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This chapter describes the properties of any system where superconducting regions are coupled together by links which transmit phase coherence as the superconducting wire. Microscopic theories for the current flowing through a weak link coupling together two superconductors are divided into two types, based on either perturbation theory or the Green's function method. The Green's function method is applied only to equilibrium situations, and it has the advantage over the perturbation theory method in that the latter is valid only when the weak link is a tunneling barrier. An alternative formula for the current through a weak link, in which the propagation of electrons through the link is described in terms of the electron Green's function instead of the tunneling Hamiltonian, has been derived by Josephson. The excess current is seen to be strongly dependent on the electromagnetic properties of the barrier.

This paper describes the events leading to the discovery of coupled superconductors, the author's move in the 1970s to a perspective where mind plays a role comparable to matter, and the remarkable hostility sometimes encountered by those who venture into unconventional areas., Invited paper for special issue of Low Temperature Physics/Fizika Nizkikh Temperatur devoted to "Quantum Coherent Effects in Superconductors and New Materials". 6pp. v5: open-access published version

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers.

It is argued that at a sufficiently deep level the conventional quantitative approach to the study of nature faces difficult problems, and that biological processes should be seen as more fundamental, in a way that can be elaborated on the basis of Peircean semiotics and Yardley’s Circular Theory. In such a world-view, Wheeler’s observer-participation and emergent law arise naturally, rather than having to be imposed artificially. This points the way to a deeper understanding of nature, where meaning has a fundamental role to play that is invisible to quantitative science.

The perception of reality by biosystems is based on different, and in certain respects more effective, principles than those utilized by the more formal procedures of science. As a result, what appears as random pattern to the scientific method can be meaningful pattern to a living organism. The existence of this complementary perception of reality makes possible in principle effective use by organisms of the direct interconnections between spatially separated objects shown to exist in the work of J. S. Bell.

The task of understanding how the brain works has met with only limited success since important design concepts are not as yet incorporated in the analysis. Relevant concepts can be uncovered by studying the powerful methodologies that have evolved in the context of computer programming, raising the question of how the concepts involved there can be realised in neural hardware. Insights can be gained in regard to such issues through the study of the role played by models and representation. These insights lead on to an appreciation of the mechanisms underlying subtle capacities such as those concerned with the use of language. A precise, essentially mathematical account of such capacities is in prospect for the future.

Current methodologies in the neurosciences have difficulty in accounting for complex phenomena such as language, which can however be quite well characterised in phenomenological terms. This paper addresses the issue of unifying the two approaches. We typically understand complicated systems in terms of a collection of models, each characterisable in principle within a formal system, it being possible to explain higher-level properties in terms of lower level ones by means of a series of inferences based on these models. We consider the nervous system to be a mechanism for implementing the demands of an appropriate collection of models, each concerned with some aspect of brain and behaviour, the observer mechanism of Baas playing an important role in matching model and behaviour in this context. The discussion expounds these ideas in detail, showing their potential utility in connection with real problems of brain and behaviour, important areas where the ideas can be applied including the development of higher levels of abstraction, and linguistic behaviour, as described in the works of Karmiloff-Smith and Jackendoff respectively.

It is hypothesised, following Conrad et al. (1988) (http://www.tcm.phy.cam.ac.uk/~bdj10/papers/urbino.html) that quantum physics is not the ultimate theory of nature, but merely a theoretical account of the phenomena manifested in nature under particular conditions. These phenomena parallel cognitive phenomena in biosystems in a number of ways and are assumed to arise from related mechanisms. Quantum and biological accounts are complementary in the sense of Bohr and quantum accounts may be incomplete. In particular, following ideas of Stapp, 'the observer' is a system that, while lying outside the descriptive capacities of quantum mechanics, creates observable phenomena such as wave function collapse through its probing activities. Better understanding of such processes may pave the way to new science., Comment: 6 pages. Invited contribution to the forthcoming issue of BioSystems in memory of Michael Conrad. Now includes links to references on the Web

It is argued that cognitive capacities can be understood as the outcome of the collective action of a set of agents created by tools that explore possible behaviours and train the agents to behave in such appropriate ways as may be discovered. The coherence of the whole system is assured by a combination of vetting the performance of new agents and dealing appropriately with any faults that the whole system may develop. This picture is shown to account for a range of cognitive capacities, including language.

It is argued that purely perceptual or generative accounts of music are inadequate to account for its specificity, and that proper accounts of music must take into account also a more fundamental level of the mind (or of consciousness), a level we term the “aesthetic subsystem”. The latter constitutes a domain of universality and of meaning that acts in conjunction with more peripheral aspects of cognition. Suggestive parallels with systems such as biosystems and lasers are used to account for a number of features of musical processes in terms of the model.

David Fisher (July p22) rejects parapsychology on the basis that it is difficult to replicate positive results in the field. However, this is insufficient reason to reject its claims.

Steven Weinberg may be right to criticize aspects of Thomas Kuhn's writings, as you report in your editorial (November 1998 p3). But Weinberg's own proposals, which he discussed in the 8 October 1998 issue of The New York Review of Books, have their problems as well. I discussed such matters further in a recent review of Roger Newton's book The Truth of Science (see Endeavour 1998 22 83), and will indicate some of the arguments here. I emphasize that I am not opposed to science as such.

In our personal lives, the fact of our consciousness – in other words, the fact that we have experiences, such as hearing sounds or seeing colours – is a central aspect of existence. In contrast, science seems to, get on very well without taking explicit note of consciousness at all. Is this because consciousness genuinely does not need be taken into account in the understanding of the natural world, or is it because current science, as a result of some selectivity in its methodology, is effectively blind to the role of consciousness? There has been a considerable growth in interest in the subject in recent years, its status having changed from that of a dubious fringe subject to one that is more or less acceptable for a scientist to work on.

In what light should a scientist regard the assertions of a religion, or of religions in general? One extreme position is the atheistic one of regarding the assertions of religion as falsehoods. Such a position can be sustained only by regarding the experiences which individuals consider as validating their religious beliefs as being explicable in other ways and, in the absence of an adequate research programme to support it, must be considered more as falling within the field of opinion that as within that of science. The alternative to this atheistic position is that there exists an aspect of reality-that one may for convenience call transcendental-which embraces the subject matter of religion (or as some may prefer to term it, the spiritual aspect of life) and which is not at present encompassed by science. The question then arises whether some future science may be able to cope with this aspect of reality, or whether it will remain forever beyond the scope of science. The author attempts to explain the ways in which current scientific orthodoxies are being challenged and to convey some idea of the alternatives presently emerging. A number of important themes here include the questions of the validity of reductionism and the universality of quantum mechanics, as well as that of the relevance of mystical experience.

The magnetic field dependence of the surface reactance of superconducting tin has been measured at a frequency of 174 MHz. In the perpendicular field configuration (RF and static fields perpendicular to each other) the behaviour observed is approximately that expected from the Ginzburg-Landau theory in the static limit. In the parallel field configuration complicated behaviour is observed, even the sign of the reactance change being different at different temperatures. Near Tc there is a region where the reactance change has approximately linear dependence on the magnitude of the applied field, instead of the quadratic dependence expected in fields that not not too large.

Human skills are acquired not by a single uniform process, but in a series of stages, as Piaget has shown. We have investigated such a sequential process by taking as an illustrative example the game of table tennis. The aims in each stage of learning are qualitatively different, and we show in detail how knowledge gained during one stage provides essential information for subsequent stages. Conclusions are drawn which may be important for artificial intelligence work generally. The question of practical implementation of a system such as discussed is considered briefly.

The rigorous inequality derived in the preceding paper, together with certain plausible assumptions about the correlations in the neighbourhood of the critical point, is shown to imply the relations sv >or= 2 - α, sv' >or= 2 - α' for the exponents describing the asymptotic from of the singularities at a critical point, where -α and -ν are the exponents for the specific heat and the correlation length respectively above Tc, the primed quantities are the corresponding exponents below Tc and s is the number of dimensions of the system concerned.

The usual derivation of Maxwell's equations for magnetic materials rests on the assumption that the sources of magnetic field within the material can be split up into a magnetization density M and a current density j. In metals the same electrons (the conduction electrons) contribute both to M and to j, and one is forced to consider the question of what one means by M and what one means by j. In this paper we answer the question for systems in equilibrium, using a thermodynamic approach. The separation of sources of magnetic field into M and j is to a large extent arbitrary, but can be done in such a way that M is uniquely related to the local magnetic field and j is zero for a normal metal in equilibrium, while in the mixed state of a superconductor it satisfies the force-balance equation $\frac{(\mathbf{j}\ifmmode\times\else\texttimes\fi{}\mathbf{B})}{c}+\mathbf{P}=0$, P being the pinning force. The stress tensor for a magnetic system is derived from first principles (not assuming the field equations), and used to obtain the force-balance equation by an alternative method. Finally, two-dimensional systems such as superconducting thin films and surface sheaths are examined by similar methods.

Superconducting systems partitioned by barriers which are thin enough to allow supercurrents to pass through them are discussed. The implications for such systems of superconducting long-range order are considered, and a phenomenological theory developed and applied to a number of topics: penetration of a magnetic field into a barrier, interference of supercurrents in the presence of a magnetic field, the cut-off frequency associated with the propagation of electromagnetic waves along a barrier, a.c. supercurrents, and structure in the d.c. current-voltage characteristics of a barrier resulting from an applied microwave field or the a.c. supercurrent. The phenomenological theory is justified by the use of microscopic theory, and a new approach, based on the Gor'kov method, is described. The results of this approach, which is of more general validity than the tunnelling Hamiltonian method, are shown to be expressible in terms of Feynman diagrams. Attention is drawn to the analogy between supercurr...

The events leading to the discovery of tunnelling supercurrents are discussed. The devopment of the theory for d.c. and for a.c. supercurrents is discussed. 24 references.

A rigorous inequality is derived relating the specific heat of a system, the temperature derivative of the expectation value of an arbitrary operator and the mean-square fluctuation of the operator in an equilibrium ensemble. The class of constraints for which the theorem is shown to hold includes most of those of practical interest, in particular the constancy of the volume, the pressure, and (where applicable) the magnetization and the applied magnetic field.

Two functions of state ξ and η are derived, such that any equation of state for the critical region consistent with the scaling hypothesis can be expressed in the form η = (ξ). The representation has the useful property that the function has no unphysical singularities (such as the branch points associated with the critical isotherm or elsewhere in the usual representations of scaling-law equations of state).

In higher states of consciousness the process of thinking is more finely adjusted to the demands of a situation than would normally be the case. We propose a mathematical model for this, based on the hypothesis that thoughts are created in part by an instability mechanism; learning establishes the instabilities, while when a situation has become familiar a compensating stability mechanism cuts out unnecessary thought. Meditation is interpreted as a process in which processes increasing stability dominate. The analysis should provide impetus for a wider examination of the value of higher states of consciousness.

A number of different approaches to the study of the brain and nervous system are reviewed, with particular reference to those of artificial intelligence, psychology and psychiatry.

Relations are derived between the superfluid density, the order parameter, and the specific heat singularity for superfluid helium near the lambda point.