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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


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