2. The Structure of 'Unimpaired' Human Behavior

 

C. A. Hilgartner & John F. Randolph

 

ABSTRACT

 

In a previous publication (Hilgartner & Randolph, 1969), we derived a logical calculus of behavior, and deployed it in several situations. In particular, we hypostatized a visitor from another planet, Myth1; and we credited him with 'perceptual' powers of the same form as those found in terrestrial animal and human organisms. We then used our logical calculus to show the general form of any encounter between Myth1 and a terrestrial object. Finally, in order to test the adequacy of our formulations, we examined situations of ordinary physiological 'need' and satisfaction, of frustration, and of danger. As judged by its handling of these situations, our model appeared adequate.

 

VI. Contact with the Windows

 

(A) MYTH1 AND THE RECTANGULAR WINDOWS

 

At this point, it is no longer necessary to stipulate in detail every step involved in the formation of Gestalten; instead, let us now show the exact form of the Gestalten formed by Myth1 as a result of three encounters with rectangular windows.

 

(a) Encounter1

 

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(b) Encounter2

 

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(c) Encounter3

 

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(d) Discussion of Myth1 and the rectangular windows

 

The expression G1 Ç G2 Ç G3 gives a succinct statement of the 'rectangular assumptions', as described by Ames (1951). These assumptions can be seen to express the relationships between rectangular objects and the images of rectangular objects on the plate (retina) of a simple camera (eye). Since the 'rectangular assumptions' can b formalized (as we have done) in terms of ordinary Cartesian co-ordinates, they demonstrably imply and assume Euclidean geometry.

 

In accordance with their view of the transactional nature of 'perception', Ames, Ittelson and others maintained that the 'rectangular assumptions' are entirely learned, as a consequence of encounters with rectangular objects; this, then, constitutes a special case of the 'transactional' view.

 

There are few experimental data bearing on this crucial transactionalist principle -- that assumptions about the properties of the distal forms determines the experience and not just the interpretation of the pattern of proximate stimulation (Ittelson, 1962). Allport & Pettigrew (1957), in one of the few direct tests, presented the trapezoidal illusion to Zulus, who were thought to live in an environment that would not be conducive to the formation of assumptions about rectangular distal objects. There results were equivocal, though Slack (1959) has suggested that perhaps even the Zulus did not lack rectangular assumptions. (Haber, 1965, p. 651)

 

Let us remember at this point that, certainly in Western cultures, and perhaps throughout the whole human race, virtually the whole untutored population appears tacitly to operate in terms of Euclidean geometry; and non-euclidean geometries were unknown, not invented, until about 150 years ago. On these grounds alone, it would appear that assumptions which imply and assume Euclidean geometry give fairly reliable guides for behavior, that is to say, reliable guides for behavior in the environments of pre-scientific cultures. Indeed, "... Modern scientists say that the concepts of space and time are 'free creations of the human mind', but ... they sometimes behave as if these concepts correspond to some real 'something'." (Swanson, 1958, p. 35) The controversy here can be resolved if we discard the assumption that the notion of a Euclidean 'space' is entirely learned.

 

We have at least three physiologically sound reasons for thinking that this construction (i.e. Cartesian coordinates, a Euclidean 'space' -- Ed.) is not entirely arbitrary.

 

(1) Consider yourself standing quietly, your arms extended straight out before you. This demarcates one line of orientation, and it feels as if one set of muscles is in tension while another set is relaxed. The direction of your neck, trunk and legs gives an up-and-down line, which intersects the line of point by a 90-degree angle. Now extend your arms straight out from your sides. This gives you a line in another direction, at 90 degrees from the first two, and requires another set of muscles to attain. It is sometimes cumbersome at times, but you can describe most of your own complicated motions in terms of those three lines. However, an articulate starfish might require seven -- one for each arm in addition to up-down and parallel to the floor.

 

(2) Besides the grossly visible structure of our bodies, we have other good reasons. Our eye muscles are so arranged that our eyes make motions which feel straight up and down and straight right and left. The motions are not exactly straight, but we are hardly aware of the difference. It is easy to assume that our eyes move as directly as our arms can. We get the sense of third direction by following our line of sight straight out in front of our noses, that is when all the eye muscles are balanced in tension.

 

(3) As part of the structure of the inner ear, we have a set of semi-circular canals so arranged with respect to each other that three mutually perpindicular lines can be drawn through them. These canals are filled with a fluid which moves when the position of the head changes. The motions of the fluid set off nerve impulses from which the brain evaluates the relative position of the head. Therefore, considering our own structure the Cartesian co-ordinate system seems very logical and 'natural' to us. Other reference systems can be devised and have been, but for many purposes, the three-line system is quite adequate. (Swanson, 1958, p. 36) (our italics)

 

(B) MYTH1 AND THE TRAPEZOIDAL WINDOW

 

Thus far, the situations described have been very simple and, except for the discussion of emergencies, devoid of problems. Let us now consider a more difficult situation. In his explorations, now encounters the Ames trapezoidal window display (Ames, 1951), and explores it thoroughly enough to come to understand it.

 

(For readers who have not had first-hand experience with the Ames trapezoidal window display, a verbal description may help in comprehending the following set-theory sentences and our translation of them. In our presentation, we demonstrate that the motor which drives the trapezoidal window is capable only of rotation at a steady rate (usually between 2 and 10 rev/min), always in one direction; and we leave no doubt that the "window" is in fact trapezoidal, not rectangular. However, once it starts rotating, despite the fact that the observers 'know better', the trapezoidal window appears to 'shift' from one form to another: at one moment it may appear trapezoidal and rotating, at another moment it may appear rectangular and seem to move in one direction, come to a stop, and then rotate in the other direction; very rarely, it may appear to be a stationary object changing in shape. Many observers find the experience of watching the trapezoidal window disconcerting. We chose this deceptively simple-looking illustration of 'surprise' and 'neglected factors' rather than one of more common experience because it comprises the most efficient way of disclosing the relation which interest us here.)

 

LINE DRAWING OF TRAPEZOIDAL WINDOW

 

(A) Encounter4

 

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The operator Sp , surprise, serves as a coenetic variable to initiate a coordinated train of emergency-responses, with the focal condition of self-preservation. The initial event in this train of responses consists of the startle-response, Sl ; this is followed by these synchronous activities: muscular efforts to interrupt whatever ongoing activity the organism may be engaged in, by "muscular jamming" or retroflexion, Rf = ML Ç ML_ , and by cutting down on the organism's oxygen supply by means of breath-holding (which produces the classic symptoms of anxiety, Ax = MBr Ç MB-r- )(Perls, Hefferline & Goodman, 1951); sensory "orienting" activities, the efforts to locate and assess the severity of whatever dangers may be present, in order to decide whether to approach or avoid the further development of this situation; and autonomic discharge, Au , which serves to ready the organism for strenuous physical activity.

 

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Having sized up the situation and decided there is no danger, finds himself in the "psychotherapeutic" situation of a SAFE EMERGENCY; and so he explores the situation thoroughly. Having learned everything he can from the stationary WT , he then experiences it while it is rotating at about 6 rev/min. Then he goes back and examines again the Wr ; and finally he investigates again the Wt . (Each of these operations could be shown in set-theory notation, but since no new principles have yet been introduced, to do so is not essential.) then sits in a corner, "thinking it over", and trying to construct an intersection of all his observations. By the way, the situation of investigating in a safe emergency is intrinsically painful. (Perls et al, 1951, pp. 286 ff)

 

VII. Aristotelian vs. Korzybskian Assumptions

 

Some form of behavior which corresponds to the operator Sp, surprise, exists throughout the animal kingdom. Animal organisms in general show the basically 'rational' assumption that, if things don't work out as they expected, they must have left out some environmental variable, the 'forgotten factor', eF Î E . (Indeed, in a later section on Developmental Psychology, we shall demonstrate that all mammalian organisms, at certain points in their lives, are required to perform the operation of taking into account, and handling adequately, some previously neglected class of environmental variables {eF}.)

 

Although we have consistently spoken of our model as human, up to this point [except for sentences (43) and (44)] we have drawn a formal model of 'organism' which applies alike to human (time-binding) and sub-human (space-binding) organisms (Korzybski, 1921); but the following passage applies only to human organisms; for in order to "understand" the Ames trapezoidal window, Myth1 must be (or become) 'aware' of being 'aware'. From his investigations of the WT , and from an examination of his G1 Ç G2 Ç G3 , and how he arrived at it, would have to conclude that G1 Ç G2 Ç G3 is adequate for dealing with visual relations with rectangular objects, but that it must have left out some crucial relationship eF needed to deal with the WT.

 

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Myth1's examination of his G1 _ G2 _ G3 can be expressed by having him regard Ex24 = G1 _ G2 _ G3 as a subset of Aw , and take the first and second correspondences of this Aw . [But to regard an expectation as a subset of 'awareness' is the exact equivalent of the 'transactionalist principle' cited by Haber (1965).] This operation gives a proposition of the form "a , and b such that if c , then d".

 

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Sentence (85) asserts that the first Cq correspondence of Cs36 is made up of the same elements as is the proposition that G1G2G3 is a subset of Aw , and the first Cp correspondence of this subset of Aw , a subsidiary 'awareness' is organized, is such that, if the second correspondence of Awiv , a visual 'awareness' at time ti , is a visual Gestalt the figure of which is composed of the same elements as is the visual image of a rectangular window, then there exists at least one environmental object yi E which is such that what the organism will find by exploring (i.e. mapping into the second Cp correspondence of Aw ) this object with tactile as well as visual receptors, at time tj , will be a visual tactile Gestalt the figure of which is composed of the same elements as is a visual tactile rectangular window.

 

As already noted, G1 Ç G2 Ç G3 expresses the relations between rectangular objects and the images of rectangular objects on the plate (retina) of a simple camera (eye). Set-sentence (85) shows that G1 Ç G2 Ç G3 is equivalent to the assertion of a gross empiricist that "I only see what's there!"; and to the assertion of an orthodox psychoanalyst that "The Self (ego) is otiose, and does nothing but observe" (cf. Perls, et al., 1951, pp. 384-7). Sentence (85) shows that G1 _ G2 _ G3 demonstrably implies-and-assumes the famous "laws of thought" of Aristotle. These are traditionally stated as the laws of identity, the excluded middle, and non-contradiction. In ordinary set-theory notation, these are stated as

 

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The demonstration that G1 Ç G2 Ç G3 implies and assumes the "laws of thought" is performed by showing the relationship between the Aristotelian and the korzybskian postulates: Korzybski distinguishes between the structure of environmental objects x Î E (the Event-level), which in principle remains unknown, and an organism's pictures of such environmental objects (the Object-level and the verbal levels); whereas Aristotle does not so distinguish. The korzybskian postulates reduce to the Aristotelian "laws of thought" iff the symmetric difference between the set of characteristics of x Î E , (Y), and the set of characteristics of an organism's picture of x Î E , (Cp2(alpha)(rho)f(Y) = Z), is negligible. In our notation, "negligible" can be indicated by two different conventions, LM- (subliminal), or Î non-existent (the empty set).

 

Thus, by analogy with the statement of the korzybskian postulates, the Aristotelian postulates can be stated in the notation of the interacting (organism&environment) field as Identity, Allness, and Linearity:

 

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Linearity

 

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If we define an identity-mapping on E , such that

 

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Furthermore, since Cp1 = Sf and Cp2 = Z Ot , and V(Sf) = Ot ,

 

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Thus, G1 Ç G2 Ç G3 does imply and assume that both Cp2(alpha)(rho)f and V are indistinguishable from IE , that is to say, that seeing is believing, and that the Self is otiose. Such a formulation eliminates considerations of order from the description of the processes comprising the Self: Like the formal set-operations of projection and section, the operation of forming an identity-mapping in our notation is an instantaneous process, which takes 'no time'. (If sthis process did take time, we would have to say IE(Yi) = Yj ; but this implies that Yi +Yj =/ 0/ . In that case, what sense does it ;make to call this an "identity mapping"? If, on the other hand, ti = tj or Yi + Yj = 0/ , why bother to distinguish between the two values of the _______________________________________________________________ ________

|- Thus sentence (85) shows that G1 _ G2 _ G3 shows the formal properties of the commonly used term 'mind'; this term, as commonly used, conceals the assumption that the velocity of nerve impulses is 'infinite'.

 

time indices?|-) Since order is eliminated, relations and structure cannot be defined, and one is left with a demonological construct: sentence (85) shows that G1 Ç G2 Ç G3 conceals the assumption that there is a little "inner man" which regulates the organism. (Of the processes which occur after light impinges on the retina, G1 Ç G2 Ç G3 specifies nothing.)

 

But we initiated our analysis of G1 _ G2 _ G3 because it led Myth1 to a contradiction, i.e.d. Cs31 = 0/ .

 

Myth 1 can now correctly state the lesson he learns from experiencing the WT , in the form of a double conditional: "If a , then b , and if c , then d ."

 

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Sentence (98) asserts that G4 is composed of the same elements as is the proposition that, if the organism has a visual 'awareness' at time tj , the second correspondence of which is a visual Gestalt for which the figure is composed of the same elements as those of the visual image of a rectangular window, then the organism existed at a previous moment ti during which it explored a rectangular window and formed a subset of Cs which was not an empty set; and if now, at time tPj , there even exists an environmental object yj E , then what the organism will find by exploring this presumed environmental object with tactile as well as visual receptors, at time tk , is a visual tactile Gestalt for which the figure is composed of the same elements as is the union of a visual tactile rectangular window, or trapezoidal window, or who knows what.

 

Sentence (98) is analogous to (85), except that it obviously implies and assumes the korzybskian rather than the Aristotelian premises. If

 

Cq2(beta)(alpha)(rho)f(yk)v,t = Oek:xv,t/(E - x)|xv,t = (Wr WT ...)kv,t ,

 

by no stretch of the imagination could this expression be indistinguishable from an identity mapping. Instead, it asserts that there is an inevitable uncertainty inherent in 'perception'. Therefore, sentences (89), (91), (92), (93), (96) and (97) do not hold true as a consequence of (98); therefore, (98) implies and assumes non-identity, non-allness and self-reflexiveness.

 

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In order to explore the implications of G4 , it will be sufficient to specify the exact relations between any environmental object yi E , i.e.d. Cp2(alpha)(rho)f(yi) or Cq2(beta)(alpha)(rho)f(yi). This we shall do by showing in detail the structure of 'awareness' and of 'consciousness'.

 

VIII. The Structure of 'Awareness'

 

(cf. Hilgartner & Randolph, 1969)

 

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(a) The structure of "Sf"i

 

Although up to this point we have used a single symbol, "Sf"i , to designate the subsidiary 'awareness' of the processes of the Self by means of which any focal 'awareness' at time ti is organized, it is not to be concluded that ""Sf"i is structureless, or even that the different values of "Sf"i distinguishable. But in order to make a fundamental point, let us now attend to the details of subsidiary 'awareness'.

 

Our appreciation of the externality of objects lying outside our body, in contrast to parts of our own body, relies on our subsidiary 'awareness' of processes within our body. Externality is completely defined only if we can examine an external object deliberately, localizing it clearly in space outside. But when I look at something, I rely for my localization of it in space on a slight difference between the two images thrown on my retina, on the accomodation of the eyes, on the convergence of their axis and the effort of muscular contraction controlling the eye motion, supplemented by impulses received from the labyrinth, which vary according to the position of my head in space. Of all these I become aware only in terms of my localization of the object I am gazing at; and in this sense I may be said to be subsidiarily aware of them." (Polanyi, 1958, p. 59)

 

[Also, Polanyi does not explicitly mention the visual scanning (Atv) which is necessarily involved in examining any 'external object'.] (cf. Platt, 1965)

 

Thus, any moment of visual awareness Awiv is composed of, i.e.d. organized by means of, some combination of these processes, making each Awiv a configuration of unique structure; and thus also

 

Cp1(Awiv) = Sfv i

 

is in each instance a unique structure. For example, in Awv(S1)fj , the visual 'awareness' of a particular object, stone-1, undergoing a free fall at time tj , the actual values of the binocular projection differences, the accomodation, the convergence of ocular axes, the eye motions involved in tracking the object, whatever postural changes are involved in the tracking operations, the sequence of labyrinthine impulses, and whatever scanning of the visual fields occurs during this Awj , will each be some transform of the Newtonian equation describing the trajectories s of freely falling bodies, i.e.d.

 

s = 1/2 gt2 .

 

Let us specify this transform for one of the variables mentioned, the direction of gaze of a single eye, as it tracks the free fall of an object whose trajectory has no horizontal component of velocity. For the sake of simplicity, let us say that the horizontal (OH) distance from the anterior aspect of the cornea (O) to the trajectory EH of the falling body E is 10 m. The body starts its fall at a point 10 m above this horizontal line, and the object is of such a size that its image on the retina has about the same diameter as the fovea centralis, that sector of the retina which corresponds to the region of greatest visual acuity of the visual field. Further, let us assume that the organism is able to track a falling object with enough accuracy so that the midpoint of the image never deviates from the midpoint of the fovea centralis by more than the radius of the fovea centralis. Finally, let us say that the head of the observing organism is fixed in a "neutral" position, with neither a side-to-side tilt nor an up-down inclination; and during the tracking operation there is no postural change. Thus, the entire tracking operation is powered by the extra-ocular muscles.

 

LINE-DRAWING P. 358

 

Under these conditions, the tracking operation will consist of movements of the eye under the influence of the extra-ocular muscles such that the angle (tau) = HOE varies, on the average, as a function of t . Within the limitations stated above, the actual eye motions involved in the tracking operation could comprise anything from a smooth, continuous movement to a series of stepwise motions. A smooth motion would be described by the expression

 

DIFFERENTIAL EQUATION P. 358

 

where k is a constant. A "jerky" motion could be described as follows. If the diameter of the fovea centralis is an arc of (phi) radians, and the eye muscles can move the line of gaze at a rate of (nu) radians a second, with no correction needed for the initiation or cessation of movement, then the eye would be focussed at time t0 so that the midpoint of the (inverted) image of the object fell approximately (phi)/2 radians below the midpoint of the fovea centralis. When the midpoint of the image passed approximately (phi)/2 radians above the midpoint of the fovea centralis, then the eye muscles would move the line of gaze to such a point that the midpoint of the image again fell about (phi)/2 radians below the midpoint of the fovea, and so on. The actual angles covered by those saltatory movements would themselves form a series, each term of which consisted of two components: the angle of (phi) radians required to shift the image of the falling object the required distance with relation to the fovea centralis, and the angle through which the line of gaze had to move in order to compensate for the distance traversed by the falling object during the course of the saltatory movement. In this series, obviously, as n increases, (delta)(tau)i also increases.

 

By similar reasoning, the elapsed time between saltatory movements will be a series, with terms in which elapsed time between jumps decreases as n increases.

 

In the foregoing remarks, we have specified the structure of an environmental object

 

UNNUMBERED EXPRESSION p. 359

 

in the terms of ordinary calculus, and likewise, in those terms, we have also specified the structure of a boundary interaction with this environmental object,

 

UNNUMBERED EXPRESSION, p. 359.

 

For either expression describing the tracking operation symbolized by Awjv , the tracking operation is similar in structure to the actual trajectory of the falling body. But the tracking operation is obviously a directive correlation

 

THEOREM, P. 359

in which the coenetic variables subsumed under d are (a) the presence of (S1)jf, and (b) the organism's need to track it. The focal condition is to move the line of gaze in such a way that the distance from the midpoint of the fovea centralis to the midpoint of the image of the object never exceeds (phi)/2. The function g comprises light impinging on the object and being reflected to the eye as the object moves along its trajectory; the function f subsumes the optics of the eye, the stimulation of the photoreceptors of the retina, the mapping of the excited photoreceptor states S* onto Ep and thence into Aw, and the motor operators governing the eye motions. The components of the function (psi) comprise s , the trajectory of the object and (tau) , the changing angle of gaze.

 

All of the operations discussed above, e.g. binocular projection differences, accomodation, etc., are in a similar way directively correlated with the trajectory s of the falling body. And all of these operations are subsumed under the term "Sf"j

 

By this point it should be obvious what is meant by the perhaps annoying aphorism that "The word is not the thing it stands for", e.g. the series of events comprising the falling of an object is not the series of events comprising an organism's tracking of the falling object: "what I see:" is not "what is 'out there'." It should also be obvious that the organism's operations, in a directive correlation, are similar in structure to the environmental events they are related to.

 

In these terms, then, the cryptic term "Sf"j could be expanded into a lengthy expression involving the intersections of subsets of the operators ;involved, e.g. accomodation, tracking motions, etc., each of which were similar in structure to the actual trajectory s of (S1)fj the falling object. This expanded term would then be unmistakably different from a similar expansion of the term "Sfv"i , the first projection of Awv (S1)ir , the 'awareness' of stone-1 at rest just before its free fall.

(b) The section over "Sf"

 

The section over "Sf"j subsumes the exact relations between the accomodation changes, the tracking operations, etc., and the 'perceived' trajectory of the falling body, i.e.

 

UNNUMBERED EXPRESSION p. 360

 

However, as it stands, this relation expresses nothing more than a tautology. The operations of forming an 'awareness' Awj are useful to the organism (i.e.d. serve as reliable guides to behavior) iff these operations tell not only about the state of the organism, but also about the state of 'environmental conditions'. In our notation, this requirement is denoted by a slight expansion of the above expression.

 

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Sentence (99) asserts that the section over the subsidiary 'awareness' of the visual processes of the Self by means of which the visual focal 'awareness' is organized, at time tj , is composed of the same elements as those of the visual image of stone-1 falling at time Tj , such that its trajectory s is composed of the same elements as those of the expression 1/2 gt2 .

 

But according to G4 , if there is an 'awareness' at time tj , the organism G4 È Oj cannot be certain whether or not there even exists an environmental object yj Î E which corresponds to Awj in any sense at all; and if there does exist some yj Î E which in some sense does correspond to Awj , the organism G4 È Oj remains uncertain as to the structure of this yj Î E . Thus, every organism is required to take part in a 'guessing game'. "Adaptive behavior consists not in abandoning the guessing game (which we couldn't do even if we wanted to), but rather in testing our guesses. I remain forever uncertain whether what I see is 'really there'; but if I also hear, smell, taste, and feel it, my uncertainty is lessened." (Hilgartner, 1965).

 

Thus, if the organism is to make use of its 'awareness' as a guide to behavior, it is required to make an inference, the guess that this 'awareness' is the product of contact with something 'real'. If we borrow Frege's "signpost" notation, , to indicate "I affirm", then we can state this inference as a proposition of the form " a , and b ; and if b then c ".

 

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Sentence (100) asserts that the organism at time tj is such that there is a visual awareness of the stimuli related to stone-1 falling at time tj , and the first correspondence of this visual awareness is composed of the same elements as those of a visual subset of the Self-component of 'awareness'; and if there is a visual subset of the Self-component of 'awareness', then the organism G4 È Oj affirms that there exists at least one environmental object at time tj , such that the mapping of this object into the Other-component of 'awareness' is composed of the same elements as those of a visual Gestalt, for which the figure is composed of the same elements as those of the visual image of stone-1 falling at time Tj .

 

This expression defines the psycho-logical mechanism of projecting; but so did the conditional clause of sentence (85). The main difference between the conditional clause of sentence (85) and sentence (100) comprises the 'signpost' of affirmation in (100). According to G4 [(98) Ç (100)], every organism necessarily engages in projecting whenever it uses its 'perceptions' as a guide to behavior. The crucial question, in terms of which to discuss the differences between (85) and (100), is: with what degree of 'awareness' is this projecting done? We have seen that the conditional clause of sentence (85), by neglecting the inevitable uncertainty inherent in 'perception', assumes and implies that the relation between the environmental object yi Î E and the organism's picture of this environmental object, Cp2(alpha)(rho)f(yi), is indistinguishable from an identity mapping IE(yi) = yi . Thus we would say that the projecting is entirely 'unaware'; whereas in sentence (100), as indicated by the signpost of affirmation, this projecting is entirely 'aware'.

 

The structure of 'aware projecting', then, is such that the organism is required 'consciously' to recognize the uncertainty inherent in 'perception'; and yet, in the face of this recognized uncertainty, the organism is required to make an affirmation to the effect that the 'awareness' is the product of contact with something 'real'. These requirements are equivalent to the requirement that the organism display unmistakable faith, the confidence that the operations of the Self will somehow serve as reliable guides to behavior, with the result that the organism will once more be able to achieve the focal condition of his own preservation-and-growth.

 

Is there a rational basis for this faith? Or must we conclude that the structure of human organisms is such that they are required to act from blind and irrational optimism? A re-examination of sentence (98) reveals that, although it explicitly defines the uncertainty inherent in 'perception', it also contains the assumption that if the visual 'perceptions' are treated as hypotheses, and tested by examining the environmental object by means of tactile as well as visual receptors, or in general by means of intersecting all the boundary interactions involved and thus forming as 'complete' a 'consciousness' of the situation as can be managed, then the ambiguity will be resolved and the organism will be able to establish the actual structure of the environmental object. That is to say, what one is 'aware' of when engaging in 'aware projecting' is not only the uncertain nature of 'perceptions', but also the fundamentally self-correcting structure of organisms, as previously described (Hilgartner & Randolph, 1969). In other words, the operations of the Self are not infallable, but they are competent to serve as a guide to behavior.

 

(But the operation of forming a 'complete' 'consciousness' of a situation is equivalent to a systematic search for eF, 'forgotten factors', without waiting to be prodded by Sp , a 'surprise'.)

 

Thus, as a consequence of Encounter4, Myth1 has come to take into account a previously neglected complexity of the (organism&environment) field, namely, the certainty of uncertainty. In order to do this, he has had to modify his expectations concerning the relations between retinal patterns and environmental conditions. (As we have already pointed out, even in non-human organisms, an organism's picture of his 'environmental conditions' is inferred from the intersection of two or more modalities of sensory intake.) However, by the postulate of self-reflexiveness, in the same act he has also modified his picture of himself: If G1 Ç G2 Ç G3 leaves out some crucial environmental factor eF needed to deal with the WT , then it also necessarily leaves out some aspect of the Self.

 

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In other words, any "discrimination" or "differentiation" an organism makes concerning his own 'environmental conditions' is necessarily also a revision of his picture of himself. This is the fundamental basis for the key term "relations with self-and-others (Hilgartner, 1965), and a key relationship in our theory of the structure of human psycho-dynamics. In this instance, the EF can be summarized as the certainty of uncertainty; and the sfF can be summarized as the fundamentally self-correcting structure of organisms.

 

When he behaves in accordance with G4 , Myth1 is said to be showing 'consciousness of abstracting'. According to Korzybski, human behavior which shows 'consciousness of abstracting' is in principle more 'adaptive', more 'appropriate', than behavior which shows the absence of such 'consciousness of abstracting' (e.g. behavior in accordance with G1 Ç G2 Ç G3 ). This is the fundamental tenet of Korzybski's 'theory of sanity' (Korzybski, 1933).

 

Sommerhoff (1950, p. 151) describes a class of situation "... when experience results in a widening of the maximum variation, and hence of the degree, of the immediate adaptations involved in the behavior". In other words, an organism which, like G4 _ Myth1 , learns how adequately to take into account his own role in the situations in which he finds himself, will be able to achieve his focal conditions in situations in which he otherwise could not do so. This, then constitutes the operational basis for Korzybski's 'theory of sanity'.

 

IX. The Structure of 'Consciousness'

 

(19)

 

(20)

 

The set Cs , 'consciousness', was defined (Hilgartner & Randolph, 1969) as being composed of successive values of Awi of the several sensory modalities, intersected with the values of the coenetic variable(s), motor operators, and any other boundary interactions which may be operative in the period under consideration, such as attitudinal sets, expectations, etc. But, according to the definitions of Hilgartner & Randolph (1969), expectations, attitudinal sets, etc., are the residual of assimilated last experiences; they constitute the evidence that in past situations, the organism did achieve its focal conditions. Thus, to form a 'complete' 'consciousness' of a situation comprises bringing the organism's entire experience to bear on the situation. But let us understand very clearly that the 'entire experience' of a human organism includes some subset of the accumulated experience of the entire human species.|- For our purposes, the subset _______________________________________________________________ ________

|- Indeed, Korzybski's definition of the species Man as a time-binding class of life (Korzybski, 1921) refers precisely to these two point: that the human species accumulates human knowledge at an exponential (compound-interest) rate, and that every human being who can talk assimilates some subset of the human knowledge of his day. The present analysis deals with the mechanisms by which a human being validates, tests, and extends his own personal knowledge, including his subset of the accumulated experience of the human species.

_______________________________________________________________ ________

 

of the accumulated human knowledge which a man has assimlated si defined by the symbol systems at his command: culture, sub-culture, discursive language, specialized languages (mathematical, scientific, technical, artistic, etc.), and so on. In these terms, then, when a human organism forms a 'complete' 'consciousness' of a situation, this subset of Cs includes fundamental answers to the "orientation questions', Who am I?, Where am I?, What am I doing here-now?, and Why am I doing it? (Hilgartner, 1965); and by the same token, it involves the 'picture of self-and-others' (the theory of the structure of human psycho-dynamics), held by that human organism. So, as already indicated, a 'complete' subset of Cs includes the climax of the excitement involved in an interaction at the boundary, e.g. the "Aha!" of surprise at the moment of insight, the orgasm, the graceful energetic harmonious motion, etc.

 

As was previously pointed out, Cs , like Aw , is organized as a Cartesian product space, designates Se&Oe . The 'Other' component of Csi , Oei , itself is organized as a Gestalt, a figure of focal interest to the organism, bounded by a ground or context more or less empty of interest, as given by several sensory modalities. The main differences between Cs and Aw are related to their (a) 'inclusiveness' (Cs includes the various operators, whereas Aw does not), and (b) their relative durations. The different values of Aw could be likened to the individual frames of a movie film, viewed one at a time, whereas Cs is comparable to the configuration achieved by viewing the successive frames at a rate which exceeds the flicker-fusion time of the observing organism.

 

However, when we speak of a 'complete' 'consciousness', we imply that subsets of Cs can be graded in terms of the degree of their 'completeness'. In a later publication, we shall explore the structure of more or less 'limited' or 'impaired' subsets of Cs ; but for the moment, let us consider the 'ideal case', an 'intact' or 'unimpaired' situation, in which only the fullest, most 'complete' subsets of Cs will be formed. This will prove equivalent to considering one more implication of G4 .

 

By reasoning similar to that in the case of Awi, the second CQ correspondence of 'consciousness' of an environmental object xi Î E comprises the organism's individuated, considered picture of the characteristics of the environmental object, at time ti . The 'perceptions' were treated as hypotheses, and these hypotheses proved not to be disconfirmed by the test of intersecting them; the structure of organisms in the O&E field is such that this is the sine qua non for the 'reality' of any contact-situation at any time Ti (Meyers, 1949). Oei then comprises in each instance a configuration of unique structure, which is organized as a 'consciousness'-Gestalt; and likewise, the first Cq correspondence, Sei , also comprises in each instance a configuration of unique structure.

 

Again, as in the case of Awi , the section U(Sei) = Oei expresses only a tautology, unless the organism engages in the psycho-logical mechanism of projecting, and affirms that this Csi is the product of contact with something 'real'. However, since the formation of a subset of Cs which is not an empty set constituted the immediate criterion of the 'reality' of a situation, and involves the climax of the excitement engendered in the boundary interaction, it is likely to prove particularly difficult for us to see that the act of affirming that this Csi is the product of contact with something 'real' still comprises an inference. But to miss this point will vitiate the advantages of this theory of the structure of human psycho-dynamics, which holds that the organism's primary dealings with self-and-others are monitored by means of proprioception of the operations of its Self.

 

By analogy with sentence (100), the structure of aware projecting at the level of 'consciousness' is given in our notation as a proposition of the form " a , and b ; and if b then c ".

 

(102)

 

Sentence (102) asserts that the organism at time ti is such that there is a 'consciousness' at time ti , and the first Cq correspondence of this 'consciousness' is a subset of the self-component of 'consciousness' at time ti ; and if there is a subset of the self-component of 'consciousness' at time ti , then the organism affirms that there exists at least one environmental object yi Î E such that the mapping of this object into the other-component of 'consciousness' is composed of the same elements as is a subset of the other-component of 'consciousness' at time ti , such that there is a 'consciousness'-Gestalt for which the figure in 'consciousness' is composed of the same elements as those of the 'consciousness'-image of yi .

 

We reassert that, according to our view, special structures are required to produce 'impaired' subsets of Cs ; thus, in this context, Csi designates a moment of the highest possible '\consciousness'. Then sentence (102) asserts that if I have a moment of the highest possible 'consciousness', this is equivalent to my recognizing the existence of a subset of my Self, and then affirming that there exists in the environment an object which corresponds to this subset of my Self. If we use the expression (signpost)Oei as the equivalent of the expression

 

UNNUMBERED EXPRESSION p. 365,

 

then, by the postulate of self-reflexiveness, a corollary of sentence (102) can be stated as

 

(102a)

 

where

 

UNNUMBERED EXPRESSION P. 366.

 

In the verbal text, we shall designate this relation as the fundamental affirmations of our organism, (signpost)Oei (union) (signpost)Sei .

 

In order to show the human significance of this relation, let us now re-examine sentence (82), which shows how an organism in an emergency situation interrupts its ongoing activities by the use of its motor apparatus and its apparatus of internal secretion so as to turn and deal with the emergency. According to our view of the structure of organisms, this effort to interrupt its ongoing activities is detectable by the organism, by proprioception.

 

Given (82),

 

(103).

 

Sentence (103) asserts that, given the situation of sentence (82), i.e.d., the necessity to interrupt the ongoing activities of the organism, if there is a startle reaction at time t33 , and retroflexion, anxiety, sensory orienting, and autonomic discharge at time t34, then there are activated states of the appropriate proprioceptors at times t33 and t34 . (These activated states are then mapped by the operators (rho) and (alpha) into Ep and Aw , respectively.

 

Sentence (103) could be made shorter by subsuming these relations as the operator Sp , and proprioception of the operator Sp .

 

Likewise, the effort to 'complete' a situation constitutes a mode of using the motor and secretory apparatus, which we have thus far indicated by the operator (signpost); and this too is detectable by the organism, by proprioception. This operator indicates a set of specific, observable, proprioceptible phenomena, which form an intrinsic part of every experience, and which give an autonomous criterion of the degree of 'completeness' of the subset of Cs involved. These phenomena are described by Perls, Hefferline & Goodman (1951) as follows:

 

... The wholes of experience are definite unified structures. Contact, the work that results in assimilation and growth, is the forming of a figure of interest against a ground or context of the organism/environment field. The figure (Gestalt) in awareness is a clear, vivid perception, image, or insight; in motor behavior, it is the graceful energetic movement that has rhythm, follows through, etc. In either case, the need and energy of the organism and the likely possibilities of the environment are incorporated and unified in the figure.

 

The process of figure/background formation is a dynamic one in which the urgencies and resources of the field progressively lend their powers to the interest, brightness and force of the dominant figure. It is pointless, therefore, to attempt to deal with any psychological behavior out of its socio-cultural, biological and physical context. At the same time, the figure is specifically psychological: it has specific observable properties of brightness, clarity, unity, fascination, grace, vigor, release, etc., depending of whether we are considering primarily a perceptual, feelingful, or motor context. The fact that the Gestalt has specific observable psychological properties is of capital importance in psychotherapy, for it gives an autonomous criterion of the depth and reality of the experience. It is not necessary to have theories of 'normal behavior' or 'adjustment to reality' except in order to explore. When the figure is dull, confused, graceless, lacking in energy (a 'weak Gestalt'), we may be sure that there is a lack of contact, something in the environment is blocked out, some vital organic need is not being expressed; the person is not 'all there', that is, his whole field cannot lend its urgency and resources to the completion of the figure." Perls, et al., 1951, pp. 231-2; their italics)

 

[These phenomena are also discussed in Hilgartner (1965).]

 

In our notation, representation of these considerations is extremely simple; given the situation of sentence (102), it requires a proposition of the form of a simple conditional.

 

(104)

 

Sentence (104) asserts that if at time ti the organism is affirming that there exists at least one environmental object yi _ E which corresponds to a recognized subset of the Self at time Ti , then there is proprioception of the affirmation, at time ti .

 

The conciseness of this expression emphasizes as nothing else could the fundamental nature of these phenomena of affirmation. This expression means that if I have a moment of the highest possible 'consciousness', I can tell, by proprioception, that this is a moment of the highest possible 'consciousness'.

 

X. The Structure of 'Aware Projecting'

 

Some examples at this point should serve to make clear how these refinements of our relational language apply to human experience. In sentences (25) through (42) of our previous paper (Hilgartner & Randolph, 1969, pp. 315-6), we provided a first approximation of "The Form of Any Encounter"; in light of the later developments, let us now re-examine the behavior of our hypothetical organism, who has by now become a disciplined psycho-logician, showing in this behavior a high degree of 'consciousness of abstracting'.

 

(105)

 

(106)

 

Throughout Myth1's experience, the coenetic variables "deficit of orientation" have undergone successive redefinition; now, at time t38, Myth1 behaviorally shows the awareness that he operates of necessity from incomplete information, and thus in every situation experiences some degree of 'deficit of orientation'. This behavioral awareness might conveniently be termed 'epistemological humility', that is to say, the disinclination to act as a "know-it-all".

 

(107)

 

Two aspects of sentence (107) require emphasis here: (1) To a person who is thoroughly familiar with the Ames demonstrations in 'perception' in general and the trapezoidal window in particular, and who shows in his behavior a high degree of 'consciousness of abstracting', the raw 'perceptions' of the rotating trapezoidal window will spontaneously and freely shift from one form to another: it may at one moment appear as an 'oscillating rectangle', then as a 'rotating trapezoid', then perhaps as a 'stationary figure changing its shape', etc. What is more, the rotating rectangular window will also be perceived as shifting in form. Under more ordinary circumstances, we usually tend to exclude from awareness transient and 'unlikely' visual ambiguities of this sort; for in order to do so we are required to expend detectable effort. This effort constitutes the restricting of one's own 'creativity'. (2) It will be noticed that the affirmation in the conditional clause of (107) constitutes the formation of a hypothesis, as previously described (Hilgartner & Randolph, 1969). The expression (Wr (xunion) WT (xunion) .)v,t) is intended to indicate the organism's expectation that he will be able to distinguish unequivocally among the different possible structures of the environmental object in question (although each of us knows from our own personal experience that this is not always possible).

 

The interaction now proceeds as we have learned to expect:

 

(108)

 

(109)

 

(110)

 

(111)

 

(112)

 

(113)

 

(114)

 

The distinction between sentences (113) and (114) lies in the fact that (113) expresses only the state of the organism at time t47 , whereas (114) affirms the organism's inference (or better, conviction) that he is correctly dealing with a 'real' environmental situation, rather than with 'unaware' hallucinations, mis-perceptions, or some other class of mistakes.

 

XI. The Structure of 'Conscious Projecting'

 

We are now in a position to fulfil one of our early promises, i.e.d. "... to show the structure of some of the most baffling aspects of human experience; and further, to indicate the existence of, and to explore, essential aspects of human experience which are systematically neglected in Western cultures, and which each of us can ill afford to exclude from our behavioral repertoires" (Hilgartner & Randolph, 1969). There is a phenomenon in human 'perception' which was originally discovered centuries ago by early exponents of the Tao and Zen tradition, and which is often referred to as the phenomenon of Tat Twam Asi -- "This otherness is myself". In most people, this phenomenon is very easy to elicit; but to describe it in words is most difficult. It was used as a key demonstration in the development of the argument in Hilgartner (1965) (cf. also White, 1959).

 

In Zen Buddhism, there is an exercise or 'meditation' which goes as follows: Select some object in your actual field of vision, say a moving automobile. Try to imagine what you would be like if you were that auto: what parts of you would become the headlights? the windshield? the wheels? and so on with the other parts. Try this with other visual objects: a tree, a stone, a bird, a sunset, a carpenter's hammer. For a time, say to yourself of everything you meet, 'This otherness is myself,' and see if you can imagine how this would work.... When I am doing this with a visual object, I am aware of making more or less covert, small motions of skeletal and oculo-facial muscles, as, in imagination, I adjust the physical parts of myself into the shape of the object I am confronting.... The crux of this exercise lies in the way that in doing it, we are forced awarely to do that which we always and unavoidably do anyway, although more unawarely."

 

We propose now to specify the structure of this 'perceptual' process, which we shall designate by the term 'conscious projecting' [as opposed to the 'aware projecting' specified in sentences (98) through (114)].

 

Stated in words, 'aware projecting' at the level of 'consciousness' constitutes the affirmation, "I have made use of my sensory receptors, motor operators, etc., and by these means have set up a subset of my Self, and have encountered no detectable contradictions; therefore I infer that there exists an environmental object which corresponds to this subset of my Self".

 

As we predicted, in order to specify the structure of 'conscious projecting', we need to make use of the notion of the multi-ordinality of terms, which was defined in sentences (43) and (44) of our previous paper (Hilgartner & Randolph, 1969).

 

(43)

 

(44)

 

'Conscious projecting' constitutes a further development of a situation in which an organism has interacted with an environmental object so as to produce a visual subset of 'awareness'. By means of his proprioceptors, the organism attends to this subset of his Self, thereby producing a proprioceptive 'awareness' of this visual 'awareness'. By then visually attending to the visible details of the environmental object, while making small but proprioceptible imitative motor adjustments of his body parts, he progressively brings about a closer and closer felt-correspondence between the parts of his Self and the observable details of the environmental object, until this process culminates in the formation of a (visual (intersect) proprioceptive) Gestalt. Thus, 'conscious projecting' comprises a kind of non-verbal dialogue between observer and observed. But it is well at this point to remind ourselves that in order to carry on this non-verbal dialogue, our organism is required to affirm that the visual 'awareness' is the product of contact with a 'real' environmental object. That is to say, at every instant of the process of 'conscious projecting' our organism is required to engage in the affirmations of 'aware projecting'.

 

But the process of 'conscious projecting' can be specified in our notation only as a directively correlated activity, with a novel set of coenetic variables and a novel set of focal conditions. In our previous paper, we defined an operator, urgency (Ur), which, in an emergency-situation, involves intensified motor activity, with an affect of desperation. 'Conscious projecting' involves a kind of unhurried playfulness, with an affect of unmistakable serenity; it might well be represented as the opposite of urgency (). Thus, the coenetic variables involved in 'conscious projecting' include not only the intrinsic uncertainty we now designate by 'deficit of orientation', and the presence of an environmental object, but also the complement of urgency. The focal condition of 'conscious projecting' include not only the formation of a visual awareness of the environmental object, but also the formation of a (visual (intersect) proprioceptive) Gestalt, the figure of which comprises the affirmation of a particular relation between organism and environmental object. In order to specify this relation, it is necessary to regard the environmental object x Î E as a set which includes a set of visible details, {v|v Î x, S*(f(v)) Î S*(f(x))}; likewise, it is necessary to regard the organism as a set which includes a set of proprioceptible parts, {o|o Î O, p*(o) Î P*(O)}. It will be noticed that both on the level of elements and on the level of sets, these activated-state components stand as representations of the 'real' components of the environmental object and of the organism; and thus they can be manipulated by the organism with the freedom of symbols. Finally, we shall define an operator, imitating, (Im), which involves using the motor apparatus of the organism in such a way as to produce the "more or less covert, small motions of skeletal and oculo-facial muscles as, in imagination, I adjust the physical parts of myself into the shape of the object I am confronting". It will be noticed that this operator can be expressed as a relation, e Im o , which is read "The element o imitates the element e ".

 

After these verbal formulations, we can almost anticipate in detail the form of these interactions; but the proof of the pudding is still in the notational deployment:

 

(115)

 

(116)

 

It will be recalled that "Sf"i designates a set of activities, namely the process of detecting binocular projection differences, of accomodating, of converging the ocular axes to some degree, the movements of visual scanning and visual tracking, etc. In each instance, the component activities which make up this set are monitored by proprioception.

 

(117)

 

(118)

 

(119)

 

(120)

 

The assimilation of this experience proceeds along familiar lines:

 

(121)

 

(122)

 

(123)

 

(124)

 

Discussion

 

In order to see the human significance of sentences (115) to (124), let us first consider the course of the assimilation of our own experiences of 'conscious projecting'. Myth1 constitutes a hypothetical 'ideal' observer, ex hypothesei capable of drawing correct inferences from a single encounter, and in the process, displaying the structure of the encounter. By way of contrast, we ordinary mortals are likely at first to set about deliberately 'trying' to do the exercise of 'conscious projecting'; and, not knowing quite what to expect or how to proceed, we are likely to be a bit clumsy at it.

Discussion

 

In order to see the human significance of sentences (115) to (124), let us first consider the course of the assimilation of our own experiences of 'conscious projecting'. Myth1 constitutes a hypothetical 'ideal' observer, ex hypothesei capable of drawing correct inferences from a single encounter, and in the process, displaying the structure of the encounter. By way of contrast, we ordinary mortals are likely at first to set about deliberately 'trying' to do the exercise of 'conscious projecting'; and, not knowing quite what to expect or how to proceed, we are likely to be a bit clumsy at it. In particular, we are likely to be impressed to the point of distraction by the surprising and 'absurd' aspects of this type of experience. However, if we persist in doing it over and over again, eventually we begin to get a sense of the form of the whole process. If and when we suddenly find that we have done the exercise spontaneously, without 'trying' at all, this comes as the biggest surprise of all; and it is this experience which corresponds to G5 . At that point, we realize that, awarely or unawarely, we humans 'conscously project' in relation with any environmental object, and that this ability is an intrinsic aspect of human behavior: "The crux of this exercise lies in the way that in doing it, we are forced awarely to do that which we always and unavoidably do anyway, though more unawarely." (Hilgartner, 1965). And as is clearly indicated in the notation, this experience is very deeply felt.

 

We have called 'conscious projecting' a 'perceptual process'; but it now becomes evident that it also constitutes a direct experiencing of the structure of a human being's relations with his environment. In other words, this affirming of this relation between the organism and its environment constitutes a fully-'aware' and entirely non-verbal answering of the four fundamental 'orientation-questions': Who am I?, Where am I?, What am I doing here-now?, and Why am I doing it?

 

But we point out the possibility of engaging in the process of 'conscious projecting' 'unawarely'. We have already shown that, in our notation, the use of the "signpost" of affirmation, (signpost), corresponds to the verbal notion of projecting 'awarely'; and we have shown that the use of the "signpost" implies that the organism whose interactions are being represented is assuming non-identity, non-allness, and self-reflexiveness. The verbal notion of projecting 'unawarely', as we have shown, corresponds to the notational situation that the organism involved is assuming that the operations of the Self are indistinguishable from an identity-mapping IE(yi) = yi , which is equivalent to a demonological construct. These results apply mutatis mutandi on the level of 'conscious projecting'. Thus, the process of assimilating our own experiments with 'conscious projecting' constitutes the experience of discovering and eliminating one more set of demonological constructs from the operations of our own Selves, a major revision of our theories of the structure of human psycho-dynamics. The felt depth of the process, the affect of serenity involved, constitutes direct proprioception of our own growth.

 

Sommerhoff (1950) deals with the topic of these deeply-felt experiences in his section on The Nature of Biological Progress. As he puts it (pp. 189, 191):

 

Our investigation and analysis of the goal-directed aspects of nature touches theology in several ways. For one thing, religion is very largely concerned with just these teleological aspects of nature and human destiny. In having shown that it is possible to describe these teleological aspects of nature in terms of mathematical relations between physical variables, and in having thus shown that these aspects represent physical relationships as genuine and real as, say, gravity or magnetism, we have not given substance to any particular religious beliefs, but we can claim to have given substance to some of the particular things religious beliefs are about.... From a purely biological point of view our religious beliefs thus appear to be of the nature of an adjustment, not to any concrete set of environmental circumstances, but to the universal existence (and fundamental importance for life) of the abstract property of directive correlation as such. In short, our religious beliefs might be described biologically as an adaptation to the fact of adaptation. (Sommerhoff, 1950, pp. 189, 191)

 

These considerations, then, give the structure of the most deeply felt of human experience, e.g. what Korzybski (1933) describes as 'silence on the objective levels'; or what Maslow (1962) describes as "peak experiences", the few best, most creative moments of a man's life; or what Polanyi (1964, pp. 49-65) refers to as 'esthetic' or 'existential' 'meaning'; or what the Zen masters refer to as the experience of Satori (enlightenment) (Suzuki, 1956; Kapleau, 1965); or what has been described by many writers as the experience of 'mystic unity'.

 

XII. Summary

 

At this point, we have provisionally demonstrated the self-consistency of our axiomatic system. We started by stating our undefined terms, and our premises; we set up our logical machinery, we turned this logical machinery one complete revolution, and got our premises back. Further, by analyzing in detail just what our hypothetical organism learned from his encounter with the Ames trapezoidal window, we have provided a representation of 'sane' behavior which can be directly compared with the perceivable structure of human experience.

 

The next step will be to extend this system so as to show the structure of the integrated social relations between human organisms. Then se shall explore the structure of 'impaired' subsets of Cs ('unsane' behavior). Finally, we shall explore the mechanisms whereby a human organism can learn how to 'complete' his hitherto 'impaired' subsets of Cs.

 

REFERENCES

(P. 374)