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].
GP
definition
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
psychophysics.
Reference:
[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.
Sung
________________________________
From: Fis <[email protected]> on behalf of Michel Petitjean
<[email protected]>
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
distributions.
Probability distributions are presented on the Wikipedia page:
https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FProbability_distribution&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C171407db4122453fe72a08d5b4465e1f%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C636613136684543650&sdata=mMWRW6FO6hrflqQRGhXtoTkhDqt0FTspjtT9YGgNn2c%3D&reserved=0
Don't read all this page, the beginning should suffice.
Then, the skewness is explained on an other wiki page:
https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSkewness&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C171407db4122453fe72a08d5b4465e1f%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C636613136684543650&sdata=HQh0OOxgyE5fXZMMEfZF6mG5S0yKOPNjoEPO%2FNo28rA%3D&reserved=0
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,
Michel.
2018-05-07 19:55 GMT+02:00 Michel Petitjean <[email protected]>:
> 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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