APPENDIX THE AUTHENTICITY AND SIGNIFICANCE OF THE TEXTS ON THE RAINBOW AND PROBABILITY A. SPINOZA'S CONTEMPORARIES The most concrete and clear-cut information concerning the development of Spinoza's ideas on theoretical optics is to be found in his correspondence. It is evident from the letters that it was probably during the mid-1660's, the four years following the publication of his book on the principles of Cartesianism, that he was most actively involved in exploring the theoretical foundations of his professional concern with the grinding of lenses and the construction of optical instruments. During these years he was co-operating with Jan Hudde (1628-1704) in the preparation of lenses for telescopes. Hudde also composed a small treatise on dioptrics, which if it had been preserved would have provided us with invaluable insight into the precise manner in which Spinoza was then thinking about light and optics. It is apparent from the surviving letters not only that he thought very highly of Hudde's expertise in dioptrics, but that as might have been expected, they were both approaching the problems it presented from a basically Cartesian standpoint. In the summer of 1666, for example, when Spinoza wrote asking for advice on the possible advantages of plano-convex lenses, he also took the trouble to re-state Hudde's geometrical presentation of spheri­ cal aberration in algebraic terms.! It was also during these years that JarigJelles (1619120-1683), a close friend of Spinoza's who had paid for the publication of the book on the principles of Cartesianism, wrote asking him to explain an apparent anomaly in Descartes' Dioptrics. After some delay, Spinoza replied in two letters, the second of which con- 1. See Spinoza, BrieJwlsselmg (ed. F. Akkerman, H.G. Hubbeling, A.G. Wester­ brink, Amsterdam, 1977), letters 34 (7 January 1666), 35 (10 April 1666), 36 Gune 1666). It used to be thought that these letters were written to Huygens. 91 APPENDIX tains a not too successful attempt at explaining the working of the human eye.2 During the 1650's, several members of this Amsterdam circle, together with their associates, had had close connections with the University of Leiden through the professor of mathematics there, Frans van Schoo ten (1615-1660). Hudde, together with Christiaan Huygens (1629-1695) and Jan de Witt (1625-1672), had studied mathematics privately at Leiden under van Schoo­ ten, who in 1649 had published an annotated Latin edition of Descartes' Geometry. This work had proved to be such a suc­ cess, that he was encouraged to prepare a second edition, in which he included a number of contributions by his pupils: articles by Hudde on the reduction of equations and the rule of extreme values, by Huygens on the intersections of a parabola with a circle and an improved method of constructing tangents to the conchoid, and by de Witt on conic sections.3 The pro­ fessor of philosophy at Leiden at this time was Adriaan Heere­ boord (1614-1661), also an enthusiastic Cartesian, and with an interest in introducing the new methods of enquiry into the natural sciences. Initially, he met with uncompromising opposi­ tion to this in the University, but in 1653 the curators appointed his pupil Joannes de Raey (1622-1702)to the chair of physics.4 Claes van der Meer (1594-1654), a Leiden financier and insur­ ance broker, was then treasurer of the University, and his son Jan van der Meer (1639-1686), who was corresponding with Spinoza on probability in 1666, and in 1678 was thought by Spinoza's friend the Amsterdam physician G.H. Schuller to be in business in Amsterdam, was evidently one of the links be­ tween Leiden and the Amsterdam circle during the 1660's.5 2. BriefwlSSeling, letters 39 (3 March 1667), 40 (25 March 1667). 3. Geometria, a Renato Des Cartes (2 vols., Amsterdam, 1659/61). Spinoza evi­ dently had both the first and the second edition of this work in his library. 4. H. De Dijn, 'Adriaan Heereboord en het Nederlands Cartesianisme', Algemeen Nederlands TiJdschrtft voor Wtjsbegeerte, vol. 75, no. 1 Qanuary 1983), pp. 56-69; E.G. Ruestow, Phystcs at seventeenth and etghteenth century Letden (The Hague, 1973), pp. 34-72. 5. Brtefwisseling, letter 38 (1 October 1666); J. Freudenthal, Dte Lebensgeschlchte Spinoza's (Leipzig, 1899), p. 207. There is no evidence that van der Meer was ever in business in Amsterdam, see K.O. Meinsma, Spmoza en ziJn krmg Cs-Gravenhage, 1896), p. 259, note 2. 92 THE AUTHENTICITY AND SIGNIFICANCE OF THE TEXTS In respect of the background to Spinoza's texts on the rain­ bow and probability, it is certainly worth noting that there is evidence that the dioptrics of the rainbow and the theory of probability were topics of general discussion in this circle during the 1650's. Huygens, for example, was investigating refraction with reference to Descartes' explanation of the rainbow as early as December 1652, and five years later published the Latin version of his work on the theory of probability, a copy of which was in Spinoza's library. Since Rene-Fran~ois de Sluse (1622-1685) is mentioned in the Treatise on the Rainbow, it is also worth noting that Huygens was corresponding with him in 1657. 6 As well as providing us with insight into the ways in which Spinoza's involvement in practical and theoretical optics led to his exchanging ideas with his fellow countrymen, the corre­ spondence also seems to indicate that prior to the publication of the Tractatus theologico-politicus in 1670, this involvement con­ stituted the main basis of his international reputation. It is certainly of significance that when Henry Oldenburg (c. 1620- 1677), secretary of the Royal Society, wanted to re-open his correspondence with him, he did so by informing him of the recent publication of Boyle's Experiments and Considerations concerning Colours and Hooke's Micrographia. What is more, when Spinoza returned the compliment, he did so by sending news of Huygens' activities and information concerning discov­ eries in astronomy being made by means of Campani's tele­ scopes. 7 When Leibniz was informed that it was Spinoza who had written the Tractatus theologico-politicus, he introduced himself to him not by commenting upon the work, but by indicating that he was aware of the importance of Hudde's dioptrical writings, and asking for Spinoza's opinion on his own recently-published Note on advanced optics. Spinoza replied 6. Huygens, CEuvres XIII, 1, pp. 146-153; letters 396-404 (II, pp. 39-53). Huygens' Tractatus de ratiOClnllS In aleae ludo was published in F. van Schooten's Exerclta­ tzonum mathematicarum (Leiden, 1657), which was in Spinoza's library: Freudenthal, op. cit., p. 161, no. (53). 7. Briefwlsseling, letters 25 (28 April 1665), 26 (May 1665); d. the enquiry and response concerning Huygens' DIOptrics in letters 29 (c. 20 September 1665) and 30 (c. 1 October 1665) 93 APPENDIX expressing doubts concerning what Leibniz called his 'pan­ dochal' lenses, and informing him that he had sent the second copy of the work on to Hudde, who had replied that he had had no time to look at it, but that he hoped he would be able to do so in a week or two.8 lt is not surprising, therefore, that the mention of a lost Treatise on the Rainbow in the preface to the collected works of Spinoza, published immediately after his death in 1677, should have aroused widespread curiosity abroad. When Jelles wrote to Spinoza enquiring about the apparent anomaly in Descartes' Dioptrics, only he and a small circle of friends in Amsterdam knew that something resembling the geometrical method then being used in dealing with light and colours was also being applied, in the re-drafting of the Ethics, to questions concerning nothing less than God and mind, the emotions and human servitude, the power of the intellect and human freedom. 9 Ten years later the full text of the Ethics was about to be presented to the world in both Latin and Dutch. Anyone who knew anything of Spinoza's interest in theoretical optics was bound to search the collected works for new light on the precise connection between the geometrical order of presentation employed in his philosophical masterpiece and the analytical geometry then being applied so successfully in the various branches of the exact sciences. Unfortunately, it was by no means apparent from the material included in the Opera posthuma what this connection might be. lt was J arig J elles who wrote the preface to the Dutch edition of the collected works, and he was evidently aware that this absence of any clear indication of what the connection might be between Spinoza's metaphysics and his mathematics was almost certain to give rise to disappointment. This probably accounts, 8. Briefwzsselmg, letters 45 (5 October 1671), 46 (9 November 1671); G.W. Leibniz, Sdmtliche Schnften und Bnefe, Zweiter Reihe, Erster Band (Darmstadt, 1926), pp. 155,184,185. Leibniz read the Tractatus soon after it was published and by the April of 1671 knew that it was by Spinoza: L. Stein, Leibmz und Spinoza (Berlin, 1890), pp. 32-34. His Notztia optzc£ promot£ was published at Frankfurt-on-Main in 1671. 9. In the draft as it existed in June 1665, the work was divided into three main sections, not five: Ethica (tr. and ed. N. and G. van Suchtelen, Amsterdam, 1979), pp. 7-8. Cf. F. Mignini's edition of the Korte Verhandeling, in Spinoza: Korte Geschriften (Amsterdam, 1982), pp. 221-436. 94 THE AUTHENTICITY AND SIGNIFICANCE OF THE TEXTS in part at least, for his statement that the Treatise on the Rain­ bow was the only manuscript of any significance that the editors had been unable to obtain a copy of: This is all the material, of any value, that we have been able to gather from the papers he left behind, and from certain copies, preserved by his friends and acquaintances.