Re: Types in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg62329] Re: Types in Mathematica*From*: "Steven T. Hatton" <hattons at globalsymmetry.com>*Date*: Sun, 20 Nov 2005 04:50:32 -0500 (EST)*References*: <200511191053.FAA16418@smc.vnet.net> <dlp2ci$le$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski wrote: > > On 19 Nov 2005, at 19:53, Virgilio, Vincent - SSD wrote: > >> >> Well now it's getting philosophical. I did say "in trying to >> understand", not "in trying to use". > > Yes, indeed. But in my understanding of the preceding discussion the > advice "forget C++" referred to the attitude one should adopt when > programming in Mathematica. At least that certainly was my meaning. > Again, I will repeat what I meant: thinking in terms of C++ or Lisp > will be no help and most likely will be a hindrance in writing good > Mathematica programs. This is all I have been trying to say in this > thread and no more. The comment "forget C++" was in response to my giving an example of how I might try to create a boolean "type" in Mathematica. I stated that my example was not something I was likely to do in C++. Mathematica is not a "strongly typed" language, but there are some aspect of it which do represent a kind of "type system". People in this newsgroup have suggested that I am making a mistake by thinking in terms of data types when working with Mathematica. This, however, is not consistent with the expositions of Steven Wolfram, Roman Mæder and Michael Trott. >> Anyway, it is always helpful to revisit first principles, novice or >> not. >> And since nothing is understood in a vacuum, so the suggested >> comparisons. > > "Understanding" is a difficult "philosophical" concept. It is true > that usually people "understand" new things by trying to form > analogies with other things that they consider as "already > understood". But once they reach a certain level of understanding > these analogies usually turn out to be a ballast that needs to be > ejected in order to be able to move to a higher level of > "understanding". By telling me to "forget C++", you are suggesting that I am incapable of understanding the differences between Mathematica and C++. You are also making assumptions about my level of understanding with respect to both Mathematica, and C++. It seems to me it would be more productive to focus on the point I was making about Mathematica than it is to focus on an aside comment about C++. > There is a vast supply of examples to illustrate > this but perhaps the one that most vividly illustrates the point is > the Bohr's "planetary" model of the atom. > It is certainly not true that someone with no knowledge of other > programming languages cannot be a better Mathematica programmer > than someone who knows lots of them. the idea that the latter > person (the worse programmer who knows other languages)may have a > "better understanding" of Mathematica seems to me unimportant and > perhaps even meaningless. It is generally acknowledged in the computer science field that a person with experience in several programming languages is typically a better programmer than a person who has an equivalent number of hours of experience in one programming language. I mean to say both programmers have the same total number of hours spent programming. > Actually, I would argue that there is > another way of "understanding" that is quite different form the one > based on making analogy with the already familiar approach. Instead > it comes from developing "intuition" through practice. This is > exactly how one acquires understanding of the more abstract branches > of mathematics: abstract algebra, category theory, algebraic topology > etc. In fact, something like that is also true in quantum physics, > where "analogy with the already familiar" is a very unreliable sort > of "understanding". So, to conclude, it seems to me that either > somethings can indeed be understood "in vacuum" or perhaps that the > role of "understanding" in science, mathematics and programming is > rather overrated I agree that most attempts to use the equations of QM to "explain" what is actually happening at the subatomic scale amount to intellectual absurdity. Schrödinger's cat is alive and well. -- The Mathematica Wiki: http://www.mathematica-users.org/ Math for Comp Sci http://www.ifi.unizh.ch/math/bmwcs/master.html Math for the WWW: http://www.w3.org/Math/

**Follow-Ups**:**Re: Re: Types in Mathematica***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**Re: Re: Re: Types in Mathematica***From:*"Virgilio, Vincent - SSD" <Vincent.Virgilio@itt.com>