Re: Re: Simplifying and Rearranging Expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg95973] Re: [mg95956] Re: Simplifying and Rearranging Expressions
- From: "David Park" <djmpark at comcast.net>
- Date: Sat, 31 Jan 2009 01:13:43 -0500 (EST)
- References: <gls1u8$hjl$1@smc.vnet.net> <15441402.1233316177571.JavaMail.root@m02>
From: AES [mailto:siegman at stanford.edu] 3) Instead, if what you're doing is a complex analysis and/or exposition, tackle the analysis portion initially with paper, pencil, and a good soft eraser, the way God intended analysis to be done. ........................ And perhaps using only integers, since I read that's all that God invented? It reminds me of a story I read somewhere, I can't recall the exact book, about the history of modern physics. Robert Serber was an important physicist on the Manhattan project. He would tell the story that one night he dreamed he had died and gone to heaven. Saint Peter issued him in to see God and God said: "You probably don't remember me but I audited your course on quantum mechanics at Berkeley." That is probably the best witness we have that God did use paper, pencil and a good soft eraser! There were no CASs in those days. And to strengthen your case further we know there are good mathematicians who would never touch a computer. Not to speak of the great mathematicians of the past. Nevertheless, I would still argue that users should be encouraged to do derivations completely ACTIVELY using Mathematica. They may think about the principles, strategy and tactics of a derivation when they are away from Mathematica. But implementing a derivation or proof actively on Mathematica has many advantages. 1) You have to gather explicitly the definitions and rules used in the derivation. Knowing the starting point is often half the problem. 2) These definitions and rules are active knowledge that you not only use in the specific derivation or proof but may be useful elsewhere. The same goes for intermediate and final results. They are not just inert equations on a piece of paper but active tools. They are the fruit of your labor. You can use these tools in further derivations or in producing graphics or dynamic presentations. 3) Active derivation has a great deal of self-proofing in it. Things have to work. It is not totally foolproof, but it does impose a fair amount of discipline. 4) One can try out ideas, and see their results much faster. 5) An interactive and dynamic medium of expression is just much better than a static document. A may seem like a lot of work, but in 99.99% of the cases Mathematica users deal with it is entirely possible. The results will be well worth it. It is no more work than writing any good paper without Mathematica. Any good product requires work. It also requires learning how to use the tools, and it requires that WRI keep working on adapting Mathematica to the working requirements of mathematicians, scientists and engineers. They haven't done that badly, and we are still at the beginning of a technology and not at the end of it. Remember what the Greeks said: The past is in front of you and the future is behind you, because what you see is the past. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/