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# INVARIANT

In the first chapter of his book Transformations: Change from Learning to Growth (1965), Wilfred Bion defined the idea of the invariant and elucidated the link between transformations and the invariant. He used the metaphor of a painter, a painting, and a field of poppies to explain that the patient and the analyst have to "repaint" new realizations, starting from the primal scene, onto the canvas of the transference. In this process, a constant must be recognized for meaning to emerge. What remains unchanged between the real field of poppies and the field of poppies on the painter's canvas, that is, between the primal scene and a transferential realization, constitutes the invariant.

To develop further his ideas on the invariant, Bion turned to the notion of mathematical invariance. By way of illustration, Bion explained that the mathematical use of symbols such as ellipses, circles, dots, and lines, no matter how coherent such a use may be, must not cause us to forget that this does not involve "things in themselves," and that a change in vertex can change the data. Thus, the eye sees two parallel lines as converging at a point that, for the mathematician, does not exist. While in algebraic projective geometry, invariance makes it possible for there to be an object common to a circular object and the elliptical representation of it, this does not apply in the case of lengths, angles, and congruence, even though these data are also a part of Euclidean geometry. Why should not the same be true of psychoanalysis? What are the invariants specific to it? How are they related to one another? According to Bion, psychoanalysis involves transformations. Through interpretations, which are themselves transformations, the analyst gains access to the analysand's original experience and its realization.

In the work of interpretation, theories are like the painter's tools, and they give access to meaning only if they have invariants. These theories vary in different methods of interpretation, so that a Kleinian transformation is different from a classically Freudian one. The meaning transmitted by the theory is also different, even if the material transformed is the same in the two cases. To illustrate his thinking, Bion offered a clinical example: In a first stage, the analysis seemed to reveal a patient suffering from hypochondriacal pain, but then in the second stage, external events (a family crisis, hospitalization) disrupted the mechanism and put the treatment at risk. What had changed? What had remained unchanged, invariant? In Bion's view, the analyst must think in terms of the fate of the external and internal objects. What appeared during the second stage as external emotional objects (worried relatives, the hospital) corresponded to what remained contained, in the form of internal objects, in pains in the knee, leg, or abdomen.

What the analyst considered internal transformed into something external, but the emotional element, though disguised, had remained unchanged. Thus, the invariant provides a link that goes beyond an apparent disconnect. It ensures the continuity necessary for psychic growth and gives the interpretation its effectiveness.

Jean-Claude Guillaume

## Bibliography

Bion, Wilfred R. (1965). Transformations: Change from learning to growth. London: Heinemann.

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## invariant

invariant A property that remains TRUE across some transformation or mapping. In the context of program correctness proofs, an invariant is an assertion that is associated with some program element and remains TRUE despite execution of some part of that element. For example, a loop invariant is an assertion that is attached at some point inside a program loop, and is TRUE whenever the attachment point is reached on each iteration around the loop. Similarly a module invariant is associated with a given module, and each operation provided by the module assumes that the invariant is TRUE whenever the operation is invoked and leaves the invariant TRUE upon completion.

Note that invariants cannot accurately be described as TRUE AT ALL TIMES since individual operations may destroy and subsequently restore the invariant condition. However the invariant is always TRUE between such operations, and therefore provides a static characterization by which the element can be analyzed and understood.