A mind without confusion

At the root of Yggdrasill, the Tree of Life, lies the magical Source of Urd. There dwell the three Norns: Urd (Wyrd), Verdandi and Skuld. Now, Urd is old Norse for 'fate'. It has become the root wert-'='to turn' to mean anything prone to change. The word 'weather' (='weer' in Dutch) originating from this, the same holds for the Dutch verb 'worden' (='to become') and also the word 'versus' ('turned against'). Because of the connotations with changing behaviour, it is easy to understand that the name Wyrd has developed into 'weird', strange and unpredicted.

This in itself is an interesting piece of etymology. But the story gets better. Last week I received a small gift from Oshita sensei. He passed this eighth dan exam iaido last year. He gave me a tenugui, a small towel, that was made for the occasion. It has a nicely calligraphed text on it. The calligaphy reads fudoshin, which normally is translated as 'an unmovable mind.'



The first and the last characters are very common: 'heart'/'mind' and 'not'/'no'. The middle one I had seen before, but I had forgotten its meaning. I used my Chinese/Japanese program Wakan and found out that the middle character means 'move, motion, change, confusion, shift, shake'. Thus, the calligraphy reads (as I translate it) something like 'a mind without confusion'.
In this way I found out that also in the Far East the bond between 'change' and 'confusion' is anchored in vocabulary.

Arithmetic

"Swordsmanship is just like this. If from the time the student is a beginner without having learned any techniques well, you say something like 'Technique will come naturally without intention; establish the hard by means of the soft,' or 'Techniques are only trivialities,' he will become empty-handed and lazy, and will never know of where to stand. Thus he will be at loss both in this world and the next."
From: Issai Cholzanshi, The Demon's Sermon on the Martial Arts (tr. William Scott Wilson).

In the Netherlands a debate on education in arithmetic and mathematics has been going on for a long time. On one side there are those who say that it is no use of learning techniques, if there is no understanding. On the other hand there are those who say that understanding will come naturally after technique has been mastered.

Prof. Jan van de Craats, an important spokesman of the latter group, argues that the didactic method of 'realisitc arithmetic' give children a variety of tricks, which leaves the pupils confused. Children need structure.

Those who advocate 'realistic arithmetic' claim that old fashioned techniques like the 'staartdeling' (an algorithm in essence equal to the English 'long division') are obsolete, because 'nobody does calculations with pen and paper any more' (Adri Treffers in De Volkskrant). That is a great loss.

I strongly feel that automatisation of arithmetic techniques, together with the learning by heart of the multiplication tables are necessary for a good sense of numbers. This is, I believe, in turn needed for a good grasp of and ability to handle with more abstract objects such as functions, variables and parameters.

As long as realistic arithmetic and mathematics remain the common way of teaching, our pupils may "become empty-handed and lazy, and will never now of where to stand."