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).
>> >> >> >>>>>>>>
>> >> >> >>>>>>>>
>> >> >> >>>>>>>>
>> >> >> >>>>>>>>
>> >> >> >>>>>>>>
>> >> >> >>>>>>>
>> >> >> >>>>>>
>> >> >> >>>>>
>> >> >> >>>>>
>> >> >> >>>>>
>> >> >>
>> >>
>> --------------------------------------------------------------------------------
>> >> >> >>>>>
>> >> >> >>>>>
>> >> >> >>>>>>
>> >> >> >>>>>> -----------------------------
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