From: ingber@umiacs.umd.edu (Lester Ingber)
Newsgroups: bionet.info-theory
Subject: Re: human mind, an ergodic source?
Date: 6 Nov 92 16:58:23 GMT
Distribution: usa
Organization: UMIACS, University of Maryland, College Park, MD 20742

In reply to the posting included below, I think that it is unlikely
that the human mind can be considered ergodic over any extended period
of time, for at least two reasons:  (1) The mind is not a closed system
(although many try to keep it so), and is often driven by external
interactions.  (2) Any reasonable modeling of large-scale brain
activity generally gives rise to nonlinear stochastic nonequilbrium
probability distributions.  These can be sticky to handle correctly
mathematically, even in the limit of a "multiplciative noise" system
(essentially Brownian motion + nonlinear multivariate driving forces
+ nonconstant coefficients of the noise).  However, when properly
treated, an information expression can be calculated over the
spatial-temporal domain of neocortical activity, as has been done in
%A L. Ingber
%T Statistical mechanics of neocortical interactions:
A scaling paradigm applied to electroencephalography
%J Phys. Rev. A
%S 6
%V 44
%P 4017-4060
%D 1991
 
This is further developed in
%A L. Ingber
%T Generic mesoscopic neural networks based on statistical mechanics
of neocortical interactions
%J Phys. Rev. A
%V 45
%S 4
%P R2183-R2186
%D 1992
 
These can be retrieved via anonymous ftp from ftp.umiacs.umd.edu in
the pub/ingber directory as eeg.ps.Z and mnn.ps.Z, resp.  For those
unfamiliar with retrieving files via anonymous ftp, at the end of
this posting I include some instructions.

Ergodicity also has its "practical" side, in that for most systems
only a weak ergodicity is relevant since no one really pretends to
visit all states.  A nice discussion of the problems is in Part VII of
%A S.-K. Ma
%T Statistical Mechanics
%I World Scientific
%C Philadelphia
%D 1985

This also is relevant in computational problems.  I have addressed
this in a review article I'm preparing,
%A L. Ingber
%T Simulated annealing: Practice versus theory
%J Statistics Comput.
%V
%S
%P (to be published)
%D 1993
For example, in a sample test problem a global minimum was obtained
among 10**20 local minima using such techniques; however, visiting
each minimum for a millisecond would take about the present age of
the universe to visit all these minima.  Similarly, in another test
problem, a global minimum was obtained among 10**50 local minima;
however, most of these are beyond a typical workstation's precision
and recognition.

Lester

  |  Prof. Lester Ingber               ingber@alumni.caltech.edu  |
  |  P.O. Box 857                                                 |
  |  McLean, VA 22101       703-848-1859 = [10ATT]0-700-L-INGBER  |

In article <Bx9oo0.I5t@ncifcrf.gov> toms@fcs260c2.ncifcrf.gov (Tom Schneider) writes:
>In article <1992Oct27.164431.5092@athena.mit.edu> makra@athena.mit.edu
>(Mohamad A. Akra) writes:
>
>|Does anyone know if there has been any work justifying (or criticizing)
>|the modeling of the human mind as an ergodic process? where ergodic
>|means, in plain terms, that the model parameters can be estimated from
>|observing the output over some time, using the law of large numbers.
>
>That's an interesting thought.  My understanding is that the 'parameters' are
>the probabilities of the states.  That is, if a system is ergodic (or fits the
>ergodic theorem, help, someone!) then one can follow it over time (infinite!)
>and this will tell you the probabilities of states; those will be the same as
>if one had set up a series of parallel systems and looked at one instant
>(infinite number of parallel systems).  Brownian motion is ergodic (my
>understanding, please correct as needed), as one can do this and get the
>Gaussian distribution either way.
>
>So if the mind were ergodic, it would mean we couldn't change with time, hence
>we couldn't learn!  So the question is whether, excluding learning, one can
>look at large numbers of organisms to obtain data about how a single organism
>may act (or the other way around).  Curious and interesting.  Sounds like
>behavioral population genetics on the fruit fly Drosophila!
>
>  Tom Schneider
>  National Cancer Institute
>  Laboratory of Mathematical Biology
>  Frederick, Maryland  21702-1201
>  toms@ncifcrf.gov


              Getting (P)Reprints via Anonymous Ftp

     Please  note  that  some of my (p)reprints can be downloaded
via anonymous ftp from ftp.umiacs.umd.edu [128.8.120.23]  in  the
pub/ingber directory.  Just follow one of these two procedures on
your local machine:

                           Interactive

local% ftp ftp.umiacs.umd.edu
[local% ftp 128.8.120.23]
Name (ftp.umiacs.umd.edu:yourloginname): anonymous
Password (ftp.umiacs.umd.edu:anonymous): [type in yourloginname]
ftp> cd pub/ingber
ftp> binary
ftp> get README.file [see list below]
ftp> get file.ps.Z [see list below]
ftp> quit
local% uncompress file.ps.Z
local% lpr [-P..] file.ps [to your PostScript laserprinter]

                             Ftpmail

     Send the following electronic mail request to DECWRL:
local% mail uunet\!decwrl\!ftpmail
[local% mail uunet_or_your_internet_link\!decwrl\!ftpmail]
[Subject: Your_own_identifier_tag [e.g., Ingber file]]
connect 128.8.120.23 anonymous yourloginname
binary
uuencode
chdir /pub/ingber
get README.saga saga.ps.Z
[or any other file(s) from the list:
README.eeg README.ingber README.markets README.mnn README.saga
eeg.ps.Z ingber.ps.Z markets.ps.Z mnn.ps.Z saga.ps.Z ]
quit
^D [or however you send mail]

     If you have problems with either of these  methods,  let  me
know  and  I will be glad to prepare a uuencoded copy to email to
you.  With a uuencoded copy, first save to mailfile.   Strip  out
lines  before  "begin"  and  after  "end".   Save to mailfile.uu.
Applying `local%  uudecode  mailfile.uu'  will  leave  file.ps.Z.
Then proceed as above.

     Sorry,  but  I  cannot take on the task of mailing out hard-
copies.

-- 
  |  Prof. Lester Ingber               ingber@alumni.caltech.edu  |
  |  P.O. Box 857                                                 |
  |  McLean, VA 22101       703-848-1859 = [10ATT]0-700-L-INGBER  |