Steven, Ben, list, I do not deny that Wigner's "Unreasonable Effectiveness of Mathematics"(UEM) has empirical support, mainly coming from physics. All I am saying is that the Unreaseaonable Arbitgrariness of Mathematics (UAM) thesis is also supported by empirical results, limitted as they may be as of now, that originate from biology. (Please try to understand the figures that I attached to my prefvious emails, without which you may miss the point I am trying to make with UAM.)
Please rememgber also that UAM is an empirical fact, not a theoretical construct, although it may be theoretically derived from semiotics of Peirce and semiolotgy of Saussure (as I have been attempting to, against strong oppositions from some of you). If if this theoreticl attempt happens to fail, as some of you may predict, it would not invalidate UAM, since it is an observational fact, just as Wigner's UEM is, within its own boundary. On the other hand, if the syllogism I suggested as a means to derive the UAM thesis from first principles in semiotics and linguistics happnes to turn out to be valid, it would strongly support the theory of signs of Peirce and the principle of the aribtraness of signs in linguistics, since they would then be judged consistent with an empirical fact recently discovered in biology. With all the best. 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 > I have a concern in this discussion. First, this notion of Unreasonable > Arbitrariness, has absolutely nothing at all to do with Wigner's > Unreasonable Effectiveness. There is no similarity in an argument for > arbitrariness and one for effectiveness. Wigner's argument speaks to > scalability and applicability of technique, it speaks against the > arbitrary > and for a profound physical uniformity. Such that techniques that are > effective at one level may be universally applied. > > Regards, > Steven > > > > On Thursday, July 3, 2014, Sungchul Ji <[email protected]> wrote: > >> Edwina wrote: >> >> "The difference is as I explained in my original post: (6061-1) >> that between a model and the process of reasoning >> which are not the SAME empirical reality; . . ." >> >> Before I comment on (6061-1), let me repeat what I said about the UAM >> (Unreasonable Arbitrariness of Mathematics) thesis. >> >> Major premise: All signs are arbitrary (Saussure) >> >> Minor premise: Mathematics is an argument symbolic legisign (Peirce) >> >> Coclusion: Mathemtica is arbitrary (consistent with the experimental >> evidecen provided), >> >> where "mathematics" means "mathemtical equations" such as the Planckian >> distribution, the double exponetial function of Lu et al (1998), or the >> ex-Gaussian function of R. D. Luce (1986, p. 100), and NOT "mathematcal >> reasonig" as you wrongly assumed. >> >> Based on this anlaysis, I conclude that >> >> "Statement (6061-1) is a red herring desinged to (6061-2) >> mis-lead readers, away from the true significance >> of the UAM thesis, whihc is empiricallly substantiated" >> >> >> as evident in the graphs that I pains-takingly provided to help readiers >> to understand what I mean. >> >> With all the best. >> >> Sung >> >> >> >> >> >> > No, Sung, the difference in meaning between your terms is not similar >> to >> > 'half-empty' and 'half-full' which uses different terms to describe >> the >> > SAME >> > empirical reality. The difference is as I explained in my original >> post: >> > that between a model and the process of reasoning which are not the >> SAME >> > empirical reality; and the nature of Saussurian semiology. I won't >> repeat >> > it >> > here. >> > >> > Edwina >> > >> > ----- Original Message ----- >> > From: "Sungchul Ji" <[email protected] <javascript:;>> >> > To: <[email protected] <javascript:;>> >> > Sent: Thursday, July 03, 2014 3:10 PM >> > Subject: [biosemiotics:6057] Re: "Unreasonable >> > >> > >> >> You can read my syllogism in eithr of two ways -- as a 3-term >> arguement >> >> (as I intended) or as a 4-term argument (as you mis-interpret agaisnt >> he >> >> evidence I presented), just as there are two ways of describing a >> >> half-filled galss of water -- "half-empty" as you prefer, or >> "half-ful" >> >> as >> >> I see it. >> >> >> >> With all the best. >> >> >> >> Sung >> >> >> >> >> >> >> >> >> >> >> >>> Never mind your endless acronyms, Sung. The fallacy in your >> syllogism >> >>> remains. You can divert the issue to the triadic basis of the sign >> >>> which >> >>> is >> >>> not relevant here, but the syllogistic structure itself has to be >> >>> examined >> >>> - >> >>> and your syllogism, though formally correct (Barbara) is invalid >> >>> because >> >>> of >> >>> the ambiguity of its terms. >> >>> >> >>> Oh, and by the way, if you want to base your comments on Peirce, >> then, >> >>> using >> >>> the 'data-based' approach, it is normal to provide the exact >> reference >> >>> to >> >>> any quotes or analysis of his that you use. Your equally endless >> >>> numbers-in-parentheses does not provide the reference sources. >> >>> >> >>> Edwina >> >>> >> >>> ----- Original Message ----- >> >>> From: "Sungchul Ji" <[email protected] <javascript:;>> >> >>> To: <[email protected] <javascript:;>> >> >>> Sent: Thursday, July 03, 2014 1:36 PM >> >>> Subject: [biosemiotics:6051] Re: "Unreasonable >> >>> >> >>> >> >>>> (Undistorted Figure 1 is attached.) >> >>>> >> >>>> Edwina wrote: >> >>>> >> >>>> "The error is called 'the fallacy of four terms'. (6030-1) >> >>>> A valid syllogism must have exactly three unambiguous >> >>>> categorical terms. But the term 'mathematics' as >> >>>> outlined above is ambiguous. Mathematics is both a >> >>>> process and a producer of models. The specific model >> >>>> chosen may be 'arbitrary' in the sense that it is >> >>>> symbolic, but the process used within that mathematical >> >>>> reasoning is not arbitrary. There are two meanings of >> >>>> mathematics in the syllogism above." >> >>>> >> >>>> It seems to me that, in her zeal to apply "the fallacy of four >> terms" >> >>>> to >> >>>> my syllogism, she may have missed or conveniently ignored the >> EVIDENCE >> >>>> that I provided in my email (see the attached), which unambiguously >> >>>> indicates what is meant by the term "mathematics" appearing in the >> UAM >> >>>> thesis, i.e., "mathematical equations" - more specifically, the >> >>>> Planckian >> >>>> distribution, a double-exponential function, and the ex-Gaussian >> >>>> distribution. To prove me wrong, she should provide the EVIDECNE to >> >>>> support her own conclusion, just as I have done so to support mine. >> >>>> Her >> >>>> failing to provide any such evidence would indicate to me that she >> is >> >>>> engaged in doing "data-free philosophy (DFP)", whereas I am >> interested >> >>>> in >> >>>> doing "data-based philosophy (DBP)". No wonder we do not >> communicate >> >>>> with >> >>>> each other. >> >>>> >> >>>> It is my humble opinion that >> >>>> >> >>>> "Conflating data-free and data-based philosophies may >> (6030-2) >> >>>> underlie most, if not all, major unproductive debates in >> >>>> philosophy, semiotics, and natural sciences." >> >>>> >> >>>> To make a long story short, I am of the opinion that data-free >> >>>> philosophies do not deal with genuine triadic signs, since they >> ignore >> >>>> the >> >>>> third mapping c, in the triadic definition of the Peircean sign: >> >>>> >> >>>> a b >> >>>> Object/Referent -----> Sign/Representamen/Signifer -----> >> Interpretant >> >>>> | ^ >> >>>> | | >> >>>> |_______________________________________________________| >> >>>> c >> >>>> >> >>>> Figure 1. The triadic definition of the Peircean viewed as a >> >>>> mathematical >> >>>> category. >> >>>> >> >>>> The key to the triadic definition of sign given above is the >> >>>> composition >> >>>> condition, a x b = c, which states that >> >>>> >> >>>> "An object determines/constrains a sign (or representamen) >> >>>> (6030-3) >> >>>> which in turn determines its interpretant in such a way that >> >>>> the interpretant is indirectly determined by (or correspond or >> >>>> is correlated to ) the same object that the sign is referring to." >> >>>> >> >>>> It may be convenient to define two classes of signs - those signs >> that >> >>>> meet the requirement of a mathematical category as in Figure 1 and >> >>>> those >> >>>> lacking one or more of the three mappings essential for a >> mathematical >> >>>> category. Such latter signs may be referred to as "Pseudo-signs", >> >>>> "dyadic >> >>>> signs", "degenerate signs", or "incomplete signs." Using these >> terms, >> >>>> I >> >>>> am tempted to propose the following statement whose validity may be >> >>>> testable:": >> >>>> >> >>>> "All nonproductive debates in science, philosophy, and >> >>>> (6030-4) >> >>>> semiotics result from using pseudo or incomplete signs." >> >>>> >> >>>> A corollary of (6030-4) would be: >> >>>> >> >>>> "All intellectual debates in philosophy, science, semiotics, >> >>>> (6030-5) >> >>>> etc. may be resolved by replacing incomplete signs with >> >>>> complete, triadic signs of Peirce." >> >>>> >> >>>> With all the best. >> >>>> >> >>>> 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 >> >>>> >> >>>>> Sung wrote: >> >>>>> >> >>>>> "Mathematics is a species of the sign according to Peirce. >> >>>>> (070114-1) >> >>>>>> All signs are arbitrary according to Saussure. Therefore, >> >>>>>> mathematics is arbitrary." >> >>>>> >> >>>>> This is invalid for two reasons: >> >>>>> >> >>>>> First, it is logically invalid. The error is called 'the fallacy >> of >> >>>>> four >> >>>>> terms'. A valid syllogism must have exactly three unambiguous >> >>>>> categorical >> >>>>> terms. But the term 'mathematics' as outlined above is ambiguous. >> >>>>> Mathematics is both a process and a producer of models. The >> specific >> >>>>> model >> >>>>> chosen may be 'arbitrary' in the sense that it is symbolic, but >> the >> >>>>> process >> >>>>> used within that mathematical reasoning is not arbitrary. There >> are >> >>>>> two >> >>>>> meanings of mathematics in the syllogism above. >> >>>>> >> >>>>> Second, it is only symbolic signs that are arbitrary, in the sense >> >>>>> that >> >>>>> their models are assigned by an external agent; iconic and >> indexical >> >>>>> semiosic relations are not arbitrary. Saussure's semiology applies >> >>>>> only >> >>>>> to >> >>>>> symbols, therefore, there are also TWO meanings of the term 'sign' >> in >> >>>>> the >> >>>>> above syllogism. >> >>>>> >> >>>>> Edwina >> >>>>> >> >>>>> >> >>>>> ----- Original Message ----- >> >>>>> From: "Sungchul Ji" <[email protected] <javascript:;>> >> >>>>> To: "Malcolm Dean" <[email protected] <javascript:;>> >> >>>>> Sent: Tuesday, July 01, 2014 7:37 PM >> >>>>> Subject: [PEIRCE-L] Re: "Unreasonable Arbitrariness of >> Mathematics":: >> >>>>> Evidence >> >>>>> >> >>>>> >> >>>>>> Malcolm, >> >>>>>> >> >>>>>> Did I attach the evidence for UAM (unreasonable aribtrariness of >> >>>>>> mathematics) to this email ? If not, it is now attached below. >> >>>>>> >> >>>>>> As you can see in the table attached, each of the two sets of >> >>>>>> experimental >> >>>>>> data, i.e., the single-molecule enzyme kinetic data and the >> >>>>>> decision-time >> >>>>>> histogram, can be fit into two very different mathematical >> equations >> >>>>>> -- >> >>>>>> the Planck distribution and a double-exponential function for the >> >>>>>> former >> >>>>>> and the Planck distribution and the ex-Gaussian distribution for >> the >> >>>>>> latter. These recent findings of mine suggested to me that >> >>>>>> mathematical >> >>>>>> models may be arbitrary. In fact you do not need any >> experimental >> >>>>>> data >> >>>>>> to >> >>>>>> come to such a conclusion, since the same conclusion can be >> reached >> >>>>>> at >> >>>>>> by >> >>>>>> simply combining the definition of the sign given by Peirce and >> the >> >>>>>> linguistic principle of the arbitrariness of signs apparently >> first >> >>>>>> articulated by Ferdinand de Saussure: >> >>>>>> >> >>>>>> "Mathematics is a species of the sign according to Peirce. >> >>>>>> (070114-1) >> >>>>>> All signs are arbitrary according to Saussure. Therefore, >> >>>>>> mathematics is arbitrary." >> >>>>>> >> >>>>>> Let me refer to Statement (070114-1) as the UAM (Unreasonable >> >>>>>> Arbitrariness of Mathematics) thesis. If we apply the UAM thesis >> to >> >>>>>> quantum mechanics (as a body of experimental data on the >> microscopic >> >>>>>> world), it may be predicted that >> >>>>>> >> >>>>>> "There should exist at least two mathematical models of >> >>>>>> (070114-2) >> >>>>>> quantum phenomena that are compatible with all known >> >>>>>> experimental data." >> >>>>>> >> >>>>>> I suggest that Prediction (070114-2) based on the UAM thesis has >> >>>>>> been >> >>>>>> validated by the fact that physicists, after over one century of >> >>>>>> quantum >> >>>>>> mechanical research, are still passionately debating as to which >> of >> >>>>>> the >> >>>>>> two theories are true - i) the non-deterministic, >> probability-wave >> >>>>>> theory >> >>>>>> of Bohr, Bon, Heisenberg, etc, or ii) the deterministic, >> pilot-wave >> >>>>>> theory >> >>>>>> of de Broglie, Schroedinger, Einstein, Bohm, and their more >> recent >> >>>>>> followers, including my fellow professor at Rutgers, S. >> Goldstein, >> >>>>>> and >> >>>>>> his >> >>>>>> research group. >> >>>>>> >> >>>>>> Since Statement (071014-2) seems to be well supported by the >> modern >> >>>>>> history of physics, it may be further asserted that >> >>>>>> >> >>>>>> "The century-old debate between Einstein and Bohr on >> >>>>>> (070114-3) >> >>>>>> the mathematical nature of quantum mechanics may be >> >>>>>> ascribed to the principle of the arbitrariness of >> >>>>>> mathematics specifically and the principle of the >> >>>>>> arbitrariness of signs more generally. There may be >> >>>>>> neither winner nor loser on this debate, since both >> >>>>>> schools of thought can be judged valid within their >> >>>>>> own theoretical framework." >> >>>>>> >> >>>>>> If the above argument proves to be valid, the century-old debate >> in >> >>>>>> physics may end up being finally solved by the knowledge gained >> >>>>>> outside >> >>>>>> of >> >>>>>> physics, namely in biology, linguyistics and semiotics. It is >> >>>>>> possible >> >>>>>> that the problem under debate is/was too complex to be resoved >> >>>>>> within >> >>>>>> physics, just as some of the current probelms fased in biology >> may >> >>>>>> turn >> >>>>>> oout to be too difficult to be solved within biology or even >> within >> >>>>>> natural sciences assisted by mathemtics and high-power computer >> >>>>>> science. >> >>>>>> >> >>>>>> With all the best. >> >>>>>> >> >>>>>> 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 >> >>>>>> >> >>>>>> >> >>>>>>> Thanks. >> >>>>>>> >> >>>>>>> I think the enthusiasm with which mathematicians present their >> >>>>>>> "accuracy" >> >>>>>>> is produced by very narrow observations of the phenomena which >> >>>>>>> happen >> >>>>>>> to >> >>>>>>> match their expectations. The world is fuzzy and messy, except >> in >> >>>>>>> rare >> >>>>>>> cases. The mathematics students I have observed have little >> >>>>>>> self-reflection. They do not see that their mathematical >> >>>>>>> experiences >> >>>>>>> are >> >>>>>>> special mental abilities, similar to religious states, in that >> >>>>>>> mathematics >> >>>>>>> is a form of generalization. I once asked Sean Carroll about the >> >>>>>>> ontology >> >>>>>>> of his particle physics. "They are just numbers, statistics," he >> >>>>>>> replied. >> >>>>>>> >> >>>>>>> My departed friends, Michel and Francoise Gauquelin, once set >> out >> >>>>>>> to >> >>>>>>> finally disprove Astrology. They gathered large statistical >> >>>>>>> databases >> >>>>>>> (30k) >> >>>>>>> and compared planetary positions at birth with adult >> professions. >> >>>>>>> And >> >>>>>>> lo! >> >>>>>>> Given a complicated statistical method, they were able to >> >>>>>>> demonstrate >> >>>>>>> a >> >>>>>>> significant correlation. American skeptics decided that since >> this >> >>>>>>> was >> >>>>>>> the >> >>>>>>> most promising evidence for planetary effects in human affairs, >> a >> >>>>>>> simple >> >>>>>>> replication would provide a knock-out blow to the superstition. >> And >> >>>>>>> lo! >> >>>>>>> With a U.S. sample size of 15k, they replicated the findings of >> the >> >>>>>>> Gauquelins. Did they honestly report the results? Of course not. >> >>>>>>> The >> >>>>>>> statistical method was now "problematic" and "unclear." The >> results >> >>>>>>> were >> >>>>>>> "dubious." >> >>>>>>> >> >>>>>>> Personally, I no longer care whether planetary effects are >> >>>>>>> acknowledged, >> >>>>>>> or >> >>>>>>> whether psi is shown to exist. I'm satisfied that a bunch of >> >>>>>>> skeptics >> >>>>>>> proved that mathematicians can lie just like the rest of us. >> >>>>>>> >> >>>>>>> M. >> >>>>>>> >> >>>>>>> On Sun, Jun 29, 2014 at 4:20 AM, Sungchul Ji >> <[email protected] >> <javascript:;>> >> >>>>>>> wrote: >> >>>>>>> >> >>>>>>>> Hi, >> >>>>>>>> >> >>>>>>>> In 1960, Eugene Wigner made the following statement in a paper >> >>>>>>>> with >> >>>>>>>> the >> >>>>>>>> now-iconic title, â?oUnreasonable Effectiveness of >> Mathematicsâ?ť. >> >>>>>>>> In >> >>>>>>>> it, he >> >>>>>>>> cites a question presumably raised by one of his students at >> >>>>>>>> Princeton >> >>>>>>>> (hence I will refer to it as the â?oWerner questionâ?ť for >> >>>>>>>> convenience): >> >>>>>>>> >> >>>>>>>> ". . . someone came to me and expressed his bewilderment >> [The >> >>>>>>>> remark to be quoted was made by F. Werner when he was a student >> in >> >>>>>>>> Princeton.] . . . with the fact that we make a rather narrow >> >>>>>>>> selection >> >>>>>>>> when choosing the data on which we test our theories. >> >>>>>>>> >> >>>>>>>> â?~How do we know that, if we made a theory which >> >>>>>>>> (062914-1) >> >>>>>>>> focuses its attention on phenomena we disregard >> >>>>>>>> and disregards some of the phenomena now commanding >> >>>>>>>> our attention, that we could not build another theory >> >>>>>>>> which has little in common with the present one but >> >>>>>>>> which, nevertheless, explains just as many phenomena >> >>>>>>>> as the present theory?â?T >> >>>>>>>> >> >>>>>>>> It has to be admitted that we have no definite evidence >> >>>>>>>> that there is no such theory." >> >>>>>>>> >> >>>>>>>> Reading between the lines, it seems reasonable to infer that >> >>>>>>>> Wigner >> >>>>>>>> was >> >>>>>>>> fully aware of the incompleteness of his famous thesis that >> >>>>>>>> >> >>>>>>>> â?oMathematics is unreasonably effective.â?ť >> >>>>>>>> (062914-2) >> >>>>>>>> which we may refer to as the â?oWigner thesisâ?ť. >> >>>>>>>> >> >>>>>>>> In other words, >> >>>>>>>> >> >>>>>>>> â?oThe Wigner thesis cannot provide any definitive >> >>>>>>>> (062914-3) >> >>>>>>>> answer to the Werner question, neither positive >> >>>>>>>> nor negative, and hence is incomplete.â?ť >> >>>>>>>> >> >>>>>>>> The reason that the Wigner thesis is incomplete is because of >> >>>>>>>> >> >>>>>>>> â?oThe Unreasonable Arbitrariness of Mathematics (UAM)â?ť >> >>>>>>>> (062914-4) >> >>>>>>>> >> >>>>>>>> The purpose of this email is to bring to your attention some >> >>>>>>>> recent >> >>>>>>>> developments in theoretical biology (see Table 1 attached) that >> >>>>>>>> support >> >>>>>>>> the UAM thesis: i.e., >> >>>>>>>> >> >>>>>>>> â?oTwo or more mathematical models can simulate a given >> >>>>>>>> (062914-5) >> >>>>>>>> set of experimental data, just as two or more signs >> >>>>>>>> can represent a given object in semiotics.â?ť >> >>>>>>>> >> >>>>>>>> I think Statement (062914-5) is consistent with the facts (i) >> >>>>>>>> that >> >>>>>>>> mathematical models are examples of Peircean signs (or, more >> >>>>>>>> specifically, >> >>>>>>>> the â?~argument-symbolic-legisignâ?T) and (ii) that all signs >> are >> >>>>>>>> arbitrary , >> >>>>>>>> according to Saussureâ?Ts thesis of the â?oArbitrariness of >> >>>>>>>> Signsâ?ť >> >>>>>>>> [2]. I am >> >>>>>>>> assuming here that >> >>>>>>>> >> >>>>>>>> â?oSaussureâ?Ts dyadic theory of signs can be viewed as >> >>>>>>>> (062914-6) >> >>>>>>>> a reduced version of Peirceâ?Ts triadic theory of signs >> >>>>>>>> -- reduced in the sense that the role of the semiotic >> >>>>>>>> agent was not EXPLICITLY taken into account.â?ť >> >>>>>>>> >> >>>>>>>> >> >>>>>>>> With all the best. >> >>>>>>>> >> >>>>>>>> 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 >> >>>>>>>> >> >>>>>>>> [1] Wigner, E. (1960). The Unreasonable Effectiveness of >> >>>>>>>> Mathematics >> >>>>>>>> in the Natural Sciences. Communications in Pure and Applied >> >>>>>>>> Mathematics 13 (I). Available at >> >>>>>>>> https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html. >> >>>>>>>> [2] See, for example, >> >>>>>>>> http://en.wikipedia.org/wiki/Sign_(linguistics). >> >>>>>>>> >> >>>>>>>> >> >>>>>>>> >> >>>>>>>> >> >>>>>>>> >> >>>>>>> >> >>>>>> >> >>>>> >> >>>>> >> >>>>> >> -------------------------------------------------------------------------------- >> >>>>> >> >>>>> >> >>>>>> >> >>>>>> ----------------------------- >> >>>>>> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to >> REPLY >> >>>>>> ON >> >>>>>> PEIRCE-L to this message. PEIRCE-L posts should go to >> >>>>>> [email protected] <javascript:;> . To UNSUBSCRIBE, send a >> message not to >> >>>>>> PEIRCE-L >> >>>>>> but to [email protected] <javascript:;> with the line >> "UNSubscribe PEIRCE-L" in >> >>>>>> the >> >>>>>> BODY of the message. More at >> >>>>>> http://www.cspeirce.com/peirce-l/peirce-l.htm >> >>>>>> . >> >>>>>> >> >>>>>> >> >>>>>> >> >>>>>> >> >>>>>> >> >>>>> >> >>>>> >> >>>>> >> >>>> >> >>>> >> >>>> >> >>> >> >>> >> >>> >> >> >> >> >> >> >> >> >> > >> > >> > >> >> >
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