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Re: error with Sum and Infinity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102508] Re: error with Sum and Infinity
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Wed, 12 Aug 2009 04:32:07 -0400 (EDT)

On 8/11/09 at 4:02 AM, fateman at cs.berkeley.edu (Richard Fateman)
wrote:

>I still agree entirely.

>Where I differ is that there is a distinct possibility that a
>program could look at the definition of the summand and notice that
>it was a constant everywhere in the interval except at one place,
>which leads immediately to a method to do the summation.  This is
>what you propose that a human would do, and I suggest that a program
>could do the same thing.  Indeed, given the cleverness of
>programmers at WRI, I would not know whether or not Mathematica
>would get the right or wrong answer here without trying it.
>Furthermore, none of us can tell whether some future version of
>Mathematica might get this right, as stated.  If the summand
>violated some stated rule of construction and was not well-formed,
>then we could say that it is unexpected that Mathematica would get
>the right answer today or any time in the future.

I don't disagree with what you've written here. That is I
definitely agree to the extent possible Mathematica should do
the right thing which in this case would be to notice the series
was constant everywhere except one point. And given the
cleverness of programmers at WRI, it may well be a future
version does this. But...

No matter how clever the programmers are, there are limits to
what they can accomplish. So, there will always be similar
issues in any future version of Mathematica. It will always be
up to the user to intelligently apply Mathematica to avoid these issues.

Ultimately, Mathematica is a tool with no intelligence. It is up
to the user to understand this and apply the tool in an
intelligent manner that gets the desired result



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