---------- Forwarded message ---------- From: Sungchul Ji <s...@rci.rutgers.edu> Date: Sat, Nov 14, 2015 at 6:47 PM Subject: Re: [PEIRCE-L] The Universe as a Self-Organizing Musical Instrument (USOMI) To: John Collier <colli...@ukzn.ac.za>
John, Jerry, lists, (1) John asked, "Isn’t this just a straightforward consequence of Fourier analysis?" Indeed John is right. Any curve, including long tailed histograms, can be fit into a series of sine waves, as the Fourier theorem predicts ( https://en.wikipedia.org/wiki/Fourier_series). In fact we have found that not all long tailed histograms fit PDE (Planckian Distribution Equation), although more than 90% of them that we have examined so far do. As an example, see how a series of 8 sine waves (green curve) in Figure 1 can fit the long tailed histogram (blue curve) much better than PDE (red curve). [image: Inline image 5] Figure 1. The superiority of the Fourier series over PDE in fitting long tailed histograms. (I thank one of my students, Seungkee Kim, for producing this graph.) Several conclusions and definitions can be formulated from these observations: (i) All long tailed histograms fit Fourier series, i.e., a series of simple sine waves, confirming the Fourier theorem. (ii) Only a subset of the histograms fitting the Fourier series also fits PDE. (iii) Just as the Planckian information (I_P) is defined as the binary logarithm of the ratio of the area under the curve (AUC) of PDE over the AUC of Gaussian-like equation (GLE), i.e., I_P = log_2[AUC(PDE)/AUC(GLE)], so (111415-1) it would be logical to define as the Fourier information (I_F) the binary logarithm of the ratio of the AUC of the N-term Fourier series (FSN) fitting a histogram over the AUC of GLE, i.e., I_F = log_2[AUC(FSN)/AUC(GLE)] (111415-2) GLE is defined as the Gaussian equation wherein the pre-exponential factor, sigma x (2 x pi)^0.5, is replaced by a free parameter, A. (iv) M. Burgin, in his book, "Theory of Information: Fundamentality, Diversity and Unification" (World Scientific, New Jersey, 2010, pp. 131-133) lists no less than 35 ways of defining information. I_P and I_F are but two more such definitions. (v) Since all experimental records (some of which may be no more than half waves), including long tailed histograms, are expected to fit functions consisting of a series of N sine waves (where N could be 5-20 ?), it seems logical to conclude that all these records result from some mechanisms implicating wave phenomena, whether electromagnetic, mechanical, chemical, acoustic, or gravitational. (2) In response to Jerry's comments about what is new in my and Petoukhov's findings that the Universe may behave as a self-organizing system of oscillators, or as a musical instrument (since ancients have already thought about it), I just want to remind him that it took more than two millennia for the concept of the atom, first invoked by Democritus, to be proven scientifically. Similarly, with all due humility, I am tempted to suggest that the Pythagoras' and Plato's idea of musica universalis ( https://en.wikipedia.org/wiki/Fourier_series) may have taken more than two millennia to be proven empirically through the Fourier theorem, the universality of PDE, and the isomorphism between molecular genetics and waving phenomena discovered by Petoukhov through the application of matrix mathematics (http://sciforum.net/conference/70/paper/2812). All the best. Sung On Sat, Nov 14, 2015 at 5:49 AM, John Collier <colli...@ukzn.ac.za> wrote: > Jerry, > > > > Isn’t this just a straightforward consequence of Fourier analysis? Are you > implying that Fourier analysis has no scientific value (it is tautological, > so no additional information content – so no additional empirical content), > or do you mean to imply some other value with your use of “scientific”? I > would prefer to keep the term from being value laden, but I know it is used > that way, though usually pejoratively. I really don’t understand your usage > here. > > > > John Collier > > Professor Emeritus, UKZN > > http://web.ncf.ca/collier > > > > *From:* Jerry LR Chandler [mailto:jerry_lr_chand...@me.com] > *Sent:* November 14, 2015 7:04 AM > *To:* Sungchul Ji > *Cc:* PEIRCE-L > *Subject:* Re: [PEIRCE-L] The Universe as a Self-Organizing Musical > Instrument (USOMI) > > > > Sung: > > > > Every 'vibrational motion' can be approximated by a sequence of intervals. > > > > How does your work relate to any form of scientific conclusion? > > > > In other words, what are the premisses? > > And what are the propositions? > > And, how are these premisses and propositions related to a scientific > conclusion? > > (such as "Life is...???) > > > > Cheers > > > > jerry > > > > > > > > On Nov 13, 2015, at 6:33 PM, Sungchul Ji wrote: > > > > Hi, > > > > Charles Peirce believed that there are "simple concepts applicable to > every subject": > > > > > > “*The undertaking which this volume inaugurates is to make a philosophy > like * (111315-1) > > > > > > * that of Aristotle, that is to say, to outline a theory so comprehensive > that, for a long time to come, the entire work of human reason, in > philosophy of every school and kind, in mathematics, in psychology, in > physical science, in history, in sociology, and in whatever other > department there may be, shall appear as the filling up of its details. > The first step toward this is to find simple concepts applicable to every > subject. *“ (Heartshorne and Weiss, 1931, p. vii; emphases > were added).” > > > > The purpose of this post is to bring to your attention some recent > evidences supporting the suggestion that "vibrational motions" of material > systems may be one of the simple concepts that applies to everything in the > Universe -- from bond vibrations in molecules, to concentration waves > inside the cell, to sound waves in human speech, to electromagnetic waves > from the sun, the brain, and i-phones, and to the gravitational waves yet > to be confirmed (Ji, 2015 a, b). > > > > Evidence #1: > > > > Petoukhov (2015) has accumulated an impressive amount of evidence during > the past decade that genes exhibit properties resembling mechanical systems > executing vibrational motions, since both genetic and vibratory systems > reveal similar regularities when analyzed using matrix algebra. For > example, the Punnet squares in molecular genetics show the patterns of > allele combinations that are similar to the patterns of frequency > arrangements in the tensor products of matrices representing vibrational > motions of mechanical systems. Based on these observations, Petoukhov > concluded that *living organisms* are akin to *musical instruments: * > > > > > > “*Any living organism is a great chorus of coordinated oscillatory > * (111315-2) > > > * (also called vibrational; my addition) processes (mechanical, > electrical, piezoelectric, biochemical, etc.), which are connected with > their genetic inheritance along chains of generations*.” > > > > “*From a formal point of view, a living organism is an oscillatory > *(111315-3) > > > *system with a large number of degrees of freedom, Resonances in such a > system can serve as mechanisms for harmonization and ordering of its set of > oscillatory processes*.” > > > > “*A new slogan can be proposed: any living body is a musical > *(111315-4) > * instrument** (a synthesizer with an abundance of rearrangements * > *of resonant modes).” (For convenience, we may refer to this idea * > *as the Petoukhov hypothesis; *see *Figure 1**)* > > > > > > > <image.png><image.png> > > -- > > > > *Figure 1*. The Petoukhov hypothesis that organisms are musical > instruments. > > > > *Evidence #2:* > > > > Based on an analysis of the microarray data measured from budding yeast > undergoing the glucose-galactose shift, I was led to conclude that *genes* > act as *molecular machines *(Ji, 2009). It is very likely that the > functions of a '*gene molecular machine*' (GMM) involves coupled > oscillatory motions of component atoms under physiological conditions and > hence can be characterized in terms of the (Hessian) matrix of frequencies > and associated eigen values and eigen vectors, in agreement with the > *Petoukhov > hypothesis* described above. In other words, the > "genes-as-molecular-machines hypothesis" and the "Petoukhov hypothesis" may > be synonymous. > > > > > > *Evidence #3:* > > > In (Ji, 1974; not so recent, I admit), I postulated that enzymic catalysis > results from coordinated vibrational motions of chemical bonds in enzyme > molecules: > > > > “*An ordinary enzyme possesses 103 to 104 vibrational degrees of > *(111315-5) > > > > > > > > *freedom. It is therefore reasonable to assume that the vibrational > motions of individual bonds in the enzyme will be far more important in > enzyme catalysis than the translational or rotational motions of the > enzyme as a whole. Given all the vibrational frequencies of the > individual bonds in an enzyme, as well as their three–dimensional > arrangements, we can in principle deduce the thermodynamic and catalytic > properties of the enzyme under any conditions.”* > > > > > *Evidence #4:* > > > In 2008 (Ji, 2012), a mathematical equation, called the Planckian > Distribution Equation (PDE), was discovered at Rutgers, and this equation > has been found to fit many long tailed histograms reported in diverse > fields of inquiries, including > > > (i) atomic physics, > > (ii) protein folding, > > (iii) single-molecule enzymic catalysis, > > (iv) mitochondrial volume distributions in cells, > > (v) whole-cell mRNA metabolism, > > (vi) fMRI signals, > > (vii) decision-making time histograms, > > (viii) EEG and ECoG, > > (ix) world length frequency distributions in speeches, > > (x) sentence length frequency distribution in texts, > > (xi) US annual income distributions, and > > (xii) the polarized cosmic microwave background radiation (fitted by PDE > only partially, probably due to the randomizing effects of galactic dust). > > > > (PDE is y = A/(X + B)^5/(Exp(C/(x + B)) - 1), where A, B and C are free > parameters, x and y are, respectively the x- and y-coordinates of a long > tailed histogram.) > > > > These observations led me to conclude that the universal applicability of > PDE to long tailed histograms may be attributed to > > > > ". . . the universality of the wave-particle duality embedded in PDE." > (111315-6) > > > > The first factor in the Planck radiation formula, and hence in PDE as > well, is related to the number of the standing waves in > > the system under consideration and the second factor to the average energy > of the standing waves ( > http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html). These ideas and > observations are diagrammatically summarized in Figure 2: > > > > <image.png> > > > > *Figure 2.* The hypothesis that the Universe is a system of > self-organizing oscillators that generate long-tailed histograms fitting > PDE. This figure can be viewed as an extension of the Petoukhov > hypothesis from organisms, Figure 1, to the Universe Itself based on the > apparent universality of the PDE. > > > > > > In conclusion, the works of Petoukhov and mine over the past several > decades appear to support the notion that oscillatory/vibrational/wave > motions play fundamental roles not only in physics but also in living > systems and that mathematics, especially matrix algebra, is indispensable > in revealing the structures hidden behind empirical regularities. > > > > > > Any questions or comments would be welcome. > > > > Sung > > > > > > Sungchul Ji, Ph.D. > > Associate Professor of Pharmacology and Toxicology > Department of Pharmacology and Toxicology > Ernest Mario School of Pharmacy > Rutgers University > Piscataway, N.J. 08855 > 732-445-4701 > > www.conformon.net > > > > > > References: > > Ji, S. (1974). Energy and Negentropy in Enzymic Catalysis. Ann. N. Y. > Ac. Sci. 227:419-437. PDF at http://www.conformon.net under Publications > Refereed Journal Articles. > Ji, S. (2009) Genes as molecular machines: Microarray Evidence for > structural genes regulating their own transcripts. Abstracts, The 2009 > Joint RECOMB Satelite Conference on Regulatory Genomics-Systems Biology - > DREAM4. MIT/Broad Institute/CSAIL, Boston, December 2-6, 2009. P. 99.Ji, > S. (2012). Molecular Theory of the Living Cell: Concepts, Molecular > Mechanisms, and Biomedical Applications. Springer, new York. > > Ji, S. (2015a). Planckian distributions in molecular machines, living > cells, and brains: The wave-particle duality in biomedical sciences. > *Proceedings > of the International Conference on Biology and Biomedical Engineering*. > Vienna, March 15-17, 2015. Pp. 115-137. Retrievable from > http://www.inase.org/library/2015/vienna/BICHE.pdf. > > Ji, S. (2015b). Planckian Information (I_P): 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 > (R. Amoroso, P. Rowland and L. Kauffman, eds.) World Scientific , New > Jersey. Pp. 579-589. > > Petoukhov, S. D. (2015). Music and the Modeling Approach to Genetic > Systems of Biological Resonances (Genetic System and Vibrational Mechanics). > The 4th ISIS Summit, Vienna, 2015. Power Point slides at > http://sciforum.net/conference/70/paper/2812. > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the > BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm > . > > > > > -- Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net -- Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net
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