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Re: Re: Mathematica 220.127.116.11 and some General Comments
From: Mariano Su=E1rez-Alvarez [mailto:mariano.suarezalvarez at gmail.com] Of course, in my work as a mathematician I have seen (too!) many papers in which I could not tell why something followed from something, or why something was equal to something else. ______ Ah yes! If it is a book, then for me this usually first occurs on page 3. This all brings us back to the intent of my original posting. Instead of just thinking of Mathematica as an ancillary tool to provide material for some other purpose, we should think of it as a primary medium for technical development and communication. I would urge that all development and communication be done via active dynamic Mathematica notebooks. Everything should be developed, derived, proved or calculated ACTIVELY with no interludes of hand waving or 'word processing'. (But there should be plenty of textual discussion.) This means that all starting points should be gathered as definitions and rules, and further definitions or rules will be developed and accumulated as the exposition proceeds. This may seem to many as too much work, and some may doubt that it can be done. It can almost always be done! It IS work, but the payoffs from the work are enormous. One of the payoffs is that you will be accumulating active rules and definitions that you can use in creating graphics and other types of presentations, and for doing further exploration of the subject matter. (The graphics, presentations, or further explorations may be the first indication of errors.) You may even find it worthwhile to turn these routines into a package. This is one of the main fruits of your labor. Don't let it slip through your fingers. A second enormous payoff is that Mathematica notebooks in the active style are largely self-proofing. Yes, it is still possible to make errors or have a clumsy approach but, nevertheless, such notebooks are of a far higher quality and integrity than traditional media. Many technical writers don't use active Mathematica notebooks because they are just plain lazy. There is no other word to describe it. That is why their work is often so difficult to follow, or sometimes wrong. (Sometimes they rationalize this with: "If the reader can't follow it, he shouldn't be working in the field anyway." Come on! Let's invite more people in.) It is far easier for people to understand actions than to understand 'static' diagrams or equations. We evolved to detect actions and respond to them with our own actions. That is why a derivation that is done actively is easier to understand. We get from one expression to another expression by actively applying some axiom or theorem. Gee, that might even cause a student to actually think about the axiom and how it is used. These axioms and theorems, in turn, are encapsulated as rules or routines. The reader of an active notebook could see what rule or routine is used to get from point to point in the derivation. He could use it himself. He could try it on other cases. The reader is far less likely to get stuck at some point she has no explanation for. Fully active Mathematica notebooks: they are the path. If we could only convince WRI to take it a little more seriously. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Mariano Su=E1rez-Alvarez [mailto:mariano.suarezalvarez at gmail.com] Of course, in my work as a mathematician I have seen (too!) many papers in which I could not tell why something followed from something, or why something was equal to something else.