Beeckman, Descartes and Physico-Mathematics (original) (raw)

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The phrase, “there are very few physico-mathematicians,” written by Isaac Beeckman in his Loci communes on the occasion of his encounter with Descartes in November 1618 is well-known. The language appears to be new, and is not found in Beeckman before this date. He comments on Descartes in this way:But the compliment is odd. Beeckman had meditated on this subject for about a decade and a half; from the very first remark in his Journal (probably from 1608 to1610), he wondered why all of the arts are not subordinated to one another, why there is not “a general science or art of all mathematics, and again, of mathematics and physics, and again of physics and ethics, and again of physics and alchemy, etc.” But obviously, Descartes had had much less experience with these kinds of questions. This compliment shows the constant care with which Beeckman drafted his reading notes, experiments, and reflections over 30 years. He sometimes judges other authors on their way of harmonizing mathematics and physics, and in a more particular way, on the ways in which they agree with the small number of philosophical theses that he considers his own and to which he returns again and again. With regard to Bacon and Stevin, he writes that the first did not try hard enough to join mathesis to physics (he believed, for example, that the cause of the interval of an octave was obscure), while the second was too devoted to mathematics and dealt too rarely with physics. Thus, the phrase “this way of investigation (hoc modo studendi)” in the quotation, is what is most important. In fact, it is not just a question of unifying mathematics and physics in general, but the specific way in which it is done. In making his judgment about Descartes, Beeckman enters him into a very select list of authors, those who are most important for him in the renovation of science, and gives him the particular distinction of being a kind of alter ego. But is Beeckman right to assume, or to presuppose, that he and Descartes have a common style?

I would like to thank Daniel Garber, the translator of this chapter, and Sophie Roux deeply for their invaluable remarks.

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Notes

1. 1. “Physico-mathematici paucissimi.” Journal, vol. I, p. 244.
2. 1. This is the title Isaac Beeckman gave at the beginning of his manuscript.
3. 1. See, though, a contemporary book by Philipp Müller, De cometa anni 1618 commentatis physico-mathematica specialis et generalis.
4. 1. “Hic Picto cum multis Jesuitis alijsque studiosis virisque doctis versatus est. Dicit tamen se nunquam neminem reperisse, praeter me, qui hoc modo, quo ego gaudeo, studendi utatur accurateque cum Mathematicâ Physicam jungat. Neque etiam ego, praeter illum, nemini locutus sum hujusmodi studij,” Journal, vol. I, p. 244.
5. 1. Ibid., vol. I, p. 5.
6. 1. See Koyré, Études galiléennes, p. 121.
7. 1. On the interest in the rediscovery of the manuscript of the Journal, see Koyré, Études galiléennes, pp. 108f., n. 2.
8. 1. Thus Leibniz, Remarques sur l’Abrégé de la vie de M. Descartes, in Die philosophischen Schriften, vol. IV, p. 316: “1630. It seems that one wrongs M. Isaac Beeckman in treating him harshly solely on the basis of the reports found in the letters of M. des Cartes. I learned that one shouldn’t put your trust in them to the handicap of others, since M. des Cartes puts a strange twist on things when he is offended with someone.”
9. 1. Descartes, Œuvres, vol. X, pp. 15–169.
10. 1. Mersenne, Correspondance, vol. I, pp. 632–644 (Rules of impact).
11. 1. De Waard’s positions are repeated in the only synthetic treatment of Beeckman available, see van Berkel, Isaac Beeckman (1588–1637) en de Mechanisering van het Wereldbeeld, with English summary pp. 317–319, and van Berkel, “Beeckman, Descartes et la philosophie physico-mathématique.”
12. 1. Koyré, Études galiléennes, pp. 108f., n. 2.
13. 1. “Tum quam utile sit axioma rebus physicis indagandis: corpora magna habere superficiem parvam, parva vero magnam.” Journal, vol. III, p. 123.
14. 1. “Coelum semel motum semper movetur.” Ibid., vol. I, p. 10.
15. 1. This text from Toletus illustrates the scholastic notion of a quietatio: “Motus ex se tendit in quietem termini ad quem, in quo stat et quiescit res; unde motus quietatio quaedam, id est, via in quietem dici potest, quae partim est cum ipso motu.” Toletus, Commentaria, bk. V, chap. 6, text 54, f. 163r.
16. 1. Journal, vol. I, p. 51 à propos of the notes on music, and Lectio, in ibid., vol. IV, p. 122 regarding the architecture of the world.
17. 1. “Censendum videtur coelum nec ab intelligentiis moveri, nec continuo Dei nutu, sed sua et situs natura semel motum, nunquam per se posse quiescere. Quod ergo fieri potest per pauca, male dicitur fieri per plura.” Ibid., vol. I, p. 10.
18. 1. “Mota semel nunquam quiescunt nisi impediuntur.” Ibid., vol. I, p. 24.
19. 1. Beeckman proposes that once something is put into motion, it never ceases to move on its own, and from this fact it follows that the world does not need the continuous effort of God to move perpetually (ibid., vol. I, p. 10). But nevertheless, he needs a universal cause of motion, which he finds in God, at once the creator of bodies and of motions (thus, ibid., vol. I, p. 131).
20. 1. “Quod semel movetur, semper movetur nisi impeditur.” See ibid., vol. I, pp. 10, 24f., 44, 61, 167, 253, etc.
21. 1. Ibid., vol. I, p. 157.
22. 1. Beeckman to Mersenne, June 1629, in Mersenne, Correspondance, vol. II, p. 233.
23. 1. “[N]on circulariter, sed in rectum ad locum, ad quem eo momento quo solvebatur, spectabat.” Journal, vol. I, p. 167.
24. 1. “Id, quod semel movetur, in vacuo semper movetur, sive secundum lineam rectam, seu circularem, tam super centro suo, qualis est motus diurnus Terrae < quam circa centrum, qualis est motus > annuus. Cum enim quaelibet minima pars circumferentiae sit curva, atque eodem modo curva atque tota peripheria, nulla ratio est cur motus circularis Terrae annuus desereret hanc lineam curvam et ad rectam procederet, nam recta non magis naturalis et aequalis naturae et extensionis est quam circularis, quia pars circumferentiae se eo modo habet ad totam, quo pars rectae ad rectam totam.” Ibid., vol. I, p. 253.
25. 1. Ibid., vol. I, pp. 253f.
26. 1. Ibid., vol. I, pp. 265–267; Mersenne, Correspondance, vol. II, pp. 633–635.
27. 1. Beeckman, Journal, vol. I, pp. 271f.; Mersenne, Correspondance, vol. II, pp. 635f.
28. 1. Beeckman, Journal, vol. II, pp. 45–54; Mersenne, Correspondance, vol. II, pp. 636–640.
29. 1. Beeckman, Journal, vol. III, pp. 128–131; Mersenne, Correspondance, vol. II, pp. 640–642.
30. 1. Beeckman, Journal, vol. III, p. 369; Mersenne, Correspondance, vol. II, p. 642.
31. 1. Beeckman, Journal, vol. I, pp. 265–267.
32. 1. I read here “minima celeritate,” as in Mersenne, Correspondance, vol. II, p. 635 and p. 123, and not “maxima celeritate,” as in the edition of de Waard (Beeckman, Journal, vol. I, p. 267); see Mersenne, Correspondance, vol. VIII, p. 422 n. 4, where de Waard notes this correction in his edition of Beeckman’s Journal.
33. 1. Beeckman, Journal, vol. I, pp. 266f., also cited in Mersenne, Correspondance, vol. II, p. 633, with the collection of impact rules proposed by Beeckman. See Beeckman, Journal, vol. I, p. 196.
34. 1. The Lectio is found in ibid., IV 122–26; the cited phrase is on p. 125. Gemelli, Isaac Beeckman, atomista e lettore critico di Lucrezio, p. 26 emphasizes the importance of this principal.
35. 1. Beeckman, Journal, vol. III, p. 49, April-May 1628.
36. 1. Mersenne, Correspondance, vol. II, p. 281.
37. 1. Ibid., and note of 30 April 1618, see Beeckman, Journal, vol. I, pp. 170f.
38. 1. “Figurarum isoperimetrarum ordinatissima est capacissima.” Ibid., vol. IV, p. 122.
39. 1. “Figurarum aeque ordinatarum major minorem, respectu capacitates, habet superficiem.” Ibid., vol. IV, p. 123. This principle itself was formulated much earlier, in a note from April 1614: “Want de corpulentie ofte swaerheyt drejnckt een dynck terneder ende de superficies, die teghen de locht kompt, verhindert int vallen. Unde sequitur globum ejusdem materiae, majoris tamen quantitatis, celerius cadere globulo minoris quantitatis: ratio enim superficiei minoris globi ad corpulentiam ejusdem globi majorem habet rationem quam superficies majoris globi ad ipsum corpus majoris globi.” Ibid., vol. I, p. 31.
40. 1. On the medieval antecedents of the notion of a law of nature, see Crombie, “Infinite Power and the Laws of Nature: A Medieval Speculation.”
41. 1. Descartes, Œuvres, vol. I, p. 230.
42. 1. See Descartes to Mersenne, 13 November 1629, Descartes, Œuvres, vol. I, p. 72. The context in Beeckman is recalled in the following letter, 18 September 1629, in ibid., pp. 82–105.
43. 1. Descartes to Mersenne, 13 November 1629, in ibid., pp. 71f. The letter is in French, except for the last phrase, which is in Latin.
44. 1. Descartes to Mersenne, October or November 1631, in ibid., pp. 230f.
45. 1. Le monde, chap. 11, in Descartes, Œuvres, vol. XI, pp. 72–80.
46. 1. Descartes, Œuvres, vol. II, p. 91.
47. 1. Descartes, Œuvres, vol. XI, p. 37.
48. 1. Descartes, Œuvres, vol. X, p. 219.
49. 1. Ibid., p. 78.
50. 1. Descartes to Mersenne, 18 December 1629: “Supponit, ut ego, id quod semel moveri coepit, pergere sua sponte, nisi ab aliqua vi externa imediatur, ac proinde in vacuo semper moveri, in aere vero ab aeris resistentia pautalitm impediri.” Descartes, Œuvres, vol. I, p. 91; Mersenne, Correspondance, vol. II, p. 341. See also Parnassus, in Descartes, Œuvres, vol. X, p. 219.
51. 1. Descartes, Œuvres, vol. II, pp. 90f.
52. 1. An analogous approach à propos of the theory of refraction is suggested in Costabel, “La réfraction de la lumière.”
53. 1. Descartes, Œuvres, vol. XI, p. 38. While at the beginning of chap. 7 Descartes talks explicitly of “laws [_lois_]” (ibid., p. 36), when he comes to give them he calls them “rules” [_regles_]
54. 1. Descartes, Œuvres, vol. XI, p. 41.
55. 1. Descartes to De Beaune, 30 April 1639 (Descartes, Œuvres, vol. II, p. 543; Mersenne, Correspondance, vol. VIII, p. 421), Descartes to Mersenne, 25 December 1639 (Descartes, Œuvres, vol. II, p. 626; Mersenne, Correspondance, vol. VIII, p. 696), 28 December 1640 (Descartes, Œuvres, vol. III, p. 205; Mersenne, Correspondance, vol. X, p. 173), 17 November 1641 (Descartes, Œuvres, vol. III, p. 451; Mersenne, Correspondance, vol. X, p. 382).
56. 1. “Je pourrais mettre encore ici plusieurs règles pour déterminer, en particulier, quand et comment et de combien le mouvement de chaque corps peut être détourné, et augmenté ou diminué, par la rencontre des autres; ce qui comprend sommairement tous les effets de la Nature.” Descartes, Œuvres, vol. XI, p. 47.
57. 1. In fact, the greatest difficulty with the rules set forth in the Principia concerns again the apportioning of the case of the reflection of one body off of another and the communication of motion. The hesitations and corrections abound, but without yielding satisfactory results, as is well known. Thus, the articulation of the rules of impact (Principia II 46–52) is considerably altered in the French translation, especially in accordance with the supplementary principle proposed in the letter to Clerselier of 17 February 1645, in Descartes, Œuvres, vol. IV, p. 187.
58. 1. Descartes, Œuvres, vol. XI, p. 44.
59. 1. Descartes, Œuvres, vol. X, pp. 381f.
60. 1. Descartes to Mersenne, 23 August 1638, Descartes, Œuvres, vol. II, p. 309. See also Costabel, “La courbure et son apparition chez Descartes,” and Cassirer, “Descartes’ Kritik der mathematischen und naturwissenschaftlichen Erkenntnis,” which is the preface to Leibniz’ System in seinen wissenschaftlichen Grundlagen, which can be found in Cassirer, Gesammelte Werke, vol. I, pp. 29f.
61. 1. Dioptrique, in Descartes, Œuvres, vol. VI, pp. 86–88.
62. 1. It is obvious that this method is to be compared with that of Kepler.
63. 1. Descartes, Œuvres, vol. XI, p. 39.
64. 1. Beeckman, Journal, vol. I, p. 26.
65. 1. Ibid., vol. III, p. 310. Note that the first sentence of the quotation is a marginal summary.
66. 1. “Lapis motus τ_ῷ n ῦ_ν mathematico est in loco et sic non movetur. At τ_ῷ n ῦ_ν physico movetur.” Ibid., vol. III, p. 357.
67. 1. See Ramus, Scholarum mathematicarum libri unus et triginta, l. IV, p. 114; see also de Buzon, “Mathématique et dialectique: Descartes ramiste?”
68. 1. “The difference consists only in this, that physics considers its object not only as a true and real entity but as existing actually and as such. However, mathematics [_Mathesis_] considers it only insofar as it is possible, and which doesn’t exist in actual space, but yet could exist.” Descartes’ Conversation with Burman, in Descartes, Œuvres, vol. V, p. 160.
69. 1. Descartes, Œuvres, vol. II, p. 56.
70. 1. Ibid., pp. 70f.

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de Buzon, F. (2013). Beeckman, Descartes and Physico-Mathematics. In: GARBER, D. (eds) The Mechanization of Natural Philosophy. Boston Studies in the Philosophy and History of Science, vol 282. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4345-8\_6

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