Yes of
course. You're comparing different attributes of something, not
different time periods of the same attribute. It's also important
that you're substituting a model for a physical system, but the main reason your
comparison of doesn't follow my principle is that you're
comparing they're different things, not different times. Think
about it this way. For a continuous process to have an increase it
needs time and a rate of change. To achieve that rate of
change it first needs a finite period of acceleration. To
achieve that acceleration it first needs a finite period of jerk (3rd deriv),
and so on, etc, etc., with all higher derivatives of the same sign for
some finite period.
It may
be the general case that during the growth of a physical system you can
find many measures that change in similar ways, but you will also also find many
measures that don't. Of course any physical thing has many
kinds of measures and frequently science can only make sense of a few, or
sometimes none at all. Without searching the range of measures
available It's more or less a matter of luck whether you pick one that reflects
what's happening broadly. Energy flow is a good bet in almost
circumstances, for example, and temperature may not show any evidence of
change at all in a dramatically reorganizing complex
system.
The
theorem is about the beginning and ending of energy flows, and my
observation that the same principle also broadly applies to any kind of measure
that reflects change that begins or ends. The statement is
that you can reliably expect to find periods of time during which that
measure will imply change that is exponential-like. Models as far as
I can tell (like P = R -
C) don't ever describe their own emergence and project only
virtual worlds consuming no energy,... so my machinations about the physical
world don't seem to apply to them or any of the abstract measures they
contain. I'm only talking about real
stuff.
Phil Henshaw ¸¸¸¸.·´ ¯ `·.¸¸¸¸
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-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Robert Holmes
Sent: Monday, October 30, 2006 5:02 PM
To: FRIAM
Subject: Re: [FRIAM] Growth (was Re: so what would be wrong withsayingwhatyou think?)
On 10/29/06, Phil Henshaw <[EMAIL PROTECTED]> wrote:Robert,
<snip>Where the implication that things beginning from scratch have to display
implied derivatives of the same sign comes from is a corollary of the
conservation laws.<snip>
Consider these 3 attributes of a company: revenue R, cost C, profit P. My simple model of a company's finances say that P = R - C. Differentiate with respect to time and get dP/dt = dR/dt - dC/dt. Assume that dR/dt at t=0 and dC/dt at t=0 are both positive. Does this imply that dP/dt >0? No; not if dR/dt < dC/dt at t=0.
So the first derivatives of the attributes of a system do not necessarily have the same sign.
Robert
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