Re: Re: Re: Simplifying and Rearranging Expressions

*To*: mathgroup at smc.vnet.net*Subject*: [mg96090] Re: [mg96051] Re: [mg96008] Re: Simplifying and Rearranging Expressions*From*: "David Park" <djmpark at comcast.net>*Date*: Wed, 4 Feb 2009 05:23:06 -0500 (EST)*References*: <gls1u8$hjl$1@smc.vnet.net> <15441402.1233316177571.JavaMail.root@m02> <gm0q6p$rpr$1@smc.vnet.net> <200902010940.EAA22741@smc.vnet.net> <18977710.1233662192327.JavaMail.root@m02>

Demonstrations Project yes. It is the dynamic style one can easily get in a Mathematica notebook and not in a static document. My objection to the Demonstrations Project is that the ones I've looked at are just a single Manipulate statement with very little textual explanation or development. Much better to have a notebook that contains development, textual discussion and various kinds of presentations, dynamic and otherwise, and tools to explain and work with some concept. For human beings it is just easier to understand an action than it is to understand a static object. We evolved to respond to actions. I have a theory about great mathematicians. 1) They have the ability to visualize actions and interactions of abstract objects in their mind, probably often geometrically. 2) They are very good at calculating without mistakes, perhaps a little like some autistic people. 3) They can immerse themselves in many specific cases and calculate them out rather fast and this way they gain a lot of experience. It is just these things that Mathematica, if used properly, helps with. The newer dynamics helps with (1). And also remember that step-by-step derivations with the actual rules or definitions made explicit are a kind of 'action'. The standard CAS facilities help with (2) and because of this we can do a lot of (3). This opens up real mathematics to a much broader class of people and that is a worthy goal in itself. This won't make everybody great creative mathematicians, but it might boost a few who otherwise were weak in one of the skills. But it takes an active, interactive, dynamic and discursive style of writing Mathematica notebooks to get the full benefit. Static documents are the old technology. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Andrzej Kozlowski [mailto:akoz at mimuw.edu.pl] I think you are missing the point of what WRI is doing. Nobody is trying to impose a single format on the world of mathematics, and nobody is trying to force mathematica users to abandon other programs. The best proof of that is the large number of export formats that Mathematica supports. The whole point of Mathematica "integrated approach" is entirely different. In my opinion it lies in the idea of "Mathematica Demonstration", as exemplified here: http://demonstrations.wolfram.com/ I consider the Mathematica demonstration to be a truly remarkable and revolutionary idea. Why, I will try to explain below. First, I just want to note that this could not be achieved without a fully integrated system that Mathematica provides. That's why I don't expect that Mathematica will see any competition in this area for quite some time. Why I think these demonstrations are such a great idea? If you only glance superficially at the demonstration site you may think that they are merely cute animations and mathematical toys. Indeed, there are a few of this kind, but be not deceived. Many demonstrations contain fully functional code that can be downloaded by the user and after minor adjustment be used to solve serious real life problems. At the same time, the Mathematica demonstration provides a remarkably intuitive and lucid way of conceptualizing what otherwise would be more or less incomprehensible piece of computational code. Some of the demonstrations I have contributed are based on papers I reviewed for Mathematical Reviews. In my opinion, these demonstrations have far greater explanatory power than any number of words (certainly any number of words written by me). Some others attempt to elucidate concepts in Mathematical finance while at the same time providing code that can be actually useful in real world computations. In the case of mathematical finance, I think there is an almost universal agreement that in the past computational techniques were emphasized too much while conceptual clarity was neglected. Mathematica now offers a unique way to combine conceptual description of a model with a mathematical solution through an analytical or numerical process. If more people contribute demonstrations adopting this approach the demonstrations site could become a valuable repository of reusable code accompanied by conceptual visualizations with a very wide area of applicability. In my opinion a Mathematica demonstration is much more than a "new format", it is a completely new form of expressing and communicating mathematical ideas. As such it justifies everything that WRI has done to make it possible - which is essentially everything that you are objecting to in Mathematica. But of course, you are always free to ignore these new features if they hold no interest for you. You are also free to use CalcCenter, which may well do everything that you really wish to use Mathematica for (I can't guarantee that as I do not really know either how you use Mathematica or what exactly CalcCenter can do). Andrzej Kozlowski

**References**:**Re: Simplifying and Rearranging Expressions***From:*AES <siegman@stanford.edu>

**Re: FourierTransform**

**Re: Re: Re: Simplifying and Rearranging Expressions**

**Re: Re: Simplifying and Rearranging Expressions**

**Re: Re: Re: Simplifying and Rearranging Expressions**