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Blasphemy

To teach classical mechanics without calculus ignores cultural aspects of science, and we could say it is blasphemy against human spirit.

 No one seems to think in this way. Why? Probably, it is believed that mechanics can be taught at an elementary level, but calculus is sophisticated and difficult. This view seems to be due to multiple misunderstanding. Is mechanics that easy, and intuitive? Is calculus that hard and counterintuitive?Teachers should seriously reflect upon respectable ways to teach mechanics without ignoring why Newton needed calculus. 

 Read  The Feynman Lectures on Physics vol I Chapter 8.

Appropriate style

Here this is mentioned to illustrate that the use of appropriate tools is crucial. 

 The manuscript of this book was written alternatively in English and in Japanese for the first 10 years or so, but since the Japanese version was published first (in 2009), recently, the manuscript was polished predominantly in Japanese. Then, an English counterpart was prepared, but the translation of newly added potions was not very trivial. I was not free from the misgiving that it may be problematic to write sentences hard to translate into English in scientific books. However, when we discuss something really difficult, or something not yet completely scientifically formalized/conceptualized, it should not be surprising that there are portions hard to translate; there must be such portions.

 Japanese Novelist Minae Mizumura [from  When Japanese expires---in the century of English (Chikuma, 2008)] says roughly as follows:

In the world there are two kinds of〈truth〉: One is the truth we can obtain by reading textbooks and the other we can obtain only by reading the texts themselves. The latter truth is the truth of literature. The most typical truth of learning is represented by the textbook filled with formulas. 

 The truth we can find in a text is the one expressed only by a particular use of language chosen from many possibilities to express similar situations .  Indeed, truth resides in the style.

 If formalized as mathematics, the `genuine’ truth of learning is `translation invariant,’ but when we use mathematics as a tool to explore the world, the mathematics is not perfected nor completely formalized. As long as we try to understand this unformalizable world with the aid of mathematics, and as long as we wish to minimize the use of actual examples, untranslatable portions must remain, which need not be unimportant portions.

 This implies that to do science in a particular language (especially non-English) can have a positive significance.