Steven, Because two entirely different mathematical equations can account for the same set of empirical data, just as two entirely different words (representamens/signs) can refer to the same object in linguistics (semiotics).
With all the best. Sung > How, exactly, does this appeal to arbitrariness? > > > On Thursday, July 3, 2014, Sungchul Ji <[email protected]> wrote: > >> Steven wrote: >> >> "What empirical evidence supports unreasonable arbitrariness?" >> >> The empirical evidence consists of the following observations: >> >> (1) The single-molecule turnover times of cholsterosl oxidase fit both >> the >> dobule-exponential function of the form y = A(Exp(-Bx) - Exp (-Cx)) and >> the Planckian distribution, y = (A/(x + B)^5)/Exp(C/(x + B)) -1) (see >> the >> upper panel of Table 1 attached), and >> >> (2) The decision-time histograms fit both the Planckian distribution and >> the ex-Gaussian distribution used by R. D. Luce (Response Times: their >> roel in Infwerring Elementary Mental Organizaiton, Oxford University >> Press, 1986, p. 100), which is of the form, y = A(Exp(B+C)Exp(-Dx)[(x - >> E)/F] (see the lower two panels in Table 1 attached.) >> >> If you have any question, let me know. >> >> 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 >> >> >> >> > What empirical evidence supports unreasonable arbitrariness? In fact, >> I >> > see >> > none at all. On the contrary, I see numerous claims of arbitrary >> behavior, >> > in non-mathematical statements. In mathematical statements I see only >> > evidence for a uniform and effective world - derived from biophysics. >> > >> > Steven >> > >> > >> > On Thursday, July 3, 2014, Sungchul Ji <[email protected] >> <javascript:;>> wrote: >> > >> >> 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] >> <javascript:;> >> >> <javascript:;>> 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:;> >> <javascript:;> >> >> <javascript:;>> >> >> >> > To: <[email protected] <javascript:;> <javascript:;> >> <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:;> >> <javascript:;> >> >> <javascript:;>> >> >> >> >>> To: <[email protected] <javascript:;> <javascript:;> >> <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:;> >> <javascript:;> >> >> <javascript:;>> >> >> >> >>>>> To: "Malcolm Dean" <[email protected] <javascript:;> >> <javascript:;> >> >> <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:;> <javascript:;> >> >> >> <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:;> <javascript:;> >> <javascript:;> . To >> >> UNSUBSCRIBE, send a >> >> >> message not to >> >> >> >>>>>> PEIRCE-L >> >> >> >>>>>> but to [email protected] <javascript:;> <javascript:;> >> <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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