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Re: Re: Re: error with Sum and Infinity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102459] Re: [mg102443] Re: [mg102437] Re: error with Sum and Infinity
  • From: "Elton Kurt TeKolste" <tekolste at fastmail.us>
  • Date: Mon, 10 Aug 2009 04:14:12 -0400 (EDT)
  • References: <h5bk64$hlm$1@smc.vnet.net> <200908070932.FAA15211@smc.vnet.net>

There is a concept in the computer programming community called the
"leaky abstraction." (See http://en.wikipedia.org/wiki/Leaky_abstraction
)

The gist of this concept is that (to a first approximation) all
human-implemented abstractions leak -- no matter how hard you try, there
will always be in some circumstances manifestations of the lower-level
infrastructure that supports the abstraction.

So, for example: TCPIP always delivers correct packets -- unless the
transmission lines are down or your power supply is interrupted.

In this case, the abstraction that leaks is the ability to make a proper
symbolic sum.

The reasons that all abstractions are leaky are
   1)  it is generally not humanly possible to anticipate all of the
   situations in which the nasty plumbing will become visible
   2)  to the extent that it is humanly possible it is not generally
   practical to fix them all (you probably don't want to know what
   Mathematica would cost if it were perfect, or how long you would have
   to wait to see it)

In the real world, where cost and time matters, each of us needs to take
ultimate responsibility for the correctness of our results and not
presume that our tools are perfect. 
   

Kurt


On Sun, 09 Aug 2009 18:19 -0400, "Richard Fateman"
<fateman at cs.berkeley.edu> wrote:
> George Woodrow III wrote:...
> > Also including a private response from Richard:
> >
Regards,
Kurt Tekolste



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