Principles of Animal Taxonomy By Prof. George Gaylord Simpson. (Columbia Biological Series, No. 20.) Pp. xii + 247. (New York: Columbia University Press; London: Oxford University Press, 1961.) 35s. net.

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Principles of Animal Taxonomy

Free Random Variables

The authors of this book beautifully describe the hierarchical order of emotions, how to identify specific emotions, and ultimately how to work and restructure the client's relationship to powerful and damaging maladaptive emotions. Greenberg and Paivio reviewed a large number of taped interviews of emotionally focused therapies that were successful. The clients had a wide range of complaints, including depression, anxiety, and problems of living. The authors discovered through this research three important steps in successful treatment: 1) bonding, 2) evoking and exploring emotional experiences, and 3) restructuring the emotional schema. These steps are synonymous with the working alliance; the development of the transference and its past components; and the working-through and resolution phase of classical psychoanalytic treatment.

The first part of the book sets forth the theoretical framework for emotions and the idea of core maladaptive emotion schemas. The authors discuss the role of emotion not as an irrational feeling state, but instead as an organizer of past interactive experiences, memories, hopes, fears, and dreams that are specific for each person and arise from relationships past and present. These schemas are organizers not only of emotion, but of identity and of the subjectively felt meaning of one's self. I think this is the most important piece of their work. The notion that “bad fits” organize emotions and hence organize one's identity is a major component of my clinical experience. These authors do not specifically talk of bad fits in early life, particularly preverbal life, but the concept is inherent in their work and their book. The passion of the bad fit or the emotions that are aroused by a bad fit help to organize and concretize the emotions in the identity.

The authors' experience is that if the maladaptive emotional schemas can be restructured, clients will develop a different relationship to these emotions that have plagued them. They will also develop a different sense of themselves, in terms of how they deal with emotions generated through their relationships. In this section, emotions are broken down according to their adaptive and maladaptive functions and are differentiated as primary, secondary, or instrumental emotions. This classification is useful to all therapists; we work with emotions every day but may not have realized the importance of differentiating them as to their origins, effects, and functions.

The second section deals with the types of interventions that occur in Emotional Focused Therapy (EFT.) Emphasis is placed on the specific moment-to-moment intervention of the therapist as he or she stays attuned to the slightest changes and shifts in the emotional makeup of the client. Through this attunement the therapist and client build a working alliance, and the resultant bonding accentuates a validation of the client's feelings. Emotional evocation, which is central to their EFT, relies heavily on the “empty chair dialogue.” This dialogue is Gestalt in origin and is not meant to be just a cathartic emotional experience: restructuring and validation of the new self follows.

In the third section, the authors describe in great detail the working of EFT with different emotions, and they present a clear picture of how the therapist attempts to deal with clients in this modality. They end with a brief chapter on research and supervision.

This book carries some important assumptions that need to be examined. Is it possible for the therapist to achieve such carefully fine attunement with the client as they suggest? I doubt it, and what is not talked about is the rupture in attunement and how that affects the process and transference issues in EFT. There should be a whole chapter focused on this issue alone. The whole issue of transference and countertransference is not addressed, and it is not clear how long the clients have to be in treatment for the EFT to be effective. I think it is dangerous to assume that a therapist can stay attuned to moment-to-moment changes in a person's emotional schema, since that assumption sets up an unrealistic expectation for both parties. It makes ruptures more difficult to heal because of the mutual narcissistic injuries. And is it difficult to train new therapists to do what clearly the authors do with a long-standing natural ease?

For people who are interested in cognitive and experiential work with emotions, this book is invaluable. For those with an analytic bent, the chapters on the emotional schema will only help them to formulate what they have already been doing every day in their offices; even so, such readers will find these chapters interesting and important.

Working With Emotions in Psychotherapy

Error Analysis in Mathematics Education.

We answer three related questions concerning the Haagerup subfactor and its even parts, the Haagerup fusion categories. Namely we find all simple module categories over each of the Haagerup fusion categories (in other words, we find the “quantum subgroups” in the sense of Ocneanu), we find all irreducible subfactors whose principal even part is one of the Haagerup fusion categories, and we compute the Brauer-Picard groupoid of Morita equivalences of the Haagerup fusion categories. In addition to the two even parts of the Haagerup subfactor, there is exactly one more fusion category which is Morita equivalent to each of them. This third fusion category has six simple objects and the same fusion rules as one of the even parts of the Haagerup subfactor, but has not previously appeared in the literature. We also find the full lattice of intermediate subfactors for every irreducible subfactor whose even part is one of these three fusion categories, and we discuss how our results generalize to Izumi subfactors.

Quantum Subgroups of the Haagerup Fusion Categories

We determine the cells, whose existence has been announced by Ocneanu, on
all the candidate nimrep graphs except E(12)
4 proposed by di Francesco and Zuber for the
SU(3) modular invariants classified by Gannon. This enables the Boltzmann weights to be
computed for the corresponding integrable statistical mechanical models and provide the
framework for studying corresponding braided subfactors to realize all the SU(3) modular
invariants as well as a framework for a new SU(3) planar algebra theory.

Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs

We complete the realization by braided subfactors, announced by Ocneanu, of all SU(3)-modular invariant partition functions previously classified by Gannon.

SU(3)-Goodman-De La Harpe-Jones Subfactors and the Realization of SU(3) Modular Invariants

We complete the realisation by braided subfactors, announced by Ocneanu, of all SU(3)-modular invariant partition functions previously classified by Gannon.

SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants

We determine spectral measures for some nimrep graphs arising in subfactor theory, particularly those associated with SU(3) modular invariants. Our methods also give an alternative approach to deriving the results of Banica and Bisch for ADE graphs and subgroups of SU(2) and explain the connection between their results for affine ADE graphs and the Kostant polynomials. We also look at the Hilbert generating series of associated pre-projective algebras.

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Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3)

We determine the Nakayama automorphism of the almost Calabi-Yau algebra A associated to the braided subfactors or nimrep graphs associated to each SU(3) modular invariant. We use this to determine a resolution of A as an A-A bimodule, which will yield a projective resolution of A.

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Mathew Pugh

Papers

Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs

SU(3)-Goodman-De La Harpe-Jones Subfactors and the Realization of SU(3) Modular Invariants

SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants

Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3)

The Nakayama Automorphism of the Almost Calabi-Yau Algebras Associated to SU (3) Modular Invariants