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Re: Re: Replace and ReplaceAll -- simple application
Replying to your two emails Tony. I agree with you that there are problems (or we might say challenges!) but I disagree with you on the identification of the problems and the solutions. You see the problem in WRI trying to do too much and Mathematica being too difficult to learn with all its features. You see the solution in a pared down Mathematica, perhaps something more like a super-graphical-calculator, and better documentation. I see the challenges differently. I'm really enthusiastic about Mathematica because I see it as a revolutionary medium that allows one to write literate mathematical documents with all the power of Mathematica behind the document. Such documents have tremendous advantages over the present practice. They have a large amount of self-proofing; they create generated knowledge in the form of definitions and routines; they can be much more expressive with all the active and dynamic capabilities of Mathematica. It may take a while for this concept to be taken up by the majority of users but I am certain it will eventually win through because of its great advantages. Obviously, I wouldn't want a pared down Mathematica. That would destroy the prospects. I really don't want an application that is just a super-calculator or a programming language. I want to be able to write, communicate AND do math with it. I see the principal problem as being education and acceptance of the application. One can't just buy Mathematica off the bit-server and start using it productively. We didn't learn how to write literate essays in a week. We actually had years of schooling in the use of our language. We can't just add mathematics and the use of Mathematica in a week - especially with graphics and dynamic presentations. Mathematica may have its quirks, but most languages have their quirks also. We just have to learn about them and practice. Students who might be headed toward technical careers should really be starting in early secondary school. That's the real problem! It isn't sufficient for students to get to university, illiterate in mathematical writing, and just modify examples provided by the professor. They have to be able to think with Mathematica on their own. It isn't sufficient to do calculations without integrating them with textual discussion. (Unless you're a super genius that is.) By the time students get to university they should know the basic syntax and usage of Mathematica. They should know how to use Help. They should know how to write definitions and routines in good style. They should know how to do reasonable graphics and some dynamics. They should know how to write packages. They should have written a few mathematical essay notebooks using sectional headings and textual discussion. A second major problem is that Mathematica notebooks should be able to be read (but not written) by anyone. I think that WRI is not oblivious to the problem and it might get solved. Another problem is the cost and acceptance of Mathematica. Some people in academia resent the commercial status of Mathematica. I think this is unfair because there are LOTS of commercial products that have near monopolies in various educational niches. But the WRI use restrictions, licensing practices, and cost, do present barriers. I don't know what the answer to these problems are, but surely there are answers. Finally, this whole discussion got started with the behavior of 1., -1., I and -I, and pattern matching. Whether or not this behavior could be improved, anyone who has had an even half-way good education in Mathematica knows that looking at the FullForm is the way to diagnose pattern matching problems. And students should learn early not to mix approximate numbers or units into symbolic equations. And they should also learn early that Conjugate and ComplexExpand is the general method for taking complex conjugates. These are far more educational issues than they are Mathematica issues. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: AES [mailto:siegman at stanford.edu] In article <hhf5kg$go6$1 at smc.vnet.net>, Murray Eisenberg <murray at math.umass.edu> wrote: [Re documentation issues and I->-I] > Only gathering usage statistics, or having a focus group of users trying > stuff, might suffice to escalate some issues to the point of requiring > more prominent warnings. 1) Fully agree. My understanding is that many software vendors (and hardware equipment vendors, for that matter), at least the larger ones, do exactly this, systematically and extensively, on their products, and especially the interfaces to their products. I have no idea whether Wolfram does any of this or not. 2) On this point let's note that, to many users, the _interface_ to Mathematica -- what the user has to (learn to) type in, to get useful results out -- is the most important (and sometimes frustrating?) part of the product. What Mathematica does or can do -- it's "capabilities" as contrasted to its interface -- is of course also of primary importance; and Mathematica seems to rank very highly on this criterion. It's the user interface where many if not most of these problems arise. 3) And let's note the explicit assertions by Conrad Wolfram (in the screencasts/video gallery on the Wolfram web site), and by others, that Mathematica is intended to be a program that does *all* tasks, for *all* users, in a *single* application (with 'all' and 'single' taken very broadly). This means, necessarily: a) A *very* complex interface (with, in particular, a _huge_ vocabulary). b) And at the same time, a very broad and diverse set of users, with very different levels of education and knowledge and experience. And this may mean that this basic goal and approach of the Wolframs' for Mathematica may not be realistic or possible. The "focus groups" you suggest will have to be very diverse in makeup, corresponding to the huge diversity of the proposed users; and each different group of users will have different interface (and documentation) needs, and want very different things. If the Wolframs' are going to insist on following this path, then user documentation -- easily accessible, brilliantly designed documentation, readily available in different forms oriented to the needs of different users -- is the primary thing they have to focus on. Thus far, so far as I can see, Heikki Ruskeepaa may be the only person on the planet who recognizes this and does something about it. Mathematica's own documentation gets maybe a C- on this score. And simply expecting ordinary users to learn ever more arcane CAS concepts and terminology in order to use Mathematica effectively seems as unrealistic as it is absurd.