Page 91 - Coincidences in the Bible and in Biblical Hebrew

COINCIDENCES IN THE BIBLE AND IN BIBLICAL HEBREW
70 70 COINCIDENCES IN THE BIBLE AND IN BIBLICAL HEBREW

an electric discharge as a result of the potential (gradient) between two poles of a
battery.
The example above for a realization of Boltzmann’ s entropy demonstrates that
lower temperatures are associated with higher rates of generation of entropy. The
same result is obtained (though from different considerations, also associated with

the Second Law of Thermodynamics), in cosmology theories. The universe was at
the highest temperature at the point of the big bang, while its entropy was at its

lowest level (relate to the previously cited references). As the universe started to
expand, and still is expanding, both the average temperature of the universe keeps
falling, and its entropy is increasing.

3.2.3 About the Equivalence of the Two Concepts of Entropy

That the two concepts are indeed equivalent has been the subject of some heated
debate for some time. Weaver, a coauthor with Shannon (Shannon and Weaver
1949), in fact claims that

“the quantity which uniquely meets the natural requirements that one sets
up for “information” turns up to be exactly that which is known in thermo-

dynamics as entropy … That information be measured by entropy, is, after
all, natural when we remember that information, in communication theory,
is associated with the amount of freedom of choice we have in constructing
messages” (therein, 12–13).

A more rigorous connection between information theory (Shannon’s) and
physics (Boltzmann’s) was established by Jaynes (1957).
A demonstration for the debate that is still ongoing about the nature of the
relationship between the two concepts of entropy may be found in “Shannon said
information is physical entropy,” an Internet exchange of messages between a group

of scientists at http://webmail.unizar.es/pipermail/fis/2004-June/000661.html.

3.2.4 Summary of Main Points

• Two concepts of entropy have been developed in two seemingly unre-
lated branches of science and technology: Boltzmann’ s entropy, rooted
in thermodynamics, and Shannon’ s entropy, rooted in the mathematical
theory of communication and information.
• The first concept of entropy resulted from observations about the behav-

ior of physical systems, and it has been applied in various branches of