la-revolution-francaise-ledition-sous-controle/
2.Johnson, W. (1992). Benjamin Robins (18th century founder of scientific ballistics): some European dimensions and past and future perceptions. International journal of impact engineering, 12(2), 293-323.
3.Mathematics course, for the use of the Royal Artillery Corps: Concerning the application of the General Principles of Mechanics, in different cases of movement & balance, Étienne Bézout
4.New Principles of Gunnery: Containing the Determination of the Force of Gun-powder, and an Investigation of the Difference in the Resisting Power of the Air to Swift and Slow Motions. With Several Other Tracts on the Improvement of Practical Gunnery，Benjamin Robins