The scholastic analysis of money, exchange, and market value, already well underway in the thirteenth century, continued to evolve over the fourteenth century, with the commentaries on Aristotle's Ethics and Politics providing the most important loci for this discussion. In this chapter I discuss the advances made within each of the six categories of connection between scholastic economic thought and proto-scientific speculation. I remind the reader that these categories are heuristic constructs. My use of them to isolate the core insights underlying the scholastic model of economic exchange should not obscure the consistent, even necessary connections between these insights in the writings considered in this chapter. Dynamic equilibrium, relativity, the measuring continuum, and common valuation all work together within the new social geometry of the fourteenth century.

EQUALITY, THE MEAN, AND EQUALIZATION IN EXCHANGE

Through the fourteenth century, the controlling principle in economic thought remained equality. Without exception, thinkers defined economic exchange as a process of equalization. In the restricted case of the loan or mutuum, ideal equality continued to be determined in most cases arithmetically – the sum lent determined the sum that could be required in return, with no allowance for proportionality. However, in the broader realm of economic exchange that included buying (emptio) and selling (venditio), traditional requirements for arithmetical equality came under increasing challenge. Thinkers began to question the knowability and even the existence of definable points of exchange equality.

Intellectual innovations within fourteenth-century natural philosophy occupy an important place in the history of scientific thought. Over the course of the century, philosophers subjected elements of the Aristotelian model of the natural world to critical analysis, advancing claims of logic, mathematical consistency, and empirical evidence against Aristotelian authority. The selective critique of Aristotle was informed by a wealth of new questions and innovative speculations. Beneath these speculations lay a profound reconceptualization of nature.

In broad terms, the conceptual landscape that emerged in the fourteenth century resulted from a striking shift in the models derived to represent order and activity in the natural world: from a static world of numbered points and perfections to a dynamic world of ever-changing values conceived as continua in expansion and contraction; from a mathematics of arithmetical addition to a mathematics of geometrical multiplication, newly accepting of the approximate and the probable; from a world of fixed and absolute values to a shifting, relational world in which values were understood to be determined relative to changing perspectives and conditions; and from a philosophy focused on essences and perfections to one dominated by questions of quantification and measurement in respect to motion and change. Each of these new directions proved to be of great importance to the future of scientific thought.

Proto-scientific speculation in the fourteenth century developed within the rigorous intellectual culture of the university, particularly at Paris and Oxford.

Paul Adrien Maurice Dirac was one of the founders of quantum theory and the author of many of its most important subsequent developments. He is numbered alongside Newton, Maxwell, Einstein and Rutherford as one of the greatest physicists of all time. He was born in Bristol on 8 August 1902 and died on 20 October 1984 in Tallahassee, Florida. On Monday 13 November 1995, after evensong, a plaque was dedicated in Westminster Abbey commemorating Paul Dirac. The simplicity and almost austere beauty of the plaque's design reflected in some ways the qualities of Dirac's unique intellect.

After graduating from Bristol University with a first class degree in engineering, Dirac stayed on to study mathematics there before obtaining a studentship in 1923 to enable him to undertake research at St John's College, Cambridge. In 1925, he became a Fellow of St John's College. In 1932, he was elected Lucasian Professor of Mathematics in the University. The Lucasian Professorship was once held by Sir Isaac Newton, and the present holder, Stephen Hawking, was present in the Abbey to give an address at the service of commemoration and the text of this address is included in this volume.

Dirac shared the 1933 Nobel Prize for Physics with Erwin Schrödinger. After retirement from the Lucasian chair in 1969, he accepted a research professorship at the Florida State University in Tallahassee. There he continued to work on fundamental physics, frequently returning to St John's College for summer visits, until shortly before his death.

In the year 1902, the literary world witnessed the death of Zola, the birth of John Steinbeck, and the first publications of The Hound of the Baskervilles, The Immoralist, Three Sisters, and The Varieties of Religious Experience. Monet painted Waterloo Bridge, and Elgar composed Pomp and Circumstance, Caruso made his first phonograph recording and the Irish Channel was crossed for the first time by balloon. In the world of science, Heaviside postulated the Heaviside layer, Rutherford and Soddy published their transformation theory of radioactive elements, Einstein started working as a clerk in the patent office in Berne, and, on August 8, Paul Adrien Maurice Dirac was born in Bristol, one of the children of Charles Dirac (1866-1936), a native of Monthey in the Swiss canton of Valais, and Florence Holten (1878-1941), daughter of a British sea captain. There was also a brother two years older, Reginald, whose life ended in suicide, in 1924, and Beatrice, a sister four years younger. About his father Dirac has recalled:

It is a great privilege to speak to you on this occasion in which we commemorate Paul Dirac. In common with many of my friends in the audience, I enjoyed the good fortune of hearing the lectures on quantum mechanics delivered by him in Cambridge. Actually I was doubly fortunate as, in my year, 1959–60, he added a second course, extending beyond the material in his famous book.

Not only did we learn quantum mechanics as never before, but, very gently, we were shown a standard of logical presentation and clarity, indeed an aesthetic of logic, that was unforgettable. I believe I can say that this experience has affected many of us deeply and provided us with an ideal to which we struggle to aspire in our own research and teaching.

In Dirac's hands the beauty of mathematical logic and rational argument was not merely a tool for establishing sound proofs. Rather it could be a weapon of discovery that could lead to the most unexpected yet perfectly valid conclusions, which, once understood and assimilated, were unassailable in their beauty and Tightness. The importance of this is that it is the discovery of the unexpected truth that changes the direction of scientific development, in both theoretical and experimental work. Dirac repeatedly showed how implacable yet beautiful logic could achieve these ends, as the other speakers also demonstrate.

When historians and economists speak of the monetization of European society in the twelfth and thirteenth centuries, they are speaking in relative rather than absolute terms of a multi-faceted social process. Increases in the volume of coinage in circulation and the frequency of monetary transactions are only two of many factors involved. The process of monetization was inextricably tied to what has been called “the commercial revolution of the thirteenth century”: the rapid growth of trade, markets, and towns; the acceleration of agricultural and craft production; the evolution of specialized commercial enterprises and techniques; and the penetration of monetary and commercial values into all areas of social life. In this sense, the process of monetization is first apparent in the Italian cities of the late eleventh and twelfth centuries. For England and France, historians identify the “long” thirteenth century – that is, between approximately 1180 and 1320 – as the period of most rapid monetization.

The accelerated use of money had ever-expanding social, economic, and intellectual consequences. As the process of monetization gathered speed, habits of thought and perception initially restricted to those actively engaged in commerce came to be adopted by members of all segments of society. Among the most characteristic of these new habits were: the focus on monetary profit and loss in a wide range of decision making; the recognition of the importance of detailed written records for this calculation; the resulting broad development of literacy and numeracy; and the translation of qualitative values into quantitative, often monetary, terms as a way to simplify the process of calculation.

As important as Aristotle's economic ideas were to the formulations of Albert, Aquinas, and succeeding masters at Paris and Oxford, they constituted only a part of the textual inheritance on economic questions. In Aquinas' most thorough discussion of usury and just price in the Summa theologiae, Aristotelian insights from the Ethics and the Politics shared place with citations from the Bible, patristic authorities, post-patristic theological writings, Roman authors, and, importantly, Roman law and canon law. In varying degrees scholastic perceptions of money and market exchange were influenced by all these textual traditions.

In addition, scholastic economic thought was strongly influenced by its Christian setting – what its continuators took as their responsibility for the care and protection of souls. Economic determinations were tied not only to legal and ethical considerations but to the individual and his salvation. The primary question scholastic thinkers asked concerning economic activity was not “how does it work?,” but “what is permitted and what is not? what is sinful and what is not?” Economic positions were often justified on moral grounds and framed in terms of the moral duty to protect the weak and to enforce economic justice.

Religious, legal, and ethical principles defining economic liceity were in turn tied to conceptions of the “natural order” of things and to Nature itself. Scholastic authors consistently defined usury not only as unethical but as “unnatural.”

I already have gray hair but I belong to a generation which grew up in physics calculating Feynman graphs and using the CPT invariance of Quantum Field Theory. The world would look very different if we could reverse the flow of time (an operation denoted by T), inverse all directions in space (an operation denoted by P) and change all particles into their antiparticle (an operation denoted by C). Yet the laws of physics would remain the same and all phenomena would occur in the same way. Our present understanding of physics implies the existence of antimatter, and all the properties of antimatter are predictable from the known properties of matter. All this looked so powerful, so beautiful and almost so natural to us, as we were learning modern physics in the late 1950s and early 1960s. The two ways to read the same simple Feynman graph, using it to describe, for instance, either the exchange of a photon between two electrons, or electron–positron annihilation and formation through one photon, looked like an obvious part of the calculation rules. This is shown in Figure 2.1. One can read it horizontally. This is scattering. One can also read it vertically. This is annihilation and pair formation. The same term can be used to describe both processes.

Coleridge was firmly convinced that dreams have a unique language: a language primarily expressed in ‘Images and Sensations’ (CN III 4409, CM III 376). He argued that the linguistic and psychological structure of language undergoes a transformation, or translation, in dreams. This language is one that ensures that the dream has a visual and somatic stress: to dream is to allow the eyes to ‘make pictures when they are shut’ (‘A Day-dream’, PW i 385), or to have the sense of ‘such feelings’ as both delight and ‘perplex the soul’ (‘Sonnet; Composed on a Journey Homeward’, PW I 153). Not only is a dream language one of images and sensations, it is also antithetical to the language used in waking life.

Coleridge believed that the dream language has ‘various dialects’, which are ‘far less different from each other, than the various <day> Languages of Nations’ (CN III 4409). One special day language was the one that he used to describe his dreams, particularly in his notebooks. His notebook writings, often set down in haste and confusion, attempt to be an accurate record of the dream experience. They are also selective accounts and analyses of particular dream experiences. This hermeneutic day-time dream language can be seen as another manifestation of a somnial language, complete with its own syntax, vocabulary and connotations.

Coleridge's belief that dream languages comprise primarily images and sensations, and that this feature of dreams is readily validated by his own experiences as well as by the ‘Dream Books of different Countries & ages’, implies that he was thinking of some kind of universal and symbolic dream language, across many different societies and centuries.

This questioning opening to Byron's ‘The Dream’, written in 1816, succinctly touches upon many of the fundamental and often contradictory opinions on the nature of dreams and dreaming during the Romantic period. In the late eighteenth and early nineteenth centuries, there was no consensus on the origin and meaning of dreams. Some argued that they were miraculous, potentially divine events. Many believed that dreams revealed the powers of the imagination and that dreaming was a form of poetic inspiration. Others argued that they were entirely attributable to the dreamer's physical or psychological constitution. In seeking to formulate his own answers, Coleridge turned to the writings of antiquity as well as those of his contemporaries. From ancient writers he gleaned the notion that dreams have the potential for prophecy and can ‘speak like Sibyls of the future’. In the works of some of his contemporaries he encountered the theory that dreams are caused by spirits taking possession of the dreamer for short periods during sleep.

For most of his adult life, Coleridge was plagued by a ‘dreadful labyrinth of strangling, hell-pretending Dreams’ (CN iv 5375). There were also ‘<Scream-> Dreams’ (CN iv 5360), dreams which forced him to awake to a sense of ‘gouty suffocation’ (CN I 1833), and ‘Dreams of Terror’ (CN II 1998) which were accompanied by painful emotional and physical sensations (CN II 2838). He collectively referred to all such dreams as the ‘Afflictions of Sleep’ (CN iv 5360). However, the discomfort and anguish associated with nightmares did not prevent him from attempting to understand the many ways in which they could be distinguished from other species and genera of dreams.

In a letter to Poole of November 1796, Coleridge attempts to explain Charles Lloyd's illness. Lloyd had been staying as his pupil in Bristol for some weeks before the fits began:

Coleridge positions himself as an authority on the subject of ‘Somnambulism, or frightful Reverie, or Epilepsy … a kind of Night-mair’. He quickly distinguishes Lloyd's condition as not merely a ‘Night-mair’, but more specifically as a ‘kind of Nightmair’.