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

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