A NOTATIONAL PHYSICS WITH PHYSICISTS IN IT

                            C. A. Hilgartner

                         Hilgartner & Associates

                          254 Kensington Place

                            Marion OH 43302

 

                          Ronald V. Harrington

                          275 Susquehanna Road

                          Rochester NY 14618

 

                            Martha A. Bartter

                          Department of English

                     Ohio State University at Marion

                         1465 Mt. Vernon Avenue

                           Marion OH 43302

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               A NOTATIONAL PHYSICS WITH PHYSICISTS IN IT

 

                            C. A. Hilgartner

                            R. V. Harrington

                              M. A. Bartter

 

 

                                ABSTRACT

 

      We hold that modern physical reasoning intrinsically depends on

 the relations between two or more observers. Using an alternative

 mathematics based on a derived grammar, we examine in detail the

 situation of discovering a relativistic discrepancy, and accounting for

 it. Our frame of reference systematically takes into account the

 observer, and utilizes an explicit model for the apparently 'purposive'

 activities of living systems; we use it to examine Walter Kaufmann as

 he performs his 1901 study on the deflection of electrons by electric

 and magnetic fields and the apparent mass of the electron. Thus we

 consider not only the theoretical significance of his contribution, but

 also the self-and-social components of his study. In our notation, we

 describe a) The spatio-temporally ordered sequence of events; b) The

 hierarchically-ordered roles Kaufmann plays in designing, performing

 and reporting his experiment; c) The inter-personal and social

 components of his career; and d) The consequences to Kaufmann and to

 the scientific community. Our notational system, which cannot NOT take

 the observer into account, confers two advantages: i) It yields

 physical theory which systematically handles the relations of an

 observer with himself and with other observers, and ii) It brings our

 articulated physical knowledge and our articulated social knowledge

 into a single rigorous symbol-system.

 

.PA

               A NOTATIONAL PHYSICS WITH PHYSICISTS IN IT

 

                            C. A. Hilgartner

                            R. V. Harrington

                             M. A. Bartter

 

                      "Think in other categories!"

                                Coleridge

.HM1

.H1  -#-

.H2  A Notational Physics with Physicists

 

 

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 INTRODUCTION

 

        This paper forms the second installment in a series in which we

 set out to scrutinize the theory of relativity to see how effectively

 it manages to take the observer into account -- and what difference it

 makes how well a theory does this, or even whether it does it at all.

 To carry out this inquiry, we make use of a frame of reference which

 does systematically takes the observer into account. Thus it provides

 a suitable background against which to display the assumptions of older

 theories (such as the theory of relativity) and to highlight the

 significance of the assumptions that we disclose.

 

        Historically, the earliest exponents of relativity (and quantum

 theory) introduced a new distinction into human discourse, which they

 expressed in terms of the construct of

.UL off

 the observer, who gets either

 included (taken into account) or eliminated from consideration.

 Einstein and others developed the revolutionary precept and criterion

 that prefers a physical theory which does take the observer into

 account over any which does not. But by the latter half of his

 lifetime, Einstein seemed mainly interested in the details of his

 general theory of relativity, and he no longer made such a point of

 that precept. Today's practicing physicists do account for the

 observer in the ways that those early pioneers taught them to. But

 they have reinterpreted that precept so as to tame it -- they take the

 construct of the observer as if it had nothing to do with living

 humans, observers. Consequently, they conduct their studies as if

 divorced from any primary connections with actual humans, or from

 effective concern for specifiable human values.

 

        In our own frame of reference, we bracket the construct of taking

 the observer into account: We present one array of logically general@

 assumptions (centering about the explicit postulate of map-territory

 non-identity) that, when held, allow one to account for the observer;

 and disclose another, contrasting array of assumptions (centering about

 the restricted and restrictive tenet of map-territory identity),

 logically less general and usually tacitly held, which eliminate the

 observer from consideration.@ These latter assumptions demonstrably

 ___________________

 

 @ Criterion of logical generality

 @ Null-A vs. traditional assumptions and "taking observer into

 account"< (WHERE did we first lay out both sets of assumptions?????)

 __________________

.PA

.PA

  form a part of the premises encoded in the traditional grammar common

 to the Western Indo-European (WIE) languages, both discursive (e.g.

 Dutch, English, French, German, Greek, etc.) and formalized (e.g.

 symbolic logic, set theory, analysis, topology, etc.).@ We suggest

 that our science grants a privileged position to this WIE grammar. If

 so, then even the best theories within WIE science include these

 restricted and restrictive assumptions among their premises and so, in

 some fundamental sense, on logical levels deeper than those ordinarily

 examined, systematically eliminate the observer from consideration.

 

 ________________

 

 @CAH, "Some Traditional Assumptions...") ________________

 pa

        A. FINDINGS OF OUR PREVIOUS STUDY

 

        In Appendix 1, we summarize the findings of our previous study.

 Succinctly stated, we find that:

 

        In the period from about 1880 to about 1900 or 1910, workers

 generated a body of perhaps two hundred experiments whose results cast

 doubt on the tenets of Newtonian physics. We find that these

 anomalies or relativistic discrepancies have a common structure, which

 intrinsically depends on the relations between two or more observers.

 Specifically, before a worker can make the kinds of observations which

 logically precede and lead to one of the twentieth-century physical

 theories which take the observer into account (such as the theory of

 relativity), s/he has to rely on certain observations made by one or

 more of her/his colleague(s) with the same kind of assurance with which

 s/he relies on certain of her/his own observations. To discover an

 anomaly, a worker compares two sets of observations, performed under

 slightly different conditions; finds that they DON'T MATCH in some

 crucial fashion; and takes this mismatch seriously enough to attempt to

 account for the discrepancy -- or at least, to write it up and publish

 it. These stages in the discovery of a relativistic discrepancy

 comprise specific physical activities -- "doings" or "happenings" --

 which observably occur at finite rates, in an ordered fashion.

 

        1. In the theory of relativity, the notion of "taking the

 observer into account" occurs mostly as verbal imagery and rhetoric;

 whereas in the mathematical development, Einstein replaces this image

 with the construct of a coordinate system, and spells out relations

 between coordinate systems. To do so treats all observers as

 interchangeable ('identical' -- the same in observational powers, in

 methods and styles, in background and assumptions, etc.).

 Consequently, for most of the anomalies, the theory of relativity

 reconciles only those aspects of the observed discrepancy which one can

 render by means of a coordinate system or the relations between

 coordinate systems -- while ignoring those aspects of the discrepancy

 not representable by a coordinate system, e.g. those which depend on

 the human anatomy, physiology and the activities of an observer, on the

 relations between the two observers, etc.@ Thus the theory of

 relativity has two parts: the foreground, the explicit, visible theory;

 and a more extensive, tacit background. Furthermore, it treats those

 "doings" or "happenings" represented by the foreground AS IF they occur

 at finite rates, in an ordered fashion; but as for those "doings" or

 "happenings" represented only tacitly, in the background, it treats

 them AS IF they take place in 'no time at all', in an non-ordered

 fashion.

 

 ___________________

 @Swanson, Marjorie

 ___________________

 pa

        Consequently, as judged by its own criteria, the theory of

 relativity appears inconsistent. In our language, where it treats

 aspects of an anomaly as if the "happenings" occur at finite rates --

 as ordered-- it relies on map-territory non-identity and so takes into

 account the observer. Where it treats aspects of an anomaly as if the

 "happenings" occur in 'no time at all' -- as non-ordered -- it grants a

 privileged position to the WIE grammar and so relies on map-territory

 identity, eliminating the observer from consideration.

 

        2. Any theory which eliminates the observer from consideration (by

 relying on map-territory identity), even in part, guides its exponents

 to create, to defend and to contribute to a mutilated science, one in

 which its advocates prostitute the explanatory power of their theory to

 local patriotism, economic interest, the power of the state, and the

 like, for the sole benefit of some group smaller than the whole human

 species. But when used for a narrow goal of that sort, a powerful

 theory such as the theory of relativity guides the whole human species

 into internecine strife and "war on nature." Furthermore, the

 explanatory power of the theory expands these goals beyond previous

 human experience, perhaps stretching the former limits of human

 comprehension: When pursued with "weapons" which harness cosmic

 forces, internecine strife becomes the prospect of species-suicide and

 extinction; when conducted with the "tools" provided by the kind of

 predictability yielded by the theory of relativity and quantum theory,

 "war on nature" turns into the prospect of the annihilation of the

 biosphere.

 

        B. THE TASK OF THE PRESENT INSTALLMENT

 

        With these findings as background, the authors now ask and answer

 the following question: How can we humans use these insights into the

 construct of taking the observer into account -- the topics of self and

 the social -- so as to generate a self-consistent physical theory based

 on map-territory non-identity?@

 

 ___________________

 

 @We suggest that creating such a theory may stand as a crucial step

 toward turning ourselves away from environmental devastation and

 self-destruction, and toward celebrating and affirming the living,

 including ourselves.

 ___________________

 pa

        In developing our answer to this question, we consider in detail

 one historical example of the kind of experiment which discloses a

 relativistic discrepancy. Walter Kaufmann (1871-1947) performed a

 series of studies concerning the mass (or rather, charge-to-mass ratio)

 of electrons. He reported the most significant of his observations in

 a paper published in 1901. His findings did not match with the

 predictions of Newtonian physics (nor with the results of some of his

 own earlier studies), and so represented what we (along with Thomas

 Kuhn) would call an anomaly. We use a rigorous model for the

 apparently 'purposive' activities of living systems to account for the

 "doings" by which Kaufmann designed, performed and reported this

 experiment, In so doing, we focus on aspects of the experimenter's

 activities crucial to his experimenting but traditionally left out of

 account in the writings of physicists.

 

         Where in the earlier paper in this series, we only mentioned our

 alternative frame of reference and our non-standard notation (and

 imported a few constructs from it), in the present paper we USE our

 alternative framework.

 

        a) Our notation relies on a novel "grammar" (pattern for what

 constitutes a well-formed formulation) derived, by a small number of

 explicit logical steps, from the non-aristotelian premises proposed by

 the late Alfred Korzybski (1879-1950). By relying on mathematical

 languages built up on a derived grammar, we gain an increase in logical

 rigor.

 

        b) It systematically takes into account the observer, thereby

 eliminating that self-contradiction intrinsic to the structure of

 relativity (and of quantum theory) which we disclose above (Hilgartner,

 Harrington, & Bartter, 1989; Hilgartner & Di Rienzi (submitted for

 publication)).

 

        The present frame of reference subsumes the topics of "humans

 studying physical "doings" or "happenings"," and of "the theories

 humans generate to explain their findings."

 

        Methodologically, we employ a procedure based on a careful

 comparison between SAYING and DOING. We check (generate our own

 reading of) the verbal or mathematical constructs which Kaufmann

 actually used in his papers; and we infer that he MEANT what he SAID.

 

        Likewise, we check what he DID (as reported by his biographers,

 etc.). Then we compare (our picture of) what he said and of what he

 did; we comment on the match between these two levels; and we account

 for the disclosed congruences and/or discrepancies by means of the

 non-standard notation which we have built up on our derived grammar.  

 

 

        The trouble with using our notation comes from two facts: that it

 remains only partially published, and that, so far as we know, no one

 outside our own research group has any familiarity with it at all.

 

        We do not derive the new notation here. In Appendix 2, however,

 we do give enough information about the notation so our readers can

 make sense of what we say; and also give a glossary of notational

 terms.

.PA

 I. PRIMARY DATA

        To provide an example for our study, we examine the life of Walter

 Kaufmann (1871-1947), who in 1901 published a paper, "Die magnetische

 und electrische Ablenbarkeit der Bequerelstrahlen und die schienbare

 Masse der Elektronen," Nachrichten von der Gesellschaft der

 Wissenschaften zu Gottingen, Math.-phys. Kl., 2:143-155 (1901). We

 obtain the data from which we argue from the entry on Kaufmann in the

 Dictionary of Scientific Biography (American Council of Learned

 Societies, New York: Scribner's, 1970), from the essay on Kaufmann in

 The World of the Atom, edited with commentaries by Henry A. Boorse &

 Lloyd Motz (New York: Basic Books, 1966), and from the translation of

 Kaufmann's paper which appears there, under the title of "Magnetic and

 electric deflectability of the Becquerel rays and the apparent mass of

 the electron."2

 

        We shall consider a brief period in Kaufmann's life, during which

 he did experiments on the mass of electrons.

 

        Born in Elberfeld (Wuppertal), Germany, Kaufmann studied at

 Munich, where he received his doctorate in 1894. In 1896-98, he began

 research on the magnetic deflection of low-velocity cathode rays,

 obtaining a first approximation to the ratio of electron charge to

 mass.  

 

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       During this period a controversy arose over whether electrons,

       believed to be the ultimate constituents of matter, could have

       "apparent" mass in addition to "real" (material) mass. Apparent

       mass would be the "electromagnetic mass" gained from the

       interaction of the moving charge with its own field. (Dictionary

       of Scientific Biography, p. 263).

 

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 We take the above comment as expressing Kaufmann's experimental focus

 (fragestellung).

 

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             During the Gottingen years, 1899-1902, Kaufmann conducted

       research on the magnetic and electric deflection of radium

       emanations -- then known as Becquerel rays. From the Curies he

       obtained several radioactive particles of radium chloride and set

       about measuring the [charge/mass (epsilon/mu)] ratio. Since

       these newly discovered rays had velocities approaching the speed

       of light, it was assumed that the maximum possible

       electromagnetic charge was imparted to them. On the basis of his

       initial epsilon/mu measurements in 1901, Kaufmann asserted that

       the apparent mass was appreciably larger than the real mass -- by

       an estimated magnitude of at least three to one. (Dictionary of

       Scientific Biography, p. 263)

 

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       Thus the results which Kaufmann obtained from his 1901 experiment

 did not match with his earlier findings.

 

       The essay in Boorse & Motz (1966) clearly sets the overall

 theoretical context for Kaufmann's study.

 

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             With the discovery that cathode rays consist of negatively

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 charged particles (electrons, as they came to be called),

 physicists began an intensive study of the properties of these

 particles; one of the most interesting and important questions

 dealt with their mass. With the equipment that was available

 immediately after the electron had been discovered, only the

 ratio of its charge to its mass could be measured directly. Only

 after Millikan had measured the charge on the electron first with

 charged water drops in 1909 and then with his famous oil-drop

 experiment in 1910-11 was it possible to obtain a precise value

 for the mass of the electron.

 

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             Although the electronic mass could not be measured directly,

       some important observational conclusions could be drawn,

       particularly since the various applicable theories pointed to

       some unusual properties of the mass. The problem that arose in

       connection with the mass of the electron is essentially the

       following one.

 

             Since an electron has an electrostatic field surrounding it

       because of its own charge, we must picture this field as moving

       along with the electron. Moreover, if the electrostatic field is

       set moving, it should, in principle, be accompanied by a magnetic

       field according to Maxwell's electromagnetic theory. Indeed,

       Rowland in 1878 had demonstrated experimentally that a moving

       charge is accompanied by a magnetic field whose lines of force

       form concentric circles about the line of motion of the charge.

       From this we can see at once that setting an electron in motion

       requires a greater push than setting an uncharged particle in

       motion, if we consider the situation in terms of Newton's laws of

       motion and Maxwell's electromagnetic theory.

 

             Let us consider an electron and an uncharged particle of the

       same mass at rest, and let us accelerate these particles by

       applying the same force to both of them. According to Newton's

       second law of motion, the force applied to either of these

       particles, divided by the acceleration imparted to this particle

       by the force, is the mass of the particle. In the case of the

       uncharged particle, this ratio (that is, the way a particle

       responds to a force) was referred to as the "true" mass of the

       particle.

 

             The situation for the charged particle is much more

       complicated because of the electrostatic and the magnetic field.

       The same force that imparts a given acceleration to the uncharged

       particle cannot impart the same acceleration to the electron

       because, to begin with, the entire electrostatic field of the

       electron must also be set moving. Moreover, the moving electron

       immediately finds itself surrounded by a magnetic field that

       (according to the laws of induction) is always so directed as to

       oppose the force acting to accelerate the electron. In other

       words, the electron behaves as though it were more massive when

       it is set moving than when it is at rest. When Kaufmann

       undertook his experiments on the variation of the mass of an

       electron with velocity, physicists differentiated between what

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 they called the "true" mass and the "apparent" mass of the

 electron. The "true" mass referred to the mass of the electron

 when it was not in motion and the "apparent" mass to its mass in

 virtue of its motion. (Boorse & Motz (1966), pp. 502-3)

 

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             Since Kaufmann had no high-energy accelerators to obtain

       electron speeds sufficiently high to show an appreciable increase

       of the mass, he used Becquerel rays, the electrons emitted by

       radioactive atoms, now called (beta)-rays. These were much more

       energetic than the cathode rays that were available to him. In

       the first few paragraphs of his paper, he gives arguments in

       support of the belief that Becquerel rays are the same as cathode

       rays despite their much higher speeds. Then he outlines his

       experiment and describes his apparatus. The theoretical aspects

       of the experiment are discussed in terms of the arrangement of

       Fig. [34-1] taken from Kaufmann's paper.

 

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 FIGURE [34-1] ABOUT HERE

 

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             We shall use this figure for a brief description of his

       experiment. A speck of radium bromide was placed at A , just

       below a pair of closely spaced and electrically insulated square

       metal plates K . A difference of potential of about 7,000 volts

       could be applied to the plates to produce a strong electric

       field. The whole region represented by Fig. [34-1] could also be

       subjected to a uniform magnetic field generated by an

       electromagnet, the field direction being perpendicular to and

       into the plane of the paper. The vertical line x1x2 determined

       by A and a fine circular opening at B , terminates on a

       photographic plate lying in the xy plane at C . In the

       absence of the electric and magnetic fields (beta)-rays

       (electrons) from the radium bromide source could reach the

       photographic plate only along x1x2 . Thus C on the

       photographic plate was a reference point for the undeflected

       rays. When only the magnetic field was applied electrons of the

       proper velocity initially directed along x1 were forced along

       the circular arc ABQ of radius (rho), by the action of the

       field. When both electric and magnetic fields were applied

       simultaneously, the path of all the electrons that could get

       through the hole B , terminated on the curve CP on the

       photographic plate. Thus the point P lying on the yz plane

       has coordinates y0 and z0 . From his measurements Kaufmann

       deduced values of (epsilon/mu) for electrons of five different

       velocities. These values are listed in Table [34-1]. It is

       clear that as the velocity of the electrons increased, the value

       of (epsilon/mu) decreased, thus showing that since the

       electronic charge (epsilon) is constant, the mass of the

       electron increased with velocity. If the ratio M+m0.(eta)/M

       +m0 is calculated from Kaufmann's data for his given values of

       v and plotted against the corresponding values of (beta)=v/c,

       the open circles shown in Fig. [34-2]

 

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 FIGURE [34-2] ABOUT HERE

 

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       result. This figure appears at the end of the paper. It is

       evident that the mass of the electron is tending to very large

       values as v approaches the speed of light. For reference, the

       full line in this figure is the graph of the Lorentz-Einstein

       relation. The dots on the lower part of the curve are the values

       of m/m0 found by Bucherer in his experiments eight years later.

       (Boorse & Motz (1966), pp. 504-5)

 

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 II. APPARENTLY 'PURPOSIVE'

 

       We systematize these primary data using the resources built into

 our notation. For example, our notation presupposes the construct of

 directively correlated (DC) (Hilgartner & Randolph, 1969a; Ashby,

 1962; Sommerhoff, 1950; Singer, 1946). In other words, we consider the

 "doings" of any organism in its environment in general, or Kaufmann's

 in his environment in particular, as apparently 'purposive'.

 

 

       SP <DCk> {<HCTe, HFTe>

 

 

                  {.:k <.:h <f(HCTe)f, g(HCTe)f>

 

 

                            {psi(f(HCTe)f, g(HCTe)f)g} OhOt>

 

 

                       {Saj <HFTe>

 

 

                            {HOci} OhOt}j OhOt}k OhOt} O . (2)     

 

       The construct of directively correlated consists of the following

 four terminological parts:

 

       a) Coenetic terming (CT), signifying "exigencies (of both

 organism and environment) which require behavior" -- e.g., in this

 situation, "initial conditions that affect both Kaufmann and his

 environment";

 

       b) Focal terming (FT), signifying "criteria for what would

 constitute a 'favorable' outcome for Kaufmann";

 

       c) Negotiations (e.g. .:, f(CT), g(FT), (psi)) between Kaufmann

 and his environment initiated by the coenetic terming; and

 

       d) Outcome (Oc) , which either does or does not satisfy the

 criteria of the focal terming.

 

       We show these parts as related in the following ways:

 

       i. Coenetic and focal terming: we regard these as mutually

 necessary, "complementary or polar-opposite."

 

 

        (nu) <CT> {FT} OpOs                (3)

 

.PA

       (This says: Our organism's polar-opposed termings (nu), specified

 as: background, CT; figure, FT; polar and synchronous ordering.)

 

       ii. Coenetic terming (CT) and negotiations (psi): we regard these

 as ordered spatio-temporally (Ot) and hierarchically (Oh) .

 

       iii. Negotiations and outcome (Oc): we regard the outcome Oc as a

 particularizing PZ of the negotiations (psi) (e.g. the transactings

 between Kaufmann and his environment), namely, that which we select as

 the terminus, "the ending of the story."

 

 

       PZ <psi> {Oc} O                     (3a)

 

 

       iv. Outcome and focal terming: we regard the outcome as an

 empirical terminus and the focal terming as the logical standard set up

 to judge it by.

 

       To facilitate translating expression (2) into English, we print it

 again here, with the various parentheses indexed with left

 superscripts:

 

 

       SP 4<DCk> 4{3<HCTe, HFTe>

 

 

                   3{.:k 2<.:h 1b<f(HCTe)f, g(HCTe)f>

 

 

                             1b{psi(f(HCTe)f, g(HCTe)f)g} OhOt>

 

 

                        2{Saj 1f<HFTe>

 

 

                             1f{HOci} OhOt}j OhOt}k OhOt} 4O . (2a)

 

 

       Expression (2) says: The specifying of our organism, spelled out

 as: 4background, the construct of DC, directively correlated; 4figure,

 a compounded expression, specified as: 3background, the coenetic term

 CT , along with the focal term, FT , for our organism at time e;

 3figure, the compounded expression that at time k, from the

 background follows the figure, specified as: 2background, the

 compounded expression that at time h, from the background follows the

 figure, specified as: 1bbackground, happenings f (consequential to the

 CT for our organism at time e ) at time f; 1bfigure, the happenings

 psi (consequential to the happenings f along with the happenings g

 ), at time g ; 2figure, the compounded expression that the figure

 satisfies the background, specified as: 1fbackground, the focal terming

 for our organism at time e ; 1ffigure, the outcome for our organism at

 time i .

 

       We can express Kaufmann's coenetic terming as deficit of

 orienting (Df(Or)) . (We can particularize this as his fragestellung,

 "What charge/mass ratios do I obtain by deflecting Becquerel rays by

 means of magnetic and electric fields?") Here we use the construct of

 orienting (Or) to signify that combination of motoric and neural

 activities (e.g. attending (At) and interest (In) (Hilgartner &

 Randolph, 1969a, pp. 303-8)) by which an organism increases its

 sensitivity to and awareness of its immediate environment. Think of a

 dog "cocking an ear" at an unexpected, unexplained sound, or of a human

 "getting his bearings" so as to avoid falling off the edge of the Grand

 Canyon, or down a flight of stairs. We also use the term orienting to

 designate longer-term, more elaborate human "doings." For example, the

 social institution of science serves as one way for the human species

 as a whole to orient more accurately or more comprehensively

 (Korzybski, 1921; see also Einstein, 1955, p. 1). Kaufmann, as he

 prepares to perform his 1901 experiment, has oriented himself to

 Newton's mechanics and Maxwell's field theory (and the most recent

 permutations of these), and has made himself aware of the evidence

 explained by postulating cathode rays and Becquerel rays (or

 electrons), and has made himself competent to study them. In other

 words, in the midst of his excellent general orientation, he

 experiences a deficit of orienting: he feels curious.

 

       Further, we can express Kaufmann's focal terming as obtaining an

 answer to his fragestellung, which we could express in notation as the

 'awareness' (Aw) of an aspect of his environment (Y) , or Aw(Y) .

 If the outcome of his experiment gave a definite answer -- the

 photographic plate showed a line or an arc, or a patterned array of

 discrete spots, as the trace produced by the deflected electrons --

 that would, in effect, relieve his deficit of orienting. If, however,

 the photographic plate showed only a blur, that would not permit

 Kaufmann to answer his fragestellung, but instead would suggest that he

 had framed his key question wrongly.

 

 

 III. COMPONENTING

 

       Our viewpoint leads us to component the information concerning

 Kaufmann's life into two mutually-necessary themes, which we call

 'self' and 'other'.

 

       A. Kaufmann's 'other': fast vs. slow electrons

 

       In dealing with his 'other', which he called electrons (fast vs.

 slow), Kaufmann showed a high degree of skill in handling all the

 facets needed to experiment successfully.

 

 

.RR L-----------------------------------------------------------------R

       ... His research was marked by great proficiency in

       experimentation, especially in the techniques for obtaining the

       high vacuums necessary for cathode ray discharge tubes. His most

       notable contributions to this art was the construction of the

       first rotary high-vacuum pump; it was very artfully made of

       loops of glass tubing through which separate columns of mercury

.RR----!---------------------------------------------------------------R

 forced trapped volumes of gas out of the vacuum space. Although

 the pump was extremely fragile, unwieldy, and temperamental,

 Kaufmann used it with great success in his celebrated electron

 mass research. (Boorse & Motz (1966), p. 505)

.PA

 

             B. Kaufmann's 'self':

 

       Although few references explicitly discuss the topic of Kaufmann's

 (or any other experimenter's) 'self', we consider this topic central to

 our investigation (cf. below, sections V, VI). Among other topics, we

 shall consider Kaufmann's (a) acts of affiliation, (b) self-esteem, (c)

 trustworthiness and ability to trust others, and (d) the sense of

 having an audience.

 

 

 IV. SPATIO-TEMPORALLY ORDERED STORY

 

       In discussing the study in question, let us start with the

 Kaufmann who has everything ready to go -- and for the first time

 starts the two-day experiment.

 

       CT: Our organism (Kaufmann) has mastered the relevant theory

 (theories), framed his hypothesis, designed the experiment, developed

 the new tools he needs, assembled the equipment (he has the radium in

 place, the orifice in place, the field generators in place, the

 photographic plate in place, etc.), and so on.

 

       FT: Our organism intends to USE the equipment, CARRY OUT the

 experiment, TEST the hypothesis, and JUDGE the theory (theories).

 

 

        HO <CP1 <CT0> {Df(Or)0} O>

 

             

              {CP2 <FT0> {Aw(Y)} O} OpOs           (4)

 

 

       This says: Our organism at moment 0, specified as including:

 background, a compounded expression, namely: background, our organism

 generating the first component (CP1) of a term at moment 0, specified

 as: background, the construct of our organism's coenetic terming (CT)

 at moment 0 ; figure, our organism's deficit of orientation (Df(Or)) at

 moment 0 ; figure, our organism generating the second component (CP2)

 of a term, specified as: background, the construct of focal terming

 (FT) at moment 0 ; figure, our organism's awareness of some Y (Aw(Y))

 at a subsequent unspecified moment; polar and synchronously ordered.

 

       Expectings Ex at instant t0 derived from past experiencing:

 We shall not spell these out in our alternative notation at this point,

 because we have not yet developed what Kaufmann brings to bear on this

 experiment. As the remainder of our text, we shall develop a

 vocabulary and a way of talking/writing which allows us to get specific

 about Kaufmann's background.

 

       "Alerted": As he enters his laboratory to begin his experiment,

 Kaufmann appears fully alert -- attending to (At) and interested in

 (In) his experimental system (Sy) .

 

.PA

       O-1 <At1 In1 , Sy1> {Aw(Sy1)2)} OhOt           (5)

 

 

       This says: Our organism abstracting (theta), specified as:

 background, our organism attending (At) and interested (In) at moment 1

 along with his experimental system (Sy) at moment 1 ; figure, our

 organism's awareness of his-experimental-system-of-moment-1 (Aw(Sy1))

 at moment 2 ; hierarchically and spatio-temporally ordered.

 

       Our organism motors (M*) over so as to approach (Ap) the

 three-way vacuum stopcock (Stk) , and closes (Cls) it.

 

 

       O-3 <M*(Ap(Stk))3> {Cls(Stk)4} OhOt           (6)

 

 

       This says: Our organism abstracting at moment 3, specified as:

 background, our organism motoring so as to approach the stopcock at

 moment 3 ; figure, our organism closing the stopcock at moment 4 ;

 hierarchically and spatio-temporally ordered.

 

       Our organism motors over to the vacuum pump off/on switch (Von)

 and turns it on (Ton) .

 

 

       O-5 <M*(Ap(Von))5> {Ton(Von)6} OhOt           (7)

 

  This says: Our organism abstracting at moment 5 , specified as:

 background, our organism motoring so as to approach the vacuum pump

 off/on switch at moment 5 ; figure, our organism turning on the off-on

 switch at moment 6 ; hierarchically and spatio-temporally ordered.

 

       After a suitable interval, our organism "motors" over to the

 off/on switch for the electric/magnetic fields (Mon), and turns it

 on.

 

 

       O-7 <M*(Ap(Mon))7> {Ton(Mon)8} OhOt           (8)

 

 

       This says: Our organism abstracting at moment 7, specified as:

 background, our organism motoring so as to approach the off/on switch

 for the electric/magnetic fields at moment 7 ; figure, our organism

 turning on the switch at moment 8 ; hierarchically and

 spatio-temporally ordered.

 

       In a similar fashion, he motors to the photographic plate and

 uncovers it. Then, at intervals during the two-day experiment, our

 organism reads the meters concerning the performance of the equipment,

 and records his readings.

 

       After two days, our organism (a) stops the vacuum pumps, (b) turns

 off the electric and magnetic fields, (c) opens the stopcock to release

 the vacuum, (d) removes the photographic plate, and (e) develops it.

 Since these "doings" closely resemble those already described in

 notation, we will not write out further notational sentences to

 describe them.

 

       Subsequently, our organism makes his measurements on the

 photographic plate, producing a table of numbers (Table 1).

 

       Kaufmann's paper gives the details of his mathematical

 computations. Table 1 (Boorse & Motz, 1966) presents the first results

 of his measurements. Here z0 signifies the magnetic deflection of

 the electrons, y0 signifies the electric deflection, (rho) signifies

 the radius of curvature of the deflected trajectories, s1 signifies

 the projection of half the path traversed in the electric field, s2

 signifies the projection of the path from the fine circular opening to

 the photographic plate, v.10-10 signifies the velocity of the

 electrons, and (epsilon)/(mu).10-7 signifies the charge-to-mass ratio.

 

 TABLE 1*

 _______________________________________________________________________

 

 

  z0   y0 (rho)      s1      s2     

 v.10-10 e/m.10-7

 _____  ______ __________     _____     

 _______ _______

 0.271  0.0621 15.1 0.888     2.02      2.83

        0.63

 0.348  0.0839 11.7 0.888     2.03      2.72

        0.77

 0.461  0.11758.9 0.889     2.06      2.59

        0.975

 0.576  0.15657.1 0.889     2.09      2.48

        1.17

 0.688  0.198 6.0 0.890     2.13      2.36

        1.31

 _______________________________________________________________________

 

       * All numbers in absolute units.

 (Boorse & Motz, 1966, p. 509)

 

       Our organism translates these "results" into "findings" (Cs) .

 

 

        O-11 <".:10 <O-3, O-5, O-7>9



 

                   {Table 1}10 Oh10Ot10>

 

 

              {Cs11} Oh11Ot11                    (9)

       

 

       This says: Our organism abstracting at moment 11, specified as:

 background, a compounded expression that from the background follows

 the figure (.:) at moment 10 , specified as: background, our organism

 abstracting (theta) as of moment 3 along with that as of moment 5 along

 with that as of moment 7, at moment 9 ; figure, table 1; hierarchically

 and spatio-temporally ordered as of moment 10; figure, our organism's

 consciousness as of moment 11; hierarchically and spatio-temporally

 ordered as of moment 11 .

 

       Our organism repeats the experiment during the interval t12-22 .

 

       Our organism reaches "conclusions": (Gt) .

.PA

       O-24 <Cs11, Cs22>

 

 

        {.: <Gt23>

 

 

                       {"The mass of electrons increases with increasing

                        velocity. As velocity approaches c , mass

 approaches

                       infinity. This conflicts with Newton's dm/dv = 0

 ."24}

 

                  OhOt} Oh24Ot24               (10)

 

 

       This says: Our organism abstracting as of moment 24, specified as:

 background, our organism's consciousness as of moment 11 along with

 that as of moment 22 ; figure, a compounded expression that from the

 background follows the figure, specified as: background, our organism's

 Gestalt or generalization as of moment 23 ; figure, the English

 paragraph, "The mass of electrons increases with increasing velocity.

 As velocity approaches c , mass approaches infinity. This conflicts

 with Newton's dm/dv = 0 ." as of moment 24; hierarchically and

 spatio-temporally ordered; hierarchically and spatio-temporally ordered

 as of moment 24.

 

       Our organism writes his ms.

 

       Our organism drops his ms into the delivery system, so that it

 will go to the journal for possible publication.

 

 

 V. HIERARCHICALLY-ORDERED STORY

 

       Let us continue discussing the study in question.

 

       In addition to and synchronous with the spatio-temporal story, we

 discern also a hierarchically-ordered story, that spells out Kaufmann's

 expectings Ex involved in his doing his experiment. In effect,

 Kaufmann expects of himself that he function on a number of different

 levels: instrument-handler, instrument-maker, experiment-designer,

 hypothesis-framer, and theory-writer.

 

       1. Instrument-handler

 

       In order to perform his experiment, Kaufmann has to gather the

 required parts, assemble them into a functioning experimental

 apparatus, and manipulate it so as to do the experiment.

 

       In so doing, he operates in a directively correlated sequence in

 which he monitors and interacts with both 'self' and 'other.' As

 preconditions, Kaufmann shows high self-esteem (Hilgartner &

 Harrington, 1984) and high skill with his chosen tools, which he has

 earned through his previous experience.

.PA

 

 

       1O-0 <1Gt-1> {1Ex0} Oh0Ot0                (11)

 

 

       This says: The first-ordered abstracting of our organism at

 moment 0 , specified as: background, the first-ordered Gestalt derived

 from past experiencing (1Gt-1) at moment -1; figure, the expectings

 based on the Gestalt (1Ex0) at moment 0; hierarchically and

 spatio-temporally ordered.

 

 

.RR L-----------------------------------------------------------------R

             "His successful measurements apparently were made possible

       by his experimental apparatus, which attained a more complete

       vacuum than other experimenters could produce in their vacuum

       tubes."

       (Dictionary of Scientific Biography, 1970, p. 263d)

 

.RR----!---------------------------------------------------------------R

 These measurements also entail high skill in handling, assembling,

 etc., the parts which make up Kaufmann's experimental apparatus.

 

       (Alternatively, if Kaufmann had low self-esteem as an

 instrument-handler and KNEW it, he could depend on someone else to

 handle the instruments; if he had low self-esteem and DENIED it, he

 could do the job himself in a bungling fashion.)

 

       2. Instrument-maker

 

       In order to design and build an instrument that he feels confident

 will accomplish a certain task, an instrument-maker has to have had

 experiences with instruments that DIDN'T do the job, and with

 instruments that DID.

 

       In designing and building a new instrument (such as a high-vacuum

 pump made of glass and mercury) to do a new job, Kaufmann operates in a

 directively correlated sequence in which he monitors and interacts with

 both 'self' and 'other' on a higher logical level than that discussed

 in the previous section. As preconditions, Kaufmann shows high

 self-esteem as an instrument-maker and high skill with the chosen tools

 of instrument-making.

 

 

       2O-0 <2Gt-1> {2Ex0} Oh0Ot0                (12)

 

 

       This says: The second-ordered abstracting of our organism at

 moment 0, specified as: background, the Gestalt derived from past

 experiencing (2Gt-1) at moment 0; figure, the second-ordered expectings

 based on the Gestalt (2Ex0); hierarchically and temporally ordered.

 

       Success in designing and building an instrument to do a certain

 task increases the instrument-maker's skill on the lower level -- as an

 instrument-handler.

 

       (Alternatively, he could belong to the Lumpy School of

 Glass-Blowing, and clumsily make his own instuments, or could depend on

 someone else to make his instruments for him.)

 

       3. Experiment-designer

 

       In order to design an experiment that uses the given instruments,

 Kaufmann has to

 

       a) Intuit how he might arrange to make the physical "happenings"

 predicted by the hypothesis/theory detectable by his senses.

 

       b) Intuit how he might relate this sensing of the physical

 "happenings" to logically-distinct alternatives, so he can make the

 judgment, "Hypothesis disconfirmed/not-disconfirmed."     

 

       In so doing, he operates in a directively correlated sequence in

 which he monitors and interacts with both 'self' and 'other' on a

 higher logical level than that discussed in the previous section. As

 preconditions, Kaufmann shows high self-esteem as an

 experiment-designer, and high skill with the tools of

 experiment-design.

 

 

       3O-0 3Gt-1 3Ex0 Oh0Ot0                (13)

 

 

       This says: The third-ordered abstracting of our organism at

 moment 0 , specified as: background, the third-ordered Gestalt derived

 from past experiencing (1Gt-1) at moment -1; figure, the

 third-ordered expectings based on the Gestalt (1Ex0) at moment 0;

 hierarchically and spatio-temporally ordered.

 

       Success in designing an experiment which uses given instruments

 increases the experiment-designer's skill on the lower levels.

 

       (Alternatively, Kaufmann could depend on someone else to design

 the experiment, could design it poorly, etc.)

 

       4. Hypothesis-framer

 

       In order to frame a hypothesis (derived from theory) which one

 could design an experiment to test, Kaufmann has to have

 

       a) A working knowledge of what the available equipment can and

 cannot do;

 

       b) A working familiarity with the available theory (or the rival

 theories) and some of its (their) implications;

 

       c) Awareness of a topic on which his preferred theory says, "Yes,"

 and some rival theory says, "No." (Or on which the whole spate of

 current theories don't express an opinion.) "Are Becquerel rays and

 cathode rays the same thing, except the Becquerel rays are going

 faster?"

 

       In so doing, he operates in a directively correlated sequence in

 which he monitors and interacts with both 'self' and 'other' on a

 higher logical level than that discussed in the previous section. As

 preconditions Kaufmann shows high self-esteem as a hypothesis-framer,

 and high skill with the tools of hypothesis-framing.

 

       In effect, he must solve the problem of deriving from theory a

 hypothesis which one could TEST with the available equipment.

 

       Scientists credit the person who frames the hypothesis with

 authorship of the study.

 

.RR L-----------------------------------------------------------------R

             It was during his period at Gottingen that [Kaufmann] did

       his most important experimental work, in particular the

       experiment which yields the dependence of the mass of the

       electron on its speed, a classic investigation that after sixty

       years is still cited in the textbooks of modern physics. (Boorse

       & Motz, 1966, p. 505; italics ours)

 

 

.RR----!---------------------------------------------------------------R

       4O-0 4Gt-1 4Ex0 Oh0Ot0                    (14)

 

 

       This says: The fourth-ordered abstracting of our organism at

 moment 0 , specified as: background, the fourth-ordered Gestalt derived

 from past experiencing (1Gt-1) at moment -1; figure, the

 fourth-ordered expectings based on the Gestalt (1Ex0) at moment 0;

 hierarchically and spatio-temporally ordered.

 

       Success in framing a hypothesis (derived from theory) that one

 could design an experiment to test increases the hypothesis-framer's

 skill as an experiment-designer.

 

       (Alternatively, Kaufmann could depend on someone else to master

 the theory and frame the hypothesis, or could frame it imprecisely,

 etc.)

 

       5. Master Scientist and Theorist

 

       The theories which humans generate start out in principle

 implicit; scientists seek to make theirs explicit, and to subject them

 to testing. While functioning only at the logical level of

 hypothesis-framer, a scientist can depend on someone else's theory or

 theories, which he masters and uses as the basis for the hypotheses he

 frames. A master scientist and theorist, however, generates his own.

 To develop his theory far enough to make it accessible to testing,

 Kaufmann has to

 

       a) Know the previous relevant work in the field;

 

       b) Select a problem to solve (the predicted dependence of the mass

 of the electron on its velocity).

 

       c) Solve it, and derive a hypothesis.

 

       d) Test the hypothesis experimentally.

 

       e) From his findings, draw inferences, spell out implications, and

 so modify the theory (theories) he started with.

.PA

 

       At the beginning of his experiment, Kaufmann shows high

 self-esteem in the domain of theorist, but he has not yet demonstrated

 high skill with the tools of theory-writing. Instead, he has depended

 on others to provide the articulated theories which guide him in

 selecting which "phenomena" to consider "interesting": He has

 functioned as a disciple of Thompson, Searle, Lorentz, et al. --

 Kaufmann's own theory appears inarticulate (embedded in his experiment,

 but not clearly stated as HIS theory.) After he completes his

 experiment, Kaufmann then makes his own theory explicit:

 

 

       "dm/dv --> infinity as v --> c ."

 

 

       In so doing, he operates in a directively correlated sequence in

 which he monitors and interacts with both 'self' and 'other' on a

 higher logical level than that discussed in the previous section.

 

       By the time he has performed his experiment, interpreted his

 results, and submitted his ms for publication, Kaufmann has

 demonstrably become a master scientist/theorist.

 

 

       5O-0 5Gt-1 5Ex0 Oh0Ot0                    (15)

 

 

       This says: The fifth-ordered abstracting of our organism at

 moment 0 , specified as: background, the fifth-ordered Gestalt derived

 from past experiencing (1Gt-1) at moment -1; figure, the

 fifth-ordered expectings based on the Gestalt (1Ex0) at moment 0;

 hierarchically and spatio-temporally ordered.

 

       Success in theory-writing increases the master

 scientist/theorist's skill in framing hypotheses.

 

       (In Section IV above, under the rubric of Expectings, we brought

 up the topic of "Expectings Ex at instant t0 derived from past

 experiencing," but deferred considering the details. Now, we would go

 back and write in 1Ex0, 2Ex0, 3Ex0, and 4Ex0 -- but, for Kaufmann

 at the beginning of his experiment, we would NOT write in 5Ex0 .)

 

 

 VI. INTER-PERSONAL AND SOCIAL STORY

 

       Besides these immediate spatio-temporally and hierarchically

 ordered "doings," an adequate discussion of Kaufmann's experiment

 requires considering more remote "doings."

 

       In performing his experiment and accounting for his results,

 Kaufmann displays consequences of past choices, inter-personal and

 social.

 

.PA

        PZ <FT> {As} O                    (16)

 

 

        PZ <FT> {So} O                    (17)

 

 

 

       This says: (16) Our organism particularizing a term, specified

 as: background, the construct of focal terming (FT); figure, the

 construct of forming an associating with

 self-and-other-member(s)-of-the-species (As); ordered. (17) Our

 organism particularizing a term, specified as: background, the

 construct of focal terming (FT); figure, the construct of continuing

 the associating (So); ordered.

 

       A. Apprenticeship (cf. Polanyi, 1964, pp. 206-9)

 

             i. Affiliating1 (as a student)

 

       At some (probably early) age, Kaufmann said (we conjecture)

 something like "When I grow up, I'm going to be a scientist" -- and

 subsequently, he progressively affiliated himself with the company of

 scientists. As Polanyi (1964, pp. 216-7) points out, from the current

 self-selected group of applicants, the company of scientists selects

 its own successors.

 

 

        PZ <FT> {1As} O                     (16A)

 

 

        PZ <FT> {1So} O                     (17A)

 

 

 

       This says: (16A) Our organism particularizing a term, specified

 as: background, the construct of focal terming (FT); figure, the

 construct of affiliating oneself with a community. (17A) Our organism

 particularizing a term, specified as: background, the construct of

 focal terming (FT); figure, the construct of self-selecting as a

 candidate for membership in a community (accepting apprenticeship).

 

             ii. Fostering/emulating (as a student)

 

       In undertaking apprenticeship, a human credits certain other

 humans as having mastered that which he aspires to practice, and he

 voluntarily submits to their authority.

 

       In accepting him as an apprentice and undertaking to teach him,

 these humans engage in fostering (Fo) . This term subsumes a sequence

 of inferences: The fostering organism affirms (-|) that another

 human (Pe) (who might imitate (Im) his "doings") does actually

 exist, and further affirms that should this person's "doings" or

 "happenings" imitate his own, the outcomes of this person's "doings"

 will satisfy (Sa) this person's focal termings (fundamental needs or

 goals).

 

 

       SP <Foi> {<Pei, Pc(Pei)i+1>

 

 

              "{O-|(.:) <Im <Hi> {Pei+j} OhOt>

 

 

                   {Sa <PeFTi> {PeOci+k} OhOt} OhOt}"i+1 OhOt} O . (18)

                                                                       

 

 

       This says: our organism specifying a term, specified as:

 background, the construct of fostering at moment i; figure, a

 compounded expression, specified as: background, our organism

 recognizing a person at moment i, along with our organism's conscious

 projecting with respect to this person-at-moment-i at moment i+1;

 figure, our organism affirming that from the background follows the

 figure, specified as: background, a compounded expression that the

 figure imitates the background, specified as: background, our organism

 at moment i ; figure, the person at moment j ; hierarchically and

 spatio-temporally ordered; figure, a compounded expression that the

 figure satisfies the background, specified as: background, the focal

 termings for the person at moment i ; figure, the outcome for the

 person at moment i+k ; hierarchically and spatio-temporally ordered at

 moment i+1 ; hierarchically and spatio-temporally ordered; ordered.

 

       This seems equivalent to saying that one of the focal terms of the

 fostering organisms gets satisfied when the relevant focal terms of the

 apprentice get satisfied.

 

 

       SP <HFoi> {<HFTi>

 

 

                   {Sa <PeFTm> {PeOcn} OhOt}i O.           (19)

 

 

       This says: Our organism specifying a term, specified as:

 background, our organism fostering at moment i ; figure, the compounded

 expression that the figure satisfies the background, specified as:

 background, the person's focal terming at some moment m ; figure, the

 person's outcome at some subsequent moment n ; hierarchically and

 spatio-temporally ordered; ordered.

 

       The apprentice, in submitting to authority, engages in emulating

 (Et). This term also subsumes a sequence of inferences: The emulating

 organism affirms that there actually exists another human (whose

 "doings" he would imitate), and further affirms that should his own

 "doings" imitate those of this person, the outcomes of his own "doings"

 will satisfy his own focal termings.

 

 

              SP <Eti> {<Pei, Pc(Pei)i+1>

 

 

                  {-|(.:) <Im <Hi+j> {Pei} OhOt >

 

 

                   {Sa <HFTi> {HOci+1} OhOt} OhOt"i+1 OhOt} O . (20)

 

 

       This says: Our organism specifying a term, specified as:

 background, the term emulating at moment i ; background, the construct

 of emulating at moment i ; figure, a compounded expression, specified

 as: background, our organism recognizing a person at moment i along

 with our organism engaging in conscious projecting with respect to this

 person-at-moment-i at moment i+1 ; figure, a compounded expression that

 our organism affirms that from the background follows the figure,

 specified as: background, a compounded expression that the figure

 imitates the background, specified as: background, our organism at

 moment i+j ; figure, the person at moment i ; hierarchically and

 spatio-temporally ordered; figure, a compounded expression that the

 figure satisfies the background, specified as: background, our

 organism's focal terming at moment i ; figure, our organism's outcome

 at moment i+k; hierarchically and spatio-temporally ordered;

 hierarchically and spatio-temporally ordered at moment i+1 ; ordered.

 

       The fostering organism holds the results (Rsl) obtained

 initially by the emulating organism as less important than the skills

 (Skl) he may develop while performing the procedures. In other words,

 in the Gestalt of the fostering organism, the emulator's skills occupy

 the figure, while his results occupy the background.

 

 

       FoO- <PeRsl> {PeSkl} OhOt                (21)

 

 

       This says: The abstracting of the fostering organism, specified

 as: background, the person's results; figure, the person's skills;

 hierarchically and spatio-temporally ordered.

 

       When the apprentice emulates the teacher and finds that the

 outcomes of his "doings" satisfy his relevant focal terms, the teacher

 finds his own focal terms satisfied. This amounts to saying that the

 apprentice fosters the teacher (on the next logical level). In other

 words, any fostering/emulating entails mutual fostering,

 [HFo(Pe), PeFo(H)]

 

 

        "[HFo(Pe), PeFo(H)] <Sa <HFTm> {HOcn} OhOti> {PeFT} OhOt

                        |           | | |     

                        |           | | |     

                        <Sa <PeFTm> {PeOcn} OhOt}i> {HFT }(22)

 

       This says: Our organism fostering the person along with the person

 fostering our organism, specified as two parallel compounded

 expressions; background1, the figure satisfies the background,

 specified as: background, our organism's focal termings at some moment

 m ; figure, our organism's outcome at some subsequent moment n ;

 hierarchically and spatio-temporally ordered; background2, the figure

 satisfies the background, specified as: background, the person's focal

 terming at some moment m ; figure, the person's outcome at some

 subsequent moment n ; hierarchically and spatio-temporally ordered at

 moment i ; figure1, the person's focal terming; figure2, our organism's

 focal terming; hierarchically and spatio-temporally ordered.

 

             iii. "Graduating" (a "rite of passage")

 

       Kaufmann, once a novice, learned how to use the relevant tools by

 emulating skilled tool-users committed to fostering. The standards or

 criteria concerning how to use the tools which he mastered don't

 "exist" "OUT THERE," independent of humans, but rather, they became

 manifest when someone in some sense or other said to him, with a

 particular attitude and in a particular tone which we might call the

 fostering voice, "Do it this way, and don't do it that way."

 Eventually he made the fostering voice his own, and used it with

 himself.

 

       The performances of our novice with his tools elicited judgments

 from teachers and peers on his skill. Furthermore, he incorporated the

 judgments on his skill and other aspects of the esteem of others into

 self-esteem, and came to assess the degree of his skill. In the

 process, he also judged the degree of skill of his predecessors,

 teachers and peers.

 

       When both Kaufmann and his teachers considered that his degree of

 skill surpassed some minimum standard, he graduated from the role of

 apprentice. Thereafter he associated with the community of scientists

 as a peer.

 

 

 B. Functioning as a peer

 

             i. Affiliating2 ("continuing the associating")

 

       After his graduation, Kaufmann answered inquiries about his

 occupation (we conjecture) with something like, "I am a physicist." As

 a member of the peerage, he began taking part in the process of

 training and selecting his own successors.

 

 

       PZ <FT> {2As} O                    (16B)

 

 

       PZ <FT> {2So} O                    (17B)

 

 

       (For rough translations, cf. (16), (17), (16A), and (17A).

 Consider 2As as signifying "accepting a person as a student," and

 2So as signifying "engaging in teaching this person."

.PA

 

             ii. Fostering/emulating (as a teacher)

 

       Functioning as a teacher, Kaufmann treated the skills developed by

 his students by performing procedures as figure, and the results they

 may obtain as background. (cf. (21))

 

       Regarded as a researcher, Kaufmann and his peers treated

 Kaufmann's results as figure, and the skills required to produce the

 results as background. In effect, he acted on the assumption that "The

 group (guild) will take me and my result seriously."

 

 

       HO- <HSkl> {HRsl} OhOt                    (23)

 

 

       This says: Our organism's abstracting, specified as: background,

 our organism's skills; figure; our organism's results; hierarchically

 and spatio-temorally ordered.

 

             iii. Mastery (a "rite of passage")

 

       Most of what scientists do and publish fills in details of the

 dominant paradigms of the time. Occasionally, however, a member of the

 community, using available equipment and acceptable methodology applied

 with high skill, gets results which do not fit with these paradigms.

 

       At the point when this scientist acknowledges his results as

 anomalous, and judges that since the experiment meets his criteria his

 results merit his own trust, he becomes a master scientist. In writing

 up his results and submitting them for publication, he asserts his

 mastery, and invites his community to scrutinize his results from

 logical and theoretical viewpoints, to replicate his experiment, and in

 general to put his findings to use. We can see how this worked for

 Kaufmann: According to the Dictionary of Scientific Biography (1970,

 pp. 263d, 264a,b), Lorentz and Bucherer subsequently discussed the

 topic of the mass of electrons; Abraham and Planck and Einstein

 specifically discussed Kaufmann's 1901 results, and Einstein in 1907

 fitted Kaufmann's findings into the special theory of relativity.

 

 

 VII. CONSEQUENCES

 

 A. Changes brought about in the guild

 

       A scientist expects the universe (both non-living and

 inter-personal) to foster him in his scientific work. In the process

 of the dialogue between theory and experiment, he improves his

 orientation in his directively correlated efforts toward individual and

 species survival.

 

       With respect to the non-living, Kaufmann's 1901 experiment yielded

 findings which Newtonian physics could not account for. Contemporary

 physicists used it to argue in favor of revising Newtonian dogma.

.PA

.RR L-----------------------------------------------------------------R

             As early as 1901 Kaufmann reviewed the history of electron

       theory in his address "Die Entwicklung des Elektronenbegriffs,"

       delivered at the seventy-third Naturforscher Versammlung at

       Hamburg. He noted the fruitless efforts in the past to reduce

       electrical phenomena to mechanical phenomena and advocated

       reversing the process by attempting to reduce mechanics to

       electrical principles. Acknowledging the contributions of

       Lorentz, J. J. Thompson, and W. Wien in this direction, Kaufmann

       reasoned that if atoms consisted of conglomerates of electrons,

       then their inertia resulted as a matter of course. (Dictionary

       of Scientific Biography (1970), p. 264 b,c)

 

.RR----!---------------------------------------------------------------R

       As for the inter-personal aspects, physicists do not customarily

 describe, or even acknowledge, the effects on the experimenter or on

 other physicists produced by performing any particular experiment. But

 to write up results and submit them for publication comprises a SOCIAL

 act, with SOCIAL consequences. The following expression states the

 relation of "continuing the associating between our organism H and a

 person Pe ", So(H,Pe), as " H abstracts so as to generate a gestalt

 Gt ("publishable findings") from his outcome Oc ("results"); and the

 person Pe takes in the (transmitted, e.g. published) gestalt Gt so

 as to generate an 'awareness' Aw ."

 

 

       So(H,Pe) <HO- <HOcg>

 

 

                   {HGth} OhOt>

 

 

              {PeO- <HGti>

 

 

                   {PeAwj} OhOt} OhOt           (24)

 

 

       This says: Continuing the associating between our organism and a

 person, specified as two compounded expressions: background, a

 compounded expression that our organism abstracts, specified as:

 background, an outcome for our organism at moment g ; figure, our

 organism's Gestalt or generalization at moment h ; figure, a compounded

 expression that the person abstracts, specified as: background, our

 organism's Gestalt at moment i ; figure, our person's awareness at

 moment j ; hierarchically and spatio-temporally ordered; hierarchically

 and spatio-temporally ordered.

 

       In keeping with custom, Kaufmann focussed on the inanimate and

 left un-discussed the possible personal and social effects of

 performing and publishing his 1901 experiment.

 

       As it turned out, the social aftermath of this experiment included

 the personal growth which Kaufmann underwent in the process of

 designing, performing and reporting this experiment (cf. above, V 5),

 and the attention subsequently paid to Kaufmann by the theorists

 mentioned above. The entry on Kaufmann in the Dictionary of Scientific

 Biography (1970) backhandedly acknowledges his originality, as

 follows:

 

.RR L-----------------------------------------------------------------R

             The significance of Kaufmann's experimental evidence that

       electron mass varied with velocity, coupled with his belief that

       mass could be expressed as essentially electromagnetic phenomena,

       has rarely been recognized. He outlined a major pathway along

       which research in twentieth-century physics would be directed.

       (Dictionary of Scientific Biography, p. 264a)

 

.RR----!---------------------------------------------------------------R

       In short, Kaufmann's study entails expectations concerning the

 inanimate, which he makes quite explicit. These expectations got

 tested and not-disconfirmed, and so yielded an advance in articulated

 physical knowledge. The cognate Newtonian tenets did get disconfirmed.

 Kaufmann's study also entails expectations concerning self and the

 social. However, Kaufmann did not make these explicit at all. Hence

 he provided no way to disconfirm these expectations. He may have

 erred, but he had no protocol, no way of ESTABLISHING whether he did or

 not. Hence his study provided no explicit advance in articulated

 SOCIAL knowledge.

 

 

 B. Eliminating vs. including the observer

 

       As just noted, in his 1901 experiment Kaufmann failed to make

 explicit his expectations concerning self and the social. By so doing,

 he continued to associate himself with the Newtonians, who, in their

 theorizing, SYSTEMATICALLY eliminate the observer (or self) and the

 relations between self and other humans from consideration.

 

       1. The structure of "eliminating the observer"

 

       The Newtonians never SAID (prior to 1900-1905) that they eliminate

 the observer from consideration (Hilgartner & Harrington, 1984a).

 Instead, they never discussed the topic of the observer -- of how a

 physicist builds up his picture of the physical happenings which occur

 in and around him -- at all.

 

       In accounting for this omission, we attribute to the Newtonians a

 special, restricted and restrictive assumption which has the effect of

 eliminating the observer from consideration -- namely, a tacit form of

 "absolute certainty." Furthermore, we attribute to the quantum

 theorists and relativists and Newtonians alike still another hidden

 assumption, distinguishable from the one disclosed in Newtonian physics

 by the early quantum theorists and relativists, which also has the

 effect of eliminating the observer from consideration by failing to

 consider the hierarchically-ordered relations of an experimenter with

 himself and with other scientists -- another tacit form of "absolute

 certainty" (Hilgartner & Harrington, 1984).

 

       Still further, we say: If in his theorizing a human relies on some

 special assumption which eliminates from consideration a crucial aspect

 of the situation, or certain facets thereof -- e.g. the self-component

 or observer -- he unavoidably leaves out of account some crucial aspect

 of the environmental component of the situation as well.

.PA

 

       CP <ZF> {SfF OtF} O                    (25)

 

 

 and likewise,

 

 

       CP <O-F> {(sigma)F (rho)F} O                (26)

 

 

       This says: (25) Our organism componenting a term, specified as:

 background, left-out-of-account aspect of organism's map (ZF); figure,

 left-out-of-account self-component (SfF) along with left-out-of-account

 other-component (OtF); ordered.

 

       (26) Our organism componenting a term, specified as: background,

 left-out-of-account aspect of organism's abstracting (O-F); figure,

 left-out-of-account self-referential abstracting ((sigma)F) along with

 left-out-of-account hetero-referential abstracting ((rho)F); ordered.

 

       In other words, like the early quantum theorists and relativists,

 we impute to the Newtonians (including Kaufmann) at least one

 fundamental theoretical error concerning self-and-environment -- and

 to the quantum theorists and relativists themselves, another. On the

 topic of such errors, Perls, Hefferline & Goodman (1951) lay out the

 crucial issues trenchantly:

 

.RR L-----------------------------------------------------------------R

             Fundamental theoretical errors are invariably

       characterological, the result of a neurotic failure of

       perception, feeling, or action. (This is obvious, for in any

       basic issue the evidence is, so to speak, 'everywhere' and will

       be noticed unless one will not or cannot notice it.) A

       fundamental theoretical error is in an important sense given in

       the experience of the observer; he must in good faith make the

       erroneous judgment; and a merely 'scientific' refutation by

       adducing contrary evidence is pointless, for he does not

       experience that evidence with its proper weight -- he does not

       see what you see, it slips his mind, it seems irrelevant, he

       explains it away, etc. Then the only useful method of argument

       is to bring into the picture the total context of the problem,

       including the conditions of experiencing it, the social milieu

       and the personal 'defenses' of the observer. That is, to subject

       the opinion and his holding of it to a Gestalt-analysis. A basic

       error is not refuted -- indeed, a strong error, as St. Thomas

       said, is better than a weak truth -- it can be altered only by

       changing the conditions of raw experience.

 

             Then, our method is as follows: We show that in the

       observer's conditions of experience he must hold the opinion, and

       then, by the play of awareness on the limiting conditions, we

       allow for the emergence of a better judgment (in him and in

       ourselves). We are sensible that this is a development of the

       argument ad hominem, only much more offensive, for we not only

       call our opponent a rascal and therefore in error, but we also

.RR----!---------------------------------------------------------------R

 charitably assist him to mend his ways! Yet by this unfair

 method of argument, we believe, we often do more justice to an

 opponent than is common in scientific polemic, for we realize

 from the start that a strong error is already a creative act and

 must be solving an important problem for the one who holds it.

.RR L-----------------------------------------------------------------R

       (Perls, et al., 1951, pp. 243-4)

 

.RR----!---------------------------------------------------------------R

       The opinion rigidly held by Kaufmann centers about the way he

 linguistically "cut[s] nature up [and] organize[s] it into concepts"

 (to use Whorf's (1956, p. 213) phrase), and the degree of reliability

 he attributes to this arbitrary, linguistically-determined pattern.

 Kaufmann symbolically cuts up nature into two distinct and disparate

 realms, namely, "the objective" vs. "the subjective," which he

 maintains in "logic-tight compartments" (Cartier, 1963). As we have

 already shown, Kaufmann treats his expectations concerning the

 inanimate, e.g. electrons, as hypothetical and tentative, and subjects

 them to experimental testing -- the most devastating kind of criticism

 yet devised. And his findings violate the predictions of Newtonian

 theory -- mass, he finds, increases with velocity. In contrast, by not

 making explicit his expectations about self and the social, Kaufmann

 treats them as NOT in any way hypothetical or tentative, but rather as

 beyond scrutiny or criticism -- as "The way things REALLY ARE."3 Since

 he does not subject his expectations in this domain to scrutiny, he

 tacitly assumes that they reach "absolute certainty." Or, stated in

 logical terms, Kaufmann TREATS his picture or map of self and the

 social as identical with the territory referred to -- he attributes

 absolute certainty to unscientific views in that arena. Absolute

 certainty logically precludes any role for the observer.

 

       In the end, by adhering to a fundamental theoretical error, each

 member of the Newtonian guild denies to his unscientific expectations

 concerning self and the social the scrutiny he gives to his disciplined

 expectations concerning the inanimate -- and in so doing, represents

 his most fundamental needs as insatiable and his self as dissociated

 (Hilgartner & Randolph, 1969a,b,c,d; Perls, Hefferline & Goodman, 1951;

 Whyte, 1949).

 

 

       SP <OGtd>i                         

                   __

        {.: <O -|>i {OPr}j OhOt }

        |             |

        |             |

        {.: <OIr(O -|>i {OSv}j OhOt }

        |             |

        |             |

        {.: <OSv}j > {OIr(O -|}k OhOt}           (27)

 

 

 

       This says: Our organism specifying a term, specified as:

 background, our organism's dissociative Gestalt at moment i ; figure,

 an expression composed of three compounded expressions taken in

 parallel, namely, figure1, our organism's Gestalt that from the

 background follows the figure; background, our organism's affirming at

 moment i ; figure, our organism's total destruction

 (not-preservation-and-growth) at moment j ; hierarchically and

 spatio-temporally ordered; figure2, our organism's Gestalt that from

 the background follows the figure, specified as: background, our

 organism interrupting his affirming at moment i ; figure, our

 organism's bare survival at moment j ; hierarchically and

 spatio-temporally ordered; figure3, our organism's Gestalt that from

 the background follows the figure, specified as: background, our

 organism's bare survival at moment j ; figure, our organism

 interrupting his affirming at moment k ; spatio-temporally and

 hierarchically ordered.

 

       Logically speaking, dissociating the self and eliminating the

 observer follow from a single hidden untenable assumption (a tacit form

 of "absolute certainty"), and so seem equivalent. Furthermore,

 developmentally speaking, when a human generates the dissociative

 Gestalt (Gtd), he imparts to his experiencing an affect

.UL on

 ive tone which

 we                     call the sense of isolation (ORe-).

 

              __

       .: <Gtd> {ORe} OhOt .                    (28)

 

 

       This says: Our organism generating the Gestalt that from the

 background follows the figure, specified as: background, the organism's

 dissociative Gestalt (Gtd); figure, the organism's sense of isolation

 (ORe); ordered.

 

       2. Consequences of eliminating the observer

 

       A human or group that tacitly regards its views as absolutely

 certain (and thus eliminates the observer), and that encounters another

 human or group whose views do not exactly match its own, manifests

 counter-fostering of that human or group by defending the rightness of

 its own views. In other words, it perpetuates an ethos of

 power-struggle. This in turn has serious consequences, which we

 discuss in detail in the next installment of this series.

 

       3. The structure of including the observer systematically

 

       We humans can eliminate the fundamental theoretical errors and the

 underlying untenable assumption discussed above by treating our

 expectations concerning self and the social as also hypothetical and

 tentative, and subjecting them to experimental testing. In so doing,

 we distinguish between our pictures of self-and-the-social and what our

 pictures represent.

 

 

 POSTULATE 1:

 

 

       Non-identity: 1=_/ <oZ> {eHeY} OhOt          

 (29)

 

 

       This says: Our organism (first-ordered) non-identifying (=_/),

 specified as: background, our organism's (object-leveled) map (OZ);

 figure, the (event-leveled) self-component (eH) along with the

 other-component (eY) of the environment; hierarchically and

 spatio-temporally ordered.

 

       That means that we explicitly regard our pictures in principle

 both as incomplete and inaccurate, and as containing some kind of

 representation of the human who generates the pictures.

 

 

 

 POSTULATE 2:

 

 

       Non-allness:(rho) <v0> {y0} OhOt                

             ___

                  (rho) <v0> {y1} OhOt      

                  ___

                  (rho) <v1> {y0} OhOt

                  ___

                  (rho) <v1> {y1} OhOt           (30)

 

 

 POSTULATE 3:

 

 

       Self-reflexiveness:(sigma) <u0> {h0} OhOt

                        _____               

                        (sigma) <u0> {h1} OhOt

                        _____

                        (sigma) <u1> {h0} OhOt

                        _____

                        (sigma) <u1> {h1} OhOt      (31)

 

 

       A human who operates from these premises does not represent his

 self as dissociated; he represents his transacting with his environment

 as directively correlated, and as competent to satisfy the fundamental

 needs of organism and group. In other words, he shows an attitude

 which we call O-|i , affirming.

 

 

       SP <O-|>i {OPrj} OhOt                    (32)

 

 

       This says: Our organism specifying a term, specified as:

 background, our organism affirming at moment i; figure, our organism's

 preservation-and-growth at subsequent moment j; hierarchically and

 spatio-temporally ordered.

.PA

       Logically speaking, affirming of self-and-other and taking the

 observer (or self) into account appear equivalent. Furthermore,

 affirming imparts to the experiencing of a human who does it an

 affective tone which we call the sense of relatedness-in-a-field,

 (ORei).

 

 

       .: <O-|i>: {ORej} OhOt                (33)

 

 

       .: <(29), (30), (31)> {ORe} OhOt           (34)

 

       

       This says: (33) Our organism generating the Gestalt that from the

 background follows the figure, specified as: background, our organism

 affirming at moment i ; figure, our organism's sense of

 relatedness-in-a-field, at moment j ; hierarchically and

 spatio-temporally ordered.

 

       (34) Our organism generating the Gestalt that from the background

 follows the figure, specified as: background, the premises (sentences

 (29), (30) and (31)); figure, our organism's sense of

 relatedness-in-a-field.

 

       4. Consequences of including the observer systematically

 

       To date, not many workers explicitly operate from theories which

 systematically include the observer. Instead, most subscribe to

 theories which posit absolute certainty in some arena (most often, that

 of self and the social), and so surround themselves with a dissociated

 setting which endorses counter-fostering in an ethos of power-struggle.

 Therefore, the consequences of including the observer remain as yet

 inadequately experienced.

 

       From our preliminary assessment of this topic, it appears that

 systematically taking the observer into account eliminates the basis

 for dissociating one's self, and for the inter-personal transactings we

 could call

.UL off

 institutionalized counter-fostering in general and

 power-struggle in particular.

 

       We parochial humans have grown up in a dissociated social

 environment, characterized by an ethos of power-struggle. When we hear

 of a practicable way toward an alternative ethos, we feel stunned.

 Somehow we can't quite imagine what it would look like.

 

       The present frame of reference provides guidance in our endeavors

 to develop such an alternative ethos. Our non-standard notations

 cannot NOT take the observer into account. Hence our mathematics makes

 the crucial relations clear, and shows us when we have left out some

 central factor of our relations with self-and-other. The third paper

 in this series will discuss some of the implications for physics of

 this frame of reference.

 

.PA

                                FOOTNOTES

 

 1. At the current stage of development of our notation, we use a total

 of five ordering terms: Besides spatio-temporal and hierarchical, we

 utilize synchronous with Os ("occurring along with, as viewed from a

 specified position"), co-ordered with Oc ("occupying one and only one

 position in an ordering on abstracting"), and polar to Op ("mutually

 necessary, opposing").

 

 2. We quote at length from these sources for at least three reasons:

 

.RR L-----------------------------------------------------------------R

       a) Few readers, we expect, will find themselves fully conversant

       with the details;

 

       b) It takes special care to reconstruct the setting for

       Kaufmann's experiment convincingly; and               

 

 

       c) The "fit" between our integrative framework and the details

       presented in these sources makes one of the most striking

       features of our framework which our study discloses. If we

       should paraphrase instead of quoting, we would deprive our

       readers of their opportunities to sense this "fit."

 

.RR----!---------------------------------------------------------------R

 3. One might excuse Kaufmann from any necessity to deal with such

 expectations, on the grounds that they lie outside the field of

 physics, or that he does not claim competence in such areas. To do so

 not only begs the questions we raise, but also endorses eliminating the

 observer.

 

.PA

                               REFERENCES

 

 Ashby, W. Ross (1962): "The Set Theory of Mechanism and Homeostasis."

 Technical   Report No. 7, Electrical Engineering Research

 Laboratory, University of Illinois, Urbana, IL.

 

 Boorse, Henry A. & Lloyd Motz (1966): The World of the Atom. New York:

 Basic       Books.

 

 Cartier, Francis (1963): "Three Misconceptions of Communication." ETC.:

 A Review of      General Semantics 20:135-145

 

 Dictionary of Scientific Biography (1970): American Council of Learned

 Societies, New York: Scribner's.

 

 Hilgartner, C. A. (1978f): "'International' or 'One-World' Languages:

 "You Can't Get There From Here"." Eco-logos: A Magazine of

 One-World Environmental Concepts, Vol 24, No. 90, Appendix V.

 

 Hilgartner, C. A. (1978g): "The Method in the Madness of Western Man."

 Communication 3:143-242.

 

 Hilgartner, C. A. (1979a): "A Complete Severance from Traditions."

 Presented at the Centennial Conference on General Semantics, New

 York City, 27 October 1979. Printed in the General Semantics Bulletin

 No. 47, 112-9 (1980).

 

 Hilgartner, C. A. & Ronald V. Harrington (1984): "Relativity Revisited:

 The Case for Hierarchical Ordering" (Submitted for publication.)

 

 Hilgartner, C. A. & John F. Randolph (1969a,b,c,d): "Psycho-logics: An

 Axiomatic System Describing Human Behavior. 1. A Logical Calculus of

 Behavior." Journal of Theoretical Biology 23:285-338. "2. The

 Structure of 'Unimpaired' Human Behavior." Journal of Theoretical

 Biology 23:347-374. "3. The Structure of Empathy." Journal of

 Theoretical Biology 24:1-29. "4. The Structure of 'Impaired' Human

 Behavior."      (Submitted for publication.)

 

 Kaufmann, Walter (1901): Nachrichten von der Gesellschaft der

 Wissenschaften zu Gottingen, Math.-phys Kl., 2:143-155.

 

 Korzybski, Alfred (1921): Manhood of Humanity. New York: Dutton. Second

 edition (1950), Lakeville CT: Institute of General Semantics.

 

 Korzybski, Alfred (1933): Science and Sanity: An Introduction to

 Non-Aristotelian Systems and General Semantics. Chicago:

 International Non-Aristotelian Library Publishing Co. Fourth edition

 (1958), Lakeville, CT: Institute of General Semantics.

 

 Perls, Frederick S., Ralph Hefferline & Paul Goodman (1951): Gestalt

 Therapy: Excitement and Growth in the Human Personality. New York:

 Julian Press.

 

 Polanyi, Michael (1964): Personal Knowledge: Toward a Post-Critical

 Philosophy. Chicago: University of Chicago Press, 1958. Torchbook

 edition, New York: Harper & Row.

 

 Singer, E. A. (1946): "Mechanism, Vitalism, Naturalism." Philosophy of

 Science 13:81-99.

 

 Sommerhoff, G. (1950): Analytical Biology. London: Oxford University

 Press.

 

 Whorf, Benjamin Lee (1956): Language, Thought, and Reality. John B.

 Carroll, editor. New York: Wiley/MIT Press.

 

 Whyte, Lancelot Law (1950): The Next Development in Man. New York:

 Henry Holt, 1948. Paperback edition (1950), New York: Mentor Books

 (New   American Library).

 

.PA

                            GLOSSARY OF TERMS

 

       In general, treat each of these terms as some kind of a

 verb-form.

 

 -|    Affirming          HOur (human) organism

                                      

 Rsl   Results          InInterest          

 

 Ap    Approach          M*Motor          

 

 At    Attend               MonOff/on switch for the

                                       electric/magnetic fields

 Aw    Aware                          

                                 OOrder          

 CP    Component                         

                                 OcOutcome          

 Cs    Consciousness                         

                                 PZParticularize     

 CT    Coenetic term                         

                                 PePerson          

 Cls   Close                          

                                 ReRelatedness          

 Df    Deficit                         

                                 SaSatisfy          

 DC    Directively correlated                    

 

                                 SklSkill          

 Et    Emulate                         

                                 SoContinue the associating

 Ex    Expect                              

                                 SPSpecify          

 FT    Focal terming                         

                                 StkStopcock          

 Fo    Foster                              

                                 TonTurn switch on     

 Greek letters:                         

                                 SySystem          

  Theta (Overall) abstracting                    

                            VonVacuum pump off/on switch

 

  Rho Hetero-referential

        abstracting.          YEnvironment     

 

  Sigma Self-referential      ZMap or representation

 

        abstracting                    

                                      

  Psi In DC, the interacting of f(d) and g(d).          

             

                                      

 Gt    Gestalt          

                                      

 Gtd   The dissociative Gestalt

                                      

.PA

                               APPENDIX 1

 

       A. SUMMARY OF PREVIOUS PAPER

 

       In the first paper of this series,@ we utilize our frame of

 reference to look at how the theory of relativity does the job of

 taking the observer into account. To make our first point, we use

 selected ones of our own constructs (mainly the undefined term

 ordering) to see how much of the theory of relativity fits within our

 theory, as a kind of special case. In the process, we differentiate

 between those aspects of the theory of relativity which amount to

 taking the observer into account and those aspects which do not.

 

 ___________________

 

 @Criterion of logical generality

 

 @Null-A vs. traditional assumptions and "taking observer into account"

 (WHERE did we first lay out both sets of assumptions?????)

 

 @"Anomalies Generated by Contemporary Physics"

 ___________________

 pa

       A) Using the special case of spatio-temporal ordering, we

 account, with considerable economy of means, for some of the positive

 accomplishments of the theory of relativity. Our constructs handle

 with particular ease the dispute over relativity, manifested in the

 well-known opposing tenets: the one attributed to Newtonian mechanics,

 a) that light travels from one point to another in 'no time at all',

 vs. the one Einstein offers, b) that light travels at a finite

 velocity which remains constant for all observers, regardless of their

 motion relative to each other or relative to the light source. The

 complex of relations which Einstein's tenet makes it possible to handle

 provides the grounds for saying that his theory of relativity takes the

 Observer into account.

 

       B) Using the special case of hierarchical ordering, we examine the

 process of discovering the kind of anomaly (also known as a

 relativisitc discrepancy) which logically precedes and leads to the

 theory of relativity. We find that the discovery of an anomaly or

 relativistic discrepancy hinges on key relations with self and the

 social. Moreover, our examination discloses certain previously

 unnoticed assumptions within the theory of relativity, specifically,

 tacit assumptions concerning how an investigator deals with self and

 the social. In detail, we find that these anomalies have the following

 common structure:

 

       a) Observer B makes some observations;

 

       b) B takes in some observations made (under slightly different

 conditions) by Observer A; or else B considers observations that B

 made at a different date, and under slightly different conditions;

 

       c) B finds that the two sets of observations DON'T MATCH in some

 crucial fashion; and

.PA

       d) B takes seriously (eventually, takes on the job of accounting

 for) this mismatch, this anomaly.

 

       The discovery of a relativistic discrepancy requires, and signals

 the presence of, a new level of trust between the scientists involved

 -- a trusting of themselves and of each other. If, like the

 traditional Newtonians, Observer B should seek to invalidate and

 discredit the findings of Observer A which don't match with her/his own

 observations/conclusions, then s/he could never discover a relativistic

 discrepancy in the first place. The trusting must precede the

 discovering. The increase in predictability delivered by the theory of

 relativity (and quantum theory), then, follows from this increase in

 intra-personal and interpersonal trusting.

 

       As noted, Einstein takes into account certain aspects of

 spatio-temporal ordering in human experiencing -- e.g. the finite

 velocity of light, and thus the finite interval it takes for Observer

 A's observations to reach Observer B. But by neglecting to discuss the

 specific patterns of dealings with self and the social -- e.g. the

 nervous system activities by which B makes her/his observations --

 Einstein tacitly REPRESENTS observable physical "happenings" which

 occur at finite velocities AS IF they occurred in 'no time at all'.

 That, however, involves a chain of implications which Einstein himself

 first disclosed: It treats ordered activities as non-ordered -- and in

 the process, eliminates the Observer from consideration.

 

       Thus we demonstrate that, within a limited arena, the theory of

 relativity does effectively deviate from the tenets concealed in the

 WIE grammar so as to rely on map-territory non-identity, and so does

 take the observer into account; whereas, elsewhere throughout the

 theory, it still grants a privileged position to the WIE grammar and so

 relies on map-territory identity, and so systematically eliminates the

 observer from consideration.

 

       As the second point of our previous paper, we address the question

 of what difference it makes whether one takes the observer into

 account, or does not. We show the importance of this issue in terms of

 the role which the practice of science plays in species-survival.

 

       In the largest perspective, we humans practice science in order to

 increase human knowledge and our ability to predict accurately, so we

 can increase the likelihood that individual, group and species will

 survive.

 

       Today, however, when we humans generate and apply new knowledge --

 when we practice science -- we bring the human species closer and

 closer to species suicide and extinction (and in the process, push the

 rest of the biosphere toward annihilation too). The authors hold that

 the disjunction between what we see going on around us -- the headlong

 rush toward species suicide, extinction and pan-biocide -- and the

 reason we humans practice science in the first place constitutes an

 anomaly. It represents "findings which we must take seriously, that

 current theory cannot adequately account for."

 

       In order to account for the current anomalies, we start with the

 supposition that humans expect or assume. Then what one DOES follows

 from what one ASSUMES, as theorems follow from premises. We hold that

 every human transacts with her/his environment -- s/he continuously

 undergoes two-way interchanges with her/his environment, which leave

 both participants fundamentallly and profoundly altered, in some sense

 that affects the further living of the living system(s) involved.

 Furthermore, every human transacts AS IF from some theory or other,

 some structure composed of assumptions, which we call a lived theory --

 whether s/he notices or not. Still further, we regard it as possible,

 feasible and desirable for any human to make her/his lived theory

 explicit, and to subject it to scrutiny, revising it as needed.

 

       Lived theories have a creative aspect, functioning like

 self-fulfilling prophecies. As we humans transact on the basis of

 lived theory, our "doings" remake everything involved in the

 transacting into a closer approximation to the pictures of "what goes

 on" in the theory which we live. For example, a lived theory which

 tacitly posits map-territory identity and so systematically leaves out

 of account the observer also systematically leaves out any transacting

 between organism (observer) and environment, and thus in turn leaves

 out the environment. Such a theory thus provides the symbolic means to

 represent only inanimate mechanisms, e.g. those that maximize a single

 variable (e.g. power, or status, or profits). In general, when we

 humans live a theory which systematically leaves out of account the

 observer -- ourselves-in-our-environments -- we transform the

 environment so that it becomes more hospitable to mechanisms and less

 hospitable to living systems, while we transform ourselves so we more

 resemble the types of mechanisms depicted in the theory --

 machine-tending machines, or businessmen, etc. -- than we do persons

 engaging in mutually-altering transacting.

 

       Conversely, a theory which explicitly posits map-territory

 Non-identity and so systematically takes the observer into account --

 in her/his dealings with self, with the non-living environment, with

 other humans and with other species -- provides the symbolic means

 adequately to represent living systems transacting with

 themselves-and-their-environments. So far, we humans have few worked

 examples of this kind of theory to consider. But in principle, when we

 live such a theory, we provide ourselves with the possibility of

 transforming our environments so as to make them more diverse, more

 hospitable to transacting persons; and of transforming ourselves so we

 resemble not mechanisms, but rather, transacting persons --

 participants in an ecology -- (co-)operating on a people-centered,

 life-centered basis.

 

       In this light, we find that although, historically speaking, the

 theory of relativity served as the focus for introducing the construct

 of taking the observer into account, for the most part its exponents --

 in company with the rest of the practitioners of WIE science -- still

 grant a privileged position to the WIE grammar, and so maintain their

 tacit reliance on map-territory identity. This reliance leads them

 both to keep the doctrines they hold concerning self and the social

 concealed, and to protect those concealed doctrines from scrutiny and

 revision. Even the advocates of the very best of the scientific

 theories of the WIE tradition, then, split their science into two

 components: In the foreground part, the exponents operate from

 disciplined observing/inferring from shared explicit assumptions which

 they acknowledge, question and test, while defining as 'favorable' any

 outcome which increases knowledge. In the background part, they

 operate from secretly shared tacit assumptions which they do not

 acknowledge, question or test, while treating as 'favorable' any

 outcome which both keeps those tacit assumptions concealed and

 maintains or increases the power or prestige or profits of some

 specified group (at the expense of other groups), for the sole benefit

 of the specified group.

 

       Thus scientists and non-scientists alike have cooperated in

 exploiting modern science, including modern physics, with no concern or

 responsibility for the welfare of the human species in its environment,

 and with no concern for the internal structure of science itself, its

 logic and ethics. In the process, we have created a mutilated

 science,@ committed to maintaining certain hypotheses, views, opinions,

 beliefs or guesses as hidden, tacit, unrecognized, unexamined and

 untested. We have subjugated our advances in explanatory power to

 local patriotism, economic interest, the power of the state, and the

 like. Thus we have created a social institution of "science" with a

 different, darker goal: To use the explanatory power of modern

 science, especially modern physics, to produce physical power in the

 service of power struggle, for the sole benefit of some group smaller

 than the entire human species. By so doing, we have created the modern

 anomalies, and so threaten ourselves with species-suicide,

 self-inflicted extinction.

 

       In conclusion, we assert that:@     

  The currently-dominant forms of human knowledge -- standard-brand

 Western logics, mathematics, sciences, philosophies, jurisprudences,

 religions, along with the lived theories of their exponents -- appear

 incompatible with species-survival. And in their present stages of

 development, none of our Western scientific theories -- in "natural

 science or psychology," as Einstein puts it -- shows us how to arrange

 our personal lives and our social systems so as to replace the

 non-viable pattern of power struggle with some alternative, viable

 pattern. None rigorously accounts for how the terrible dangers which

 constitute the modern anomalies can arise out of modern physics.

 

       We summarize our findings as follows:@

 

.RR L-----------------------------------------------------------------R

             In casting about for a way to talk about our current

       species-suicidal impasse, the authors... explore [the]

       possibility ... [t]hat, as organisms who guide what we DO by the

       assumptions encoded in the theories we hold, we humans HAVE DONE

       exactly what the currently dominant assumptions have told us to

       -- to our immediate peril -- and that we can change what we do

       ONLY by changing our assumptions.

 

             As our considered opinion, the authors suggest that the

       assumptions encoded in our currently dominant theories include at

.RR----!---------------------------------------------------------------R

 least one now-disclosed tacit assumption which directs us humans

 in self-defeating, self-eliminating, suicidal directions. We

 further suggest that we now have the resources -- alternative

 assumptions and the beginnings of an alternative scientific frame

 of reference based on them -- with which to reject and replace

 this dangerous tacit assumption. We hold that the time has come

 for us humans to revise our traditional premises.

 

 ________________

 

 @Polanyi

 

 @Anomalies, p. 138b

 @"Anomalies...", p. 139a,b

 ________________

.HM3

.HM1

.H1        APPNDX2.TNL October 28, 1990 at 8:40

.H2        PM

.PA

        October 23, 1990 at 11:54 AMOctober 23, 1990 at 12:32 AM10/17/90 at

        23:41:0910/16/90 at 22:18:5510/15/90 at 23:47:0110/15/90 at

        15:33:31heWORKOVR7                                    10/15/90 at

        13:48:1410/13/90 at 00:05:0610/12/90 at 21:59:5610/12/90 at

        12:05:3810/10/90 at 10:41:2810/09/90 at 20:41:27heAPPNDX2.TNL                        10/09/90 at 11:56:3310/08/90 at

        21:48:1810/08/90 at 18:18:5310/08/90 at 00:28:1610/07/90 at

        16:43:5010/03/90 at 10:01:0110/03/90 at 01:30:5210/02/90 at

        22:30:1410/01/90 at 23:13:5509/30/90 at 23:01:07APPENDIX 2

 

.RR-----!--!----!----!----!----!----!----!----!----!----!----!----!----R

        In this Appendix, we give enough information about our

 non-standard notation so our readers can make sense out of what we say

 with it. However, here we do NOT undertake to derive the notation in

 any formal sense.

 

        As noted in the text, we have embarked on the task of generating

 physical theory which systematically takes the observer into account.

 The present non-standard frame of reference and notation started out as

 a deliberately generated axiomatic system. It arises out of an ongoing

 study aimed at exploring the consequences of taking Korzybski's

 non-aristotelian premise of Non-identity seriously. To that end,

 elsewhere we have already generated a frame of reference and a notation

 based on map-territory non-identity as our most fundamental postulate.@

 In the current series of papers, we begin develping the constructs we

 believe necessary to elaborate a physical theory that cannot eliminate

 the observer from consideration. The main limitation on the growth of

 this non-standard notation has come from its unfamiliarity.

 

 

 ___________________

 @Elsewhere

 ___________________

 pa

         In approaching our non-identity-based notation, almost everyone

 trained in WIE science will do so expecting the formalized expressings

 in our text to work somewhat the way the equations or formulae of the

 familiar identity-based WIE notational languages do.

 

        They don't. They have their own pattern, radically different from

 that of the formalized or discursive WIE languages. Let's start with

 two main examples of expressings from our non-standard notation, with

 interpretations in English; then, for those who want more details, we

 compare the pattern of the WIE languages with that of our own, so as to

 highlight both the differences and the similarities between them.

 

 

        1. A NON-STANDARD NOTATION

 

        From our point of view, any written text (in any language) -- even

 a laundry list -- presumes a speaker, addresses an audience, and posits

 a dramatic situation.

 

        (a) Interacting: WIE notational languages

 

        In general, texts written in a WIE language posit some dramatic

 situation which centers about one or more "thing(s)" interacting with

 one or more "thing(s)." The term interacting (modified from Dewey &

 Bentley@), suggests a kind of "one-way causality." Consider, for

 example, Newton's second law of motion:

 

           f = ma                                        (1)

 

 "Force," "mass" and "acceleration" exemplify the kind of "things" known

 as quantities, while "equals" and "times" or "multiplied by" exemplify

 the kind of "interactions between things" known as operations or

 relations. Moreover, this famous equation describes the "motion" of

 physical "bodies," in a world thought to consist of more or less

 discrete objects of different sizes, which follow trajectories and

 sometimes collide. (The descriptions it generates prove quite

 accurate, as long as the dimensions of the "bodies" or "things"

 examined remain within a few orders of magnitude of the dimensions of a

 human body.)

 

        (b) Transacting: Our non-standard notation

 

        In our frame of reference, in general we posit "doings" or

 "happenings" which consist of the two-way transacting between a human

 organism-as-a-whole and her/his environment, over a specific period --

 as viewed by a particular observer, who writes out her/his observations

 in our alternative notation. The term transacting (modified from Dewey

 & Bentley) suggests a kind of two-way interchange between organism and

 environment which profoundly alters the living system(s) involved, in

 some way that affects its/their further living.

 

 ___________________

 @Dewey & Bentley, 1949

 ___________________

 pa

        Our demonstration consists of four parts, ending up with an

 expressing which corresponds roughly to an English-language

 characterization of our non-standard theoretical system as "An

 accounting for how humans account for human accounting."

 

        (1) For our purposes, we consider the topic of what our observer

 regards as the kind of primary, first-order transactings by which our

 organism accounts for and deals with what goes on in and around

 her/himself. In generic terms, our observer designates this kind of

 accounting by the defined term abstracting, which s/he symbolizes with

 O- .

 

           O- .                                     (2a)

 

 To interpret (2a) in English: "Our organism abstracting."

        Put into idiomatic English: "Our organism accounting for and

 dealing with what goes on in and around her/him."

 

        (2) Given that our observer wants to say more about what s/he sees

 going on than just O- , "our organism abstracting": S/He spells out

 more details using a kind of topic-comment "template," which has four

 "places" within it.

 

        1O- <HY> {Z} OhOt                               (2b)

 

         (i) In the first of these places, the "topic" term (e.g. O- ,

 abstracting) expresses the organism's "doings" or "happenings" of the

 moment, in context, as viewed by our observer.

 

        In the remaining three terms our observer specifies a "comment" on

 this topic, framed as a Gestalt. To do this, s/he writes a

 "background" term set off by French brackets < > , followed by a

 "figure" term set off by braces { } , followed by a term which spells

 out how the background and figure terms hang together.

 

        (ii) In the second place, the "background" term <HY> , our

 observer refers to what s/he regards as the "territory" which our

 organism accounts for, and includes H , a designation for the "doings"

 or "happenings" occurring within our organism, and Y , a designation

 for the "doings" or "happenings" occuring in the vicinity of our

 organism.

 

        (iii) In the third place, the "figure" term {Z} , our observer

 refers to what s/he regards as the "map" which our organism generates

 in the process of "accounting for what goes on in and around her/him"

 at present.

 

        (iv) In the fourth place, the "ordering" term OhOt , our observer

 spells out how the background and figure terms relate to each other.  Here, Oh , hierarchically ordered, means "One term (here, the figure)

 occupies a position in a hierarchical order one logical "level" higher

 than does the other (the background)." Likewise, here Ot ,

 spatio-temporally ordered, means "One term (here, the figure) occurs

 later and/or in a different location than does the background."

 

 To interpret (2b) in English: Topic, our organism abstracting:

 background of the Gestalt, the "doings" or "happenings" occurring in

 and around our organism; figure, our organism's map of these "doings";

 ordering, the figure (map) occurring one logical level higher than does

 the background, and also occurring later and/or in a different location

 than does the background.

        Put into idiomatic English: "Our organism accounting for what

 goes on in and around her/himself."

 

        (3) In expressing (2b), our logician focuses on "the map" or "the

 accounting" which our organism generates, and relegates "what goes on

 in and around our organism" -- the details that the map represents or

 refers to -- to the background. S/He can reverse this stance, treating

 HY as figure and Z as background, which allows focusing on "what

 goes on in and around our organism" instead of on "the map of what goes

 on in and  around her/him."

 

        1O- <Z> {HY} OhOt                                (2c)

 

        Our logician defines this process of reversing the positions of

 figure and ground as negating -- s/he produces (2c) by negating (2b).

 

 

        (4) Finally, in this notation we can nest expressings to make

 compounded expressings. For example, in place of a single term used as

 background or as figure, we can insert a whole well-formed expressing,

 e.g.

 

        ... <O- <HY> {Z} OhOt> ....

.PA

 

 This makes it possible to deal with some of the complexities of human

 behaving-and-experiencing which otherwise escape our efforts to account

 for them.

 

        The process of nesting produces expressings of considerable

 complexity. In order to keep track of the way we terms in our

 notation, we can index any term T in various ways, for example, by

 means of right and left superscript and right and left subscript. For

 example, our logician uses the left superscript, aT , to spell out the

 logical level of that term (position in a hierarchical ordering,

 relative to the positions of the other terms or expressings present).

 With the right superscript, Tb , s/he spells out the position of that

 term in a spatio-temporal ordering (relative to the positions of the

 other terms present). With the right subscript, Tc , s/he

 individuates that term (relative to the other terms present), e.g. O

 signifies some ordering term (in a generic sense), but does not

 particularize a specific one; whereas the indexed Oh signifies one

 particular ordering, namely, hierarchical ordering; while Ot

 signifies another, namely, spatio-temporal ordering.@

 

 ___________________

 @Footnote 1 (5 ordering terms)

 ___________________

 pa

        Sometimes it appears necessary, or at least useful, to index terms

 in an ordinary English sentence. The characterization, above, of our

 non-standard theoretical system in particular might profit from such

 indexing, yielding the compounded construct of "3Accounting for how

 humans 2account for human 1accounting." Expression (2d) gives a

 notational version of this compounded construct.

 

        To produce (2d), we treat our expressing for 1accounting (viz.

 (2b)) as the background. Then a similar expressing for 2account,

 indexed as occupying a second logical level, makes up the figure. Then

 the construct of 3accounting, the main expressing, indexed as occupying

 a third logical level, expresses our organism's main activities of the

 moment, as viewed by our logician.

 

 

        3O- <1O- <HY> {Z} OhOt> {2O- <HY> {Z} OhOt} OhOt      (2d)

 

 To interpret (2d) in English: Main topic, our organism abstracting:

 main background, the nested expressing (12b): <1sub-topic, our organism

 abstracting (first-ordered or occurring on the "lowest" logical

 "level"); background, the (mainly non-verbal) "doings" or "happenings"

 occurring in and around our organism; figure, our organism's

 first-ordered (mainly non-verbal) "map" of those (mainly non-verbal)

 "doings" or "happenings"; ordering, the figure (map) occurring one

 logical level higher than does the background, and occurring later than

 does the background>; main figure, the nested expressing (22b):

 {2sub-topic, our organism abstracting (second-ordered or on a

 "middle" logical "level"); background, the first-ordered "doings" or

 "happenings" represented by (12b), the process by which our organism

 generates a first-ordered "map" of mainly non-verbal "doings" or

 "happenings"; figure, the second-ordered "map" of those "doings" or

 "happenings," the process by which our organism accounts for

 first-ordered accounting; ordering, the figure (map) occurring one

 logical level higher, and later, than does the background}; main

 ordering, the figure occurring one logical level higher, and later,

 than does the background.

        Put into idiomatic English: "Our organism 3accounting for how

 humans 2account for human 1accounting."

 

        These remarks probably do not contain enough detail to enable our

 readers to WRITE in the non-standard notation; but, like a

 foreign-language phrase-book, (when coupled with the Glossary of Terms)

 they should make it possible for you to read the notational sentences

 in the text.

 

        For those who want more background, the following section compares

 the pattern of symbolizing within WIE languages such as the

 mathematical theory of sets with the pattern of symbolizing within the

 present non-standard notation.

 

 

        2. COMPARING THE PATTERNS OF WIE AND NON-STANDARD NOTATION

 

        A. OVERVIEW OF THE WIE PATTERN

 

        In our frame of reference, we regard the obvious "structural"

 features of a symbolic system such as a grammar as evidence which

 manifests what the exponents of this symbol system assume.

 

        A WIE discursive language such as English has a vocabulary

 composed mostly of two main categories of terms, known respectively as

 nouns and verbs. Between them, these two categories make up some 70 to

 80 percent of the entries in a big dictionary. Furthermore, we

 distinguish between the two categories relationally, by regarding and

 treating the nouns as "identical with themselves" and the verbs as

 "not-identical with themselves." In so doing, we define the binary

 relation of identical with as signifying "entire and absolute agreement

 or negation of difference."@ Identical with itself, then, comes out

 meaning "permanent" or "persisting" or "really existing" or (as little

 as we may like to admit it) "unchanging."@ To form a complete

 sentence, we place at least one noun -- or, better, noun-phrase -- next

 to at least one verb-phrase:

 

         The cat grinned.

 

 

 ___________________

 @Webster's Second, 1961, p. 1236

 

 @CAH, "Some Traditional Assumings" -- GSB 1977/78, p. 140-1

 ___________________

 pa

        A WIE formalized language such as a symbolic logic or one of the

 mathematical theories of sets also has a vocabulary composed of two

 main classes, which we variously call things and relations (between

 things), or quantities and operations, etc. Again, we tell the classes

 apart by regarding and treating the things or quantities, etc. -- the

 terms which substitute for nouns -- as "identical with themselves," and

 the relations or or operations -- substitutes for verbs -- as

 "not-identical with themselves." To generate a well-formed

 formulation, then, we place at least one noun-substitute next to at

 least one verb-substitute:

 

         Not-A .

 

         x [element of] A .

 

 

        1. MAP-TERRITORY IDENTITY

 

        The WIE grammar makes no provision for distinguishing between

 "map" and "territory," or alternatively, between "a word" and "that

 which the word represents or stands for." For example, it includes no

 mandatory prefix, suffix, infix, no special grammatical forms, etc., by

 which a speaker/writer can keep track of this distinction. Of course,

 a speaker/writer CAN arrange to differentiate "map" from "territory,"

 by secondary means, whenever s/he wants to (or remembers to) -- but

 underneath such locutions, the primary structure of the WIE grammar

 still does not make this distinction.

 

        But in our frame of reference, the construct of "does not

 distinguish between" appears equivalent to "holds or treats as

 identical with." In other words, where by presupposition the WIE

 grammar provides an exponent with no primary means to distinguish

 between "map" and "territory," by that presupposition it constrains

 this exponent to hold that "the territory" -- ultimately, "the world"

 or "the Universe" or "the Cosmos" -- has a structure which precisely

 matches that of the WIE grammar. "The world," it says, REALLY DOES

 consist of (a) static-and-unchanging "objects," precisely suitable for

 anyone to represent in "language" by means of self-identical

 noun-phrases; and of (b) more or less transient "relations between

 objects," precisely suitable for anyone to represent by means of

 not-self-identical verb-phrases.

 

        In WIE mathematical terms, we can express this tenet by means of

 the construct of an exhaustively complete, entirely accurate one-to-one

 relation, such that every point of "the territory" or "the world" gets

 represented by one and only one point of our exponent's "map" of "the

 world," and that our exponent's "map" contains no extraneous points (no

 points which do NOT represent or refer to points of "the world").

 

        We designate this presupposition as map-territory identity or

 tacit identity. Elsewhere, we have demonstrated that this (silent)

 postulate of tacit identity underlies the standard logical sense(s) of

 the term identity (or the relation of identical with).@ We designate

 this latter construct as explicit identity.

 

 ___________________

 @CAH, "Some Traditional Assumptions ..."

 ___________________

 pa

        Our frame of reference and notation contrast sharply with the WIE

 discursive and formalized languages at precisely this point. The WIE

 frame of reference and the various WIE notations stem from tacit

 identity, from explicit identity, and either from Aristotle's Law of

 Identity or from the modern Logical Axiom of Identity. Hence we refer

 to these languages as identity-based or as generically Aristotelian.

 Our frame of reference and notation stem from a central premise known

 as Korzybski's Postulate of Non-identity, which rejects (disallows as

 valid) the construct of identity in any guise or form, explicit or

 tacit. Hence we refer to these languages as non-identity based or

 generically non-aristotelian.

 

 

        B. AXIOMATIC SYSTEMS

 

        To facilitate making the comparison between the WIE and our own

 non-standard frames of reference and notations, let us review the

 general outlines of what we call an axiomatic or postulational system.

 One difference shows up immediately: In the WIE view, an axiomatic

 system "exists" as a thing, independent of any observer, logician, or

 other human. In our non-standard view, what we call "an axiomatic

 system" "exists" or "occurs" solely and exclusively as HUMAN ACTIVITIES

 -- "something someone does." Thus, someone (a logician or "observer"

 or "organism") chooses a) some setting or other@ and b) a small number

 of undefined terms; s/he selects c) some postulates, which s/he

 expresses by means of the undefined terms; s/he arranges for d) rules

 of inference, and e) standards of proof; etc. With these "pieces" in

 place, s/he then derives and prove one or more theorems, or formal

 conclusions. In so doing, s/he satisfies our minimal criterion for the

 "completeness" of an axiomatic system.

 

 ___________________

 @Note on Euclid and Russell -- construct of setting.

 ___________________

 pa

        Except for the difference of opinion concerning the "locale" of an

 axiomatic system, we expect that exponents of standard WIE axiomatic

 systems would agree with this way of naming the "parts" that make up

 such a system.

 

        However, we discern some key connections between these "parts" not

 previously described. For example, in keeping with our views on the

 "locale" of an axiomatic system,

 

        1) We regard the setting, and also the undefined terms, as human

 "doings" -- something someone DOES. Specifically, we hold that each of

 these constructs operates as a special kind of postulate: namely, as a

 silent postulate, the tenets of which the person who relies on it

 cannot state in words.

 

        2) We posit a further connection between setting and undefined

 terms, such that for one to occur requires the occurrence of the other.

 In other words, we posit a polar relation between them.

 

           (a) In choosing a setting, our logician (to use a

 characteristically WIE image) chooses the way in which her/his frame of

 reference "slices up the world."

.PA

 

           (b) In selecting undefined terms, our logician puts

 limitations on the "slicing-up" process, so as to get "elements of the

 lexicon" -- terms or "words" or "sentence-parts" which will fit into

 the "slots" of the template or grammar of the notation in question.

 

           (c) In articulating the setting and the undefined terms, our

 logician produces a version of the logic of opposites, which amounts to

 a pattern for handling defined terms -- in particular, one which

 specifies the connections between a term or construct and its opposite

 or contradictory or negation or complement.

 

        3) We maintain that our logician obtains the grammar by somehow

 inter-defining the undefined terms.

 

        Thus, taken together, setting and undefined terms specify the

 conventions for symbolizing of the notation in question.

 

 

 heWORKOVR8                                    10/22/90 at 16:03

 10/18/90 at 00:26:0710/17/90 at 10:12:0310/17/90 at 00:43:07     C. WIE

 LANGUAGES AS AXIOMATIC SYSTEMS

 

        We regard English as a traditional discursive language of the

 Western Indo-European family. It did not arise as a deliberately

 generated axiomatic system. For example, no one consciously chose a

 setting or undefined terms for it. The WIE mathematical languages,

 e.g. the various mathematical theories of sets, stand as axiomatic

 systems, but the innovators who generated them grant a privileged

 position to the WIE grammar and so tacitly rely on its conventions for

 symbolizing -- rather than questioning and disclosing these conventions

 and characterizing them in general terms, as we do here.

 

        By analogy with the pattern laid out in B above, let us now infer,

 and then supply, the missing "parts," and so frame English or set

 theory as a version of an axiomatic system. In the process, we shall

 account for (or at least incorporate) the features of WIE languages

 mentioned above, in our overview of the identity-based WIE pattern.

 

        1) Setting: As noted, we regard setting and undefined terms as

 human "doings", silent postulates of an exponent. The setting for a

 WIE language, in our view, consists of a distinction -- a pair of

 opposites, an "empty" dichotomy which we may indicate generically as x

 and     not-x .

 

        2) Undefined terms: As undefined terms, we propose noun, verb,

 and the copula (e.g. 'is').

 

        3) Interconnections between setting and undefined terms: The

 interconnections in question generate the conventions for symbolizing

 of WIE languages such as English or set theory.

 

        (a) Someone who chooses the above setting thereby "slices up the

 world" into two "KINDS." Or, to use an image that begs fewer

 questions, s/he CREATES two disparate "kinds." In any case, s/he

 treats them as polar; or in other words, treats her/his "process of

 slicing" or "process of creating" as if it necessarily generates both

 "kinds." Further, s/he utilizes this process of dichotomizing over and

 over again within the grammar of a WIE language, on various logical

 levels.

 

        (b) Someone who chooses the above undefined terms thereby puts

 constraints on the "process of slicing" just described. S/he

 subdivides one "kind" into noun and verb, where noun 'is' noun, while

 she does NOT hold that verb ("not-noun") 'is' verb . In the same

 breath, s/he subdivides the other "kind" into two sub-classes, one of

 which s/he treats as precisely suitable to represent by means of

 self-identical noun-forms or noun-phrases, and the other of which s/he

 treats as precisely suitable to represent by means of

 not-self-identical verb-forms or verb-phrases.

 

        These arrangements not only yield terms or "words" or

 "sentence-parts" which will fit into the "slots" in the template or

 "grammar" of the notation or discursive language in question -- they

 also support the conviction that there "exist" two disparate domains:

 one which has something to do with "words" or "language," and another

 which seems somehow "non-verbal," e.g. a "reality" or "world" that

 "exists" "out there," independent of any "speaker" or "observer" or

 "organism," and also independent of any "words" the "speaker" may

 utter. Finally, these arrangements support the conviction that these

 "sentence-parts" uniquely "represent" this non-verbal "reality".

 

 (c) Logic of opposites: As noted, the logic of opposites amounts to a

 pattern for handling defined terms (in a WIE language, nouns or

 noun-substitutes), one which specifies the connections between the

 noun-phrase in question and its negation (or other polar-opposite).

 The WIE tradition has included at least two distinctly different

 versions of the logic of opposites, commonly known as undelimited and

 delimited.

 

           (i) Undelimited: The undelimited version of the WIE logic of

 opposites utilizes two key terms, namely, some (defined)

 noun-substitute x and its negation, not-x . When expressed in a

 discursive language, this version of the logic of opposites contrasts

 "a thing" (e.g. day) against its negation (not-day),@ which eventually

 consists of "everything else." In addition to the discursive language

 example, a simple Venn diagram makes this relationship clear:

 

           FIGURE 1 ABOUT HERE

 

        Critics point out that the construct of "everything else" proves

 unsatisfactory, undefinable -- for the term day, it not only includes

 "night," but also "pollywogs," "foreign policy," "Cantor's transfinite

 cardinal numerals," etc.

 

 ___________________

 @We Westerners treat opposing terms as somehow separable, "unrelated."

 Watts remarks on this attitude, and calls it an "illusion":

.PA

 By and large Western culture is a celebration of the illusion that good

 may exist without evil, light without darkness, and pleasure without

 pain, and this is ture of both its Christian and secular, technological

 phases. Here, or hereafter, our ideal is a world iln which "there

 shall be no more death, neither sorrown, nor crying, neither shall

 there be any more pain; for the former things are passed away."

 (Revelations 21:4) (Watts, Alan W.: The Two Hands of God: Myths of

 Polarity. New York, Brazillier. Paperback edition, 1969, Collier

 Books, p. 48)

 ____________________

 pa

        (ii) Delimited: This version of the WIE logic of opposites

 utilizes three key terms, namely, a delimited domain D , within which

 "exists" the noun-substitute x and its negation not-x . Here not-x

 comprises "everything else within the domain D ". No one has yet

 modified a WIE discursive language so as to make use of the delimited

 version of the logic of opposites, so we have examples only from WIE

 notational languages.@ A Venn diagram displays these relationships

 clearly:

 

           FIGURE 2 ABOUT HERE

 

        In this version of the WIE logic of opposites, not-x proves

 readily definable, avoiding most of the logical difficulties of the

 earlier version.

 

 ___________________

 @Some discursive languages outside the WIE family routinely utilize a

 delimited version of the logic of opposites. Sino-Tibetan languages,

 for example Mandarin, treat term-pairs, e.g. buy and sell, as defined

 on a common domain. As Chu puts it,

 

.RR L-----------------------------------------------------------------R

       ... Ideas are often denoted [in Mandarin] by compound expressions

       composed of antonyms: for examples, "buy-sell" for "trade,"

       "advance-retrea" for "movement," "rule-chaos" for "political

       condition," etc. The antonyms are not thought of as

       irreconcilable opposites but as being united to form a complete

       idea. One of the most important concepts in Chinese philosophy

       is expressed in a compound of antonyms, yin1yang2. These two

       terms denote two opposing but complementary forces in the

       universe, the interaction of which produces all things and the

       unity of which reposes in the Ultimate. (Chu, Yu-Kuang:

       Interplay between language and thought in Chinese. ETC.: A

       Review of General Semantics 22:307-329 (1965), p. 316.)

.RR----!---------------------------------------------------------------R

 ___________________

 pa

       4) Grammar: The pattern for a "complete sentence" or "well-formed

 formula," requires someone to place at least one noun-phrase or

 noun-substitute next to at least one verb-phrase or verb-substitute.

 But since any noun 'is' 'identical with' itself, this grammar consists

 precisely of the undefined terms inter-defined.

 

       5) Postulates: So far as we know, no one within the WIE tradition

 has exhaustively characterized the postulates of the WIE frame of

 reference. These postulates include (for the undelimited version of

 the logic of opposites) the "Laws of Thought " of Aristotle of Samos

 (384-322 BC). Aristotle called them laws of thought; today, it becomes

 clear that they spell out the rules for naming or "nouning":

 

        The law of identity: Whatever is, is.

 

        The law of contradiction: Nothing can both be, and not be.

 

        The law of excluded middle: Everything must either be, or not

 be.

 

       For the delimited version of the logic of opposites, replace the

 "Law of Identity" with the modern Logical Axiom of Identity:

 

        For all x which belong to the delimited domain D ,

 

        x =_ x .

 

       6) Rules of inference, and

 

       7) Standards of proof: We have little to add to the traditional

 characterization of these topics.

 

 WHAT WE CAN TALK ABOUT IN THIS LANGUAGE:

       "Things" interacting with "things".

       In a larger sense, the frame of reference here consists of a

 dualism, e.g. framed as 'mind' vs. 'matter', where the "words" stand

 for or represent "things," and both follow the same patterns, both

 follow the same grammar.

 

 

 rm 72heWORKOVR9       October 28, 1990 at 6:39

 PMOctober 27, 1990 at 1:56 PMOctober 27, 1990 at 9:48 AMOctober 25,

 1990 at 10:50 AMOctober 24, 1990 at 2:41 PMOctober 23, 1990 at 2:25 PMD. THE PRESENT NOTATION AS AN AXIOMATIC SYSTEM

 

 

       As noted above, we treat the constructs of setting and undefined

 terms as designating human activities: "something someone does."

 

       1) Setting: We can express the setting for our non-standard

 notation by means of a run-on phrase, such as "One particular

 human-organism-as-a-whole-dealing-with-her/his-environment-at-a-date."

 More succinctly, we can express it by means of single terms such as

 "transacting" or "contacting" or "living." With the Gestalt therapists

 Perls, Hefferline & Goodman@, we say,

 

 We speak of the organism contacting the environment, but it is the

 contact which is the first and simplest reality.

 

       2) Undefined terms: As undefined terms, we follow Korzybski's

 example and choose structure, order, and relation (Korzybski, 1943).@

 In our non-standard notation, we signify these by means of S , O , and

  R . When we write these in English, we treat them as verb-forms:

 (to) structure, (to) order, (to) relation.

 

       3) Interconnections between setting and undefined terms: When

 dealing with the present non-standard notation, the image of "slicing

 up the world" has seriously misleading implications. It suggests an

 already-existing dualism, e.g. a dichotomy between "the world" and "the

 one who slices." Such a construct might work well as an image for a

 WIE frame of reference -- which makes it inappropriate for the present

 one. Instead of regarding "organism" and "environment" as separate,

 disparate "things" which occasionally collide with each other, the

 present frame of reference treats "the environment" as the other side

 of the organism's skin, and treats "the organism" as the other side of

 the environment's skin.

 

       (a) When we choose the above setting, we thereby create the main

 pattern which the non-standard notation expresses. By adopting this

 non-standard notation, a user thereby restricts her/himself to a single

 point of view, and can discuss "doings" or "happenings" solely and

 exclusively from a standpoint of this created pattern, which we can

 indicate by some run-on phrase such as the one stated above, or by a

 single term such as transacting.

 

  (b) When we choose the above undefined terms, we thereby put

 constraints on the pattern generated by the setting. In particular,

 when we use an undefined term, we designate, or postulate, some example

 of "a transacting" or of "the dealings of an organism-as-a-whole with

 its environment at-a-date."

 

  (c) Logic of opposites: As noted above, the logic of opposites

 amounts to a pattern for handling defined terms. In our non-standard

 frame of reference, it consists of five points:

 

       1. Our incompletely-informed and inaccurately-informed (symbolic)

 'organism'

 

       2. Consists of spatio-temporally ordered "doings" or "happenings"

 which occur within a (specific, delimited) setting known as

 transacting.

 

        3. By her/his abstracting, our 'organism'elaborates a 'gestalt'

 composed of

 

       a) a 'figure' which focally interests the 'organism'

 

       b) specified against a 'background' which does not (at present)

 interest her/him.

 

       4. Any 'gestalt' further consists of two 'components'

 

       a) one of which tells about the 'environment', and

 

       b) the other tells about the 'organism' who elaborates the

 'gestalt'.

 

        5. In negating a 'gestalt', our 'organism' interchanges the

 'figure' and the 'background', and alters none of the other

 considerations listed here.

.PA

       When we negate a 'gestalt', and then re-negate it, that does not

 bring us back exactly to our starting-place.

 

       EXAMPLE: Consider the positive degree of an ordinary English

 adjective vs. its negated negation: not unhappy does not qualify as an

 exact synonym for happy.   

 

       4) Grammar: We obtain our grammar by inter-defining the undefined

 terms. For example, where we designate or posit a structuring S ,

 that already gives us a "bridge" from the non-verbal to the verbal.

 Wheneverf we want to give more details about that S , we use the other

 two undefined terms, as follows:

 

 SRRO or

        SOOR or

        ORRS or

        OSSR or

        ROOS or

        RSSO.

 

       Where we use an undefined term twice in an expressing, we intend

 that no one take the two usages as identical.

 

       5) Postulates: In a formal presentation of an axiomatic system,

 one uses the undefined terms to state the postulates. Here, for the

 sake of intelligibility, we state Korzybski's non-aristotelian

 postulates in terms of the map-territory analogy, which holds that to

 say that an organism lives means that it makes some kind of maps of

 (or guesses about) that territory composed of "what goes on in and

 around our organism" -- and then it guides its "doings" or "choosings"

 by these maps. Stated colloquially, then, these postulates become:

         Non-identity: The map is not the territory it stands for.

 

         Non-allness: The map represents not all of the aspects of    the territory.

 

         Self-reflexiveness: Any map contains some kind of    representation of the map-maker (organism).

 

       6) Rules of inference: For the purposes of this appendix, it

 suffices merely to name the rules of inference of the non-standard

 notation: Generalizing, Particularizing, Componenting, and Specifying.

 

       7) Standards of proof: Again, for the purposes of this appendix,

 it suffices to say that to "prove" an expressing, one demonstrates that

 s/he can both derive it from an expressing composed solely of undefined

 terms, and can "decompose" it back into an expressing (or a number of

 expressings) composed solely of undefined terms.

 

       WHAT WE CAN TALK ABOUT IN THIS LANGUAGE: "An observer observing

 the observed," as viewed by another observer ("logician"), who writes

 down her/his observations.

.PA