Re: Range of Use of Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg88823] Re: [mg88810] Range of Use of Mathematica*From*: DrMajorBob <drmajorbob at att.net>*Date*: Sat, 17 May 2008 23:27:54 -0400 (EDT)*References*: <3902281.1211029361739.JavaMail.root@m08>*Reply-to*: drmajorbob at longhorns.com

I think David's right on! His Derivations sub-package is phenomenal, and I only wish I had more occasions to use it. Bobby On Sat, 17 May 2008 04:30:16 -0500, David Park <djmpark at comcast.net> wrote: > For some years now 'AES' (actually Professor Anthony E. Siegman, McMurty > Professor of Engineering Emeritus at Stanford University) and I have > engaged > in a running dialog on the extent of Mathematica's usefulness in > preparing > research material for publication. I believe that AES's basic position is > that Mathematica is fine for doing computer algebra (traditional CAS > operations), numerical calculations and generating starting graphics for > publications. But then he advocates using outside programs for perfecting > the graphics, doing typesetting and preparing the final publication. He > thinks that "..even attempting (to combine these functions in > Mathematica) . > is inherently a bad idea." > > > I suspect that this is, in fact, the procedure employed by most > Mathematica > users involved in research and publication. Not being myself extremely > prolific in publishable ideas, and in recent years only publishing a few > Mathematica papers, which were in notebook form, I'm not in a position > to be > too critical of AES's position and I do respect his experience and > knowledge > in these matters. > > > What I have been interested in is using Mathematica to study various > textbooks and subjects to attempt to learn some modern mathematics and > physics. In doing this I have always wanted to produce notebooks that > looked > like textbooks or research papers. Not having publication as a primary > objective, I have been willing to stay with Mathematica all the way. > What I > have learned is that with Mathematica I can produce notebooks that look > like > regular publications. I have to admit that this does require extra > effort in > the way of writing convenience routines that define and format various > objects one may be dealing with. But it does not involve more work that > buying additional, often expensive, applications and learning their > installation, syntax and operation, and how to export Mathematica > results to > these programs. If one already has and knows well these additional > applications, before coming to Mathematica, then AES's approach is the > natural one. For those who come to Mathematica first, I think it would be > far easier to work in Mathematica as far as possible. I don't see why one > couldn't write an entire paper in Mathematica and then print it as a PDF > document. > > > Even if one uses Mathematica strictly for CAS work and numerical > calculations, it is still necessary to write definitions and routines for > processing the objects one deals with. I do not see why there should be > an > artificial line between extra routines that calculate and extra routines > that format. And, in any case, having nice presentations of objects is > often > an integral part of calculating with them and understanding the theory. > > > Having this preference for Mathematica notebooks, and looking at many > textbooks and papers, I will go one step further, many will say right off > the edge! Mathematica notebooks are inherently FAR SUPERIOR to static > printed documents. They are so superior that I can't understand why > anyone > would want to transform to printed documents. A Mathematica notebook is > to a > printed document as the Parthenon is to its floor plan. Forget that > static > printed papers are the standard of today. They won't be in the future. > > > I'll give two examples where printed documents fall short. The first is > the > general matter of presenting mathematical proofs in textbooks. I find > proofs > difficult and the limitations of the printed page do not make them any > easier. Proofs usually have structure, but in books and especially with > poor > typographic layout, they often look like a run-on paragraph. Proofs often > need commentary and sometimes extended examples or subparts. Putting > these > in the middle of a proof disrupts the structure of the proof and putting > them before or after disconnects them. So I take it as something of a > challenge to learn how to better present proofs using the active > features of > Mathematica. I've written a Derivation container that can contain comment > and command expressions. The comments can be used to annotate the steps > of a > proof or derivation. A command gives evaluated results of a Mathematica > statement, with a Tooltip of the generating statement. I've also designed > Sidebars, which are notebooks embedded within the main notebook that can > be > launched by a button. These provide methods to clarify proofs and > derivations but there may be other and better methods, such as using > TabView > for various sections of a proof. Every proof may require its own style of > presentation. I think there is much that can be done with Mathematica to > make the presentation of proofs clearer, more elegant and easier for > students and readers than anything possible in printed documents. If we > always think in terms of static printed documents we won't even take up > this > challenge. > > > As a second example, my wife and I are reading 'King of Infinite Space: > Donald Coxeter, the Man Who Saved Geometry' by Siobhan Roberts. Excellent > book! There, in discussing methods to visualize four dimensional space > Coxeter used the idea of slicing, and slicing from 3-dimensional space to > 2-dimensional space as practice. So there were pictures of sequences of > parallel sections slicing the Icosahedron (vertex first, edge first and > face > first) and Dodecahedron. But these are very difficult to follow on a > static > page. I could partially follow them and my wife was rather lost. How much > better to see these in a Manipulate statement where one could set the > normal > to the slicing plane and slowly move through a regular polyhedron. It > would > be especially nice if we could get the 3D slicing picture in one pane and > the 2D outline in a second pane. It sent me to the Demonstrations > project to > see if this had been done but I couldn't find it, and I suspect it might > be > somewhat difficult. But I did find some nice animations demonstrating > Euclidean solid geometry theorems by Isidor Hafner! > > > Still, I have some reservations about the Demonstrations Project, as > popular > as it is. If forcing everything onto a static printed page is one > restrictive mode or presenting material, then forcing everything into a > Manipulate statement is another restrictive mode. Generally the > Demonstration projects are lacking in textual discussion, derivations, > methods of calculation, and because of that, generally difficult to > actually > follow and learn from. The lesson to me is that we should not > artificially > restrict Mathematica but use its full powers to present topics in > notebooks > that follow a classical style of writing but employ the active > capabilities > of Mathematica. > > > > David Park > > <mailto:djmpark at comcast.net> djmpark at comcast.net > > <http://home.comcast.net/~djmpark> http://home.comcast.net/~djmpark > -- DrMajorBob at longhorns.com