Hi, Don Watson wrote:
"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." I do not think any users would want to be without many of the hundreds of named functions listed in User Manual / Script Libraries / Definition Summaries. The user obtains brevity by using these simple function names. The J primitives are a basic set of elements which obey the structural rules, have been given short names for convenience and brevity and have given names (word-choices) which convey a lot of meaning to those who do not yet know the language. Like Alex Rufon, I have found new users find it easier to work with words as names for the J primitives, and find them much simpler than learning the inflected primitives. For me the whole point of J is that it is a powerful means of structuring ones thoughts about a computation. In most cases that involves combining many J functions in a set of new functions which are designed to achieve tasks in some subject area. These new functions become the 'primitives' for clarifying and specifying computations in that area. They all just have character names. Whether the J primitives are denoted by a single character, two characters or words is totally inconsequential compared with the power of the J language structure to facilitate rapid expression and solution of computational tasks. >From that perspective the contributions which many users have been making to packages available through the Project Manager are much more important than finding some new symbols which old and new users alike will have to learn for a set of functions which already have very brief names. Fraser ----- Original Message ----- From: "Don Watson" <[email protected]> To: "General forum" <[email protected]> Sent: Tuesday, February 24, 2009 11:13 AM Subject: Re: [Jgeneral] Teaching > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
