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 <fis-boun...@listas.unizar.es> on behalf of Michel Petitjean <petitjean.chi...@gmail.com> 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 <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. > _______________________________________________ Fis mailing list Fis@listas.unizar.es https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flistas.unizar.es%2Fcgi-bin%2Fmailman%2Flistinfo%2Ffis&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C171407db4122453fe72a08d5b4465e1f%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C636613136684543650&sdata=SGe1nIzwBEg%2BzgW58GSDulk015IzSdlQqTQB7XhEBcE%3D&reserved=0

_______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis