Stephen P. King (stephenk1@home.com)
Wed, 05 May 1999 22:13:57 -0400
Dear Hitoshi,
I have the book on order...
Here is a critique by Chris Hillman et al:
http://members.home.net/stephenk1/Outlaw/Frieden.txt
I got:
Fisher's arrow of time in quantum cosmology (1998)
by Frieden, B. Roy & Rosu, H. C.
Journal Title: Modern Physics Letters A
Volume Number: 13
Page Number: 39
I is awesome! I am putting a summary together. Perhaps I'll finish
tomorrow. I am convinced that his work dovetails into ours! We need to
seriously think about the information theoretical aspects of LS theory!
I have some interesting ideas but not words. :( I think in pictures ->
dyslexia! I hate it, I like a person struck deaf when trying to say
Eureka! :( But I shall try:
The fundamental assumptions, such as Noeter's theorems need to be
looked at very carefully within the LS theory! No connections between
LSs -> no Universal Absolute Unique space-time with a priori
Langrangians -> Conservation Laws are <<glocal>>? since they only apply
to finite clusters of interacting LSs...
I have said before that there is no unique manifold X (Riemannian or
other wise) for all LSs to be fibered into; I think that this relates to
the "operator ordering problem for coherent states". This also plays
into our thinking about histories (sum over histories, etc.!) as an
aspect of time.
Clocks merely gauge the "flow" of the LS scattering propagation, they
do not define a unique ordering in themselves unless we could show that
the ordering of the configurations of the quantum mechanical particles!
This is like how the numbers on the face of an analogue clock are
ordered mod 12: ..., 1, 2, ..., 11, 12, 1, 2, ... . We could also think
of a of a non-cyclic model of clock that uses an endless paper tape with
numbers: ..., n-1, n, n+1, ...
I see these as an example of the "streams" in Peter's work! I think
there are a minimum of three components to a clock: Two disjoint sets of
streams and a mapping between the two. The configurations of positions
and velocities are streams and the mapping -the quotient operation-, is
maybe, their mutual entropy (how much of the whole of one is a subset of
the other's powerset) - (there is something missing in this line of
thought!) I think that the infomorphism maps LS clocks into (up to onto
at the limit m -> +/- \infinity) each other.
How this works into Frieden's thinking I am working on... ;) It does
begin to answer Lance's challenge to me. :)
Onward,
Stephen
Hitoshi Kitada wrote:
>
> Dear Friends,
>
> Is there anyone who has Frieden's book?
>
> Best wishes,
> Hitoshi
>
> ----- Original Message -----
> From: Stephen P. King <stephenk1@home.com>
> To: <time@kitada.com>
> Sent: Wednesday, May 05, 1999 11:12 PM
> Subject: [time 276] [Fwd: Fisher information]
>
> ----- Original Message -----
> From: Christopher Brown <cbrown@chem1.chem.dal.ca>
> To: <stephenk1@home.com>
> Sent: Wednesday, May 05, 1999 11:53 PM
> Subject: Re: Fisher information
>
> > > I have assembled a link page on Fisher information and have a
> > >definition: "The Fisher Information about a parameter is defined to
> > >be \theta the expectation of the second derivative of the
> > >loglikelihood."
> > >http://members.home.net/stephenk1/Outlaw/fisherinfo.html
> > > But I am still needing an intuitive grasp of that it means. :)
> >
> >
> > In short, when you estimate a parameter, you estimate it's value usually by taking
> > the estimate of the parameter to be the maximum likelihood value. So we get an
> > estimated parameter value, and we know it's uncertain. Imagine it as a normal
> > distribution, the center of which is our estimate, and the variance of which is the
> > uncertainty we have in the location of our estimate. The Fischer Information
> > essentially describes how sharp that normal distribution is around our estimate.
> > More Fischer Information roughly implies a more informative estimate (i.e. tighter
> > spread around the MLE).
> >
> > Hope it helps,
> > CDB
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