Re: question about ODEs and processes they describe

From: Edward Green (spamspamspam3_at_netzero.com)
Date: 06/14/04 

Date: 14 Jun 2004 01:36:40 -0700

"Justin Davis" <jkd3@duke.edu> wrote in message news:<Mw_yc.22890$tH1.1549672@twister.southeast.rr.com>...

> "Alexander Korovyev" <korovyev@rambler.ru> wrote in message
> news:26c82787.0406130553.6b5a4a8a@posting.google.com...

> > ... Since
> > every state must determine some phase trajectory (process' past,
> > present and future relative to the state's time-point), phase
> > trajectories clearly must not intersect. Ok, so far so good. But what
> > about ODE of this kind: dx/dt = x^(2/3)? How many parameters are
> > needed to characterize a state of a process described by this ODE? It
> > looks like the phase space is 2-dimensional but it is not! Suppose the
> > process starts at x = 0, is it possible to tell its evolution? What
> > information do we need for this? Was I told a lie that all ODEs
> > describe finite-dimensional, deterministic and differentiable
> > processes? ...
 
> "This theory helps to describe and study finite-dimensional, deterministic,
> and differentiable processes" does not imply that "all ODEs describe
> finite-dimensional, deterministic and differentiable processes" in the same
> way that "water helps to put out fires" does not imply that "all water is
> used to put out fires." Not sure why it was necessary to include the idea of
> a "lie." Sorta antagonistic.

But it's a very common complaint/reflex/trope. I guess we have to
study literature or psychoanalysis to understand why: it's part of a
personal mythos, like the idea that one's real parents are royalty.
 
> If your system starts at x = 0, why would it move, since at that point,
> dx/dt = 0?

I think he was implying that the future evolution of the system from
this point was indeterminate.

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