[Scientific Essay] What is the second language you learned first?
Age of Languages
We live in the age of language. As the market becomes global, more and more people are learning not only just one second language but also another second language. Companies also require language skills for job seekers. When filling in an application form, engineering students think it would be great if they could write C #, C ++, JAVA or Python as language skills. If so, they could write 4 more languages as well as their second language. But, I have this kind of idea. "Why do not they write down those kinds of languages? The application form does not say 'foreign language' but just 'language'. In addition, the definition of language according to the dictionary is "the method of human communication, either spoken or written, consisting of the use of words in a structured and conventional way". A programming language is also the method of communication. The only difference is that a listener is a computer. Do you agree that it is also a language? So, this is the beginning of my article. What is the second language you learned first?
The lingua franca of the world
My guess is that the second language you learned first is mathematics. Since after you cried out "M...m..om!", you would have begun playing with the alphabet cards with the letters A, B, C, etc, and the numbers cards with 1, 2, 3, etc. Then, since your first word was "mom", English is your first language you learned. And since you learned the letters 1, 2, 3, etc that are the basics of mathematics, mathematics is your second language you learned first. Because nobody start to learn other letters before A,B,C and 1, 2, 3, mathematics must be your second language you learned first. Of course, 'mathematics' itself is not a language. Strictly speaking, it would be better to call it as 'mathematical language'.
The 'mathematical language' is a language system that consists of many symbols and conveys information only in letters. Because the letters of most ordinary languages are associated with their spoken language, the language system without spoken language is not a familiar concept. But it is certainly also a language. For example, sign language does not correspond to the spoken language but has its own grammar, because the deaf people have never heard the spoken language. Sign language is not associated the spoken language but transmits information in the form of a hand gesture. The same is true of 'mathematical language'. It does not associate with the spoken language but transmits information independently in the form of a letter.
The writing systems that conveys information in letters can be broadly categorized into alphabet, syllabary, and ideography. alphabet and syllabary are the phonetic system that only corresponds to sounds, not meanings. And ideograms correspond to meanings. There is a way to read the ideogram verbally, but how to read it is not a big issue. Typical examples are alphabet for Hangul(Korean), syllabary for kana(Japanese), and ideography for Hanzi(Chinese). It is interesting that the three countries that located side by side have very different languages and writing systems.
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According to the classification of letters, the mathematical language can be divided into ideography. Chinese, Korean, and Japanese each read the letters "天" in different ways as "tiān", "cheon", and "ten", but all three countries get the same meaning of "sky" from the letter. We read the expression below, " One plus one is two" in English, but Korean read it like "il deohagi il eun ee". Nevertheless, you can get the same information no matter who speaks Korean or English.
A mathematical language can not convey information of daily life, but it conveys mathematical information very efficiently. Even if you cannot switch to spoken language, you can see the meaning of it. Rather, translating it into a spoken language often causes the distortion of its meaning. It is also thanks to the mathematics language that non-English-speaking pupils studying math or science can easily see difficult major books in English. This is because just one or two lines of formula will give you the most information contained in a lengthy English sentence. Currently, mathematical languages, which consist of Arabic numerals, Greek letters, and various symbols, are the most widely used common language in the world.
Why is math difficult?
Frankly, the first reason that mathematics is difficult is because it requires a high level of logic and creativity in problem solving. It is too obvious. And here, one more reason why mathematics is difficult is in 'mathematics language'. You have to become accustomed to the 'mathematical language' to do mathematics well. It is as if you need to know French to write a literary work in French. I have watched Many of the students, and most of them are having problems in translating the problem into a "mathematical language" or accepting the meaning of the problem in the form of "mathematical language". For example, let's say that the following equation is given to the problem
What information do you get about
Most students, although they are not given a real problem yet, feel difficulty from here. In reverse, If I ask students to write down a function with a width of 2 triangular signals that goes to the right of the x axis as t increases, they feel even more difficult to do that. The problem of them is in "mathematical language". They're not used to "mathematical language".
To be good at mathematics, you have to get used to "mathematics language" somewhat. Of course, the essence of mathematics is not here. However, to compare it with a general language, literature becomes a masterpiece not because of its flamboyant style but because of its philosophy and content, but it can not be written without knowing how to write properly.
Most people don't know that they have to get used to mathematical language, so they don't go through the language learning process. Especially, since most of the tests in the school require just results of solution, they practice solving the problems given in mathematics language, but they rarely practice to translate the their daily language into mathematical language. To learn a language, you must speak it with your own mouth or write it down your own hand. And when I look at the students' workbook, it is rambling. Instead of setting the proper equations, they write only numbers and letters here and there in their workbook. As if to learn a language, you must first make a habit of speaking the whole sentence, you should make a habit of setting whole equations. Finally, the most important point of language learning is persistence. Even languages that you already know will be rusted, if you don't use them for a few months. 'Mathematics language' is the same, so you can not get used to it without steadiness.
Translation of Mathematical Language
In [Appendix] Quantum Mechanics for General Knowledge, I tried explaining quantum mechanics in the ordinary language. However, it is really difficult to explain physics without 'mathematics language'. Moreover, It is likely to cause misunderstanding. Scholars who study literature or philosophy say that they read the original book rather than translation, because when language changes, meaning can not be fully communicated. The same goes for mathematics. The physicist Michio Kaku also explained this in his book "Parallel Worlds". He said that a representative example of misunderstanding of the language is that the public accepts "the principle of uncertainty" simply as a limitation of measurement technology. But, "The principle of uncertainty" is a conclusion derived entirely from mathematical logic.
Originally, mathematical language belonged to ordinary daily life without any difference from any other language. As if seeing the blood from a wound and the flower on a field, people abstracted the attribute "red" and coined the language, people abstracted the numerical properties like 1, 2, 3 between objects. After that they got the fundamental arithmetic operation like addition and subtraction. And people abstracted a higher level concept using mathematical language, and that concept abstracted the following concept. People got the multiplication from the addition, the power from the multiplication, and from the power again the concept of the square root and the log. The language of mathematics that has not been based on the ordinary life has moved away from the ordinary language. Translation between the two has become difficult.
But at the same time, the mathematics language has had its own value as it has become far apart from ordinary language. What can not be explained in ordinary language can be expressed in mathematical language. At present, human has reached a very high level of scientific knowledge that you wouldn't understand if you were not a professional. The language of mathematics has led us to the knowledge of science beyond the reach of ordinary language.
Well, I guess it would be good to be proud of ourselves, everyone. The language we learned next to the mother tongue was mathematical language. I think we can boast to the savage alien who lives on the planet a few million light years away, even though we do not know math well, but we know a little bit of 'mathematical language' that developed humanity.