Hi Michel,

Thank you for your informative comments and helpful suggestions in your earlier 
post (which I happened to have deleted by accident).  In any case I have a copy 
of the post so I can answer your questions raised therein.

(1)  I am defining the Planckian information, I_P, as the information required 
to transform a symmetric, Gaussian-like equation (GLE), into the Planckian 
distribution.  which is the Gaussian distribution with the pre-exponential 
factor replaced with a free parameter, A,   i.e., y = A*exp(-(\m - x)^2/2\s^2), 
which was found to overlap with PDE (Planckian Distribution Equation) in the 
rising phase.  So far we have two different ways of quantifying I_P: (i) the 
Plamck informaiton of the fist kind, i_PF = log_2 [AUC(PDE)/AUC(GLE)], where 
AUC is the area under the curve, and (ii) the Planckian information of the 
second kind, I_PS = -log_2[(\m -mode)/ \s], which applies to right-skewed 
long-tailed histograms only.  To make it apply also to the left-skewed 
long-tailed histograms, it would be necessary to replace (\m - mode) with its 
absolute value, i.e., |\m - mode|.

(2)  There can be more than two kinds of Planckian information, including what 
may be called the Planckian information of the third kind, i.e., I_PT = - 
long_2 (\chi), as you suggest.  (By the way, how do you define \chi ?).

(3)  The definition of Planckian information given in (1) implies that  I_P is 
associated with asymmetric distribution generated by distorting the symmetric 
Gaussian-like distribution by transforming the x coordinate non-linearly while 
keeping the y-coordinate of the Gaussian distribution invariant [1].

              Gaussian-like Distribution -------------> PDE 
--------------------> IP

Figure 1.  The definitions of the Gaussian process (GP) and the Planckian 
information (IP) based on PDE, Planckian Distribution Equation.  GP is the 
physicochemical process generating a long-tailed histogram fitting PDE.

(4)  I am assuming that the PDE-fitting asymmetric histograms will always have 
non-zero measures of asymetry.

(5)  I have shown in [1] that the human decision-making process is an example 
of the Planckian process that can be derived from a Gaussian distribution based 
on the drift-diffusion model well-known in the field of decision-making 

   [1] Ji, S. (2018).  The Cell Language theory: Connecting Mind and Matter.  
World Scientific Publishing, New Jersey.   Figure 8.7, p. 357.

All the best.


From: Fis <fis-boun...@listas.unizar.es> on behalf of Michel Petitjean 
Sent: Monday, May 7, 2018 2:05 PM
To: fis
Subject: Re: [Fis] Are there 3 kinds of motions in physics and biology?

Dear Karl,
In my reply to Sung I was dealing with the asymmetry of probability
Probability distributions are presented on the Wikipedia page:
Don't read all this page, the beginning should suffice.
Then, the skewness is explained on an other wiki page:
Possibly the content of these two pages is unclear for you.
In order to avoid a huge of long and non necessary explanations, you
may tell me what you already know about probability distributions and
what was unclear from my post, then I can explain more efficiently.
However, I let Sung explain about his own post :)
Best regards,

2018-05-07 19:55 GMT+02:00 Michel Petitjean <petitjean.chi...@gmail.com>:
> Dear Karl,
> Yes I can hear you.
> About symmetry, I shall soon send you an explaining email, privately, because 
> I do not want to bother the FISers with long explanations (unless I am 
> required to do it).
> However, I confess that many posts that I receive from the FIS list are very 
> hard to read, and often I do not understand their deep content :)
> In fact, that should not be shocking: few people are able to read texts from 
> very diverse fields (as it occurs in the FIS forum), and I am not one of them.
> Even the post of Sung was unclear for me, and it is exactly why I asked him 
> questions, but only on the points that I may have a chance to understand (may 
> be).
> Best regards,
> Michel.
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