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MathGroup Archive 2004

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Re: Energy content of a mathematical result.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48680] Re: Energy content of a mathematical result.
  • From: "Fred Klingener" <gigabitbucket at brockeng.com>
  • Date: Thu, 10 Jun 2004 02:43:34 -0400 (EDT)
  • References: <ca3gnu$rri$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

<Matthias.Bode at oppenheim.de> wrote in message
news:ca3gnu$rri$1 at smc.vnet.net...
> Dear Colleagues,
>
> is there a theory - or hypothesis - which share of the processors energy
> consumption goes into the result when e. g. a system of equations is being
> solved or a list is being subjected to Sort (by Mathematica)? - The
> processors output cannot be just 100 per cent hot air.

I would understand your question better if I could cast it in terms of the
thermodynamics. On Google, "thermodynamics computation" gets 65,000 hits and
"entropy computation" gets twice that.  So it's safe to conclude that
there's an established theoretical basis (more likely 65,000 different and
mutually exclusive bases) for the discussion.

If you're saying that Sort reduces the entropy of a List, ("entropy sort"
gets 127,000 hits) then you have some basis for establishing what is useful
work and what is not.  I think it's a common school exercise to compare the
energy expenditures for a given entropy change realized by different sort
algorithms (the implication is that any notions of the "energy of a result"
are kind of bogus because they're path dependent - the path-independent
state variable is going to be the entropy), but the inclusion of interaction
with the OS would be an interesting complication.  Pretty clearly, the time
expended on 'System Idle Process' would be "100 per cent hot air" (an
innappropriate analogy, because you can do lots of useful work with hot
air), but would servicing a Travelocity pop-up window increase or decrease
the entropy?

Advice is usually worth what you pay for it.
Fred Klingener


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