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Re: Re: More /.{I->-1} craziness. Schools are conservative. So are

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  • Subject: [mg106643] Re: [mg106638] Re: More /.{I->-1} craziness. Schools are conservative. So are
  • From: "David Park" <djmpark at comcast.net>
  • Date: Wed, 20 Jan 2010 06:46:34 -0500 (EST)
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Again, I have to strongly disagree with AES and RJF. Active, dynamic
textbooks and papers backed by a good CAS will displace static documents.
They are better for learning, teaching and communication. I will repeat my
arguments again, just so newcomers won't get the wrong impression.


1) Think of Mathematica as a 'piece of paper' on which you are developing,
writing and communicating your technical ideas. Don't think of it as just a
'super graphical calculator' or a 'programming language'. The object is to
learn, or develop and express mathematical ideas in as clear and elegant a
fashion as possible. 

2) Mathematica coupled with mathematics is complicated. It really takes long
years of study and practice to get good at it. This would be true of any
comparable medium. How long did it take just to learn how to write
reasonably good English? Learning how to write good technical documents is
even more difficult. Early exposure and practice is essential. It is an
intrinsic problem.  There is no easy way around it.

3) Mathematica can't make the big breakthrough until WRI provides a free
Mathematica Player that will allow anyone to read, evaluate and operate
dynamic controls in any Mathematica notebook. (But not edit, and maybe not
print or save.) Users don't write notebooks for communication now because
most other people can't read them. So there are presently very few good
examples. When there are more good examples, more people will be impressed
with them and want to do the same. In my opinion, this issue is more
important than anything else for WRI. (But the licensing and business model
also need critical examination.)

A few other preliminary comments.

It is not obvious or necessarily easy to write good active, dynamic
mathematical documents. People haven't tried to do it much. It is easy to
fall into traps and fill up a notebook with 'computer junk'. There are so
many tools at our disposal that it is difficult to know which ones are best
for a given situation. It is a little like Tufte with data graphics. There
are good and bad ways to do things and we just don't know all the good ways
yet. Also, the very process of trying to present something clearly, using
the new dynamic tools, will often bring us to a deeper understanding of the
subject. "He who makes the graphics often makes the discoveries."

Unfortunately, I think the common present usage of Mathematica is just to
calculate some things and then copy them out to some other document. Then
what would be the use of all the dynamic features, other than our own
pleasure? (And AES recommends that WRI drop all these features and stick to
basic CAS.) I'm trying to convince more people to go beyond that restricted
usage. Of course, the main reason we have the restricted usage is that most
other people can't read the notebooks.

How should such notebooks be written? They should have structured sections
(with group openers) and otherwise look like classical technical papers.
They will probably contain a Routines section where developed routines are
placed. Everything should be actively calculated. If it sounds too
difficult, try anyway.

Now, why do I say that active, dynamic mathematical documents are orders of
magnitude better than the present static documents? Here are the reasons:

1) Embedded knowledge. Good notebooks can generate embedded knowledge:
active usable definitions that result from derivations. This embedded
knowledge can then be used within the notebook itself, in extended
applications in other notebooks and can form the basis for writing a general
purpose package. This is some of the principal fruit of your labor. Don't
let it slip through your fingers. (I will discuss how to better organize
this below.)

2) Actions are better than static presentations. It is always easier to
understand an action than a static diagram or a set of static equations.
Animations can be used to show what is being changed and how it affects a
derivation. A Step by step derivation using rules is something like an
animation as it shows exactly what principles or identities or substitutions
are required to advance an argument and exactly what effect they have.

3) Self-proofing. An active Mathematica notebook is to a large extent
self-proofing. Cells that contain typographical errors generally will not
evaluate properly or often not evaluate at all. Equations that are nonsense
will similarly fail. All of the elements necessary to a derivation must be
present and explicit. It is certainly still possible to make errors or
muddled arguments but not nearly as easy as without active mathematics.

4) Integrated graphics and presentations. The active mathematics can be
integrated with the graphics and dynamic presentations. That is, the
definitions and embedded knowledge developed in the notebook is used to draw
the graphical elements. This not only makes the presentations easier, but
the graphics can also validate the mathematics and may often be the first
indication of errors.

One can go even further and organize work into applications using
Workbench/DocuTools. This could be used for 1) Writing a book, 2) Setting up
college course material, 3) a research project, 4) a study project. An
application could contain 'finished' work: a package, documentation and
notebooks (chapters, lessons or papers), and a Workbooks (say) folder that
contained working notebooks where most day to day work would be done. This
is a very good way to organize and preserve work.

AES and RJF look for flaws in Mathematica (and certainly it's worthwhile to
have skeptics and critics) but what about flaws in present practices? There
are plenty of them and they are glaring. What about all the typos and errors
in printed texts and papers? What about being referred to an equation in a
previous chapter, which is difficult to find, and then this just refers to
another previous equation? Reading some books is like being a real estate
lawyer doing a title search! Why not reprint the equation? Oh, they wouldn't
want to waste some paper and ink. With a notebook you could recall the
equation (by bringing it up at the place where it is used, not by jumping
out of place.) Suppose you are asking a student to do derivations using
axioms. You could bring up all the axioms in a separate window whenever and
wherever you needed them. Better yet, you could have the axioms in active
form so a student could apply them in seeing how derivations are done. Texts
often have skipped steps that can cause students immense aggravation and
loss of time. What about proofs or derivations that run on for a number of
pages and which must be presented in a serial manner? With a notebook one
can organize an extended proof in a compact space, and in a structure that
follows the structure of the proof. Then one can look at the individual
parts by clicking buttons, or bring up parts of the proof in separate
windows. What about the restrictions and artifacts of a fixed length printed
page? Putting content aside and just considering form, I think it's fair to
say that static printed documents are generally chock full of deficiencies
that are significant impediments to communication. 

Now to your questions and objections.

I readily admit that there are HUGE problems to solve to make these ideas
work. (Universal ability to read notebooks, early training, preparation of
adequate material.) That doesn't mean it wouldn't be worth it.

I don't know of any studies to test if this will work. I doubt if any such
test has been done. I don't know how one could set up such a test without
the preconditions above.

I don't think that a professor should be told to teach Mathematica instead
of quantum mechanics. Unfortunately, that is what happens now! My point is
that students should know Mathematica BEFORE they take the quantum mechanics
course.

An Extra course might help, in freshman year. But students with a potential
for a technical career should be introduced to Mathematica in secondary
school.

When active and dynamic Mathematica notebooks can be freely read,
researchers WILL write their papers as notebooks (or applications). They
want to sell their ideas and they can do that much better with active,
dynamic notebook papers. Printed journals have the same future as
newspapers. They will eventually fade away. More and more people take papers
from the Internet. I don't even have access to a technical library. The only
journal I look at is Science, which the local library carries. (I used to
sometimes visit the NIST library in Maryland, which is not too far away, but
since 9/11 it is closed to ordinary American citizens.) So I don't give a
damn about the printed journals; they're useless to me.

I wouldn't attempt to convince printed journals to accept Mathematica
notebooks. The journals are way too expensive, too slow, and way outdated.
The only thing they offer is a 'stamp of approval' and that isn't worth
much. The real scientific world is much more lively.


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


From: AES [mailto:siegman at stanford.edu] 

In article <hj12vo$bbu$1 at smc.vnet.net>,
 Richard Fateman <fateman at cs.berkeley.edu> wrote:

> But telling professors that Mathematica version 7.0 should be taught 
> instead of (say) quantum mechanics, won't work.  And to tell them that 
> it should be taught as an EXTRA course won't work.  And to tell them 
> that it will be more useful than some other programming language in 
> which most of their colleagues' work is written, won't work.  And to 
> tell them that they should write their papers (at some additional 
> effort) in this new way, and then present them to journals that will 
> just flatten them out into static page images, probably won't work.

Don't know how long Professor Fateman has been in a major ".edu" 
institution, but in my case it's 50+ years.  Seen a lot of things come 
and go.

And I'd say that every word of the preceding paragraph is absolutely 
correct, beyond further discussion.

> So you might start by trying to reform the publication system. 
> Convincing a journal to publish papers that can only be fully viewed by 
> readers who have a computer running Mathematica [which version?] is
> a tough sell.

Also spent a fair amount of volunteer time myself at upper levels of 
major professional societies and dealing with scientific publication 
matters over the years; and this paragraph is equally valid.

And there are a lot of other equally compelling reasons why Mathematica 
won't be the standard scientific publishing system of the future.




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