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by Paulo Cesar Sandler
"And finally we must not forget that the analytic relationship is based on a love of truth– that is,on
a recognition of reality– and that it precludes any kind of sham or deceit" (Freud, 1937, p. 248)

W.R. Bion
The Grid is Bion’s attempt towards simplifying the communication between analysts as well as a personal communication of an analyst with himself (Bion, 1962b, p. 38, para 2). This specific project was felt by many readers as a complication. Perhaps an attempt to synthesise his proposal can prove to be timely. This synthesis does not replace Bion’s texts but tries to orient a reading to the reader who unfamiliar with them. The Grid is a device intended for an outside analytic session critical scanning of psycho-analytic material (Bion, 1965, p. 128). It was formulated circa 1960 (Bion, 1992, p. 195) through the integration in a hitherto unavailable form of Freud’s Two Principles of Mental Functioning with Klein’s Interplay of Positions (Freud, 1910, 1920; Klein, 1940, 1946, 1947). It was first published in ‘Elements of Psycho-Analysis’ and ‘Transformations’ and subjected to more extensive explanations (pp. 39-47, 167-169) especially through its clinical use in a mobile, dynamic non-patterned form (pp. 50, 74-75, 96-100; 126). The reading of those selected parts of ‘Transformations’ seem to me mandatory for the reader who is not familiar with the Grid. There ensued some improvements (1967 and 1971; published in 1992, pp. 325, 357): two of its ‘categories’ (line C and column 2; see below) were considerably developed fourteen years later in a short paper, ‘The Grid’ as well as in Bion’s (1977) talks in New York City (Bion, 1977b; 1977c, pp. 57 and 92, published in 1980). The Grid is not ‘appropriate to the actual contact with the patient’. It may be used as a prelude as well as an aftermath to it: it trains the analyst’s gauging of the analytic work done and it also may help future work. It ‘provides practice, analogous to the musician’s scales and exercises, to sharpen and develop intuition’ (Bion, 1963, p. 73). This gauging is made in terms of the success or lack of it to approximate to the patient’s truth as well as the truth of what occurs in a session. In other words: to what extent and under what parameters were the insights gained, intrapsychically and in the relationship of analyst and analysand, truthful? The raw material to be examined are the analyst’s and the patient’s verbal statements. ‘The two axes should thus together indicate a category implying a comprehensive range of information about the statement’ (p. 73).
The Grid contains dynamically linked categories formed by the intersection of two axes in an Euclidean bi-dimension representation (fig. 1). A statement may fall simultaneously in different categories and one category may fall into another (Bion, 1965, p. 116). This can kaleidoscopically change in a next ‘decisive moment’ (Cartier-Bresson, 1952). Each axis expresses basic psycho-analytic theoretical-practical, intra-session activities. Each axis can be regarded as a synthetic epistemological searchlight that represents the underlying rationale of the psycho-analytic endeavour. Therefore the Grid is an epistemological tool. The horizontal axis (columns) includes the functions of the ego according to Freud, as outlined in his paper ‘Formulations on the Two Principles of Mental Functioning’(Freud, 1910): notation, attention, inquiry and action. To those functions Bion ascribes numbers in order to facilitate categorisation. This axis also includes two Kantian categories akin and more primitive to the ego-functions adumbrated by Freud. I surmise that those two categories were implicit in Freud’s work but they were not yet named. Bion makes them explicit through naming them:

(1) a primitive equivalent of pre-conceptions in the area of thought processes, which Bion names definitory hypothesis, probably linked to instinctual endowment;
(2) column 2 is a non-saturated category, plenty of unknown, purposefully named ‘y .’ It corresponds to false statements known as such by analyst and analysand. If its begetter is the analyst, it indicates his need of further analysis. The statements appertaining to this category are not amenable to be understood, but rather to be perceived and used as pointers. In fact, a telling example of statements appertaining to column 2 are explanations and rationalizations.
During the development of the Grid, Bion stressed the phantastic nature of projective identification, already stated by Mrs. Klein herself (Klein, 1946, p. 298) as well as its constant relationship with hallucination and lie: ‘indeed her [Melanie Klein’s] theory of projective identification could itself be presented, in the course of analysis, as a series of lying statements’ (Bion, 1977b, p. 11). This seems to me a turning point in Bion’s practical approach during the actual session. It sharply contrasts with a tradition, probably initiated by Paula Heimann, that ascribes actual and factual properties to projective identification, extrapolating its effects in the area of thought (splitting) to a real inoculation of thoughts or feelings into the analyst’s or other onlookers’ minds. Bion had previously distanced himself from this trend when he re-published his paper on schizophrenic processes of non-thinking in Second Thoughts. A synthetic formulation depicting y statements appears in John Milton’s A Second Defence to the English People: ‘To be blind is not misery. Misery is not to be able to endure blindness’ (Milton, 1654, p. 205). Projective identification ‘attains’ the status of a non-lie when there is an ‘adequate receptor’, which demands discrimination from a container (in Bion’s sense) or a good-enough mother (in Winnicott’s sense). In psycho-analysis, the ‘adequateness’ inheres in the lack of discrimination of what a lie is and the analyst becomes prey to it. Therefore, successful projective identification depends on collusion, the stuff of column 2 (in fact, C2). Bion proposes to typify lies in order to sharply differentiate them from false statements: ‘the false statement being related more to the inadequacy of the human being, analyst or analysand alike, who cannot feel confident in his ability to be aware of the "truth" and the liar who has to be certain of his knowledge of the truth in order to be sure that he will not blunder into it by accident’(Bion, 1977b, p. 11). He synthesizes: ‘it is simplest to consider column 2 as relating to elements known to the analysand to be false, but enshrining statements valuable against the inception of any development in his personality involving catastrophic change’ (p. 11). The Grid helps us to deal with lies not under a moral, but rather under a scientific vertex: what is at stake is the scientific endeavour: the apprehension of reality.
The vertical axis (lines) of the Grid is to be used in David Hume’s sense, that is, constantly conjoined with the horizontal axis of functions and uses. The falsity of a statement as well its truth is a ‘function of its relationship to the other element in the scheme’(Bion, 1977, p. 9). This axis has lettered categories, A to H. It furnishes an (onto)genetic view of the development of the thinking apparatus, a spectrum that ranges from primitive sensa stimuli to the most sophisticated expressions of human thought hitherto known. The former are felt as things-in-themselves: psychotic feelings of attainment and ownership of absolute truth, no-thinking at all, which Bion named ‘b-elements’. The latter corresponds to algebraic calculus. In between A and H we have: line B, ‘a-elements’, that is, "de-sense-yfied" b-elements that can be used to think and for dream work; dream thoughts; line C, that comprises dreams, myths, dream thoughts, to which I would add metaphors. It corresponds simultaneously to Plato’s Ideal forms and to Aristotle’s ‘nous’: the mind thinking about itself and presenting the real universe, human nature and, above all, itself to itself. This is a remarkable category; myths are powerful enough to convey macro, universal truths and they also are valid at the micro, individual level, as part ‘of the primitive apparatus of the individual’s armoury of learning’. Bion considers the myth as a ‘fact-finding tool’ and states explicitly: "I wish to restore its place in our methods so that it can play the vitalizing part there that it has played in history and in Freud’s discovery of psycho-analysis’ (Bion, 1963, p. 66). Bion scrutinizes the Oedipus Myth (Bion, 1963) and the myth of Babel (Bion, c. 1960, published in 1992, p. 226).This Grid category would be noticeably expanded in 1977 to the point of meriting a Grid of its own. Line D lodges Kantian pre-conceptions, which correspond to Freud’s protophantasies (Freud, 1920); conceptions, concepts (E) and scientific deductive systems (F) compose lines D to F. In order to better apprehend the ethos of line C onwards, one should firmly grasp the conception of psychic reality as a different form of existence from material reality (Freud, 1900)--i.e., one must not be ‘too concrete’ as Hanna Segal puts it (Segal, 1979, p. 62; Sandler, 1997b).

The Grid is an embryonic search for a discriminatory and epistemological tool that doubles as a communicational tool between analyst and patient as well as among psycho-analysts. It enhances the intrinsic scientific nature of our activity, an issue very dear to Freud. It may be stated in terms of concern toward truth (Bion, 1960, in Cogitations, p. 125; 1970, p. 26). The Grid has an empirical, observational nature, seemingly stemming from Bacon and Locke. It is a commonsensical tool in that it uses our commonality of senses. Although the two axes of the Grid 'may appear arbitrary' they stem 'from the analytic situation itself’ (Bion, 1963, p. 91). They take into account the uses the analysand ‘makes of the analytic situation’(p. 91) through scrutinising the patient’s most evident activity in analysis: thinking and lack of it. The two axes measure uses and functions (horizontal axis) of statements vis-à-vis the ontogenetical value (vertical axis) of statements, which reflects growth (Bion, 1963, pp. 63, 92). The statements, being verbal statements, are a function of thinking processes. The realness of a clinical occurrence is stated in clearly explicit terms: the various Grid categories.
The term ‘commonsense’ in Bion’s work is used according Locke’s original concept – to have at least two senses in common. It is as a kind of Geiger-device to ‘detect’ the presence of truth (reality) as it is (Locke, 1690). This seems to me to be the basic ‘episteme’ and rationale of what I suppose that Bion tried when he devised the Grid, an exercise in discrimination for practising psycho-analysts. He was searching for a psycho-analytical method to discriminate elemental ‘facts as they are’ (Samuel Johnson, often quoted by Bion; for example, ‘Cogitations’, p.6, 13, 114; circa 1959; also 1970, 1975).
I assume that the permanently therapeutic effect of a psycho-analysis, if any, depends on the extent to which the analysand has been able to use the experience to see one aspect of his life, namely himself as he is. It is the function of the psycho-analyst to use the experience of such facilities for contact as the patient is able to extend to him, to elucidate the truth about the patient personality and mental characteristics, and to exhibit them to the patient in a way that makes it possible for him to entertain a reasonable conviction that the statements (propositions) made about himself represent facts.
It follows that a psycho-analysis is a joint activity of analysand and analyst to determine the truth; that being so, the two are engaged – no matter how imperfectly – on what is in intention a scientific activity’ (Bion, circa 1959, in Cogitations, 1992, p. 114; Bion’s underscore)
Since self-knowledge is an aim of psycho-analytic procedure the equipment for attaining knowledge, the function and apparatus of pre-conception, must be correspondingly important’ (Bion, 1963, p. 91)

Later he would call the endeavour as ‘transformations in O’ (for example, Bion, 1965, pp. 147 and 148; 1970, pp. 148, 26, 28, 29, 70-71, 89; 1975, p. 8 and pp. 87, 96-98). In order to know models (Bion, 1962b, p. 79, in the strict Kant’s sense p. 105, 162 p. 98 in the English version; Freud, 1937, p. 225; 1938c, 191-192) and approximations towards what may ‘elucidate the truth about the patient personality and mental characteristics’, relentlessly considering the hindrances and obstacles to such a task.
A central role is performed by ‘reversion of perspective’, a fact dependent on projective identification that happens to occur in an analytic session. It is amenable to be used, provided the analyst developed his (her) ability to ‘make the best from a bad job’. Reversion of perspective is one of the tools to see beyond the material, overt, acted-out appearances (Bion, 1963, p. 54, 60; 1975, p. 11-37). An example of reversed perspective at work is the scrutiny of emotions of hate and love during an analysis, under the vertex of tolerance of paradoxes (Sandler, 1997b). It is expressed by the analyst’s realization that ‘if the hate that a patient is experiencing is a precursor of love its virtue as an element resides in its quality as a precursor of love and not in its being hate’ (Bion, 1963, p. 74). This includes the appearances of manifest discourse, talk. The Resistance, in Freud’s sense, expresses itself even in discrete words uttered by our patients, which are counterparts during the actual session of the manifest discourse as it is traditionally regarded in the dream. Therefore the words, phrases, facts, events, reported by the patients may be dreams being dreamed during the actual session. Also, they may be hallucinations and delusions. Therefore, it is a matter of discrimination. If they constitute dreams, resistance and manifest content simultaneously point to the truth and equally disguise this very same truth. As in Bion’s metaphor in ‘A Memoir of The Future’, we psycho-analysts are ever at the risk of aping a dog that looks at his master’s pointing hand instead of paying attention to the object the hand points to. It is a matter of intuiting the existence of the moon’s dark side, of intuiting the obverse of whatever appears, what remains hidden, lurking – but what nevertheless is there. This allows us to close a true circle, returning to our epistemological point of origin of this brief précis of Bion’s Grid -- the real value of statements that avoid descriptions of ‘particular clinical entities’ being subjected to fit to ‘some quite different clinical entities’: ‘Correct interpretation therefore will depend on the analyst’s being able, by virtue of the Grid, to observe that two statements verbally identical are psycho-analytically different’ (Bion, 1963, p. 103).

Some authors, including Bion himself, repeatedly emphasized the damage provoked by a rigid, I dare to say, ‘wooden’ use of the Grid (Bion, 1963, p. 25; 1965, p. 132, Matte-Blanco, 1981; Sandler, 1987; Green, 1992). Pretty serious warnings appear in volume II of ‘A Memoir of the Future’ and in a talk in New York City (1977, p. 11; 1980, p. 56). Distinguished by its static, mechanistic approach, this use transformed the Grid into a harrow or a rail. As a matter of consequence it wastes the ‘grid’ nature of the grid. They tried to use the Grid as if it was a drawer to pigeon-hole statements, inserting ad hoc clinical facts into the device: ‘This is column 4’, ‘This is a b-element’ and so on. This use dismantled right from the start the conjoined use of the two axes (Bion, 1965, p. 43; 1977b, p. 9). I am afraid that it perverted the nature of the Grid, for here an intuition-training tool turns into a pre-conceived, pre-patterned repository for Memory. Also, this use reduced it to still another ad hoc theory that would function as a clever manipulation of symbols. In brief, something Bion refused to do during his whole professional life. Irony of ironies: perhaps an expression of man’s prohibition to knowledge (Thorner, 1981), that the theories are used in the exactly opposite sense from that for which they were originally devised? I think that Bion’s Grid had a ‘distributing’ and ‘flowing’ as well as ‘transducer’ nature. Distributing and flowing to the extent that it redirects and transforms inputs, much like the starting grid in horse or automobile races, or of a polarizing photographic filter. ‘Transducer’, like a living filter such as the frog’s gallbladder structure as used in studies of physiology, which lets pass some elements and bars others selectively (Sodium and Potassium). Being a live device, it is ever-changing and in some cases useless. (Bion, 1978; Sandler, 1987).
It is of no use to criticize without an accompanying attempt to remedy the issue. From experience with groups of candidates studying the Grid, I think that a preventive measure helps to to not take the device too concretely: to describe the categories employing the cogent wording, as if reading a graph of x, y co-ordinates; the analogy is with a beginner learning musical notation in the score who must repeat it aloud until automatic memorisation ensues. It helps to consciously avoid saying ‘C3’ or ‘F4’ or ‘B1’. Instead, one should clearly state to oneself, ‘the patient is making a notation of his dream’ (C3), or ‘his attention is directed to the formation of a concept’ or this statement refers to a ‘definitory hypothesis which already contains this or that psychic feature’ (B1), a kind of solfeggio. When one has introjected the concepts, thus achieving an inner, personal realization of it, one is enabled to use the shorthand quasi-mathematical notation. It is of no use to the child to learn by heart the four arithmetical operations unless he or she firmly grasps their real mathematical ethos.
I can say that an early casualty in trying to use the Grid is the Grid itself...anyone who examines the Grid both in psycho-analytical grounds and for scientific methodological rigour will be dissatisfied’ (Bion, 1977b, pp. 12 and 20). Bion and Freud, being scientists, maintained the same posture. Both recommend using their observations as starting points to further developments. Klein and Bion did this when they expanded the venues opened by Freud in what regards to, respectively, death instincts and disturbances of thought, dream work and other inroads into the unconscious. Bion requested that readers should actively seek to expand his theory of H, L and K links, hoping that someone could try to discover other links. Among others, I suppose that Money-Kyrle extended some of Bion’s concepts on cognitive processes; Grotstein, on binocular vision and in the realm of ‘O’; Green on the "negative", Britton on some amendments to K link and Sandler on anti-alpha-function (Money Kyrle, 1968, 1970; Green, 1986; Grotstein, 1991; 1995; Sandler, 1997, Britton, 1997). The present proposal does not intend to replace Bion’s Grid, but it tries to accept Bion’s invitation: ‘in time someone may evolve ... the formation of grids suitable to particular types of difficulty, different disciplines...’ (Bion, 1977b, p. 12). To use Bion’s metaphors in his expansions of C-category (Bion, 1977b, p. 2 and 17), I hope my ‘dissatisfaction’ may share more features with the tomb robber’s dissatisfaction than with Palinurus’. I suppose that the tri-dimension Grid addresses the special difficulty presented by diagnostic assessments that can furnish a global picture of the various types of psycho-dynamic assessments often found in clinical practice. It is a visual way to present some psycho-dynamic diagnoses. Hopefully, their outstanding psycho-analytic features will appear more clearly, and at a glance. It can be regarded as a quasi-photographic depiction of types commonly found. The tri-dimension Grid is intended to be a representation, a model which depicts the instantaneous state of some nosographical entities. The problem I faced was this: is it possible to get a speedy, instantaneous way to diagnose those states? Can the Grid be helpful to get a status of the mental functioning of particular types of persons or a given moment of a particular being? I also use the tri-dimension Grid to scrutinize a paradigmatic clinical, intra-session situation.

Bion, probably inspired by Whitehead (1911), reminded us on many occasions (for example, Bion, 1977a, pp. 7, 21, 27) that Descartes was able to expand Thales’ and Euclid’s bi-dimension space of lines, triangles, parallels and circles. The tri-dimension system of Cartesian co-ordinates opened a whole field, hitherto unknown, to exploration. This was my clue: why not to try the expansion of the system of two co-ordinates composed by the Grid’s two axes, Uses and Genetic (figs. 1 and 2), with a third axis that could still furnish – always following Bion’s provisos - still more information about the statements we make? In fact it seemed to me that this third axis was implicit in Bion’s practical use of his original Grid, specially when he furnished his clinical examples in ‘Transformations’. I thought that a graphic way could be used to express what already was there, albeit implicitly: a question of intensity in and of the various grid categories (fig. 3). I resort to the concept of ‘intensity’, that already has a penumbra of accepted meanings. Nevertheless, this axis cannot, by the very nature of the Grid model as well as the nature of Psycho-analysis itself, follow any kind of positivistic tenets. As stated by Freud many times, Psycho-analysis is not amenable to quantifying procedures. I consider Psycho-analysis as a step furthering the advance of science beyond the limits of the ‘naive realism’ which takes data apprehended within the restricted range encompassed by human sensory apparatus, irrespective of its augmenting by artificial devices such as microscopes, telescopes, and nowadays computerized scanners or whatever it be, as if they were reality itself. As was the case in other sciences, as discussed for example by Adorno et al. (Adorno, 1967), it is a very controversial epistemological issue, to say the least, if some established tenets of the positivistic schemata, chief among them, the need to quantify and measure, (‘How can something people ‘feel’ be measured?’; Bion, 1959a, p. 2); as well as the criteria of reproducibility and falsifiability of data, masterfully depicted by authors such as Braithwaite, Carnap, Popper, Hempel (Carnap, 1950; Hempel, 1962, 1966; Popper, 1963) among others, have a place in psycho-analysis, modern physics and mathematics, after the observations of Freud, Einstein, Heisenberg, Gödel among others. I cannot dwell on this now, something that can be seen in other authors.
Both bi- and tri-dimension Grids are mere models that try to depict or analogically resemble clinical experience in order to provide training of intuition and critical thinking after the session (‘models’ and ‘criticism’, in Kant’s and Bion’s sense). They are not intended to present clinical experience; failure to realize this renders the tool incomprehensible. The realization of those models depends upon the psycho-analytical clinical practice and intuiton of the reader. As a consequence, exact quantification of the sort that characterizes some very specific areas of macroscopic, sensuously based scientific experimentation as adumbrated by Carnap and others would be misplaced here. If it can be accepted without demanding precise quantification of grades or scales in its three axes, especially the ‘intensity’ axis I am proposing, this tri-dimension Grid can prove to be a viable exercise that will compensate for its inherently cumbersome nature.
The tri-dimension Grid depicts a space that in reality does not exist, even though we humans, who possess very limited resources both in what concerns the range or reach of our sensory apparatus (for example, our eye encompasses electromagnetic wavelengths ranging only from red to violet; our ear, acoustic mechanical wavelengths ranging from 18 to 18.000 dB), as well as in our mental abilities, do think that tri-dimension space exists. It is a figment of imagination, rather than a realistic presentation of reality itself. This seems to be important when we try to psycho-analyse someone, for the unconscious has no space and is timeless. In other words, Freud perceived that Euclid’s bi-dimension schemata as well as Kant’s a priori categories, as such, were too weak to deal with mental phenomena. There are no tri-dimensions, cause/effect Cartesian reasoning in the unconscious either. In our present times, perhaps only mathematicians are able to perceive and utilize systems of n co-ordinates instead of simply three. Matrix calculus, as well as the phase-space (Hamilton, Liouville and Minkowsky) in Physics, which has six co-ordinates, is a more apt presentation of real space. It allowed for no less than the most precise and successful depiction of reality as it really is, in terms of getting most near ‘O’ as the human being was able to get until now, namely, Poincaré and Einstein’s descriptions of stellar gravitational forces and the relationship of matter and energy (Sandler, 1997b).

It is a kind of mental functioning where/when it prevails there is an excessive clinging to the paranoid-schizoid position. There are plenty of b-elements. The person thinks that he or she ‘owns’ the thing-in-itself, ultimate truth. b-elements are the stuff of definitory hypotheses which practically do not reach the status of a-elements, that is, they go straight into acting-out. Thus column 6 depicts acting-out in its purest form. For example, a patient diagnosed as schizophrenic felt that all motor car's licence plates which contained the number "24" were owned by people who said that he was a sissy. (There is a popular Brazilian numbers game; animals mean the various numbers; the number 24 is attributed to a Bambi, which also means a sissy). Therefore he violently shouted at the drivers and unscrewed the plates from the bumpers of the cars, displaying them as "proof" of his idea. Seemingly less disturbed people can interpret an analyst's countenance as "a proof" of his or her dislike of the patient. b-elements also compose line C as hallucinations which are indistinguishable in this case from dreams -- usually wish-dreams. b-elements are in their almost entirety bizarre objects, a special kind of b-elements tainted with ego and super-ego traces, or ‘seemingly intelligible b-elements’ as I proposed elsewhere (Sandler, 1997a). a-function almost does not exist, except in column 2 as well as in acting-out. This is a serious matter, for it builds up a network of lies destined to prove something the person already has in his or her mind. Rational abilities are used; the person knows the truth in order to avoid it. Or one knows the stuff of which truth is made in order to ‘tell ‘truths’ so well told, that nobody suspects they are lies’ (‘Emilia’, a character of Monteiro Lobato, a very popular Brazilian author of children’s stories). F and G in this case appertain to minus K. G is represented by a dotted line to display its virtual nature. For example, an schizophrenic patient who was a mathematician built a mathematical model to explain the origin of mankind. F and G usually have an impeccable internal coherence, in the logical sense and qualify for scientific deductive systems in y and in acting-out (columns 2 and 6). They preclude ego functions which appertain to observation of facts (one may say ‘empirical’ if one stretches the term in order to allow its semantic field to encompass infra-sensuous as well ultra sensuous stimuli). Psychiatric practice with the so-called schizophrenics furnishes many examples of this kind of F and G productions; some schizophrenics who are also mathematically trained are able to build whole mathematical systems which are false but cannot be demonstrated as such unless one examines their premises. Those are deductive systems dissociated from reality and full of reasoning – but devoid of intuition. Probably what passes for scientific production, even in academic institutions which enshrine method, appertains to this realm (Adorno et. al, 1967). Less concrete mental activities, typical of line C and outside of the realm of hallucination, are much less intense. Its coverage of the area of notation is at the service of pre-conceptions in y . The matching of pre-conceptions with realizations is utterly rare and circumscribes itself to matters of pure physical survival. The areas of attention and inquiry are useless in this kind of mental functioning. When active, they constitute themselves as a source of remarkable anxiety, due to the pain induced and inception of doubt. This doubt is usually extinguished through rationalizations in F6 and G6.
This figure is an attempt to roughly depict a professional who is able to occupy the depressive position in that fleeting transience that characterizes it. For example, in the transient moment one is able to perceive a selected fact amidst a wealth of seemingly non-coherent and scattered observations and occurrences. This may take days, weeks, months to occur; it also may occur in different moments of the session. The practising psycho-analyst therefore tries to construct (Freud, 1937) something in order to propitiate an environment that may allow for an insight by the patient. This construction has some minimally useful (or good-enough, to paraphrase Winnicott) degree of contact with an invariance present in the transformations just made by the analysand. It is considered that there is always some degree of A1, A2. That is, b-elements that to a certain extent debase the analyst’s analytic capacity, as well as a constant presence of productions of y, granted that the psycho-analytic discipline, including discipline on memory and above all on desire and understanding, maintains this kind of production outside column 6. Those are some of the effects of the analyst’s personal analysis. This ‘decisive moment’ must happen -- even rarely – some time during an analysis to confer the status of analysis upon the job done. The analyst’s a-function is ever present, even though it lowers in the extent it comes the moment to furnish the construction to the patient in a verbal form. [Please clarify the foregoing, it's meaning is not clear] For a-function is a prelude to action, and constructions, when they reach a verbal form, are actions. Column 6 encompasses both action and acting-out according to Bion. Line C is constantly present. I suppose it should not be repetitive, that is, it should not be a product of memory or imitation. Its content may be constructed in the spur of the decisive moment. Derived from free associations, or better to say, from the analyst’s free floating association constantly conjoined with his artificial blinding of himself, it composes each analyst’s own inventory of myths. It is, at least as far as my practice goes, instantly available. Nevertheless, it is not an act of conscious will. It seems to be rather out of necessity and custom tailored to that moment with that patient. This inventory of myths is formed through the analyst’s learning from experience since his infancy. Those myths are mainly for private use as fact-searching tools; sometimes they serve to communicate colloquially with the patient [should there be a period here? and then a new sentence?]  I think that there is a painful heightening of D2 that can be counterbalanced by some other heightening in 3, 4, 5. Line E maintains the very same profile of D; the lessening of intensity pays respect to the fact that not all pre-conceptions will find their realizations. Many times this is dependent upon evolving situations through time and upon the transformations occurring in the analytic pair that are amenable to creative growth. It is doubtful that G and H do exist in psycho-analysis; deductions in the rational sense, intuition-less, may be part of pure desire and acting-out.

A BEGINNER (fig. 6)
By ‘a beginner’ I mean a young professional as well as an experienced professional who experiences memory and desire during a session. There is a fairly common expression of death instincts that one should name, after Bion (1975), a ‘thus far and no further’ tendency. This is an attempt to freeze the living march into the unknown, which is ever-present but may be subjected to denial. This term applies to any professional who acts according to the following conditions, discretely or in different combinations: (a) tries to bear [not sure what you mean by your use of the word "bear" and "bear in" here, please clarify] in readings and imitations; (b) who can be erudite with respect to the written work of known authors but remains blind to the things they described; (c) who follows the ‘research of psycho-analysis’ but is not able to penetrate into the psyche it reveals, in the recommendation to the practising analyst contained in Bion’s A Memoir of the Future (1975, p. 9, 122) [how does this last phrase relate to the foregoing thought? I mean, what does Bion's recommendation have to do with the point about one who follows the research but is unable to penetrate into the psyche it reveals?] . Therefore one may see that columns 4 and 5, attention and inquiry, are almost non filled [empty?] – he who acts out under the aegis of memory and desire can dispense with attention and inquiry, for any doubt is hurriedly ‘answered’ in advance. Column six depicts acting-out and is overloaded of b-elements disguised as a-elements, with traces of ego and super-ego. They [who?] acquire a form of jargon and can be gullible [not sure you mean "gullible" here; a person is gullible; who or what is the subject here?] as ‘psycho-analytically correct’, for they have an external armour of wording drawn from what in its origin was a psycho-analytic theory. This may be regarded as the effect of anti alpha-function in the mind of the psycho-analyst (Sandler, 1997a). The pre-conceptions are violently transformed at their birth into prejudices. They remain as definitory hypotheses that constantly conjoined with lies (D1 and D2) jump to conclusions as acting-out over the patient who usually colludes with this attitude. They prevail over C-productions, that is, dreams, intuitive reverie and freedom. What passes for a-elements, as stated above, are in fact seemingly intelligible b-elements. According to Bion’s earlier observations, this corresponds to the psychotic part of the personality, or psychotic personality, using the neurotic personality (Bion, 1957). All steps appertaining to the realm of Observation are disposed with. The practising professional replaces the fact there occurring in the here and now of the session with some preferred theory, all flowing to acting-out.
AN ARTIST (fig. 7)
Perhaps the reader may gather interest and patience to make the exercise for himself, that is to translate the visual scheme into verbal thought in order to ‘read’ the visual image of an artist as obtained through the use of the tri-dimension Grid. I think that this exercise is seminal and may be made with the previous examples too. This exercise is the tri-dimension extension of my idea expressed above on trying to avoid saying "D4" and so on. It cannot be replaced by my wording, at the risk of transforming either Grids with its ‘picture-power’ into senseless concrete imagination. Perhaps this kind of workout is analogous to a dreamer’s inner workings – as well as an analyst’s task. Both have at their disposal visual images that once were verbal thoughts and re-claim their return to the verbal thought status. To be fettered by verbal formulations precludes their living experience -- perhaps for this reason many highly articulate persons, such as philosophers, cannot be wise; this also differentiates the erudite person who talks about some issue and the expert who has an actual experience of this issue (Bion, 1975, p. 9), whatever it may be. All the same, to be fettered by the ‘visual’ or the sensuously based precludes the full use in a less unconscious way (to turn the unconscious, conscious) [this last phrase needs clarification]. It also precludes to run [reformulate] the full cycle of the back-and-forth negotiation between the Paranoid-Schizoid and Depressive positions.

One may use the tri-dimension Grid for whatever diagnostic category one wants or needs. Among possible ideas, the two Grids can be drawn to depict and study groups, as for example a group gathered around a messianic leader, a flight-fight group; a maternal moment of the interaction of mother and baby, using a Grid to the baby and one to the Mother, whether she is in a moment of reverie, being able to accept the baby’s projective identifications or not; or a greedy and envious baby who cannot match his pre-conception of a breast with the real breast that is offered; or a tolerating baby who puts up with the fact that the breast (or the realization of his pre-conception which never matches completely the latter); or a political leader, the liar, the sceptical, the cynic, a person involved in catastrophic change (either trying to avoid it or putting up with it), the traitor, the ungrateful, the grateful, the learner from experience, the psychosomatic diseased, the envious, the greedy. The verbal formulations as well as the graphical representation of these ideas are not included as to do so would render this paper impossibly long. It can perhaps constitute an exercise for the interested reader to build the corresponding Grids. Moreover, and more useful, may be the alternative that each reader may choose a specific problem to address.
The visual patterns thus obtained allow for comparison (they could be drawn over transparent films to further facilitate this task). The images can be likened to ‘mental functioning architectural blueprints’ or ‘aerial photos of "personality cities"’. When I drew the first tri-dimension Grids, I had no intention to compare them but the comparison was unavoidable as soon as the drawings were ready. There appeared an underlying invariance, irrespective of the ‘nosographic entity’ each drawing represented originally. For example, one can take ‘A Psychotic moment’ and ‘A Beginner’ (figs. 4 and 6), as well as ‘A Psycho-Analyst’ and ‘An Artist’ (figs. 5 and 7). The latter group forms a less fragmentary whole and the former group of outlines has remarkably ‘isolated’ visual edifices. One may not be surprised to find that Melanie Klein’s observations on splitting are visually observable here, even at the cost of serious re-evaluations on what we are doing with our patients, or to what extent one is allowed to act-out one’s psychotic nuclei during one’s professional work. One may say that two different methods of approaching the mental apparatus – Bion’s Grid and Klein’s discourse -- came to the same point: disintegration. Not only the similarities but the dissimilarities as well should be the object of study when one compares an analyst and an artist at work. The images visible through the tri-dimension Grid allow us to spot that the mental state of an analyst is analogous, but not identical, to the mental state of an artist. Perhaps the tri-dimension Grid may overcome its status as a merely cumbersome exercise of imagination and can win the status of a legitimate exercising of an analyst’s discriminative powers and a critical scrutiny of his work, in the same league as the original bi-dimension Grid.
Let us examine some possibilities of scrutinizing a statement one finds in clinical practice in a different way from that depicted in fig. 4. We will now use the tri-dimension Grid not to examine broad diagnostic assessments, but in the same way Bion used the original Grid – with verbal statements uttered during analytic sessions. The Grids so constructed may correspond to the patient and to the analyst.
Statement 1: A mildly frightened patient reports, ‘I dreamt with an atomic bomb’.
Possibility I: The analyst thinks, ‘he is expressing his aggression and destructiveness’. He does not deal with the statement trying to link it to previous experience with the patient. Nor does he wait for more associations. This is to say, he does not deal with it as a free association. One may say that the statement does not extrapolate the status of a definitory beta-element hypothesis (A1); the Z axis displays a highest degree possible intensity. The Tri-dimension Grid thus construed shows a high concentration in A1 and a relative poverty in all other areas except A2 and A6. Interpretation in this case is hastily linked to the manifest content, the spoken version of the patient without further elaboration and transformation. In Bion’s later notation, Tp b, or in more normal verbal formulation, the final product of the transformations that the patient makes out from his initial inner stimulus, ‘Op’. The patient’s Grid, both in his bi and tri dimension versions and the analyst’s Grid are identical. The analyst takes the patient’s statement at its face value and even though it is reported as if it is a dream, it is not in fact a real dream; this is a conscious, assigned value; it does not conform to C-categories. Both analyst and analysand will rely in column 2 beliefs. Consciously constructed, deductive rational explanations will follow – G6 and H6. There will be direct, non-complex ideas on the ‘patient’s destructiveness’ beared  [beared?  what are  you trying to say with this word?] in the statement.

Possibility II: If the analyst can observe that Possibility I occurred, during his tranquil session’s recollection [by "tranquil session's recollection" do you mean something occurring outside the session or inside it?  this is not clear here] of the out-of-session reflexive exercise (be it aided by a supervisor, by his personal analysis, by the Grid or whatever it be). Perhaps he will allow his Grid to develop from the b element definitory hypothesis (A1) status of the statement ‘I dreamt with...’. He considers that the statement indicates that the patient is dreaming that he is in a session of analysis, and sets up an exploration to see the analyst’s reaction. After almost one century from the inception of the psycho-analytic movement, it is quite common to find the prejudice that one must report dreams before an analyst. Therefore in this case the statement qualifies to C1: the patient has a day dream that he is in a session of analysis and a growing intensity in column C can be drawn: a myth of a session of analysis. Both ‘dream’ and ‘atomic bomb’ are not [to?] be dealt with as if they were absolute truths, of things-in-themselves. If the analyst does this, he can propitiate a movement for the patient to do this too. Thus the Grid helps the practising analyst to gradually get hold of the psycho-analytical vertex: from the superficial approach to an interpretative approach toward hidden meanings. Let us now consider that the analyst can spontaneously be reminded – as a product of his free floating attention – of his experience with the patient. He can know, for example, that the patient usually resorts to hyperbolic augmentation of feelings; the statement may appertain to A6, C6 and D6.
Possibility III: Let us suppose now a third situation, where there is a still more ample field for the practising psycho-analyst's exercise, his ‘mental fitness training’ provided by the Grid, outside the session, when he wishes to gauge the extent of his grasp of the psycho-analytic vertex. The analyst hears the patient’s utterance ‘I dreamt with an atomic bomb’ and says to himself: ‘I do not know what this man is saying’. This propitiates not only the inception, but the building of the analyst’s Grid, as different from the patient’s Grid. Or in Bion’s later notational system, there begins Tp a out from Tp b. Putting up with a state of uncertainty, he waits and hopes that a pattern will emerge; he allows a space and a time (probabilistically) where and when more material may, with luck, appear, even if it comes from his experience with the patient. He provisionally sees (not knowing it during the session) that the statement corresponds to A1 in a high degree: a b-element. During his watchful, waiting pause, he spontaneously is reminded (his own free association emerges to his conscience [consciousness?]) that this very same patient, months ago, stated that in his opinion ‘Churchill could well be made good use of the atomic bomb, [ unclear what the patient is saying here] he would never drop it on Hiroshima...He was not a crook like that man Truman. Poor Einstein. He counselled Roosevelt to develop the bomb but he never thought that Roosevelt could die. Santos Dumont, the inventor of the aircraft, committed suicide when he saw his invention being used to make war’. The tri-dimension Grid will depict the situation, accordingly. The analyst uses it as his own B1, C1, C3 categories (his a-element definitory hypothesis, that is, he used the patient’s A1, raw sensory data, the statement, transformed it into an a-element and began not only to make a notation but to be attentive to it, reaching C4 and C5. He uses his own memory as a self-warning: I cannot hastily drop an atomic bomb – A6, hasty interpretation – here. I can wait. Then the person says that he ‘loves mushrooms’ – ‘mushrooms are the stuff of life’, ‘my grandfather used to say that babies are like mushrooms – especially Japanese babies, they procreate faster than mushrooms...grandfather loved children, he was a schoolmaster all his life’. Those statements modify radically the Possibility I. The analyst perceives that the patient is trying to work though not his aggressiveness but quite the contrary, his love and life instincts. In his unconscious transformation, ‘atomic bomb’, the ‘atomic mushroom’, has the value of babies and life. The reference to the grandfather is also linked to the fact that this man suffered a lot in the war but survived against all odds. The Grid seems to allow the analyst to perceive the initial statement’s nature as a kind of deductive scientific system made by the psycho-analytic function of the patent’s mind, for he is researching with it the nature of life itself. Thus the statement and the associations conform to D, E and F rows, encompassing all functions of the ego (columns 1-6) in a high intensity.

Five years after devising this Grid, during a research that intended to verify if there were relationships between Mathematics, Physics and Psychoanalysis and, if positive, what those relationships were (Sandler, 1997b), I came across fractals theory (Mandelbrot, 1989) and its complex numbers-generated visual images. At that time, it seemed to me that there were epistemological similarities between the detection of invariances with the help of Bion’s observations in psycho-analysis and with another tool which detects invariances, namely, fractals theory. Fractals were initially visual patterns resulting from computer treatment [of?] [out from] a complex numbers equation. The images are computer-generated and the computer functions as a transducer that creates analogies visually formulated, starting from formulations which were previously numerical. The "O" which those different formulations refer to and express is the same. The formulations, or better to say, the presentations (in Kant’s sense) vary according to some criteria that may render them more interesting to some specific groups of observers or people with different abilities to observe. Time allowed [Over time it became clear that] to conclude that fractals also had counterparts in Nature – including Biology. Perhaps the Grid, like any transducer (for example, pressure transducers that can turn acoustic stimuli into electricity – we call them ‘microphones’), is also generating visual imagery starting from psycho-analytical descriptions of mental states. It is the intersection between the mental reality’s ontogenesis as discovered by Freud and Melanie Klein with their epistemological foundations in Locke, Hume and Kant’s work (Sandler, 1997b). This intersection, that is, the description of personality traits, seems to me to be amenable to being conceptualized as a counterpart, in Psycho-Analysis, of complex numbers. The Grid can be regarded as an equivalent of Mandelbrot’s equation and its image generator computerized treatment. Those comparisons, that can be only hinted at within the scope of this paper, may be a signal which points out, in the guise of an analogy, how real are the scientific foundations of our field.
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Note: This is a modified version of a paper previously published in Portuguese as "Um desenvolvimento e aplicação clinica do instrumento de Bion, o grid." Rev. Bras. Psicanal, 33 (1999): 13-38.  It was awarded the "Durval Marcondes Prize" as the best paper given by a training analyst at the XVII Congresso Brasileiro de Psicanalise (1999).
Acknowledgements: to Dr. Arnaldo Chuster for reminding me of this proposal on the ‘Bion list’ associated with the internet website established by Dr. Silvio Merciai in connection with Bion’s Centennial; to Dr. Jorge Ahumada for his useful suggestions regarding illustrations of the clinical utility of the device; to Dr. Antonio Carlos Eva, Dr. Antonio Sapienza and Dr. Luiz Carlos Uchoa Junqueira Filho for their comments in two Scientific Meetings at the S.B.P.S.P. dedicated to these ideas; to Prof. Marc de la Ruelle for correcting the originals and putting them into vernacular English; to Drssa. Parthenope Bion Talamo for her unprejudiced and unconditional stimulus to pursue this path. Her untimely disappearance precluded the development of a joint study, doomed to be stillborn, on the possibilities of the tri-dimension Grid.
PAULO CESAR SANDLER is a Training Analyst at the Sociedade Brasileira de Psicanalise de Sao Paulo where he conducts courses and seminars on the work of Freud, Klein and Bion. He has translated many of Bion's books into Portuguese, including the first foreign version of A Memoir of the Future, as well as works by Meltzer, Milner, Winnicott and others.  His published books encompass a 10-volume series, A Apreensão da Realidade Psíquica ("The Apprehension of Psychic Reality"), a clinical study dealing with the origins of psychoanalysis and its scientific status.  He has published many papers in Brazilian journals and some in the IJPA, as well as chapters in books published in Europe, all of them dealing with clinical extensions of Bion's contributions dealing with psychotic phenomena as they appear in everyday life.  He is a member of the Editorial Board of Kleinian Studies.






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