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Re: Re: error with Sum and Infinity

• To: mathgroup at smc.vnet.net
• Subject: [mg102453] Re: [mg102439] Re: error with Sum and Infinity
• From: "Elton Kurt TeKolste" <tekolste at fastmail.us>
• Date: Sun, 9 Aug 2009 18:21:17 -0400 (EDT)
• References: <h5jdfe$152$1@smc.vnet.net> <200908091006.GAA16066@smc.vnet.net>

A software product of any nontrivial level of complexity will have never
provide perfect solutions to the following.

Design decisions:  
For a concept such as "SymbolicProductThreshold" there are many possible
implementations, one of which must be selected in spite of the fact that
there are advantages and disadvantages (known and unknown) to each
option.  Any choice, when made, will be based upon logic that will be
transparent to some users under some circumstances and opaque to other
users or in other circumstances.

Documentation Limitations:
It is prohibitively expensive to design the documentation for a system
so that just the right entry magically appears after the user follows a
search path that makes sense to them while they are thinking about the
particular syntactical and semantic concerns of the moment.  The best
that we can hope for is that there is always some way to discover the
Mathematica construct needed.  

Alternative syntax:
As with a natural language, a well-designed technical language will
incorporate redundancy that allows its users to reach a solution without
necessarily having to find the unique solution (costly and
time-consuming).  This, of course, means that there are often many
alternative ways to achieve some immediate objective, some of which are
better than others (with the ordering depending on circumstances).  

Neither programming nor mathematics is a discipline in which the path to
the solution to any particular problem is discovered merely by following
the signposts left by some previous traveller.  These are creative
processes in which there is a responsibility on the part of the user to
test their product and use appropriately robust development processes so
as to minimize the likelihood that some nuance of the program and its
environment yields an incorrect result.

I see a discussion groups such as this as forum by which we help each
other through these inherent difficulties -- it is one part of the
"appropriate development process."
Regards,
Kurt Tekolste

• References:
  • Re: error with Sum and Infinity
    • From: Richard Fateman <fateman@cs.berkeley.edu>