Upper bounds for Kruskal's stress

In this paper the relationships between the two formulas for stress proposed by Kruskal in 1964 are studied. It is shown that stress formula one has a system of nontrivial upper bounds. It seems likely that minimization of this loss function will be liable to produce solutions for which this upper bound is small. These are regularly shaped configurations. Even though stress formula two yields less equivocal results, it seems to be expected that minimization of this loss function will tend to produce configurations in which the points are clumped. These results give no clue as to which of the two loss functions is to be preferred.This study has been supported by the Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek (Netherlands Organization for the Advancement of Pure Research), under grant 56-146.Comments by Willem Heiser and Frank Critichley have been very helpful.The second author presently is employed by the Netherlands Central Bureau of Statistics, Voorburg.     

In defence of the criticism of the Defence Mechanism Test (DMT): A reply to Kragh (1998)

Kragh ( Scandinavian Journal of Psychology , 1998, 39, 123–124) criticises a recent empirical study of the Defence Mechanism Test (DMT) conducted by the present authors (Zuber & Ekehammar, 1997) concerning methodological and other shortcomings. The present paper reviews and responds to Kragh's critical points. As to the most serious criticism, the methodological, the main conclusion is that Kragh's own published empirical studies of the DMT, and also those of other researchers, can be criticised along similar lines. Furthermore, and surprisingly, in contrast to our study, Kragh's main DMT studies do not employ the DMT picture(s) at all.     

A note on keats' generalization of the rasch model

An alternative derivation is given for a simple test model which incorporates anability parameter for the subject anddifficulty level andguessing parameters for the problem. The probability of a correct response to the problem is a projective transformation of the problem difficulty. The ability and difficulty parameters separate into additive components.     

The art of the tincture: analytical supervision

Using the alchemical metaphor, effective supervision can be seen as an excellent example of the tincture: a little goes a long way. This paper offers a model of the dynamics in analytical supervision: a mirroring of the professional-self of the supervisee, the opportunity to learn through empirical factual knowledge, and, most importantly, experiential, interactive and dynamic learning. The container of supervision will be amplified using an image of the triple vessel of alchemy. The materia of supervision is discussed as 'amalgams' of complex related material. The supervisory field is seen in a triadic intersubjective and interimaginal manner. Jung's diagram of all the possible conscious and unconscious connections between patient and therapist is expanded to include the supervisory situation. Moving beyond projective identification as explanatory process, the concept of the mundus imaginalis is used as the medium for this triadic structure. The 'analytic third' expands to include the 'supervisory fourth' while incorporating the supervisor's imaginings of the patient as the quintessential experience of the imaginal other. The supervisor's attitude and state of mind are seen through the paradigm of active imagination. This state of mind is called supervisory reverie.     

From Inexactness to Certainty: The Change in Hume's Conception of Geometry

Although Hume's analysis of geometry continues to serve as a reference point for many contemporary discussions in the philosophy of science, the fact that the first Enquiry presents a radical revision of Hume's conception of geometry in the Treatise has never been explained. The present essay closely examines Hume's early and late discussions of geometry and proposes a reconstruction of the reasons behind the change in his views on the subject. Hume's early conception of geometry as an inexact non-demonstrative science is argued to be a consequence of his attempt to discredit geometrical proofs of infinite divisibility of extension by anchoring the meaning of geometrical concepts in inherently inexact qualitative measurement procedures. This measurement-based attack on the exactness and certainty of geometry is analyzed and shown to be both self-refuting and inconsistent with the general epistemological framework of the Treatise. The revised conception of geometry as a demonstrative science in the first Enquiry is then interpreted as Hume's response to the failure of his earlier attempt to discredit geometrical proofs of infinite divisibility of extension. This revised version was published online in August 2006 with corrections to the Cover Date.     

Working with psychosis Part 4: Therapy online – ending by email

This is the fourth and concluding paper from a series about psychotherapy with a man suffering from a psychotic illness. The paper describes the ending of the therapy which was precipitated by my decision to leave the country. News of ending was extremely disturbing for my client and stirred fears that he would again break down and need re-admission to hospital. Six weeks before the ending he stopped attending but continued to stay in contact by email. I decided to reply to his emails during the session times, and we developed what he came to call his ‘email therapy’. This online technology provided a means for my client and me to separate, to find a third perspective and to begin to mourn this ending without him losing his mind and breaking down. Following James Fisher's ideas about ‘mourning in the presence of the loved object’ I understand aspects of this email ending as enabling a relinquishing of projective identification used to possess and control, a recognition of the freedom of the other and of the need to mourn omnipotence. I discuss some of the problems presented by premature ending with a vulnerable client – problems which can be seen in my difficulty of mourning and working through the ending reflected in the long time it has taken to finish writing this paper.     

The Meaningfulness of Helping Others: Loren Eiseley's “The Star Thrower”

Freud and Klein describe projective processes—projection, projective identification, and the repetition compulsion—that cause interpersonal distortions not only in the psychotherapy relationship but in adult intimate relationships as well. Winnicott's theory of the use of an object describes a way of relating that is free of the distortions of projection, opening up the possibility of differentiation between intimate partners. Two case examples illustrate how addressing projective processes assisted one patient in extricating herself from a psychologically abusive relationship and helped a couple in treatment to move from object relating to object use. It is argued that the use of these psychoanalytic theories has an important role within a modern relational social work practice.     

“A Failure of Curiosity”

ABSTRACT

This essay discusses the clinician's defense against and resolution of the experience of boredom in the countertransference as an incident of projective identification in the treatment of a woman with dissociative identity disorder. The essay details the inner mind of the therapist as she discovers both her own feelings and judgements of those feelings. As the essay progresses, she begins to grasp the significance of her discomfort in informing the therapeutic process. We watch as this material is made use of to move forward a stalled therapy into new territory.     

Ernst Cassirer's Neo-Kantian Philosophy of Geometry

One of the most important philosophical topics in the early twentieth century – and a topic that was seminal in the emergence of analytic philosophy – was the relationship between Kantian philosophy and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but instead develops a kind of logicism modeled on Richard Dedekind's foundations of arithmetic. Further, because he shared with other Neo-Kantians an appreciation of the developmental and historical nature of mathematics, Cassirer developed a philosophical account of the unity and methodology of mathematics over time. With its impressive attention to the detail of contemporary mathematics and its exploration of philosophical questions to which other philosophers paid scant attention, Cassirer's philosophy of mathematics surely deserves a place among the classic works of twentieth century philosophy of mathematics. Though focused on Cassirer's philosophy of geometry, this paper also addresses both Cassirer's general philosophical orientation and his reading of Kant.     

A new counter-example to Kelvin's conjecture on minimal surfaces

A survey of the published literature on undercooled metallic and oxide melts suggests that phase selection during solidification can be categorized as nucleation controlled or growth controlled. Common characteristics governing the phase-selection pathway have been identified for various alloy systems. It is recognized that when competing stable and metastable phases share the same crystalline characteristics and have comparable interface kinetic coefficients, the principle of nucleation control applies for primary phase formation in a deeply undercooled melt. However, there can be a difference of two or three orders of magnitude in the interface kinetic coefficients for competing phases, either between an ordered intermetallic compound and a disordered solid solution, or between a crystalline phase with a high level of complexity and a simple crystal. In such cases, the principle of growth control will apply; more specifically, the phase with the faster growth kinetics should be favoured and the competing counterpart with sluggish interface kinetics should be suppressed at high undercoolings. Some simple predictions are suggested on the basis of this principle when considering stable and metastable phase diagrams. The specific conditions under which the present categorization is applicable are outlined. Future work is required to elucidate phase competition under conditions of very rapid solidification.