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Re: More /.{I->-1} craziness

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106489] Re: More /.{I->-1} craziness
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Thu, 14 Jan 2010 05:49:24 -0500 (EST)

On 1/13/10 at 5:56 AM, fateman at cs.berkeley.edu (Richard Fateman)
wrote:

>Bill Rowe wrote:
>>On 1/11/10 at 5:27 AM, fateman at cs.berkeley.edu (Richard Fateman)
>>wrote:

>>>When one first reports a behavior that one believes is a bug, the
>>>natural hope is that it will be fixed.

>>Which is very reasonably when what is reported as a bug is indeed a
>>bug. But it is not reasonable to expect something reported as a bug
>>to be changed when it is not a bug.

>It seems to be inevitable that people will, with such a complex
>system as Mathematica, have differences of opinion as to whether
>some behavior constitutes a bug or not.  When WRI declares "this is
>a feature not a bug", that does not necessarily change peoples'
>opinions.  In fact, WRI has, from time to time, changed its opinion
>on what is a feature or a bug.

Certainly it is true a declaration from WRI might have little or
no effect on someone's opinion. And it is certainly true there
will be those who have different opinions as to what a bug is.
But in the final analysis, it only matters what WRI defines as a
bug in Mathematica. I don't expect WRI to change Mathematica to
fix a "bug" if the behavior being changed is not a bug from
their perspective. And in this thread, it seems very clear the
behavior of ReplaceAll with respect to complex values is not a bug.

>>Nor is it reasonable to expect WRI to intuit your meaning of bug
>>when it differs from the standard accepted difference. That is, the
>>behavior being discussed is simply not a bug. It is exactly the
>>behavior the documentation indicates should occur.

>Especially when the documentation is vague or lacking on what should
>occur, the difference between a feature and a bug is elusive.

No disagreement here.

>>You appear to be suggesting Mathematica should be written to enable
>>someone to do mathematics without understanding much in the way in
>>which Mathematica works.

>Yes.  One of the goals of the people who have been developing
>software for "symbolic mathematical computation" starting in the
>1960s, was that, to the largest extent possible, the newly
>discovered and implemented algorithmic underpinnings of constructive
>mathematics should be merged with the natural notations and usage of
>practicing mathematicians, scientists, engineers, etc, so these
>computer systems could be used most widely and most effectively.

>>While I can there are those who want something to just work without
>>additional effort on their part,

>Yes.

>>I don't see this as happening with anything as powerful and complex as
>>Mathematica.

>It is a particular conceit of Stephen Wolfram that he has invented a
>new and improved notation and method for designating computation,
>and that if only everyone learned it, mathematics and perhaps all of
>science would be so much better for it. And I see it echoed here --

I've no specific knowledge of Steven Wolfram's views regarding
what you write above, but this totally misses my point. I make
no claim as to whether notation used in Mathematica is superior
or inferior to notation used in mathematics or that anyone will
be bettered by learning Mathematica notation.

But to use Mathematica efficiently and effectively, it is
essential to learn the notation used in Mathematica. Failure to
do so severely limits what you can do with Mathematica. The
point is effective use of any software tool requires
understanding that tool. This point has absolutely nothing to
say about whether the tool that is Mathematica is better or not
for some particular use. Nor does it say someone who has learned
to use Mathematica is in anyway "better" than someone who has not.

>why don't we have all high school students learn Mathematica?

>(Uh, answer: maybe Mathematica is (a) unnecessary,

Clearly true to a large extent since mathematics has been done
long before any version of Mathematica existed.

>(b) unnecessarily complex,

Given the complexity of mathematics and what Mathematica is
designed to do, I don't see Mathematica as "unnecessarily complex.

>(c) not as powerful as you think,

Since I've yet to fully master all of the capability in
Mathematica (and probably never will), it seems clear
Mathematica isn't significantly less powerful than I think.

>(d) the complexity is not required to provide the power,

Possibly true, but I very much doubt that it is true.

>(e) Have you really examined all the history of introducing computing
>to lower grades in school?

No, I have not. But my knowledge of the history of introducing
computing in to lower school grades is not germane to this
thread. In fact, the whole question of why Mathematica is not
widely used in high school really has little to do with this
thread. Given funding made available to high schools, the cost
of a Mathematica license almost certainly puts Mathematica out
of reach regardless of complexity and capability.

>(f) Even if we agree that "algorithms and/or computing" is a good thing
>to know, is Mathematica the tool?)

There may be better tools than Mathematica. But that is beside
the point. Making efficient/effective use of Mathematica entails
more than just a passing knowledge of algorithms and computing.
A lack of knowledge in these areas will severely limit what can
be done with Mathematica.

>>Someone who "merely knows" mathematics and has no interest in
>>FullForm, Reduce, Eliminate, ReplacementRule etc would be well
>>advised to do mathematics by hand and not use Mathematica at all.

>You know, there are a few alternatives other than doing mathematics
>"by hand" va. Mathematica that do not require knowledge of these
>items, and I hope you and other readers of this note consider that
>your comment it is an example of your "drinking the {wolfram} kool
>aid".

>Is the choice "learn internals of Mathematica" or "don't use
>computers"?

No. The advise is if you want to master the use of Mathematica
as a problem solving tool, you need to learn something about the
design of Mathematica. If you are unwilling to do that, you
would be well advised to use a different tool. This in no way
says Mathematica is essential to solving a particular problem. I
do not have the view it is the "Mathematica way" or the highway.
I do have the view effective problems solving using Mathematica
requires more than just a knowledge of mathematics.

Note, the point I am expressing here is applicable to any CAS
not just Mathematica.

>>It simply is not reasonable to expect good results from a tool if
>>you are unwilling to learn how to use the tool.

>One of the attributes of computer software is that it is almost
>infinitely malleable.  When a particular design of a software tool
>turns out to be ill-suited to a particular task, it is worth
>considering whether a better alternative or additional tool can be
>designed. Even if you have learned to use the existing tool, that
>does not mean you are constrained to use it to the exclusion of
>others, nor that you are forbidden from designing another, or
>suggesting that other people help design other tools.

I've no disagreement with the above. But none of what you say
here changes the need to learn how to use a tool in order to
make effective use of that tool to obtain good results.



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