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2. Experimentation and Quantification

Medieval world

At the end of the 1970s, sociologists of science and sociologically-orientated historians of science began to pay attention to experimentation. Even if their claim that experimentation had been neglected was overstated, it is true that historical literature is rich neither in works dealing with experimentation nor with systematisation.

Uncertainties persist regarding experimentation in the medieval world before it began to occupy, jointly with quantification, the centre-stage of scientific activities in the seventeenth century.

This has something to do with the course of the discussion regarding the medieval origins of normal science, stimulated by Alistair Crombie in the early 1950s. It became overshadowed by the debate on the structure of scientific revolutions, engendered by Kuhn’s seminal essay and lasting from its publication in 1962 to about the mid-1980s.1

Medieval science as such was not a concern of Kuhn’s except in the context of his interpretation of scientific revolutions as paradigm shifts. Not surprisingly, to the author of the renowned The Copernican Revolution (1957) the emergence of Copernican astronomy represented a classic case of a paradigm change. Kuhn acknowledges, we should note, the role played by ‘external’ factors in the emergence or transition to new paradigms. Regarding the replacement of Ptolemaic astronomy by Copernican astronomy, Kuhn lists among external factors: calendar reform, medieval criticism of Aristotle, the rise of Renaissance Neoplatonism ‘and other significant historical elements besides’. Nevertheless, he chooses not to address them:

In a mature science – and astronomy had become that in antiquity – external factors like those cited above are principally significant in determining the timing of breakdown, the ease with which it can be recognized, and the area in which, because it is given particular attention, the breakdown first occurs. Though immensely important, issues of that sort are out of bounds for this essay.2

By contrast, Crombie was concerned with the medieval origins of modern science which he associated with the use of experiment and mathematics. First he traced them back to the thirteenth century, if not to earlier times. But by 1961, he stated: ‘I have been responsible for claims that now seem to me exaggerated’.3

Even so, Crombie’s approach to medieval theoretical and practical engagement with the natural world is still valuable. As, for example, when he underlines the importance of the study of medieval technical texts for the understanding of the evolution of experiment:

The technological writings of the Middle Ages are still relatively unexplored, and yet it seems to me that it is there that one must chiefly look for those habits developed by the demands made by the problems themselves for accurate, repeatable results. These are of the essence in practical life where it matters if you are given short measure or the wrong product, are subjected to incompetent surgery, or arrive at an unintended destination. They are also of the essence in experimental science. For the history of science in the whole medieval and early modern period, the relations between the intellectual habits and methods of theoretical science and of practical technology present a vast field of research that has scarcely been investigated. The history of ‘practical mathematics’ in the Middle Ages would especially repay systematic study.4

Let us look at the approach of another authority in this field of historical research – Edward Grant. On the question of experiments in the Middle Ages, taken up in the book in which, as one reviewer put it, he distilled ‘a lifetime of scholarly research’, Grant has this to say:

Occasional experiments had been made, and mathematics had been routinely applied to hypothetical, though rarely real, problems in natural philosophy. In the seventeenth century, the new scientists applied mathematics to real physical problems and added experiments to the analytic and metaphysical techniques of medieval natural philosophers. The developments did not emerge from a vacuum.5

No doubt, Crombie would have had agreed. The problem is the difference in the thinking of the two historians on what constitutes the milieu or, in Grant’s words, the ‘societal environment in the Middle Ages that eventually enabled a scientific revolution to develop in the seventeenth century’. Basically, Grant equates this environment with (1) the translation of Greco-Arabic works on science and natural philosophy into Latin, (2) the formation of the medieval university and (3) the rise of the theologian-natural philosopher.6

What emerges from Grant’s account is that medieval savants set themselves suppositional problems and sought intellectual solutions to them.

Crombie impressively returned to this problematic in his massive three-volume Styles of Scientific Thinking in the European Tradition (1994), where he discusses the apparent predisposition of Western society to experimental investigation of nature in conjunction with the medieval philosophical theology of the Creator as a divine mathematician. According to this way of thinking, God created the world in which all things were ordered by measure, number and weight. God also created man in his image, endowed with senses and reason to unriddle God’s thinking. Such a belief, Crombie argues, offered the way not only to the systematic use of observation, experiment and logical argument to bring nature under control, but also to the improvement of the human condition. But Crombie contends:

The habit of systematic measurement and its instrumentation by appropriate procedures was characteristically a response not to the theoretical demands of natural philosophy but to the practical demands of the technical arts. Academic natural philosophy put a premium on logical precision and internal coherence; practical life required exact and repeatable measures of the external world as experienced and used. Technical ability to specify the conditions for producing a desired result was an essential need of theoretical science and of practical art alike; a quantified experimental science depended on a dialogue between the two. That could take place at a suitable level of education. The technical innovations which came to quantify many aspects of practical medieval life in the 12th century were being matched from early in the 12th century by an increasing attention of scholars to the practical arts, both within general encyclopedias and in more specialized treatises. Intellectual contact was encouraged at once by the improved education of superior craftsmen and by the enlargement of the technical content of the university curricula especially in the mathematical quadrivium.7

Crombie found confirmation for this viewpoint when he considered the evolution of quantification of fundamental entities during 1200-1500: time, space and weight.

Quantification of time: mechanical clock

Regarding the measure of time, it is accepted that the spread of the mechanical clock effected a radical change in Europe beginning around 1300. Its operation depended on the ingenious combination of a driving mechanism (falling weight) and a regulating mechanism (‘foliot-and-verge’ escapement).

The perception of time as a continuum was transformed by slicing it into concrete, identical small-time portions (minutae). This was due to the mechanical clock’s capability to indicate the time of the day – reckoned from one midnight to the next – split into equal 24 hours, each containing 60 minutes of 60 seconds. It should be added that the weight-driven mechanical clock was not accurate enough for measuring small intervals of time. Nevertheless, in comparison with the contemporary methods of telling day time, by the sundial and astrolabe respectively, the superiority of the mechanical clock as a timer was obvious. Of the two, the fixed sundial was simpler to handle – shadow indicated the sun’s progress through the sky. Though portable and usable by day, or night, the astrolabe was a more complicated timekeeping implement, as was the armillary sphere. They were devices for measuring the position of stars; from the obtained values, it was possible, in the thirteenth century, to calculate time reliably to 2-5 minutes.

When and who actually invented the mechanical clock is unknown – the first firm date is 1286.8 As the eminent historian of technology Donald Cardwell states:

Its design may have resulted from the speculations of some millwrights who knew about gearing and the problems of uniform motion, and who, moreover, had astonishing insight into mechanical principles.

All we can suppose is that there must have been many attempts to devise a machine to indicate the position of the sun in its daily journey round the earth, and therefore to tell the time. Certainly many of the first clocks were astronomical ones, some of them of such elaborate design that the positions of the sun, the moon, the other five planets and even the motions of the tide could be displayed.9

Undoubtedly we are on firmer ground when we inquire about social conditions that favoured the invention of this crucially novel device for measuring time. The mechanical clock was a product of the need to regulate the timing of religious and burgeoning multifarious urban (civic) activities as well as a factor in achieving this regulation. It is no accident that the clock ostentatiously came to adorn monasteries, churches and town halls.

Fig. 3 The Prague Astronomical Clock (Prague Orloj)
in Old Town Square, Prague, Czech Republic.

Especially during its early phases, clockmaking was professionally intertwined with astronomy. The ingenuity underlying the making of clocks was regarded so highly that Nicole Oresme (c. 1325-1382), the great French medieval savant, was prompted to visualise God the Creator as a clockmaker. Just as man contrived to produce a self-moving clock, so ‘did God allow the heavens to move continually according to the proportions of the motive powers to the resistances and according to the established order (of regularity)’.10 An early instance of invoking the image of God as the heavenly clockmaker!

Quantification of space: compass and cartography

In some ways, the part played by the magnetic needle compass in the history of space measurement was analogous to that of the mechanical clock in the history of time measurement. The compass is described for the first time in a Chinese text dating to about 1088, whereas in Europe the first reference occurs in Alexander Neck(h)am’s (1157-1217) De naturis rerum (c. 1200). A letter known as Epistola de magnete by Petrus Peregrinus (Pierre de Maricourt) (fl. 1269) contains a summary of the European knowledge of magnetic phenomena in the late Middle Ages. Peregrinus conceives the compass both as an astronomical and a navigational instrument.11

He describes magnetic compasses without and with a pivot and scale. They were in use in the Mediterranean, clearing the way for the drawing of the first medieval maps, known as portolani (compass-charts). Made by practical men, Crombie states,

and based on the direct determination of distances and azimuths by using log and compass, they were specifically guides to coastlines. From the earliest extant examples of the Carte Pisane (1274), the portolans showed scales of distances. By the 16th century they gave two essential pieces of information for navigation: the route to follow and the angle it must make with the north-south axis as given by a magnetized needle; and the distance to run in the direction thus determined.12

Compass-bearing in conjunction with observations of currents and winds, rather than methods of astronomical observation, guided the first Portuguese and Spanish voyages of discoveries, including Columbus’s transatlantic crossing, in the late fifteenth century.13

Against this it is pointed out that Ptolemy’s influential Geography had become well-known in Portugal and Spain before Bartholomew Diaz, Vasco da Gama and Christopher Columbus embarked on their voyages and thus played a role therein. The Latin translation of the work appeared in print for the first time in Florence in the early fifteenth century. It contained maps drawn on a gridwork of parallels and meridians located with respect to the positions of celestial bodies. Of Ptolemy’s coordinate system, Crombie notes that ‘by its emphasis on an accurate linear measure of the arc of the meridian it came to transform quantitative mapping’.14

Crombie also accepts that Ptolemy’s work played a part in the rediscovery of linear perspective. That is, Ptolemy showed how to draw a map as a projection from a single viewpoint. It is generally acknowledged that the technique of linear perspective was invented and demonstrated by Filippo Brunelleschi (1377-1446), the eminent Florentine architect, between about 1413 and 1425. Whether he was acquainted with Ptolemy’s work is unclear. Be that as it may, the latter guided multitalented men such as P. dal Pozzo Toscanelli (1397-1482), L. B. Alberti (1404-1472), L. Ghiberti (1378-1455), Nicolaus of Cusa (1401-1464) in ‘their common search for a quantified space and techniques for its measurement in astronomy, cartography, optics and painting alike’.15

Quantification of weight: statics and assaying

Historically, the quantification of weight by measurement has empirical origins going back to the invention of the balance with equal arms. This was in use in Egypt and Mesopotamia from 2700 BC. It seems to have taken about two and a half millennia before the balance with unequal arms was invented.16 Its principle was known to the author of Problems of Mechanics who, it is now accepted, was a follower of Aristotle. He was familiar with the use as well with the properties of the lever. Thus, for instance, he asks:

Why is it when two men carry a weight between them on a plank or something of the kind, they do not feel the pressure equally, unless the weight is midway between them, but the nearer carrier feels it more? Surely it is because in these circumstances the plank becomes a lever, the weight the fulcrum, and the nearer of the two carrying the weight is the object moved, and the other carrier is the mover of the weight.17

What we have here is an empirical recognition of the law of the lever as later presented by Archimedes (287-212) in a formal mathematical language. Archimedes’s status as a great researcher in pure and applied mathematics was already acknowledged in antiquity. What has remained unclear was his attitude to practice. On the one hand, the biographer Plutarch (fl. 83) refers to Archimedes’s disdain for the work of the engineer and for artisanal activities in general. On the other hand, his own inventive abilities are praised by authors such as Polybios (fl. 164 BC) and Livy (59 BC-AD 17). Apart from the device known as the Archimedean screw, he was said to have invented powerful contrivances for lifting and moving heavy loads, and the steelyard.

What cannot be disputed is that Archimedes thought deeply about methodological questions. That is, he was concerned about the truth of a theorem deduced geometrically. He believed that the truth of the proof demonstrated by geometry follows more easily from knowledge acquired previously through contemplation of a mechanical problem.18

Archimedes conceived of a mechanical problem as belonging to statics. In effect, he brought into being scientific statics and hydrostatics as a branch of mechanics with weight as its foundational category – a branch that originated empirically and was rooted in reality. This is clearly shown in the well-known, albeit apocryphal, story of Archimedes’s discovery of the hydrostatic principle named after him. It enabled him to solve the problem posed by King Hiero of Syracuse as to whether the royal crown was made of pure gold.

Archimedes’s prestige was so great that the authorship of medieval works on statics was wrongly ascribed to him. In comparison with his original text, however, a discernible shift occurred in the attitude towards practice. To the ‘science of weights’ (sciencia de ponderibus), as medieval statics was called, the theory underlying the mechanics of moving heavy objects was of interest. Thus the Toledan translator Domingo Gundissalvo (fl. 1140), drawing on Arabic authors, has this to say about the science of weights:

The science of weights considers weights in two ways: either (1) according to the weights themselves that are being measured or according to what is measured with them and by them; and this is an inquiry about the principles of the doctrine on weights. Or (2) it considers them in so far as they are moved or according to the things with which they are moved; and this is an inquiry about the principles of instruments by means of which heavy bodies are lifted and on which they are changed [or carried] from place to place.19

Evidence for the rising awareness of worldly affairs in medieval intellectual circles is provided by the unknown author of the pseudo-Archimedean treatise De insidentibus in humidum (c. 1250). He displays distinct familiarity with price-fixing in the market-place and transfers this insight to the solution of hydrostatic problems:

Since the size of certain bodies cannot be found geometrically because of their irregular shape, and since the price of certain goods is proportional to their sizes, it was necessary to find the ratio of the volumes of bodies by means of their weights in order to fix their definite prices, knowing the volume ratios from the weight ratios.20

Propelled by the silver-based economy, the quantification of weight by measurement came into its own in assaying during the Middle Ages. The purpose of assaying was particularly to test for the amount of gold and silver that could be extracted from ores and to find out whether coins and the precious metals used in jewellery were pure.21

The assayer essentially reproduced the large-scale smelting operation quantitatively on a small scale. The process involved the recovery of silver and gold, in a stream of air, from lead beads placed in a shallow dish made of bone ash (cupel). The end of the process was signalled by the appearance of a bead of the precious metal in the dish which could then be weighed. The balance’s limit of accuracy was about 0.1 milligram.

In a noteworthy characterisation of the assayers’ and the refiners’ craft, Rupert Hall observes that it was

a quantitative craft; profit arose from successful use of the balance, for margins were small. Here, as in navigation, science and craft came close together; but while the navigator was the astronomers’ pupil, the chemist descended from the assayer.22

A striking early illustration of science and craft connecting, in the context of assaying, is by provided by an edict of Philip de Valois in 1343.23 It contains two caveats, as it were, to be observed by the assayers. First, the balance is to be accurate – leaning neither to right nor left. Second, the assayers are advised to perform a blank test on a sample of the lead to be assayed. The idea was to find out whether it contained silver and, if so, how much. This is not quantitative chemical analysis, but it is a step towards it.24

It was in the late Middle Ages that experimental weighing was beginning to interest the learned as a means of acquiring natural knowledge. Among those who realised its importance and wrote about it was that audacious thinker Nicolaus of Cusa, in his Idiota: De staticis experimentis (1450). As Crombie points out, Cusa envisaged a programme and proposed experimental procedures for measuring a wide range of properties and for determining by measurement the composition of different materials. Because, according to Cusa,

By the difference of weights, I thinke wee may more truly come to the secret of things, and that many things may be known by a more probable conjecture.25

Cusa himself did not perform experiments. But the idea of comparing the weight of materials, before their starting and after their finishing, was eventually to lead to one of the great scientific generalisations by Lavoisier – the principle of conservation of matter (1789).

Fig. 4 Portrait of Nicolaus of Cusa wearing a cardinal’s hat,
in Hartmann Schedel, Nuremberg Chronicle (1493).

Fermentational and metallurgical contexts26

That Lavoisier formulated the principle of conservation of matter – weight of products equals the weight of reactants – from observing the chemical changes that underline the natural process of fermentation has been regarded as somewhat puzzling. But it should not be cause for surprise, seeing that historically a good deal of chemical knowledge evolved from the experience and problems of fermentation.

In effect, the formulation of the principle was the fruit of the interaction of experimentation, quantification and the theory of phlogiston, created by the German chemist Georg Ernst Stahl (1659-1734). Stahl’s thinking about chemical transformation owed a good deal to the examination and discussion of processes associated with the preparation of fermented drinks and the making of bread. This was certainly one of his major interests, as indicated by his first significant chemical work, Zymotechnia Fundamentalis, published in Latin in 1697 and posthumously in German in 1734.

Fig. 5 Georg Ernst Stahl. Line engraving (1715).

It is noteworthy that one of the driving forces behind the translation of this work was the high expectancy of its economic effect. In the preface the anonymous translator claims, in the spirit of mercantilism, that Germany could save millions on imports if more attention were paid to the ways in which wines, beers and spirits were produced.

There can be no doubt that the close connection between theoretical chemical knowledge and its practical use accorded well with Stahl’s views. Indeed, the actual impetus that got him developing the phlogiston theory was his interest in the process of smelting ores. Stahl elaborated a picture of the reduction process revolving around the release and transfer of a subtle material to the ore, postulated to be present in charcoal, that he came to call phlogiston. That is, he explained the reduction of ores as ‘phlogistication’ and the combustion of metals as ‘dephlogistication’.

Moreover, he envisaged that phlogiston embodied the subtle matter of combustibility that linked the vegetable, animal and mineral kingdoms. In fact, he visualised a global circulation of phlogiston. Underlying it was the conjecture that the phlogiston of the air was absorbed by plants during their growth, then taken up in the way of vegetable food by animals, and then passed back into air through breathing.

Regarding Lavoisier, what emerges clearly is the initial impetus he received from the prize-winning essay on wine fermentation and the best way of obtaining alcohol by Abbé François Rozier in 1770. This contained the suggestion that common air played a part in the souring of wine, a process that has worried man since he became involved in its preparation. It was this idea that may have provided the first clue leading to Lavoisier’s subsequent interest in the aeriform state: the physical and chemical properties of ‘elastic fluids’ or ‘airs’, including the phenomenon of heat and the composition of common air and water. Through investigations of these problems Lavoisier eventually arrived at a new conception of acidity, calcination and reduction of metals – that of combustion and respiration based on oxygen – turning on the principle of conservation of matter.

The analogy between respiration and slow combustion yielding carbonic acid and water was recognised in 1784 by Lavoisier in the quantitative work he did on a guinea pig in an ice calorimeter, conducted jointly with Pierre-Simon Laplace (1749-1827). But it was almost a decade later that this analogy, which included the generation of animal heat, was explained in the light of the transformed chemical thinking by Lavoisier in collaboration with Armand Seguin (1767-1835).

Quantification of qualities: motion, change and money

The reference to the world of commerce in a pseudo-Archimedean medieval treatise may surprise. However, during the last quarter of the twentieth century, studies appeared substantiating the thesis that medieval scholars owed more to their monetised societal setting than was previously conceded or even considered. This is brought to light when we examine the medieval approach to local motion as a problem of quantifying a quality against its socioeconomic background.

But before we return to this, it is useful to recall the strict Aristotelian separation of quality and quantity as incommensurable categories. The Aristotelian denial that qualities could be quantified was called into question, during the fourteenth century, by some of the most eminent scholastics then active in the universities of Oxford and Paris – acknowledged centres of medieval scholarship. Underlying their discussion of ‘intension and remission of forms and qualities’ was the belief that variations in degree of qualities were measurable (latitudo qualitatum).

Their work included queries into the quantifiability of divine grace but also into the quantifiability of local motion, or velocity, comprehended as continuous magnitudes. Here, as in other areas of inquiry into natural and social phenomena, medieval scholarship was confronted with Aristotelian generalisations. Regarding the speed of a body in motion, Aristotle argued that it was directly proportional to its weight (‘force’) and inversely proportional to the resistance of the medium in which it moved (‘density’). Accordingly, any force, however small, could move any resistance, however large.

Perceiving the paradox in Aristotle’s position, scholars in Oxford associated with Merton College – known as the Merton School or the Oxford Calculators – challenged it.27 Conceiving variations in velocity as variations in the intensity of a quality mathematically, they arrived at what became known as the ‘mean speed theorem’. It proposed that a uniformly accelerated velocity could be measured by its mean speed. The proposal has been hailed as ‘probably the most outstanding single medieval contribution to the history of mathematical physics’.28

Other historically notable fourteenth-century challenges to Aristotle’s approach to the motion of bodies came from Paris. Certainly Jean Buridan (c. 1300-c. 1350) was critical of Aristotle’s notion that the movement of a projectile depended on the propelling action of the air. He found Aristotle’s explanation unsatisfactory because it was contradicted by experience:

The first experience concerns the top (trocus) and the smith’s mill (i.e. wheel-mola fabri) which are moved for a long time and yet do not leave their places. Hence, it is not necessary for the air to follow along to fill up the place of departure over a top of this kind and a smith’s mill. So it cannot be said [that the top and the smith’s mill are moved by the air] in this manner.

The second experience is this: A lance having a conical posterior as sharp as its anterior would be moved after projection just as swiftly as it would be without a sharp conical posterior. But surely the air following could not push a sharp end in this way because the air would be easily divided by the sharpness.

The third experience is this: a ship drawn swiftly in the river even against the flow of the river, after the drawing has ceased, cannot be stopped quickly, but continues to move for a long time. And yet a sailor on deck does not feel any air from behind pushing him. He feels only the air from the front resisting [him]. Again, suppose the said ship were loaded with grain or wood and a man were situated to the rear of the cargo. Then if the air were of such an impetus [that it] could push the ship along so strongly, the man would be pressed very violently between that cargo and the air following it. Experience shows this to be false. Or, at least, if the ship were loaded with grain or straw, the air following and pushing would fold over (plico) the stalks which were in the rear. This is all false.29

The point of this is to bring to attention that practical activities had affected medieval scholastic thinking. Without doubt Buridan, who was Rector of the University of Paris according to documents in 1328 and again in 1340, took them on board. In the course of his studies of motions of material bodies, Buridan developed the notion of impetus. He associated it with the motive force imparted to the body by the agent that set it in motion. Viewed in retrospect, Buridan was coming to grips with the tendency of bodies in motion towards inertia which was to occupy the minds of René Descartes (1596-1650), Gottfried Wilhelm Leibniz (1646-1716) and Newton (1643-1727).30

It is noteworthy that Buridan employed impetus to discuss whether God is in need of assistance to move celestial bodies. Buridan found that God can do without it – his pervasive sway is sufficient to keep them going. Prefiguring Newton, in fact, Buridan proposed that once launched by God such bodies are on their own – possibly for eternity. However, in order to avoid accusations of advancing opinions contrary to the teachings of the Church, Buridan was at pains to stress:

But this I do not say assertively, but [rather tentatively] so that I might seek from the theological masters what they might teach me in these matters as to how these things take place.…31

It remains uncertain whether Buridan’s impetus theory influenced Nicole Oresme when he compared God to a celestial clockmaker allowing the heavens to move, like clockwork on their own.32

Oresme is celebrated more often than not for employing geometrical lines and figures to represent and quantify qualities and motions.33 His novel method is comprehensibly described in Kaye’s account as follows:

[Oresme’s] new approach, which he outlined clearly in the first part of his De configurationibus, was to construct a dual system of coordinates capable of representing at the same time the intensity of a quality and the extension of the subject in which the quality inhered. In Oresme’s scheme, the extension of a given subject in space or time was measured by a base line [longitude], and the intensities of the quality or motion in that subject were represented by perpendicular lines erected on the base line [latitude]. Greater or lesser intensities at various points in the subject were represented by proportionally longer or shorter lines erected on the base line at these points. When drawn, these measuring lines along two coordinates formed two-dimensional surfaces of varying geometrical configurations and sizes.34

Thus the configuration of a quality or motion of uniform intensity – the heights of all vertical lines being the same – had to be a rectangle. A quality or motion of uniformly varying intensity was categorised by Oresme as ‘uniformly difform’, e.g. uniformly accelerated motion. It was represented by a right triangle.

Oresme was interested not only in the geometric representation of quality and motion but also in the measurement of the quantity of the quality of motion, a quantity which he imagined to be equal to the product of intensity and extension. Moreover, he arrived at what amounted to a geometric proof of the mean speed theorem in which the areas of the rectangle (representing a uniform motion) and the right triangle (representing acceleration) are shown to be equal. The geometric demonstration of the theorem was to influence the analysis of motion for the next 250 years or so.

To view Oresme’s two-dimensional procedure as foreshadowing Cartesian analytical geometry is problematic. The simultaneous representation of the extension of a given subject in space or time and the intensity of a quality or motion was not equivalent to the axial system, named the ‘Cartesian coordinate system’. Rather, it was a device to demonstrate geometrically that ‘quantity (extension) and quality (intension) were bound together in a dynamic proportional relationship’.35

What marks Oresme off from medieval scholars concerned with proportionality was, as Grant puts it, his ‘fascination with the subject of commensurability and incommensurability in mathematics, physics and cosmology … [as] evidenced by a number of treatises in which he saw fit to discuss or at least to mention it’.36

In fact, Oresme’s intellectual interests extended beyond the natural world. Among other works, he wrote a very influential treatise on money and minting known under its abbreviated title De moneta.37 The question suggests itself as to whether Oresme’s scientific and economic thinking connect and, if so, in which context. This issue has been perceptively addressed by Kaye in his treatment of areas of historical investigation that are rarely considered together: economic history, the history of economic thought and the history of science on which much of what follows is based.38

Monetisation and market developments

Kaye’s point of departure is the development of the power and weight of the market place within European feudal society during the twelfth and thirteenth centuries. This growth had to do with the development of towns as centres of trade and handicraft production. Factors in this process, as well as products of it, were widening monetisation and heightening monetary consciousness. These connect to the subject of Oresme’s De moneta, in which the state’s policy of debasement of coinage is critically examined. The devaluation and revaluation of coins were undermining money’s role as a socially-accepted general equivalent to the value of commodities. Here was a situation, as Kaye notes, in which society experienced relativity and proportionality on a grand scale. It furnishes the social background to analysis, for instance, of Oresme’s and Buridan’s relativistic ideas about whether the earth is always at rest in the centre of the universe.

There is a good deal of evidence that the scholastic thinkers of Oxford, Paris and elsewhere were not cloistered intellectuals but engaged in academic and ecclesiastical administration, financial operations and politics. They could not avoid becoming aware of the pervasive social and economic impact of expanding merchant capital on the feudal economy and society.

Indeed, the term ‘capital’ in its Latin version capitale here enters the economic vocabulary for apparently the first time. It appears in a thirteenth-century work entitled De contractibus usurariis, composed by Peter John Olivi (Pierre de Jean Olieu), who hailed from the Provence and lived from 1248-1298. He was a member of the Franciscan order and a leader of the faction pressing for a return to the order’s original commitment to spiritual things and values. In fact, after Olivi’s death the Franciscan superiors deemed his works to be heretical and ordered their destruction.

Though Olivi opposed Franciscan participation in the economic process, he understood that it constituted a core element of social reality, one cardinally affected, as it were, by the exchange of commodities for money. Versed in Roman and canon law-thinking on lending, and familiar with lending practices in the commercial world, Olivi arrived at the notion of capitale. At its simplest, it represented the accrued value of borrowed money due to the skilful activities of the investor. Olivi speculated that the relationship between a striker or thrower of an object and the object he sets in motion corresponds to the relationship between an investor and the borrowed money he turns into capitale. It has been argued that this analogy amounted to the first formulation of the concept of impetus.39

Be that as it may, we have here medieval perceptions of economic and natural phenomena interacting which, on examination, led Kaye to conclude:

While the physical basis of reality does not change, the social basis of reality does. Over this period society was transformed through the many-faceted social processes of monetization and market development. Every level of society and every layer of institutional growth was affected. Philosophers, from their earliest days as students, were presented with social and economic experiences, rules of conduct, avenues of advancements and models of success unknown by previous generations. As social experiences change, so too do perceptions about how the world functions and is ordered.

The rigorous intellectual training of the university and its intense atmosphere of challenge and disputation transformed raw perceptions into insights capable of being elaborated through the technical instruments of mathematics and logic. The scholastic habit of synthesis encouraged the linking of insights and principles between different spheres of thought, between the comprehension of the economic order and the comprehension of the natural order. The result was the creation of a new image of nature based on the experience and observation of monetized society: a dynamic, relativistic, geometric, self-ordering, and self-equalizing world of lines. It was upon this model of nature, first imagined in the fourteenth century, that thinkers from Copernicus to Galileo constructed the ‘new’ science.40

Edward Grant’s depiction of the medieval societal environment in which knowledge of nature developed appears distinctly narrow in this light. It is insufficient to equate this environment with the translation of Greco-Arabic learning into Latin, the formation of the medieval university and the rise of the theologian/natural philosopher.

Social relations of experimentation

The historic issue is the role of the form of capital, termed merchant capital, in the first phase of the transition from feudalism to capitalism. These are Marxist conceptions advanced for the understanding of the pre-industrial phase of capitalism in Europe. That is, the phase in which the control of capital over the monetary exchange was of greater importance than its domination over the production process, constrained, as it was, by urban guilds.

This dynamic certainly emerges from David Abulafia’s incisive review of Italian banking in the late Middle Ages. But, along with other historians, Abulafia appears to be reluctant to employ the term ‘capitalism’ in the context of pre-industrial economies.41 Be that as it may, it is worth noting that the prominent non-Marxist student of the Scientific Revolution, Steven Shapin, has recourse to the concept of the transition from feudalism to capitalism in Europe between the fifteenth and seventeenth centuries. He identifies this period as one of recognisable societal change, during which mechanical modes of explaining natural phenomena were in the ascendancy. The transformation of the intellectual climate during this period was fuelled by the mounting awareness of mechanical devices in everyday life, symbolised by the clock:

The allure of the machine, and especially the mechanical clock, as a uniquely intelligible and proper metaphor for explaining natural processes not only broadly follows the contours of daily experience with such devices but also recognizes their potency and legitimacy in ordering human affairs. That is to say, if we want ultimately to understand the appeal of mechanical metaphors in the new scientific practices – and the consequent rejection of the distinction between nature and art – we shall ultimately have to understand the power relations of an early modern European society whose patterns of living, producing, and political ordering were undergoing massive changes as feudalism gave way to early capitalism.42

Thus reflecting the course of events, Leibniz acknowledges in 1671 the preference of contemporary natural philosophers for a mechanistic interpretation over the dominant organicist philosophy of Aristotle: ‘All modern philosophers desire to explain natural phenomena mechanistically’.43 Around this time the term ‘mechanical philosophy’, coined according to all accounts by Robert Boyle, entered scholarly vocabulary.

Fig. 6 Portrait of Robert Boyle by Johann Kerseboom (c. 1689).

Among the numerous publications dealing with the work and life of the ‘father of the steam-engine’, Steven Shapin and Simon Schaffer’s Leviathan and the Air-Pump has attracted wide attention. They wanted ‘to understand the nature and status of experimental practices and their historical products’ and they wanted their ‘answers to be historical in character’. To that end they write:

we will deal with the historical circumstances in which experiment as a systematic means of generating natural knowledge arose, in which experimental practices became institutionalized, and in which experimentally produced matters of fact were made into the foundations of what counted as proper scientific knowledge. We start, therefore, with that great paradigm of experimental procedure: Robert Boyle’s researches in pneumatics and his employment of the air-pump in that enterprise.44

Here the reader is reminded that the two essential and intertwined aspects of science – systematic and quantitative experimentation, on the one hand, and institutionalisation (about which later), on the other – were coming into their own in the seventeenth century.

In fact, the vacuum pump was one of the first of the complex and large machines to be developed for laboratory use (the electrical machine was the other).45 According to Shapin and Schaffer, it was the intellectual production (‘matters of fact’) by means of a purpose-built scientific machine that made Boyle’s experimentation an historical milestone. For one thing, the novel technology for the experimental investigation of air-pressure (‘spring of air’) clarified why suction pumps would not raise water more than about ten metres – an obstacle for the development of mining in the deep. For another, it gave the lie to the denial of a void in nature – an essential component of Aristotelian physics. Last but not least, from the tabulated measurements of pressures and volumes of air it emerged that their product is the same (1662). Historically, the reciprocal relationship, known as Boyle’s Law, is considered to be the first experimental physical law.

There is widespread agreement, however, that the celebrated air-pump experiments were performed by Robert Hooke (1635-1703) and not by Boyle, his employer and backer of many years. All the same, Boyle wished to make a personal point when he stated:

And though my condition does (God be praised) enable me to make experiments by others’ hands; yet I have not been so nice, as to decline dissecting dogs, wolves, fishes and even rats and mice, with my own hands. Nor, when I am in my laboratory, do I scruple with them naked to handle lute and charcoal.46

Here Boyle, the wealthy gentleman, clearly signalled that it was not socially demeaning to engage in hands-on experimentation. Moreover, he exhorted scientists

to disdain, as little as I do, to converse with tradesmen in their work houses and shops ... he deserves not the knowledge of nature, that scorns to converse even with mean persons, that have the opportunity to be conversant with her.

In general, what the natural philosophers endeavoured to comprehend in their workshops (laboratories) was matter in motion. It underlay the processes that craftsmen and artisans were empirically mastering while plying their trades in their workshops. The natural philosophers’ growing awareness of the contiguity of these activities weakened the reasoning that underwrote the traditional distinction between nature and art – it was not confined to England.

Take the sixteenth-century Czech polymath Tadeáš Hájek z Hájku (1525-1600), also known as Thaddeus Hagecius or Nemicus. He was ennobled on being appointed in 1571 to the post of Chief Medical Officer of Bohemia; moreover, because of his astrological and alchemistic interests he became an influential figure at the court of Emperor Rudolph II (1576-1612) in Prague. In 1585 he published in Frankfurt am Main a small book on brewing: De cerevisia eiusque conficiendi ratione natura viribus et facultatibus opusculum.47

What lay behind Hagecius’s interest in beer? There was the medical and pharmaceutical dimension. It appears that the suggestion to write the booklet came to Hagecius from a personal physician of Rudolph II. But beyond that, there is the growth of a large scale manorial economy in Bohemia to consider. Centred on sheep-farming, brewing and raising fish (carp), as well as on glass and iron making, this economy was directed towards augmenting the declining cash income of the lord of the manor.48 Thus the lord evolved into a large scale entrepreneur within the feudal system and, unwittingly, into an accessory to its dissolution.

The steps taken by Hagecius to become acquainted with brewing practice recalls Boyle’s advice to natural philosophers not to shy away from seeking enlightenment from socially inferior practitioners. Ignorant of brewing, Hagecius consulted with humble brewers who provided him – as he acknowledges – with information that was full, though simple and unsystematic. Poignantly, he regarded the production of beer as a legitimate field for scientific inquiry and rejected the notion that it was an undignified scholarly pursuit. Clearly, Hagecius did not perceive the worlds of intellectual and manual labour to be separated by an impervious wall.

It is in this context that it is convenient to turn to Shapin and Schaffer’s account of Thomas Hobbes’s (1588-1679) critique of Boyle’s methodology. He took issue with the notion that trustworthy natural knowledge can come by way of (air-pump) experimentation.

For Hobbes, the idea that the Boyleian pneumatic experiments, including crucial measurements of ‘the spring of air’, could establish the existence of the vacuum was defective in three related ways. To begin with, Hobbes held labouring in a laboratory to be akin to the labours of ‘workmen’, ‘apothecaries’, ‘gardeners’ and, therefore, a class-bound manual activity beneath a philosopher’s dignity. Experiment was one thing, philosophy another. By its very nature, knowledge produced by the former was inferior to that generated by the latter.

As to philosophy proper, Hobbes subscribed to plenism, a form of materialism asserting that the world of nature is a plenum made of bodies in motion, there being no room for ‘free space’, i.e. vacuum.

Finally, Hobbes was in matters of politics a fervent advocate of absolute monarchy. Shapin and Schaffer stress that ‘Hobbes’s philosophical truth was to be generated and sustained by absolutism’.49 This serves to remind us that they – unorthodoxly – seek ‘to read Leviathan as natural philosophy’.50 Unorthodoxly in the sense that the book has been perceived as a political tract, indeed, as ‘the greatest work of political philosophy ever written in English’.51

Shapin and Schaffer’s exegesis of Hobbes’s rejection of vacuism on political grounds is bold:

...the argument against vacuum was presented within a political context of use … He recommended his materialist monism because it would assist in ensuring social order. He condemned dualism and spiritualism because they had in fact been used to subvert order … For Hobbes the rejection of vacuum was the elimination of a space within which discussion could take place.52

The employment of the term ‘social order’ is not clear. Does it refer to a ‘political order’ (probably) or to a type of society (feudal, capitalist – less likely)? At all events, the cited passage and other statements hinge on Shapin and Schaffer’s introduction and usage of the term ‘space’ in a wider sense. Thus ‘experimental space’ refers to congregations in laboratories for performing/witnessing experiments. Whereas ‘philosophical space’ or ‘intellectual space’ bear upon participation in scientific debates and the meetings of groups such as the newly founded Royal Society.

Hobbes denies natural philosophers the right to such activities because they could undermine the sovereignty of absolute monarchy, in his understanding of it. As noted by Shapin and Schaffer:

Speech of a vacuum was associated with cultural resources that had been illegitimately used to subvert proper authority in the state.53

The state in question is absolute monarchy. Absolutism is said to be ‘the first international State system in the modern world’.54 Concurrent to its development, the institutional pursuit of natural knowledge (through scientific societies and journals) was evolving and transcending national boundaries. The contemporaneousness is not accidental: both realms, the political and the scientific, were products of and agents in the transition from feudalism to capitalism. The complexities of the transition over time, involving multiple factors (politics, economy, ideology, wars, etc.), do not allow here for an analysis directed towards a primary cause. But it is worth noticing that during its early phase, systematic and quantitative experimentation became an integral part of the pursuit of natural knowledge opposed by Hobbes, acquiring in the long run a degree of relative autonomy in relation to the state.

Regarding the status of experiment in scientific advancement, Boyle prevailed over Hobbes. What about the status of hypothesis which, famously, was of great concern to Newton? Can it be said that Boyle’s empiricism triumphed over Hobbes’s rationalism? That would be a simplistic choice with regards to the philosophies of both protagonists. Certainly, it does not reflect the position of the Royal Society, which from its inception (1600) until the early eighteenth century ‘was the chief European centre of experimental physics’.55 As Marie Boas Hall puts it in her close analysis of science in the Royal Society in the seventeenth century:

However much the Society as a body might hesitate to favour hypothesis, its aim was to establish something more than a collection of random experiment. Mere matter of fact was not valued for itself, but for light it could shed on the Society’s object, the establishment of a true philosophy of nature.56

1 For what is probably the earliest public presentation of the ideas developed in the essay, see T. S. Kuhn’s paper ‘The Function of Dogma in Scientific Research’, presented at the Symposium on the History of Science, University of Oxford, 9-15 July 1961. See A. C. Crombie (ed.), Scientific Change, Symposium on the History of Science, University of Oxford 9-15 July 1961 (London: Heinemann, 1963), pp. 347-69. The paper was commented on by A. Rupert Hall and Michael Polanyi, respectively (pp. 370-80). Curiously, neither Kuhn nor Hall mentioned that the latter had already employed the term ‘paradigm’ in the paper ‘The scholar and the craftsman in the scientific revolution’ (Hall uses the lower case). It was presented to a history of science conference, also attended by Kuhn (Madison, 1-11 September 1957). See M. Clagett (ed.), Critical Problems in the History of Science (Madison, WI: University of Wisconsin Press, 1959), pp. 3-29 (p. 19). Here Hall famously states that although the roles of the scholar and the craftsman in the Scientific Revolution are complementary ones, the former holds the prime place in its story (p. 21).

2 T. S. Kuhn, The Structure of Scientific Revolutions, 2nd revised ed. (Chicago, IL: University of Chicago Press, 1970), p. 69.

3 See Crombie’s ‘Contribution to Discussion of Part Three: Science and Technology in the Middle Ages’, pp. 272-91, in his (ed.), Scientific Change, pp. 316-23. For Crombie’s erstwhile statements, see his Augustine to Galileo: The History of Science A.D. 400-1650 (London: Falcon Press, 1952); Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (Oxford: Clarendon Press, 1953).

4 Crombie (ed.), Scientific Change, p. 319.

5 E. Grant, The Foundations of Modern Science in the Middle Ages (Cambridge: Cambridge University Press, 1996), p. 202.

6 Ibid., p. 171.

7 A. C. Crombie, Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation Especially in the Mathematical and Biomedical Sciences and Arts (London: Duckworth, 1994), Vol. 1, pp. 416-17. The notion of a ‘superior craftsman’ originates with Edgar Zilsel’s ‘superior artisan’. See his ‘Sociological Roots of Science’ (1942), reprinted in D. Raven et al. (eds.), Edgar Zilsel The Social Origins of Modern Science (Dordrecht, Boston, MA and London: Kluwer, 2000), pp. 7-21. The historian T. Inkster differentiates between ‘higher artisanal’ and ‘lower craftsman’ knowledge. See his ‘Thoughtful Doing and Early Modern Oeconomy’, in L. Roberts, S. Schaffer and P. Dear (eds.), The Mindful Hand Inquiry and Invention from the Late Renaissance to Early Industrialization (Amsterdam: Koninkliijke Nederlandse Akademie van Wetenschappen, 2007), p. 445.

8 By and large, scholars do not accept the claim by Joseph Needham (and his collaborators Wang Ling and D. J. de Solla Price) that the hydro-mechanical escapement of the astronomical clock described by the eminent Chinese scholar and state servant Su Sung (1088) represents an important stage in the development of the mechanical clock, with its verge-and-foliot escapement of late thirteenth-century Europe. ‘The Chinese measured time by the continuous flow of water, the Europeans, by the oscillatory movement of a verge-and-foliot. Both techniques used escapements, but these have only the name in common. The Chinese worked intermittently, the European, in discrete but continuous beats’. D. S. Landes, Revolution in Time (Cambridge, MA: Harvard University Press, 1985), p. 21.

9 D. Cardwell, The Fontana History of Technology (London: Fontana Press, 1994), p. 41.

10 Quoted in J. Kaye, Economy and Nature in the Fourteenth Century: Money, Market Exchange, and the Emergence of Scientific Thought (Cambridge: Cambridge University Press, 1998), p. 224.

11 For an English translation, see The Letter of Peregrinus, in E. Grant (ed.), A Source Book in Medieval Science (Cambridge, MA: Harvard University Press, 1974), pp. 368-76.

12 Crombie, Styles, Vol. 1, p. 420.

13 D. Goodman, ‘The Scientific Revolution in Spain and Portugal’, in R. Porter and M. Teich (eds.), The Scientific Revolution in National Context (Cambridge: Cambridge University Press, 1992), p. 166.

14 Crombie, Styles, Vol. 1, p. 433.

15 Ibid., p. 455. For a valuable contribution on the relationship between mathematics and painting in the late Middle Ages, see J. V. Field ‘Mathematics and the Craft of Painting: Piero della Francesca and Perspective’, in his and Frank A. J. L. James (eds. and intr.), Renaissance and Revolution: Humanists, Scholars, Craftsmen and Natural Philosophers in Early Modern Europe (Cambridge: Cambridge University Press, 1993), pp. 73-95. Field underlines the Euclidian rather than the Ptolemaic impulse. English seamen in the sixteenth century began to employ astronomical observations and mathematical calculations in navigation instead of relying largely on practical experience. See S. Rose, ‘Mathematics and the Art of Navigation: The Advance of Scientific Seamanship in Elizabethan England’, Transactions of the Royal Historical Society, 14 (2004), 175-84.

16 Here, and in what follows, I draw on P. Damerow, J. Renn, S. Rieger and P. Weinig, Mechanical Knowledge and Pompeian Balances, Preprint 145 (Berlin: Max-Planck-Institut für Wissenschaftsgeschichte, 2000). See also G. E. R. Lloyd, Greek Science after Aristotle (London: Chatto and Windus, 1973), p. 48.

17 See Grant (ed.), Source Book, pp. 223-24, n. 22.

18 Archimedes’s thoughts on this are enshrined in The Method, an incomplete treatise. They are addressed to Eratosthenes, renowned for his remarkable method of calculating the circumference of the earth. See the translation in T. L. Heath, The Works of Archimedes (Cambridge: Cambridge University Press, 1912). Professor Lloyd has commented to me: ‘I don’t think you have got mechanics in Archimedes quite right. It is not that he tried a mechanical problem first and then turned to a geometrical analysis. The problem is mathematical from the outset. The use of mechanics is limited to the application of the two ideas that a geometrical figure can be thought of as balanced around a fulcrum’.

19 See Grant (ed.), Source Book, pp. 75-6.

20 Quoted by O. Pedersen and M. Pihl, Early Physics and Astronomy: A Historical Introduction (London: Macdonald and Jane’s and New York: American Elsevier Inc., 1974), p. 210.

21 It is of interest that the words ‘test’ and ‘testing’ relate to the Latin ‘testa’, meaning an earthenware pot or vessel employed in metallurgical operations.

22 A. Rupert Hall, ‘Early Modern Technology to 1600’, in M. Kranzberg and C. W. Pursell, Jr. (eds.), Technology in Western Civilization, Vol. 1 (New York: Oxford University Press, 1967), p. 94.

23 Here I draw heavily on F. Greenaway’s ‘Contribution to the Discussion of Part Three: Science and Technology in the Middle Ages’, in Crombie (ed.), Scientific Change, pp. 329-31.

24 A. J. Ihde, The Development of Modern Chemistry (New York: Evanston; London: Harper and Row, 1964), p. 23.

25 Crombie, Styles, Vol. 1, pp. 421-22.

26 See M. Teich, ‘Circulation, Transformation, Conservation of Matter and the Balancing of the Biological World in the Eighteenth Century’, Ambix, 29 (1982), 17-28.

27 The Merton School included Thomas Bradwardine (c. 1290-1349), John Dumbleton (died c. 1349), William Heytesbury (fl. 1235), Richard Swineshead (fl. 1340-1355).

28 Grant, Foundations, p. 101.

29 J. Buridan, The Impetus Theory of Projectile Motion. Transl., intr., and annotated by Marshall Clagett, in Grant (ed.), Source Book, pp. 275-76.

30 According to Buridan, ‘by the amount the motor moves that moving body more swiftly, by the same amount it will impress in it a stronger impetus’. Ibid., p. 277. This measure of impetus, as has been often observed, recalls Newton’s momentum as defined by the product of mass multiplied by velocity.

31 Ibid., pp. 277-78.

32 See Crombie, Augustine to Galileo, p. 255.

33 See N. Oresme, The Configurations of Qualities and Motions, including a Geometric Proof of the Mean Speed Theorem. Transl., intr., and annotated by Marshall Clagett, in Grant (ed.), Source Book, pp. 243-52.

34 Kaye, Economy and Nature, p. 204.

35 Ibid., p. 206.

36 Grant (ed.), Source Book, p. 529.

37 The work’s title is given as Tractatus de origine et natura, iure, et mutationibus monetarum and is said to have been written sometime between 1355-1360. See Charles Johnson (ed. and transl.), The “De moneta” of Nicholas Oresme and English Mint Documents (London: T. Nelson, 1956).

38 Kaye, Economy and Nature, pp. 9-10. For a related study, see A. W. Crosby, The Measure of Reality: Quantification and Western Society, 1250-1600 (Cambridge: Cambridge University Press, 1998).

39 Here I draw on M. Wolff’s stimulating Geschichte der Impetustheorie (Frankfurt am Main: Suhrkamp, 1978), pp. 163f.; see also idem, ‘Mehrwert und Impetus bei Petrus Johannis Olivi’, in J. Miethke and K. Schreiner (eds.), Sozialer Wandel im Mittelalter (Sigmaringen: Thorbecke, 1994), pp. 413-23. For a biological Aristotelian approach to impetus theory, see J. Fritsche, ‘The Biological Precedents for Medieval Impetus Theory and its Aristotelian Character’, The British Journal for the History of Science, 44 (2011), 1-27. For further information, see R. W. Hadden, On the Shoulders of Merchants Exchange and the Mathematical Conception of Nature in Early Modern Europe (Albany, N.Y.: State University of New York Press, 1994), p. 100.

40 Kaye, Economy and Nature, pp. 245-46. See also J. Day, ‘Shorter Notices’, The English Historical Review, Vol. 109/432 (1994), 701.

41 D. Abulafia, ‘The Impact of Italian Banking in the Late Middle Ages and the Renaissance, 1300-1500’, in A. Teichova, G. Kurgan-van Hentenryk and D. Ziegler (eds.), Banking, Trade and Industry: Europe, America and Asia from the Thirteenth to the Twentieth Century (Cambridge: Cambridge University Press, 1997), pp. 18, 31.

42 S. Shapin, The Scientific Revolution (Chicago, IL and London: University of Chicago Press, 1998), p. 33.

43 ‘Desiderant omnes philosophi recentiores physica mechanice explicari’. Quoted by H. Mayer, ‘Gott und Mechanik Anmerkung zur Geschichte des Naturbegriffs im 17. Jahrhundert’, in S. Mattl and others, Barocke Natur (Korneuburg: Ueberreuter, 1989), p. 12.

44 S. Shapin and S. Schaffer, Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life (Princeton, NJ: Princeton University Press, 1985), p. 1. Note: ‘The father of the steam engine would be a better title for Robert Boyle than the “father of chemistry”’. A. Rupert Hall, The Revolution in Science, 1500-1750 (London and New York: Longman, 1983), p. 338.

45 S. A. Bedini and D. J. da Solla Price, ‘Instrumentation’, in Kranzberg and Pursell, Jr. (eds.), Technology, Vol. 1, p. 178.

46 This and the following quotation are from J. G. Crowther, The Social Relations of Science (New York: The Macmillan Company, 1942), pp. 364-65.

47 Hagecius has a place in the history of astronomy. First, his findings related to the discovery of a new star in the Cassiopeia constellation (1572). He established that the star must be further from the Earth than the moon and must therefore be a fixed star. This disclosure contributed to the supplanting of the Aristotelian doctrine of two disjointed regions, sublunary and supralunary. He took a similar line in his writing on the comet that appeared in 1577. Moreover, he was behind Rudolph II’s invitation to Tycho Brahe (1546-1601) to move to Prague. The life and work of Hagecius is examined by eighteen authors in the collection edited by P. Drábek, Tadeáš Hájek z Hájku (Prague: Společnost pro dějiny věd a techniky, 2000). The stock of factual knowledge about Hagecius’s life is critically scrutinised by J. Smolka, ‘Thaddaeus Hagecius ab Hayck, Aulae Caesarae Majestatis Medicus’, in Gertrude Enderle-Burcel, E. Kubů, J. Šouša and D. Stiefel (eds.), “Discourses – Diskurse” Essays for – Beiträge zu Mikuláš Teich & Alice Teichova (Prague and Vienna: Nová tiskárna Pelhřimov, 2008), pp. 395-412. For a brief introduction in English to the period, including Hagecius’s significance, see J. Smolka, ‘The Scientific Revolution in Bohemia’, in Porter and Teich (eds.), Scientific Revolution, pp. 210-39. For an English response to the discovery of a new star in Cassiopeia, see S. Pumfrey, ‘“Your Astronomers and Ours Differ Exceedingly”: The Controversy over the “New Star” of 1572 in the Light of a Newly Discovered Text by Thomas Digges’, The British Journal for the History of Science, 44 (2011), 29-60.

48 The elements of this economy are echoed in a well-known contemporary German saying: ‘Schäfereien, Brauereien und Teich, machen die böhmischen Herren reich’.

49 Shapin and Schaffer, Leviathan, p. 339.

50 Ibid., p. 92.

51 Cf. promotional description of Hobbes and Republican Liberty (Cambridge: Cambridge University Press, 2008), authored by Quentin Skinner.

52 Shapin and Schaffer, Leviathan, pp. 99, 109.

53 Ibid., p. 91. Here, perhaps, it is appropriate to refer to the attention Quentin Skinner pays to Hobbes’s description of liberty in Leviathan ‘according to the proper signification of the word’: ‘As soon as we leave the world of nature, however, and enter the artificial world of the commonwealth, we are no longer simply bodies in motion; we are also subjects of sovereign power’. Skinner, Hobbes, pp. 162-63. Shapin and Schaffer’s book is not listed among Skinner’s ‘Printed secondary sources’.

54 P. Anderson, Lineages of the Absolute State (London: New Left Books, 1974), p. 11.

55 Rupert Hall, Revolution, p. 260.

56 M. Boas Hall, ‘Science in the Early Royal Society’, in M. Crosland (ed.), The Emergence of Science in Western Europe (London and Basingstoke: Macmillan, 1975), pp. 61-2.