Biology Reference
In-Depth Information
12.16 The Common Regularities (Isomorphisms)
Found in Physics, Biology, and Linguistics:
The Role of Gnergy
So far I have described two kinds of regularities. The
quantitative regularity
in
the form of the blackbody radiation-like equation (BRE), Eq.
11.27
(without the
additive term), that has been found to apply to blackbody radiation, single-molecule
(Sect.
12.12
) and the
qualitative regularity
in the form of the linguistic rules and
These regularities and their fields of applications are summarized in Rows 2 and 3
in Table
12.13
. The first row of this table also exhibits another quantitative
regularity, i.e., y
ax log x, which can be viewed as a generalization of both the
It may be asserted that BRE and the Boltzmann entropy-like equation (BEE),
y
¼
¼
ax log x, represent two of the very few mathematical equations that have
been found to apply to both
physics
and
biology
.
It should be pointed out that both BRE and BEE can be viewed as the “nondimen-
sionalized” version of Planck's radiation formula, Eq.
11.26
, and Boltzmann equation,
parameters (i.e., numbers without any measuring units) that can be derived from its
original physically meaningful equation based on the
Buckingham
theorem
.
According to this theorem, if a physically meaningful equation contains a certain
number, n, of physical values which can be expressed in terms of k independent
fundamental physical quantities (e.g., mass, length, charge, temperature, etc.), the
original expression can be converted into an equation involving a set of p
p
n-k
dimensionless parameters constructed from the original variables (
http://en.wikipedia.
The first two rows numbered 1 and 2 exhibit the
quantitative regularities
common to six different fields (see 1a, 1b, and 2a-2d in the second column)
and the last row numbered 3 lists the
qualitative regularities
found in two fields
(3a and 3b). Thus, the topics analyzed in this table using the “table method” of
analysis (Ji 1991, pp. 8-13) cover the widest possible range of sciences, unlike, say,
the dimensional analysis (
http://en.wikipedia.org/wiki/Dimensional_analysis
)
which is limited to analyzing
quantitative aspect
of reality (Stahl 1961). As evident
in Table
12.13
, the objects appearing in the first six categories have either some
dimensions or are dimensionless, while the objects in the last two categories
represent qualitative entities without any quantitative dimensions.
The regularities appearing in the first column of Table
12.13
, whether quantita-
tive or qualitative, can be viewed as
systems
,
machines
,
functions
,or
structure-
preserving maps
that convert an input (denoted as x on the top row) into an output
(denoted as y). In category theory (defined in Sect.
12.17
,Eqs.
12.55
and 12.56),
such regularities are referred to as
morphisms
, and x and y are referred to as the
source object
and the
target object
, respectively. A
category
is a very abstract
mathematical construction characterized by a set of
objects
that can be transformed
¼
