[time 2] [Fwd: Cramer-Rao Inequality]


Stephen P. King (stephenk1@home.com)
Thu, 11 Mar 1999 17:10:51 -0500


"Stephen P. King" wrote:
>
> Hi guys,
>
> ca314159 wrote:
> >
> > Stephen P. King wrote:
> > >
> > > Hi Robert,
> > >
> > > I hava always suspected that many people are busy building the pieces
> > > to our jig-saw puzzle! This is great!
> >
> > Dear Stephen,
> >
> > Yes. But there are probably less pieces than people realize.
>
> I agree, but we can't a priori determine or compute what they are. See:
> http://tph.tuwien.ac.at/~svozil/publ/casti.ps
>
> (Svozil's work is excellent! :) )
>
> > How does Cramer-Rao fit in with Kosko's understanding of
> > the Cauchy-Schwartz Inequality. If his view is *functionally*
> > equivalent, then there is one piece, not two, and we are
> > only seeing the same thing over and over in many different
> > *forms*.
>
> I don't know. I have not fully digested the ideas involved in
> Cramer-Rao and its possible relationship to Kosko's ideas of the
> Cauchy-Schwartz inequality...
> Yes, we are "only seeing the 'same' thing over and over in many
> different forms," it is the Universe partitioned and represented in some
> finite way. Another way of saying this is: "All signals are just noise
> run through a different filter," or Feynmann's "All electrons are one
> and the same, just at different spacetime points..."
> Contextual function defines form.
>
> > We should be aware of the need to do "data compression on theories"
> > otherwise we accumulate lots of information with no understanding
> > of them.
>
> I agree, but this can't be done in a way that is "invariant with
> respect to thinker." Such would be making the assumption of a "universal
> language" or representational or encoding scheme that works for an
> arbitrary observer, thinker, agent, etc.
>
> This is very interesting!:
> http://tph.tuwien.ac.at/~svozil/publ/time.ps
>
> > Robert
>
> this is interesting:
>
> http://www.optics.arizona.edu/News/Oscillations/July.htm
>
> "Fisher information is an old concept. It has been used since about
> 1922 to judge the quality of statistical estimates. Now it is the
> central concept in a new theory of measurement. This predicts that each
> physical phenomenon arises in response to a request for data about it.
> Roy explained, "The probe particle that initiates a measurement perturbs
> the measured particlefs wave function. This perturbs the particlefs
> Fisher information level, and initiates a variational principle whose
> solution and output is the probability law that produces the requested
> measurement. For example, the Schroedinger wave equation arises out of a
> request for the position of a particle. In this way, the phenomenon that
> is to be measured is produced eon the spot.f The result is a kind of
> local creation of reality. This appears to be an effect that is new to
> both physics and metaphysics, resembling the 'participatory universe' of
> Professor J.A. Wheeler."
>
> Roy continued, "Virtually all of known physics, from relativistic
> quantum mechanics to statistical mechanics to quantum gravity, has been
> derived by this measurement approach. The local creation of reality is a
> microscopic effect. It arises in measuring and interacting with single
> elementary particles. Itfs reminiscent of the microscopic reversibility
> to time of the laws of physics. As with the latter, we donft yet know
> how and if ereality on demandf translates into a macroscopic effect."
>
> A traditional measure of disorder, entropy, has provided the usual
> definitions of time and temperature. Said Roy, "Fisher information
> provides us with new definitions. They arise out of a newly discovered
> eH-theoremf for the information: It can only decrease with time. This
> makes Fisher information a measure of disorder and means that Fisher
> information must provide its own definitions of time and temperature.
> Time is defined to increase when Fisher information decreases.
> Intriguingly, we find that Fisher time and entropy time do not agree
> about 1% eof the time.f Temperature is defined as the resistance to a
> change in energy of the Fisher information of a system. The relationship
> of the Fisher temperature scale to the entropic, or conventional,
> temperature scale is currently not known."
> B. Roy Friedenfs fall 1998 course offering, Opti 529, crosslisted
> as Phys 529, is titled "Physics from Fisher Information, a Unification."
> It will show that Fisher information provides a basis for nearly all
> physical laws, including quantum mechanics, classical e&m theory,
> special and general relativity, diffraction optics, the statistical gas
> laws, quantum gravity, and the ubiquitous 1/f-noise power law. The
> textbook for the course, Physics from Fisher Information, a Unification
> by B. Roy Frieden will be published in December 1998 by Cambridge
> University Press."
>
> Later,
>
> Stephen

attached mail follows:


ca314159 wrote:
>
> Stephen P. King wrote:
> >
> > Hi Robert,
> >
> > I hava always suspected that many people are busy building the pieces
> > to our jig-saw puzzle! This is great!
>
> Dear Stephen,
>
> Yes. But there are probably less pieces than people realize.

I agree, but we can't a priori determine or compute what they are. See:
http://tph.tuwien.ac.at/~svozil/publ/casti.ps

(Svozil's work is excellent! :) )

> How does Cramer-Rao fit in with Kosko's understanding of
> the Cauchy-Schwartz Inequality. If his view is *functionally*
> equivalent, then there is one piece, not two, and we are
> only seeing the same thing over and over in many different
> *forms*.

I don't know. I have not fully digested the ideas involved in
Cramer-Rao and its possible relationship to Kosko's ideas of the
Cauchy-Schwartz inequality...
Yes, we are "only seeing the 'same' thing over and over in many
different forms," it is the Universe partitioned and represented in some
finite way. Another way of saying this is: "All signals are just noise
run through a different filter," or Feynmann's "All electrons are one
and the same, just at different spacetime points..."
Contextual function defines form.

> We should be aware of the need to do "data compression on theories"
> otherwise we accumulate lots of information with no understanding
> of them.

I agree, but this can't be done in a way that is "invariant with
respect to thinker." Such would be making the assumption of a "universal
language" or representational or encoding scheme that works for an
arbitrary observer, thinker, agent, etc.

This is very interesting!:
http://tph.tuwien.ac.at/~svozil/publ/time.ps

> Robert

this is interesting:

http://www.optics.arizona.edu/News/Oscillations/July.htm

"Fisher information is an old concept. It has been used since about
1922 to judge the quality of statistical estimates. Now it is the
central concept in a new theory of measurement. This predicts that each
physical phenomenon arises in response to a request for data about it.
Roy explained, "The probe particle that initiates a measurement perturbs
the measured particlefs wave function. This perturbs the particlefs
Fisher information level, and initiates a variational principle whose
solution and output is the probability law that produces the requested
measurement. For example, the Schroedinger wave equation arises out of a
request for the position of a particle. In this way, the phenomenon that
is to be measured is produced eon the spot.f The result is a kind of
local creation of reality. This appears to be an effect that is new to
both physics and metaphysics, resembling the 'participatory universe' of
Professor J.A. Wheeler."

Roy continued, "Virtually all of known physics, from relativistic
quantum mechanics to statistical mechanics to quantum gravity, has been
derived by this measurement approach. The local creation of reality is a
microscopic effect. It arises in measuring and interacting with single
elementary particles. Itfs reminiscent of the microscopic reversibility
to time of the laws of physics. As with the latter, we donft yet know
how and if ereality on demandf translates into a macroscopic effect."

A traditional measure of disorder, entropy, has provided the usual
definitions of time and temperature. Said Roy, "Fisher information
provides us with new definitions. They arise out of a newly discovered
eH-theoremf for the information: It can only decrease with time. This
makes Fisher information a measure of disorder and means that Fisher
information must provide its own definitions of time and temperature.
Time is defined to increase when Fisher information decreases.
Intriguingly, we find that Fisher time and entropy time do not agree
about 1% eof the time.f Temperature is defined as the resistance to a
change in energy of the Fisher information of a system. The relationship
of the Fisher temperature scale to the entropic, or conventional,
temperature scale is currently not known."
      B. Roy Friedenfs fall 1998 course offering, Opti 529, crosslisted
as Phys 529, is titled "Physics from Fisher Information, a Unification."
It will show that Fisher information provides a basis for nearly all
physical laws, including quantum mechanics, classical e&m theory,
special and general relativity, diffraction optics, the statistical gas
laws, quantum gravity, and the ubiquitous 1/f-noise power law. The
textbook for the course, Physics from Fisher Information, a Unification
by B. Roy Frieden will be published in December 1998 by Cambridge
University Press."

Later,

Stephen



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