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Re: How to write a "proper" math document
In article <iv45b8$es8$1 at smc.vnet.net>, "David Park" <djmpark at comcast.net> wrote: > The "two document" approach has both feet planted in the past. The first > "document" is really a "programmable super graphical calculator" planted in > the recent past. The second document is a static "text, equations, diagram" > document planted in 3000 year old technology. > > . . . the second of the current "two documents" nearly completely throws > away all of the benefits of an active and dynamic mathematical medium. Such > as: . . . > > AES, I sometimes wonder if you have ever tried to write such a document or > ever read one. You seem to be unaware of the advantages. I'll refer you once again to an article I wrote two decades ago (when the Mac was just 5 years old, and Mathematica had just appeared): <http://spie.org/etop/1991/338_1.pdf> It's opening sentence reads: "As I began preparing the talk on which this article is based its subject matter began to evolve, moving from the original topic of computer display tools for optics education toward the more general topic of personal computers in higher education, especially in science and engineering; and so this article will be directed more broadly to that topic." I've also voiced on this forum my very high opinion of Manipulate and its dynamic capabilities as providing a major and highly valuable contribution to these broad objectives. But I believe there are still multiple methods and needs for the creation and the distribution of information and knowledge, including dynamic mathematical tools that individuals can use by themselves to explore all kinds of knowledge; dynamic tools for group presentations (seminars, lectures, dynamic web sites]; and, still very important and necessary, printed books, journal articles, manuals, and other manuscripts for individual use. If I'm trying to understand and puzzle out the physical implications of some involved mathematical analysis of a physical problem, I very much want to have the equations and their derivation, along with other reference material, in a printed article or memo or book on the desktop beside me -- maybe several such items -- so I can flip through this material, or scrawl notes on it, or just stare at the derivations to see if some insight will leap out at me, AND at the same time have a dynamic mathematical tool available and running on the large monitor in front of me. Similarly, if I'm trying to program something using a new tool, I need to have one or more systematically organized manuals or collections of reference material on the desktop beside me, AND at the same time have that tool itself running on the large monitor in front of me. Trying to carry out all the activities involved in either of these two situations using only a monitor and no printed materials, so that one is continuously jumping back and forth and navigating between the active computation and the reference materials, all on a single screen (even a large one) is an exercise in frustration and inefficiency. And, trying to insist that all of this be done not only on a single screen but within a single tool or a single program, like Mathematica, with all the documentation for that tool available only on that same screen, is also an absolutely prime way to suppress the creativity of all the innumerable other people in the world who might write other better tools, or might write better documentation for some aspect of Mathematica. So: We basically agree on some things -- but, I guess, substantially disagree on others. You further add: > The solution is simple. Every technically literate person should have > Mathematica. A price of $295 (for the Home edition) is not unreasonable for > people who might at first be casual users or readers. I absolutely agree with your second sentence -- except I'd broaden it to say something like "Every intellectually active individual . . .", at almost any age from intermediate school level to senility, and in almost any field, 'technical' or not. The problem is, this is absolutely incompatible with your third sentence. For the average family in this world a stripped down "Family Edition" in the $40 range (fully usable by mom, dad, and all the kids) would be more like it; $295 is at the upper level of what I'll willingly pay for a more or less full-bore edition of Mathematica to use in my own post-retirement technical consulting and scholarly explorations (and that's for something with at least a 4 or 5-year lifetime before I have to pay for any upgrades). Mathematica needs more competition from other open-source or lower-priced or freeware tools that can do some of the things it does equally well. It also needs some form of modular restructuring, so that different grades and levels of users can be served with different levels or subsets of the capabilities built into the complete system (I appreciate this may not be easy; but that doesn't make it any less needed).