NEWTON’S ALCHEMICAL MANUSCRIPTS

It may seem suprising to present Isaac Newton, the founder of modern mathematical natural science, as a serious student of alchemy. He himself must have felt this anomaly, since at all stages of his life he was concerned to hide his occult interests from the public. Until very recently his large collection of alchemical manuscripts was hardly looked at, much less systematically sorted or studied, in contrast to his better-understood manuscripts dealing with mechanics or the theory of matter. Yet Newton dedicated at least as much time to alchemical and theological studies as to his mathematical and physical ones.

The process of dating his manuscripts has shown that Newton worked on alchemy at all periods of his productive life, in parallel with his scientific work. This evidence proves that his occult studies were not the aberrations of senility. Newton would hardly have devoted so much time to such “absurdities” if he had not been convinced that some deeper knowledge lay hidden, which he eventually believed that he had at least in part discovered.

Newton attempted to make a synthesis of his occult-alchemical and exact-scientific research. For him a means of attaining this goal was the study of the so-called “prisca sapientia,” a tradition of ancient wisdom. Newton considered that the original wisdom of the ancients, which had been gradually lost through the ages, was most fully retained in the writings of the Hermetic tradition. He saw himself as endeavoring to explain, by means of experimental science, this “sapientia,” which had grown unintelligible.

Newton's achievements in celestial mechanics tend in popular accounts to be underestimated in some respects, exaggerated in others. This chapter seeks to correct a number of misconceptions arising from inattention to the detailed history.

KEPLER’S FIRST TWO LAWS, SO-CALLED, AND NEWTON

The claim that the planets move in elliptical orbits, with the radii vectores from Sun to planet sweeping out equal areas in equal times, first appeared in Kepler’s Astronomia Nova of 1609. Since the late eighteenth century the two parts of this claim have been referred to as Kepler’s first two planetary “laws,” understood as empirical laws. According to the popular account, Newton relied on these “laws” as thus established.

Writing to Halley on 20 June 1686, Newton stated: “Kepler knew ye Orb to be not circular but oval & guest it to be elliptical.” Whether Newton ever saw the Astronomia Nova is unknown.

The Astronomia Nova is an innovative work. It establishes important empirical results, such as the passage of the planet’s orbital plane through the Sun’s center and the orbit’s oval shape. Was the orbit’s ellipticity also a straightforwardly empirical result, say by means of triangulations of Mars, as sometimes asserted? Kepler carried out many such triangulations, but they were subject to sizeable observational error, of which he was acutely aware.

INTRODUCTION

Between 1715 and 1716 Gottfried Wilhelm Leibniz and Samuel Clarke were engaged in a theological and philosophical dispute mediated by Caroline, Princess of Wales. Ten letters were exchanged, five on each side, before the controversy was brought to an end by Leibniz's death in November 1716. During the controversy those involved agreed to publish the texts, which were edited in 1717 by Clarke, who also translated Leibniz's letters into English. His editio princeps is considered to be both fair and excellent, and contains Leibniz's original French on facing pages, as well as a useful selection of additional explanatory materials. This extraordinarily influential controversy is among the most famous and heavily studied philosophical disputative texts of all times, and, in the words of a recent interpreter, its intellectual intricacies are reserved only for the very learned or the foolhardy.

Despite the extent of interest and studies the correspondence has attracted, however, we still lack a comprehensive critical edition taking into account all the relevant texts, including Caroline’s and Clarke’s. Interestingly, eighteenth-century editions did not include the private correspondence between Caroline and Leibniz, which was first made available in the nineteenth century, notably by Onno Klopp in the most complete form. The private correspondence of the Princess ofWales was probably not available to Clarke and, even if it had been, publishing it at the time would have been highly inappropriate. That correspondence, however, provides interesting perspectives on the exchange between Leibniz and Clarke.

When one speaks of Newton's “metaphysics,”it should be noted that the word itself was rarely used by Newton; further, that in point of general philosophical usage, that word has not had in our own time a fixed and well-established acceptation. For the purposes of the present study, a rather broad view will be adopted - suggested on the one hand by Newton's most influential near predecessor, the previous author of a book called Principia Philosophiae, Descartes, according to whom metaphysics treats of the principles of [all] knowledge, and serves as the root of the “tree of philosophy” (whose “trunk” is physics, and whose “branches” are what we should call the “applied sciences”);and on the other by the author of the article “Metaphysics” in the eleventh edition of the Encyclopaedia Britannica, Thomas Case, who summarizes the concern of this discipline in the two questions: “ What is the world of things we know?How do we know it?”Thus metaphysics will here be understood to be the discussion of the most general features, both of the constitution of the world, and of the principles of human inquiry into the nature of the world.

It will be useful for our discussion to put Newton’s position in comparison with that of Descartes; for the work of the latter was both enormously influential in general – in the seventeenth century, and also, so far as metaphysics (in contrast to natural philosophy) is concerned, right down to the present day – and of great moment for Newton in particular.

To those who are unfamiliar with the history of alchemy, the image of Isaac Newton poring over manuscripts illuminated strangely with dragons, sceptered gods, and couples copulating within flasks cannot fail to educe a strikingly discordant tone. How could such a great mathematical mind, the father of modern physics, concern himself with such seemingly unintelligible gibberish? Must we simply throw up our hands at the “superstitious” Zeitgeist of the age, as Newton's nineteenth-century biographers did, and conclude that he was deluded by the work of “a fool and a knave”? Should we conclude, with more recent scholars of Newton's alchemy, that he was engaged in a fundamentally religious quest in which alchemy would provide the key by which God's immaterial activity could be linked to the phenomenal world of matter? Or is there yet another answer - that Newton's alchemical research was primarily an investigation of the microstructure of matter, the forces of chemical affinity, and the ability of material substances to undergo radical transformation in the laboratory? Needless to say, the matter is not easy to decide, given that Newton copied, abstracted, commented upon, and composed about a million words of manuscript material on the subject of alchemy, over a period spanning more than thirty years. One thing, however, is sure: in order to understand Newton's fascination with alchemy, we must not consider the enterprise from an anachronistic viewpoint that equates alchemy with the irrational, the mystical, or the anti-mechanical. If we wish to comprehend Newton's deep involvement in this subject, we must have a firm grounding in the subject of alchemy as it existed in the seventeenth century.

INITIAL ENTRIES INTO FOUNDATIONAL STUDIES

Mathematics occupied a controversial place in Cambridge in the late nineteenth-century: the Tripos was being roundly criticised as a mere set of skills, and yet it must have helped the university to gain a high reputation in applied mathematics. Alfred North Whitehead (1861–1947) started off in this branch after graduating from Trinity in 1884, being quickly elected to a college Fellowship with a dissertation on Maxwell's theory of electromagnetism. Further work drew him to the algebraic methods of the German mathematician Hermann Grassmann, which he popularised in a large book called A Treatise on Universal Algebra, with Applications (1898). The title was a misnomer, in that no one algebra was presented but instead a range of them, including also George Boole's algebra of logic.

Pure mathematics at Cambridge was rather boring, with excessive emphasis laid upon linear algebras due to Professor Arthur Cayley, and rather routine treatments of the calculus and analysis. Bertrand Russell (1872–1970) took the Mathematics Tripos from 1890 to 1893 (with Whitehead as one of his tutors), but then abandoned the subject in disgust and moved over to philosophy. He united these two trainings in an attempt to find a foundations for mathematics, starting with a Trinity Fellowship dissertation in 1895 which he revised into the book An Essay on the Foundations of Geometry (1897). His philosophical training lay in the neo-Hegelian tradition then dominant, which he exercised with skill; but the results for mathematics were not satisfactory.

In 1936, I left my home town, Vienna, for Cambridge, to seek the Great Sage. He was an Irish Catholic converted to Communism, a mineralogist who had turned to X-ray crystallography: J.D. Bernal. I asked the Great Sage: ‘How can I solve the secret of Life?’ and he replied: ‘The secret of life is in the structure of proteins, and there is only one way of solving it and that is X-ray crystallography.’ So I became an X-ray crystallographer. We called him the Sage because he knew everything from history to physics. His conversation was the most fascinating of anyone I have ever come across. Actually, what had attracted me to Cambridge was not the Sage. It was the lectures of a young organic chemist in Vienna who told me of the work being done in the biochemistry laboratory headed by Gowland Hopkins, one of the founders of biochemistry.

Hopkins had shown that all chemical reactions in living cells are speeded up by enzymes. They are catalysed, chemists say. And he showed that all enzymes are proteins. The remarkable thing in the living cell is that chemical reactions go on at room temperature, in water, at near neutral pH. When chemists make these reactions happen, they need strong solvents or high pressures, or a vacuum, or strong acids and alkalis. In the living cell they take place without any of these, because there is a special protein that speeds up each particular reaction – and speeds it up by a fantastic amount.

In the mid seventeenth century, mathematics and science were accorded no greater importance in the University of Cambridge than in other universities throughout Europe. One hundred years later the position was quite different. Though the traditional academic ‘exercises’ still took place, the ability of graduands was judged by their performance in the Senate House Examination or Mathematical ‘Tripos’. During the seventeenth century, traditions of teaching mathematical subjects, ‘natural philosopy’ (i.e., physical science), and medicine were modernised in many European countries, including Britain, but the influence of Isaac Newton (1642–1727) brought about particularly swift and far-reaching changes at Cambridge, his own university.

As Lucasian Professor of Mathematics for nearly thirty years from 1669, Newton set some of his own discoveries before his auditors (few enough) without ever proposing any general reform of education, while in private – in documents long unread and showing little desire to alter the balance between humane and mathematical or scientific studies – he increased the latter's importance. Most interesting in these drafts is the new role of a mathematically based natural philosophy, for which students were to be prepared by courses in geometry and mechanics, that is, ‘the demonstrative doctrine of motions … For without a judgement in these things a man can have none in [natural] philosophy.’ The latter subject Newton explained as the investigation of those matters which he himself had so far advanced in his Mathematical Principles of Natural Philosophy [Principia] (1687), beginning with an understanding of time, space, body, and motion, moving on to rational and fluid mechanics, astronomy and cosmology, then ending ‘if the [lecturer] have skill therein’ with knowledge of minerals, vegetables, and anatomy.

Among Cambridge undergraduates there has long been an élite who have bypassed conventional studies to follow their own paths, usually to the dismay of their tutors, and gone on to make profound contributions to the sciences. Charles Babbage was an early member of this group. When Babbage went up to Trinity in 1810 Cambridge science was in a poor state. Experimental science barely existed, while mathematics languished, hampered by loyalty to Newton's inflexible dot notation for the calculus. The scene cried out for change, but as the transformation developed it became deeply involved with the contemporary political Reform movement.

Babbage and his friends fought for the systematic development of science and its application to commerce and industry on a national scale, but theirs was not the only ideology developing at the time. Against them was the curious chivalric revival which permeated the public schools and the Establishment. It has been observed that the ruling ideas of every age are the ideas of the ruling class, and Babbage and his friends lost the battle. The consequences of this defeat remain the subject of active discussion.

Babbage was born in London, south of the river in 1791. His family came from Totnes in South Devon, bankers who, like many other such families, had formerly been goldsmiths. A precocious mathematician Babbage was already well versed in the Continental mathematical notations when he went up to Cambridge.

One discovery after another in the last few years of the nineteenth century initiated so radical a change in the nature of physical science that it has become customary to distinguish between ‘classical’ and ‘modern’ physics. It was, of course, no overnight change – most active investigators continued along the lines that had brought them success, and encouraged their students to follow their example. A few, notably Max Planck, caught a glimpse of a new world and did not much like it. As usual, it was the unfledged young who broke with tradition, like Einstein who saw clearly what Planck had hardly appreciated. The process can be seen in a brief look at the first few Cavendish Professors of Experimental Physics, beginning with James Clerk Maxwell who had died well before the critical date of 1895 when Röntgen announced the discovery of X-rays. His successor Lord Rayleigh (who stayed only five years) was already in the middle of an immensely productive research career. His versatile mind continued to find new applications of the well-tried methods until his death in 1919 at the age of seventy-six, having published seven papers in his last year. The fourth Cavendish Professor, Ernest Rutherford, arrived in Cambridge from New Zealand as a new research student in 1895 at the start of the revolution and quickly developed into the greatest experimenter of his time and the pioneer of a new branch of science, atomic and nuclear physics.

The Cambridge Physiological Laboratory was formally established in 1883 when Michael Foster (1836–1907), then Praelector in Physiology at Trinity College Cambridge, accepted Cambridge University's first Chair of Physiology. From this laboratory emerged several key scientists in the study of the nervous system, principal amongst them being Foster's colleagues J.N. Langley (1852–1925) and Walter Gaskell (1847–1914). Their pupils Charles Sherrington (1857–1952), Henry Dale (1875–1968), and E.D. Adrian (1889–1977) all won Nobel Prizes for elucidating basic mechanisms of the nervous system, each of them making major contributions to modern understanding of the functional mechanisms of the nervous system. In turn, in 1963, two of Adrian–s own pupils Alan Hodgkin (1914–1998) and Andrew Huxley (b.1917) became Nobel laureates in 1963 for their investigations of the molecular mechanisms of neural activity. Also from the Physiological Laboratory in the earlier period came A.V. Hill (1886–1977) who won the Nobel Prize in 1922 for his work on heat generation by nerve and muscle. The physiological research work that Sherrington, Dale, and Adrian undertook, and the lab from which they emerged, in which Langley, Gaskell, Adrian, and Hodgkin spent almost their entire professional careers, will form the main foci of this chapter.

MICHAEL FOSTER AND THE CAMBRIDGE PHYSIOLOGICAL LABORATORY: FEW APPOINTMENTS HAVE MORE PROFOUNDLY INFLUENCED THE FUTURE OF A UNIVERSITY OR A SUBJECT

Michael Foster trained under William Sharpey, the ‘father of British physiology’, at University College London, becoming Professor of Practical Physiology there in 1867.

The reputation of William Gilbert (1544–1603) as a great scientific mind traditionally rests on three foundations, all of which are evident in the only book he published, the seminal De Magnete [On the Loadstone] (London, 1600). First, he discovered that the Earth was a giant magnet and, in order to establish the fact, inaugurated the modern science of magnetism. Secondly, he rightly boasted that the method evident in De Magnete was experimental, a radical break with the more textual methods used by his scholastic contemporaries. Finally, he distinguished between magnetism and electricity, which had hitherto been paired as similar, occult attractive principles; he even coined the noun electricitas, which was rapidly Anglicised as ‘electricity’. Gilbert has been made a hero as ‘the first experimental scientist’, and he would come first, chronologically, in many surveys of scientific minds, not just of Cambridge minds. In Cambridge, he is immortalised in the name of Gilbert Road, a development built on land belonging to his college, St John's. As a Cambridge schoolboy, I entered my primary school every day from Gilbert Road, regrettably ignorant of the existence of the eponymous scientific hero.

Nevertheless, Gilbert's inclusion in this collection is probably the most controversial.

For much of its almost 800-year history, Cambridge University's greatest minds devoted themselves to fields other than science as we know it. As this book shows, it was not until the time of William Gilbert in the late sixteenth century, already three centuries into the University's life, that science in our sense began to characterise its life and work.

Of course, as we see here, the foundations existed, especially in the mathematical studies, which later came to underlie the whole Cambridge curriculum and provided the soil in which science was to be planted and grow. Isaac Newton in particular, who shines in the firmament of Cambridge stars, continues to inspire our mathematical and physical studies, not least in the new Institute which bears his name.

In 1664, in Newton's prime, the new Royal Society of London took as its motto ‘Nullius in verba’ (‘on the word of no man’), signifying that evidence, tangible data, and experience repeated at will were to be the marks of scientific endeavour. Merely to quote opinion or authority was in future to be valueless. And so, from then, we move into what is increasingly recognisable as the modern world of scientific inquiry, and pass to the era of Cambridge's greatest contributions to our knowledge of the world.

From then until our own day the progress of Cambridge and of the World's science studies is clear, as these chapters skilfully describe.

In Cambridge University's Cavendish Laboratory, alongside intricately impressive devices such as cloud chambers and mass spectroscopes, there is preserved an intriguing ‘wheel of life’. A regularly slotted cylinder has a sequence of pictures carefully drawn on a removable strip of paper on its inner surface. As it spins vertically, persistence of vision gives a spectator peering through the slots the impression the figures are moving. This wheel is not on show merely because it was an important step towards stroboscopes and cinematography. It is there because this version was built in 1868 by a Glasgow instrument maker for James Clerk Maxwell (1831–1879), first head of the Cavendish Laboratory and supreme Victorian physicist. Maxwell put concave lenses of focal length equal to the wheel's diameter into the slits so every visible figure would be stationary. ‘The unlearned pronounce it lively.’ He designed fascinating images: boys play leapfrog, pine trees grow, acrobats leap, and fountains change colour. But he also showed cylinders in a resisting fluid, vibrating wires, and the behaviour of those interwoven vortex rings reckoned the basic constituents of matter by many nineteenth-century natural philosophers. He discussed his wheel of life with one natural philosopher, the Glasgow professor, William Thomson, then set its theory as a puzzle for the Cambridge Mathematics Tripos in January 1869. Maxwell had first played with zoetropes, to use their grander name, as a boy on his father's Glenlair estate in southwest Scotland in the 1830s.

Charles Darwin came up to Christ's College, Cambridge, late in 1827 to read for a BA degree. His intention was to prepare for ordination into the Church of England. He eventually obtained a rather undistinguished degree, but by then he had become determined to devote himself to natural history. Cambridge thus played a key role in turning Darwin to science, and it was his Cambridge contacts who arranged for his voyage on the survey vessel HMS Beagle, the event which changed Darwin's life completely. In the years following his return to England he developed the theory of evolution by natural selection, eventually published in the Origin of Species in 1859. The resulting debates made Darwin world famous. When Cambridge awarded him an honorary degree in 1877, the undergraduates in the audience dangled the figure of a monkey from the balcony. They, at least, appreciated the lesson of the Descent of Man, Darwin's analysis of human origins published six years earlier.

Historians all agree that the Cambridge years were a vital part of Darwin's development as a scientist. Although not actually studying science, he immersed himself in extra-curricular activity devoted to natural history and geology, and by the time he went aboard the Beagle he had a fair degree of competence in both areas. But the Anglican ethos of the Cambridge scientists was also a source of tension in Darwin's later life.

The inclusion in this volume of William Whewell, the historian and philosopher of science, may require some comment. Unlike Isaac Newton, Charles Darwin, or James Clerk Maxwell, he was not a major scientific discoverer and does not feature in any list of great scientific minds. On the other hand, however, as a person who lived in Cambridge from 1812 until his death in 1866, Whewell's connection with that place was arguably more continuing and deeper than that of many others who began their scientific lives there. I shall begin with this last point and then return to Whewell's contribution to the historical and philosophical understanding of science, one that fully justifies his treatment in this book.

Born the eldest son of a Lancaster master carpenter in 1794, Whewell attended Heversham Grammar School from 1810 in order to compete for a scholarship to Trinity College. He was successful and was formally entered at Cambridge in 1811, beginning his first term in October 1812 as a sub-sizar. From this time, although he kept in contact with his family in Lancaster, he rarely returned there, preferring to stay in Cambridge with his books and his new friends. In spite of the plague in Cambridge in the spring of 1815, he told his sister that he had decided to stay, because the trip home was expensive, and ‘because I can employ my time better here’.

After winning acclaim for his monumental work on the history of Chinese science, Joseph Needham was occasionally introduced to fellow scientists who expressed appreciation for what they took to be his father–s pioneering research on chemical embryology. The two women central to his adult life – his first wife Dorothy, and his long¬time collaborator and eventual second wife Lu Gwei-Djen – used to enjoy recalling the surprise on the face of new acquaintances when they realised the biochemist and the sinologist were the same man. Like A.N. Whitehead, whose philosophical views and breadth of outlook he absorbed as a young man, Needham made the history of science his priority only after first gaining a reputation as an innovative scientific researcher. His later orientation was nevertheless solidly grounded in sensibilities he cultivated from youth.

Joseph Needham was born in London in December 1900. Looking back on his life in the 1970s, he accounted for the distinctive features of his character in terms of the influence of his parents. His tendency to embark on expansive projects he saw as reflecting the artistic temperament of his Irish songwriter mother, while his scientific propensities and broad religious interests he ascribed to his English father, a physician of Anglo-Catholic conviction and Gallophile tastes. Like George Bernard Shaw, one of his youthful culture heroes, Needham later explained his creativity, and particularly his abiding desire to build bridges between various areas of interest, as the consequence of a desire to reconcile parents whose personalities and opinions often clashed.

Alan Turing was, in a phrase, the founder of computer science. But this article will not rehearse the chronology of achievement or the claims of priority but suggest deeper questions in the motivation and culture of mathematics and its relationship to science and history. There are no definitive answers to these questions, and neither can Alan Turing be comfortably classified as a Cambridge mind; he elicited the contradictions and conflicts of that ambience.

ISOLATION AND UNIVERSALITY

Science now craves public understanding, but popularity sits ill at ease with the years of dedication to learning, challenge to received ideas, and sacrifice of advantage that science requires. Science tries to explain the universe; yet to the public (and to publishers) sits in a small specialist niche. The contradiction is even more marked in mathematics; so few, even within the sciences, can picture modern mathematical research. Recent authors have won praise for conveying the sense of struggle and devotion on the unroyal road, but have done so by omitting serious mathematical content, a musicology without knowledge of music, trying to popularise the essentially unpopular.

This creates an isolation both for mathematical culture, and for individual mathematicians. There are escape routes: one is a parochial tunnel vision, or a sort of mathematical camp, making a joke of everything. But there is a heavier burden for those who see their mathematics as the foundation stone of certainty. Turing expressed this from the beginning.