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The last quarter of Newton's life was distinguished from the first three-quarters by the profusion of his written work that was published by himself or by others for him. As always with Newton, none of this publication was fundamentally new: his intellectual effort was devoted to making more perfect what had been published before (as with the Principia and Opticks), to bringing to light from his files writings and correspondence of long ago (as with Commercium Epistolicum), or to polishing for the benefit of posterity the results of studies that he had pursued for decades (as with The Chronology of Ancient Kingdoms Amended and The Prophecies of Daniel and John). In making this point I do not mean quite to assert that, had Newton died in 1705, it would have been possible to reconstruct from his papers all that was subsequently published under his name. Only of the posthumous System of the World would this be exactly true. On most of the late books Newton was always at work, modifying, adding new material from experiments and reading, extending and revising.
Of the Queries appended to the successive editions of Opticks this is particularly true. The main text of this book was not greatly changed when it was republished in Latin in 1706, nor indeed in the subsequent English editions. The Queries, however, developed into the most important series of statements that Newton released to the public about the deepest questions of natural philosophy: the concepts of matter and force, the possible role of an aether and the relation of God to the universe.
On the first of March, 1704, David Gregory noted in his diary that Newton had been ‘provoked by Dr Cheyns book to publish his Quadratures, and with it, his Light & Colours, &c.’ And just one month later Newton indeed signed and dated his “Advertisement” to this volume. Some sixteen months had passed since he had promised ‘Mr [Francis] Robarts, Mr Fatio, Capt. Hally & me to publish his Quadratures, his Treatise of Light, and his treatise of the curves of the 2d Genre [sic]’. In the interval Robert Hooke had died, thus clearing the way for the publication of Opticks,a book which Newton had sworn to keep to himself so long as Hooke lived. Opticks, like the pair of mathematical treatises that was to appear with it, had been long anticipated by Newton's friends. In 1694 Gregory had examined its three Books – hence it was substantially complete then, though Newton was not yet ‘fully satisfied about a certain kind of colours and the way of producing it’ – and summarized it in his diary of his visit to Cambridge (5 to 7 May). Newton meant to publish it after leaving the university, in English as it was written, or translated into Latin if he remained at Cambridge. By April 1695 John Wallis at Oxford knew of it (through Flamsteed's protégé Caswell) as ‘a Treatise about Light, Refraction and Colours’ already completed. ‘Tis pitty it was not out long since. If it be in English (as I hear it is) let it, however, come out as it is; & let those who desire to read it, learn English.’ Thus spoke this fervid Englishman! Through successive letters Wallis continued to prod Newton, but he would not budge.
After looking so far forward to the origins of the Principia, it comes almost as a shock to realize that young Isaac Newton was still barely twenty-four years old, not yet a Master of Arts, when he returned to Cambridge in 1667. It would be strange indeed if he were not now far more conscious of his own potentiality in the world of learning than he had been before the plague. Five years into the future he would be arguing for his own discoveries on equal terms with the acknowledged leaders of the scientific movement in Europe. As yet, however, he stood on the lowest rung of the ladder of academic promise and his name was unknown. Newton had a chance of a minor fellowship at Trinity College at the next election, in the coming October, and no doubt hoped for something from the support of his family connection, Humphrey Babington. Candidates for the fellowship had to submit, at least in theory, to four days of oral examination by the Seniors in the college chapel. By whatever means, and whoever was convinced of his merits, Newton was indeed among the chosen. He was assigned the ‘Spiritual Chamber’ to reside in, but probably remained where he was with his friend (and amanuensis) John Wickins, renting out the room allotted to him. Trinity College now paid him ‘wages’ of £2 per annum, gave him allowances for livery and commons (that is, clothing and food) and allowed him his share (‘dividend’) of the college revenues. Trinity also assigned him his first pupil, a Fellow-commoner named St Leger Scroope, who made no mark in history.
In response to my request, some years ago, Professor Karin Figala prepared an elementary account of the results of her investigation of Newton's alchemical papers and related documents. This was communicated to me privately in March 1984. In the following paragraphs Professor Figala's summary is printed, with her permission. For her technical paper on this material, see ‘Die exakte Alchemie von Isaac Newton’ in Verhandlungen der Naturforschenden Gesellschaft Basel 94, 1984, pp. 157–228.
The search for a combination of the exact sciences with magical thought was a central motive of the seventeenth-century attitude of mind: Newton was no exception to this rule. His personal attitude towards the problem is best illustrated by his (al)chemical research, for he seems to have seen in traditional alchemy – which he considered to be of divine origin – a possible synthesis of seemingly divergent lines of thought. He was convinced that God had arranged everything in Heaven and on Earth according to number and measure, thus sharing the firm belief of the ancient Pythagoreans. Harmonic proportion seems to be a key concept in Newton's thought, as mirrored in his theory of the material world. In fact, his theory of the composition of matter – laid down in principle in Opticks – centres on the material world; accordingly, contemporary alchemy immediately presented itself to his mind. It is in Newton's ‘rational alchemy’ that we can get hold of at least a small part of his attempt to reconcile magic and science.
In Newton's theory of the composition of matter, seemingly impenetrable particles are built up from cubic elementary cells, some of which hold matter, some of which do not.
Swift was in England from November 1707 to May 1709 and from September 1710 to the middle of 1713, on Irish Church business. His first known reference to Catherine Barton is in his terse accounts, where he notes a loss of two shillings at ombre, at ‘Barton's’ on 4 December 1708. Twelve days later he was there again, suffering very bad ‘fitts’ of his habitual giddiness; he was forced to take a chair home, instead of walking as usual, and next day rewarded Mrs Barton's servants with the large present of 7s.6d in gratitude for their attentions. In April, July and August 1709 he recorded letters from Catherine, and on 26 May 1709 one written to her.
During his second and longer visit to England Swift noted in his journal for ‘Stella’ (Esther Johnson) that he dined with Mrs Barton three times in thirty-three months (28.ix.1710; 30.xi.1710; 7.iii.l711); he records visits to her on nine further occasions (19.xii.1710; 23.i.l711; 2.iv.l711; 10.iv.1711; 6.vii.l711; 18.vii.1711; 14.X.1711; 25.x.1711; 20.xii.1711). It is notable that by his own record Swift saw nothing of Mrs Barton during the whole of 1712, nor during the six months of 1713 that he spent in London.
During his first visit to London Swift associated with the Whigs and became friendly with Halifax, among others. He never in any way connected Halifax with Mrs Barton, though he continued to meet both during his second visit to London, when he supported the Tory interest (and therefore disputed with Mrs Barton, who like her uncle was a Whig).
In his translation of Hermann Boerhaave's Elements of Chemistry (1741) Peter Shaw wrote: ‘It is by means of chemistry, that Sir Isaac Newton has made a great part of his surprizing discoveries in natural philosophy,’ an opinion which becomes more understandable, if no less extravagant, when related to Shaw's wide claim that ‘chemistry, in its extent, is scarce less than the whole of natural philosophy.’ Such a high view of chemistry would not have been expressed a century earlier, indeed the rise of chemistry as a department of natural philsophy had taken place in Newton's lifetime. In this rise the writings of Robert Boyle had played a principal part, exercising (as we have seen) considerable influence over Newton himself. Many considerations lead me to believe that Newton's chemical atomism was Boyle's corpuscular chemistry revised, made more precise and rendered more complete, but also more deeply speculative. However, as Shaw correctly states, the Queries in Newton's Opticks had done much to enhance chemistry's reputation as a branch of theoretical science, the science of matter.
When Newton's chemical interests first took shape, Opticks and its Queries were still half a century in the future. It would be rash indeed to extrapolate the sophisticated atomist theory of chemical reaction found in them back into Newton's initial experiments of the late 1660s. No positive statements can be made about their date, nor about what book or which individual may have inspired Newton to attempt this kind of investigation.
The Newton family belonged to the yeoman class descended from the most modest of the free landholders of manorial England. Socially beneath the esquires and knights, some members of this class had prospered greatly after the fourteenth-century decline of feudalism. Later the dissolution of the monasteries, sheep-farming and inflation had given some yeoman families, like the Newtons, means to enter the gentry class. As small landowners they lived in solid houses of brick or stone, sometimes adjacent to the barns and farmyard, like Newton's birthplace at Woolsthorpe in Lincolnshire. Yeomen, who could not prosper by idleness, constituted a great reservoir of ambition and talent, supplying Church, universities and the law, as well as commerce and industry. They wrote plays for the stage and music for the nobility; they staffed the empire. The father whom Isaac Newton never knew, also Isaac, could not sign his name but his mother and half-sisters were literate after the phonetic style also practised by the greatest ladies. When the posthumous child was three years old his mother, Hannah, remarried Barnabas Smith, rector of nearby North Witham. Smith owned a small library of theological books, works of the Fathers and so on, which passed to his stepson. Thus Isaac was born into the lower limit of landed property and learning alike. When he was old and famous he took pains to satisfy the College of Heralds of his common descent with an established armigerous gentleman, Sir John Newton, who was glad to bring so famous a man among his own kin. Sir Isaac Newton for his part responded to many begging letters from his poor relations.
With the freedom granted to all Lucasian professors to decline holy orders, Newton knew that so long as he retained that office he was assured of the tenure of his fellowship at Trinity College till death or resignation – in fact, he would hold it for another twenty-six years. He did not resign his Cambridge posts until December 1701, still not a Senior in his college though non-resident since 1696. Further, to the best of our knowledge, Newton had carried out no teaching since the Revolution.
His appearances in the public life of his college and university are poorly documented. In March 1673 he joined his relative Humphrey Babington and others, Masters of Arts, in signing a protest against the heads of houses exercising their customary but doubtful powers of nominating two candidates for the post of Public Orator, for the Senate's election. The protest failed. At an unknown date Newton attempted to secure from the commissioners of taxes for Cambridge an exemption from a property tax, on the grounds that the revenue from the Lucasian professorial estate did not belong to his college. (Later, from 1688 to 1695, Newton himself was to be one of these commissioners, a mark of his eminence in the university; the vicechancellor was one of the body ex officio.) In 1676 Newton gave £40 – then a fairly comfortable annual salary – towards the projected new library building proposed by Barrow at Trinity, since famous as the Wren Library closing the rear court of the college. This gift was followed by a loan of £100 made about the end of 1679; Newton also presented a number of books to the library.
Dagognet's work shows that making algorithmic compressions seems to be one of the major targets of scientific progress. This effort has been so successful that until recently one might have thought everything could be algorithmically compressed. Indeed, this statement, which might be seen as a scientific translation of the Hegelian thesis in its strong form (“the real is rational and the rational is real”), admits to some objective limits in computer science. Though a lot of algorithms are successful, there exist today, and perhaps forever, logical and physical limits that cannot allow us to cherish the dream of a “theory of everything.” Moreover, a complete mastery of complexity does not seem possible — because some domains of reality are too complicated to be computable, because the human brain is too limited, because computers cannot do that much better than the human brain, and because, ultimately, there are some kinds of things it would make no sense to compress. This paper shows that Dagognet's work came to recognize what a glance at the history of algorithmics has made evident.
Philosophy, a discipline without equals, seeks to account for reality, if possible in its entirety. It can be practiced only through the analysis of manifestations as diverse as art, religion, anthropology, politics, etc.
In this contribution, I argue for epistemological impurity as the key to the historical reconstruction of the proto-biological sciences of the eighteenth century.
The traditional approaches to the more or less complex and more or less stratified past of science either focus on the ideal content of that which has in the meantime been recognized as standard biological knowledge (transmitted from generation to generation by textbooks) or otherwise try to uncover the implicit cognitive principles at work in order to reveal their shortcomings (as measured against today's accepted criteria = epistemological presentism).
A closer look at the breakdown of the classical models of mechanistic explanation and the detailed analysis of the new empirico-experimental research in the neurophysiology of the eighteenth century shows, however, that eclectic procedures of various kinds have dominated the field. This eclecticism (the principle of epistemological impurity) supported, and was in turn supported by, what has recently become known as “thinking with one's hand.” The paper illustrates this specific kind of thinking (and experimental acting) with reference to the case of Nicolas Le Cat's microphysics of nervous activity.
The secret of invention or the art of inventing has recently become the object of positive or experimental research, aimed at discovering the logic of the initial mental processes that lead to “innovation.” But the problem is old and goes back to antiquity: The art of memory, rhetoric, symbolics. Does the succession of thought in invention follow a rule, such that its variations could be classified? Here I offer but a general direction: There is an analogy between the two relations: invention/innovation and fecundation/maturation – namely, a male and a female principle.
The Ancients thought that inventing was a divine art and that man receives the spark to then brood over its fruit in his mind. Today's still dominant materialist tendency insists on the importance of this secondary maturation and minimizes the role of the primordial spark.
Thus becomes possible the ranking according to a unique order — but not without hesitations and guilt — of thinkers as far apart as Mandeville, Adam Smith, Hegel, Buffon, Rousseau, and Herder, to find the contemporary trend to which François Dagognet belongs.