Hi FISers,
(I) In the post dated March 21, 2017, I attached a file entitled "What is the
Planckian information ?". The Planckian information (symbolized by I_P) is
defined as the binary logarithm of the ratio between the area under the curve
(AUC) of PDE (Planckian Distribution Equation; see Eqn (1) in the file) and
that of GLE(Gaussian-like Equation; see Eqn (2) in the file):
I_P = log_2 (AUC(PDE)/AUC(GLE))
(1)
PDE is the function for long-tailed histograms (both right and left long
tailed) and GLE is the bell-shaped curve whose rising portion overlaps with the
rising portion of the right-long tailed PDE as exemplifed by Figures 1g, 1i,
1k, 1o, 1r and 1t in the above file and in Figures 15, 16, 20, 22, and 23 in
[1]. It is clear that the greater the deviation of PDE from GLE, the greater
is the I_P value, since GLE represents randomness and the deviation of PDE from
GLE represents non-randomness, order, or information.
(2) There may be many physical, chemical, or mental processes that can give
rise to I_P by producing PDE from GLE. One such mechanism is the so-called
"drift-diffusion" mechanism well-known in the field of decision-making
pyschophysics (see Figure 6 in [2]).
(3) Another mechanism of generating PDE from Gaussian distribution is what I
call the "Rutgers University Admissions Mechanism" (RUAM). That is, if RAUM
does not take into account the students' heights in their admissions process,
the hieght distribution of the RU students would be most likely Gaussian.
However, if RUAM favors short students over tall ones, the RU students' height
distribution will be skewed from the normal curve thus producing PDE. The
degree of skewness of PDE from its Gaussian counterpart (with an equal area
under the curve) can be used as a measure of the information used by RAUM in
selecting RU students. The information derived from PDE based on its skewness
will be referred to as the Planckian information of the second kind, I_PS, to
distinguish it from the Planckian information defined previously (see Eqn (1))
which is now called the Planckian information of the first kind, I_PF:
I_PS = - log_2 (mean - mode/standard deviation)
(2)
(4) We have found that some experimetnal data (e.g., digitized water wave
patterns produced by the sonified Raman spectral bands measured from single
cells) that fit PDE are better modeled with I_PF and some others (e.g., the
mRNA levels measured from yeast cell ensembles) are better modeled with I_PS.
(5) If these considerations are substantiated further in the future, the
following conclusions may be drawn:
(a) There can be more than one kind of information that can be defined based
on the same empirically derived mathematical euqation, depending on supporting
physical mechanisms (or formal algorithms ?).
(b) The reasoning in (1) suggests that the mathematically defined
"information" is arbitrary in the sense of Saussure.
(c) The mathematically defined "information" can be viewed as a sign in the
Peircean sense and hence is irreducibly triadic as depicted in Figure 1:
f
g
Reality ---------> Quantitative Information
---------> Mechanism
|
^
|
|
|
|
|___________________________________________|
h
Figure 1. The irreducibly triadic nature of the "quantitative information" or
the "mathematical information".
f = measurement; g = mental process; h = correspondence,
grounding.
(6) Finally, it may be that PDE (or the skewed Gaussian distribution) provides
a more general model for defining what "information" is than Shannon's
communication system.
All the best.
Sung
References:
[1] Ji, S. (2016). PLANCKIAN INFORMATION (IP): A NEW MEASURE OF ORDER IN
ATOMS, ENZYMES, CELLS, BRAINS, HUMAN SOCIETIES, AND THE COSMOS In: Unified
Field Mechanics: Natural Science beyond the Veil of Spacetime (Amoroso, R.,
Rowlands, P., and Kauffman, L. eds.), World Scientific, New Jersey, 2015, pp.
579-589). PDF at
http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf
[2] Ji, S. (2015). Planckian distributions in molecular machines, living
cells, and brains: The wave-particle duality in biomedical
sciences.<http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vienna_2015.pdf>
In: Proceedings of the International Conference on Biology and Biomedical
Engineering, Vienna, March 15-17, 2015. Pp. 115-137. PDF at
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