From: <complex-science@necsi.org>
Sender: <y3list1@necsi.org> (Yaneer Bar-Yam)
To: complex-science
Date: Thu, 17 Jul 2008 11:28:55 -0400
Message-ID: <redirect-22236595@necsi.org>
Subject: Dual mechanisms of correlations--sychronic and diachronic
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It seems that "interactions" and "correlations" are two of the most widely
used terms in all intellectual discourses, ranging from physics, to
chemistry, to biology, to computer science, to mathematics, and beyond. I
have reasons to believe that "correlations" is more general than and
subsumes "interactions".  It is clear that correlations can be quantitated
using the Shannon's entropy formula.

The purpose of this post is twofold -- i) define two kinds of
correlations, and ii) apply the result to support the conclusion that the
two fundamental questions in biology, i.e., "What is life?" and "What is a
gene?", are entangled in the sense that one question cannot be answered
without taking into account the other, or that answering one automatically
answers the other.

Linguists divide their field into two branches depending on the
methodologies employed -- i) the synchronic approach analyzing language
uses going on here and now, and ii) the diachronic approach focusing on 
the historical development of languages.

Likewise, we may divide "correlations" into two classes --

   i) synchronic correlations between two or more objects resulting from
their physical interactions through space with speeds less than c, the
speed of light, and

  ii) diachronic correlations between two or more objects resulting from
their being derived from a common precursor state/object and thus
appearing to interact instantly or with speeds faster than c. These two
mechanisms of correlations are compared in Table 1.


Table 1.  A comparison between synchronic and diachronic correlations.
__________________________________________________________________________

                              Correlations
                  ________________________________________________________

                  Synchronic                 Diachronic
__________________________________________________________________________

1. Correlations   Space                      Time
   in

2. Speed          Less than c                Faster than c
                                                (i.e., instantaneous)


3. Alternative   "Physical interactions"     "Entanglement" (?)
   names         "Horizontal correlations"   "Vertical correlations"
                 "Relativistic               "Non-relativistic
                     interactions"             interactions"

4. Examples      All interactions in         "Spooky action at a distance"
                    physics and chemistry    All evolved systems
                                                including organisms

5. Scientific    Physics                     Evolutionary biology
   disciplines   Chemistry                   Cosmology
                 Reductionistic              Holistic
                    (molecular) biology         (cell) biology
                 Synchronic linguistics      Diachronic linguistics
                 Computer science
                 Applied mathematics         Pure mathematics (?)
__________________________________________________________________________

The essential point of Table 1 is the logical assertion that correlations
can be dichotomized based on the dichotomy of space and time.

As examples of the dicharonic correlations, I cited the controversial
topics of Einstein's "spooky action at a distance" or "entanglement", but
I am not a theoretical physicist so I do not know if this inclusion will
survive the test of a more rigorous mathematical-physics analysis. However
I will assume that the identification of "diachronic correlations" with
"entanglement" is reasonable for the purpose of this post.

I was motivated to formulate the dual mechanisms of correlations proposed
in Table 1 by my intuition this morning that the two questions, "What is
life? and "What is a gene", may be entangled in the sense that one cannot
be answered without taking into account the other, or that answering one
automatically constrains the answer to the other in such a way as to make
both answers together obey a common set of universal principles. This, of
course, is reminiscent of the "spooky action at a distance" or
entanglement in quantum physics.

If the above conjecture is valid, several useful conclusions may be drawn
on the basis of it:

   i)  Biology divides into two branches -- reductionistic biology (RB)
embodying physicochemical interactions in space whose speed is
constrained by c, and holistic biology (HB) embodying correlations in
the time dimension which can appear as spatial
correlations/interactions at a transluminal speed.

  ii) HB cannot be reduced to RB, nor vice versa, just as a vertical axis
cannot be reduced to a horizontal axis and vice versa in the
2-dimensional Euclidean space.

 iii) There exists a universal set of principles that constraints the
correlations between HB and RB.  One possible member of the postulated
universal set of principles may be the information-energy complementarity
(see Complementarism in my home page, under Publications).  WE may
summarize these ideas schematically as follows:


                       Universal Principles
 (e.g., the principle of information-energy complementarity)

                                ^
                              ^   ^
                            ^       ^
                          ^ ^ ^ ^ ^ ^ ^
           Reductionistic               Holistic
                  Biology               Biology

Figure 1. Reductionistic biology and holistic biology as the
          complementary manifestations of a set of universal principles.

If Figure 1 is valid, it may enable us to infer that synchronic and
diachronic correlations are the complementary aspects/manifestations of
universal principles, just as waves and particles are the complementary
aspects of quantum objects.


With all the best.

Sung

_________________________________________
Sungchul Ji, Ph.D.
Department of Pharmacology and Toxicology
Rutgers University
Piscataway, N.J. 08855