It is now fifty-six years since I wrote my first piece for Recusant History, and I am happy to have survived to welcome its reincarnation. Since its foundation in 1951 as an addendum to Gillow’s Biographical Dictionary of English Catholics it has had an honourable career, getting into print a number of essential contributions to the history of Catholics in England, mainly between the sixteenth and eighteenth centuries. It has been a companion to the distinguished bibliographical work of Anthony Allison, David Rogers and Tom Birrell. It was a creation of laymen, which is to say that it was an attempt to transcend the efforts of a period when this history had been largely a monopoly of the clergy, and ran the risk of degenerating into feuds between rival sections of that body. This lay input was much strengthened by the effect of the 1944 Education Act, which produced numbers of students keen to make a mark in the field. In view of their education, they did not necessarily alter the terms in which questions were put, and when the modest journal was launched a degree of hegemony in the Catholic Record Society was being exercised by the Jesuit side, which ought to have but failed to put out the letters and papers of Robert Persons. It had an invitation to wider thoughts in the philo-Jesuit lectures on the Counter-Reformation of the Cambridge academic Outram Evennett, delivered also in 1951.1 As these were not published until 1968 the invitation was muffled, but something of it was in the atmosphere.

The non-equilibrium behaviour of concentrated colloidal dispersions is studied by Stokesian Dynamics, a general molecular-dynamics-like technique for simulating particles suspended in a viscous fluid. The simulations are of a suspension of monodisperse Brownian hard spheres in simple shear flow as a function of the Péclet number, Pe, which measures the relative importance of shear and Brownian forces. Three clearly defined regions of behaviour are revealed. There is first a Brownian-motion-dominated regime (Pe ≤ 1) where departures from equilibrium in structure and diffusion are small, but the suspension viscosity shear thins dramatically. When the Brownian and hydrodynamic forces balance (Pe ≈ 10), the dispersion forms a new ‘phase’ with the particles aligned in ‘strings’ along the flow direction and the strings are arranged hexagonally. This flow-induced ordering persists over a range of Pe and, while the structure and diffusivity now vary considerably, the rheology remains unchanged. Finally, there is a hydrodynamically dominated regime (Pe > 200) with a dramatic change in the long-time self-diffusivity and the rheology. Here, as the Péclet number increases the suspension shear thickens owing to the formation of large clusters. The simulation results are shown to agree well with experiment.

A general method for computing the hydrodynamic interactions among an infinite suspension of particles, under the condition of vanishingly small particle Reynolds number, is presented. The method follows the procedure developed by O'Brien (1979) for constructing absolutely convergent expressions for particle interactions. For use in dynamic simulation, the convergence of these expressions is accelerated by application of the Ewald summation technique. The resulting hydrodynamic mobility and/or resistance matrices correctly include all far-field non-convergent interactions. Near-field lubrication interactions are incorporated into the resistance matrix using the technique developed by Durlofsky, Brady & Bossis (1987). The method is rigorous, accurate and computationally efficient, and forms the basis of the Stokesian-dynamics simulation method. The method is completely general and allows such diverse suspension problems as self-diffusion, sedimentation, rheology and flow in porous media to be treated within the same formulation for any microstructural arrangement of particles. The accuracy of the Stokesian-dynamics method is illustrated by comparing with the known exact results for spatially periodic suspensions.

The newly developed simulation method known as Stokesian dynamics is used to investigate the rheological behaviour of concentrated suspensions. Both the detailed microstructure (e.g. pair-distribution function) and the macroscopic properties are determined for a suspension of identical rigid spherical particles in a simple shear flow. The suspended particles interact through both hydrodynamic and non-hydrodynamic forces. For suspensions with purely hydrodynamic forces, the increase in the suspension viscosity with volume fraction ϕ is shown to be caused by particle clustering. The cluster formation results from the lubrication forces, and the simulations of a monolayer of spheres show a scaling law for the cluster size: lc ∼ [1 − (ϕ/ϕm)½]−1, where ϕm is the maximum volume fraction that can shear homogeneously. The simulation results suggest that the suspension viscosity becomes infinite at the percolation-like threshold ϕm owing to the formation of an infinite cluster. The predicted simulation viscosities are in very good agreement with experiment. A suspension with short-range repulsive interparticle forces is also studied, and is seen to have a non-Newtonian rheology. Normal-stress differences arise owing to the anisotropic local structure created by the interparticle forces. The repulsive forces also reduce particle clustering, and as a result the suspension is shear-thickening.

The title, and subject, of this piece is ‘satisfaction’, though its main locus in time is the sixteenth and seventeenth centuries. I chose the subject because it fitted in with our president’s preoccupations, and because it interested me; it turns out, to my surprise, to jog our elbow about some contemporary matters, as I guess he wished.

We had better start with the word, where there are two distinctions to be considered. The obvious one is between making up for, paying for, making amends, making reparation; and contentment, gratified desire, giving satisfaction, what you can’t get none of. I shall say that the first is the strong meaning, the second the weak one. The first is always other-directed, and entails an offence previously committed; the second is principally self-directed. ‘To content’ is a classical meaning of satisfacere, but it means to content someone else: to do something (facere), as against receiving something. A short history of the word in Latin and English records that the strong meaning emerged into late Latin as a description of church penance, and so passed into English in the fourteenth century. Its heyday was from then until the eighteenth. It referred to ecclesiastical penance (interrupted by the Reformation), the theology of the Redemption (encouraged by the Reformation), and in general public usage to the meeting of any kind of obligation, payment, atonement or compensation. From the eighteenth century it passed from public use, superseded by the weak meaning except in technical or professional fields. One professional usage, to which The Oxford English Dictionary gives a good deal of attention, is ‘to satisfy the examiners’: they think it is a case of ‘content’; may it be a case of ‘avert wrath’?

Somewhere about 1970 Gordon Leff changed his mind about William of Ockham. Earlier, in the article The fourteenth century and the decline of scholasticism’ and the survey Medieval Thought, Ockham had appeared in the conventional role of demolisher of the scholastic synthesis of reason and revelation; apologist of pure will in God and man; lock-picker of the Pandora’s box of moral and theological bugs in which the teaching of his successors consisted. Sceptic and/or fideist, he might be credited with clearing the way for natural science, and indeed for Renaissance and Reformation; but in himself he was an apostle of negation, carrying a whiff of the diabolic. Leff made public his change of heart in the massive exposition of Ockham of 1975 and the essay, The Dissolution of the Medieval Outlook, which came out the following year. Ockham was still the author of a ‘metamorphosis of scholastic discourse’ because he had excluded all but empirical knowledge of individual things and had refused to accept that rational proof could be found for more than marginal items of revealed truth. But he had, it seems, believed that ‘nature’ and ‘right reason’ were terms which might be properly used of the physical and moral worlds; random incursions of God’s potentia absoluta (what God might do) into the system of salvation constructed by his potentia ordinata (what God had actually done) were no longer to be anticipated; and Ockham was not responsible for the aberrations of some followers.

In 1945, which is beginning to seem a long time ago, Dom Gregory Dix published The Shape of the Liturgy. In the last two chapters of the book he expressed a view about the devotional and liturgical practice of the late Middle Ages which will provide a convenient starting-point for my subject. He said that the trouble about the medieval Mass was its separation of the ‘corporate offering’ assumed to have occurred in the primitive liturgy from the ‘priesthood of the priest’; the notion of worship it expressed, like the doctrine of the eucharist it exemplified, was ‘inorganic’. The effect of this was to let in, especially during the fifteenth century, non-liturgical, individualist forms of devotion which were unparticipatory and obsessed with historical facts about the life of Christ, notably with the facts of his Passion. ‘The quiet of low mass afforded the devout an excellent opportunity for using mentally the vernacular prayers which they substituted for the Latin text of the liturgy as their personal worship … The old corporate worship of the Eucharist is declining into a mere focus for the subjective devotion of each separate worshipper in the isolation of his own mind.’ Liturgical doing had subsided into inactive seeing and hearing, on the way to being engulfed in a miasma of private thinking and feeling. The Protestant reform of the liturgy amounted to pickling this pre-Reformation devotional tradition while dropping the ritual performance to which it had been loosely attached.