Hi,
The responses to my suggestion (of adding a mode to J in which users are deceived into thinking one special APL-like character is being stored instead of two ASCII) have been of three kinds: 1. Suggestions for good ways of teaching J, which I very much appreciate. 2. "It can't be done" - Except for Tracy Harms, who agrees that my suggestion can be implemented. 3. "Why would we want to do it?" When trying to write self-teaching modules with an IBM 2741 terminal in 1968, which printed at the breakneck speed of 15 characters per second, I learned the following formula for natural language: Understandability = structure + brevity + word-choice I think this formula is equally valid for notation. J has structure, but it loses its brevity when two characters are used for a symbol. Words are important for the rich associations that they bring with them. APL characters and any new APL-like symbols can be designed to bring much richer associations with them. It was not that long ago that Mathematicians tried to solve problems using equations expressed in natural language - for example, something like the following (it is a long time since I looked at the history of notation - so this is a guess): "The second unknown is equal to three times the first unknown to the power three plus seven times the first unknown to the power two plus six times the first unknown plus seventeen" In addition, it was written in Latin. Only when concise notations were developed could Mathematics advance at speed. Isn't using natural language words instead of notation going backwards? I think a valid argument has been made that many people who are taught APL or J don't like the concise symbols and respond better to replacing them with natural language words. However, isn't this a chicken and egg problem? Does a natural revulsion to Mathematical symbols mean someone won't use them or does the fact that they haven't used them produce the revulsion? Understanding the richness and value of a word comes from using it and seeing it used in practice. Recent research has established that the brain cuts off the potential for unused skills somewhere between about 10 and about 13. If you haven't thrown a curveball by age 13, you have no chance of being a major league pitcher. Similarly, if you haven't learned the richness of Mathematical symbols by age 13, you probably never will. So this has to be learned in Public School, not High School. However, it is also true that a student doesn't acquire the ability of abstract though in time. Public School is mostly about experiential learning. But aren't APL and J experiential? Wouldn't their use in Public School begin to develop an understanding of the richness of notational Mathematical words? Then wouldn't adults better understand Mathematics? There is an important educational potential here Don Watson ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
