Abstract
This Chapter brings together two lines of investigation about the natural philosophical structure and aims of Le Monde. First, it shows that Descartes’ often belittled vortex celestial mechanics was a serious intellectual construct: It was Descartes’ technical answer to the natural philosophical challenge posed by realist Copernicanism, and hence it was also a serious gambit in the natural philosophical contest. The centrality of the vortex mechanics to all the other topics addressed in Le Mondeis demonstrated. Second, this Chapter explores the celestial mechanics as a conceptually hybrid entity. On the one hand, it is shown that the vortex celestial mechanics has a genealogy reaching back through the physico-mathematics studied in earlier chapters. But, on the other hand, we also learn that the vortex mechanics was a piece of generic natural philosophical discourse, understandable as such by any member of the educated culture of natural philosophizing. This shows that Le Mondewas simultaneously the climax of Descartes’ trajectory in physico-mathematics and the first iteration of a systematic natural philosophizing, emergent from that carapace.
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Notes
- 1.
Kuhn (1959) pp. 240, 242.
- 2.
Bachelard (1965) p.79, ‘La métaphysique de l’espace chez Descartes est la métaphysique de l’éponge.’
- 3.
And, as Aiton (1972) has shown, the vortex celestial mechanics was taken seriously and articulated much further down into the first half of the eighteenth century by committed Cartesians and anti- Newtonian mechanists.
- 4.
In saying this I in no way wish to imply that I introduced Bachelard and Kuhn above as mere straw men. These two historian/philosophers of science initially most influenced my understanding of the dynamics of seventeenth and eighteenth century natural philosophy. I have argued elsewhere that Kuhn and Bachelard indeed misunderstood the nature of that natural philosophy and the contestations over it—taking it as the necessary but pre-scientific backcloth to the temporally splayed crystallization of a heterogeneous set of new ‘real’ sciences. However, as I have also claimed, that is less important than the fact that their speculations prompted more positive modeling by historians of early modern natural philosophy, its nature, dynamics and trajectory. Schuster and Watchirs (1990), Schuster and Taylor (1996), and Schuster (2002) all set the groundwork for the model of natural philosophy presented above in Chap. 2.
- 5.
Of course, if Le Mondemarked a node and climax, in Descartes’ career, it was obviously a particularly transient and occluded one, rather internal to Descartes’ development, not a public marker. Yet, to understand the later Discours, Meditationsand Principiawe need to understand how and why he arrived at this text, its genealogy, and its systematic character as a natural philosophy.
- 6.
Indeed in oral presentations of this paper at seminars and conferences I have used, not unsuccessfully, the following conceit in synthetically presenting the vortex theory: that this is a pro-Cartesian university lecture in Cartesian natural philosophy circa 1660, assuming fairly widespread consensual acceptance of the vortex mechanics. This allows the further conceit that the new diagrams and concepts I use below to explicate the vortex mechanics have actually become recognized parts of a Cartesian Scholastic tradition within a generation of his death. Perhaps if the remainder of this section is read in that spirit, the key points about the theory will come through, provided one remembers above all that I am not suggesting this was for anybody the explicit, publicly acknowledged version of the vortex celestial mechanics, but rather that this is very close, on a charitable reading, to Descartes’ own best understanding of his vortex theory, as it related to his course of work and context of natural philosophical struggle up to the early 1630s. Cf. Sect. 10.5.4below where in a similar conceit ‘Descartes’ himself speaks posthumously of the coherence of his vortex celestial mechanics.
- 7.
The more textual critical approach to teasing the underlying theory out the literal sense of Le Mondeoffered in Appendix 2 was begun in Schuster (1977). Amongst Descartes’ inadequately or misleadingly expressed analogies and claims that—revised, criticized and explicated—will find their place the synthetic presentation of the theory below are [1] the appeal to the behavior of a large heavy boat compared to random flotsam in the confluence of two parallel rivers; [2] Descartes’ mode of setting out the notion of a ‘balance’ of forces holding a planet in its orbit; and [3] the articulation of the key concept of ‘massiveness’ or ‘solidity’ of an orbiting body.
- 8.
In fact in the key analogy used by Descartes, in a strong river current boats behave like comets, and it is light flotsam that behaves on analogy to planets. Thus, untutored intuition misleads as to Descartes’ own preferred analogy (and hence misses the theoretical points he will be elucidating through the analogy).
- 9.
Additionally, as we shall see, he was also interested in relating a theory of local terrestrial gravity to his vortex celestial mechanics—a nice trick, since on Earth bodies of third element subjected to the local vortex fall down; but in the heavens, bodies of third element, subjected to the stellar vortex, find specific and stable orbital distances. Descartes thought there was a unified conceptual explication of these indubitable phenomena and he prided himself on designing it.
- 10.
Let us now call this the ‘force-stability principle’. Strictly speaking, however, more is involved in Descartes’ full conception of the orbital stability of the particles, or planets, orbiting at a given radial distance. Descartes’ articulated version of the force-stability principle will be developed below, Sect. 10.2.3.
- 11.
AT xi. 50–51; SG 33; MSM 81–83, ‘Thus, in a short time all the parts were arranged in order, so that each was more or less distant from the center about which it had taken its course, according as it was more or less large and agitated in comparison with the others. Indeed in as much as size always resists speed of motion, one must imagine that the parts more distant from each center were those which, being a bit smaller than the ones nearer the center were thereby much more agitated.’
- 12.
Note in relation to this figure, as well as Figs. 10.3and 10.4below that they of course do not exist in Le Mondeand are interpretative tools of my own design, used to picture the relationships Descartes sets out verbally. Additionally, it should be remembered that Descartes had no way of assigning empirically meaningful dimensions to the sizes and speeds of the boules. Nor would it have occurred to him to insist on any specific relationship for the variation of size and speed with distance. He limited his discussion to notions of proportionately greater or lesser increase or decrease of variables, which the figures then represent. Had Descartes sketched figures like these, we might more easily recognize the traces of his style of physico-mathematics in the vortex mechanics.
- 13.
Descartes adduces the elements at this stage in Le Mondein Chapter 8 (AT xi 51–55), but, as we have seen (Sect. 9.3 above) he has already adumbrated their properties at the end of Chapter 4, and described them in detail in Chapter 5 (AT xi 24–6; SG 17–18; MSM 37–39), writing there that, ‘I conceive of the first, which one can call the element of fire, as the most subtle and penetrating fluid there is in the world… I imagine its parts to be much smaller and to move much faster than any of those other bodies. Or rather, in order not to be forced to imagine any void in nature, I do not attribute to this first element parts having any determinate size or shape; but I am persuaded that the impetuosity of their motion is sufficient to cause it to be divided, in every way and in every sense, by collision with other bodies, and that its parts change shape at every moment to accommodate themselves to the shape of the places they enter… As for the second, which one can take to be the element of air, I conceive of it also as a very subtle fluid in comparison with the third; but in comparison with the first there is need to attribute some size and shape to each of its parts and to image them as just about all round and joined together like gains of sand or dust. Thus, they cannot arrange themselves so well, nor press against one another, that there do not always remain around them many small intervals, into which it is much easier for the first element to slide in order to fill them. And so I am persuaded that this second element cannot be so pure anywhere in the world that there is not always some little matter of the first with it. Beyond these two elements, I accept only a third, to wit, that of earth. Its parts I judge to be as much larger and to move as much less swiftly in comparison with those of the second as those of the second in comparison with those of the third. Indeed, I believe it is enough to conceive of it as one or more large masses, of which the parts have very little or no motion that might cause them to change position with respect to one another.’
- 14.
AT xi 53, MSM 85; SG 34–35.
- 15.
Descartes insists that a central star can agitate the surrounding particles of second matter of its vortex: ‘These (spherical bodies) incessantly turning much faster than, and in the same direction as, the parts of the second element surrounding them, have the force to increase the agitation of those parts to which they are closest and even (in moving from the center toward the circumference) to push the parts in all directions, just as they push one another.’ (AT XI 53 MSM 85; SG 34–35) Note that in this exposition we often speak of our central star, the sun, as does Descartes. The theory, however, is quite general and applies to each and every central star and its respective vortex. No reader of Le Mondecan be in any doubt about this fundamental point.
- 16.
The special radial locus at distance K is present in Descartes’ own discussion. Here for expository purposes I introduce the term ‘K layer’ not used by Descartes. Note as well that the existence and location of the K layer are caused by the existence and action of the sun.
- 17.
Descartes’ final distribution of the size and speed of the particles of the second element is as follows: AT XI 54–6; MSM 87–91; SG 35–37. (Fig. 10.1): ‘Imagine… that the parts of the second element toward F, or toward G, are more agitated than those toward K, or toward L, so that their speed decreases little by little [as one goes] from the outside circumference of each heaven [vortex] to a certain place (such as, for example, to the sphere KK about the sun, and to the sphere LL about the star ε) and then increases little by little from there to the centers of the heavens because of the agitation of the stars that are found there....As for the size of each of the parts of the second element, one can imagine that it is equal among all those between the outside circumference FGGF of the heaven and the circle KK, or even that the highest among them are a bit smaller than the lowest (provided that one does not suppose the difference of their sizes to be proportionately greater than that of their speeds). By contrast, however, one must imagine that, from circle K to the sun, it is the lowest parts that are the smallest, and even that the difference of their sizes is proportionately greater than (or at least proportionately as great as) that of their speeds. Otherwise, since those lowest parts are the strongest (due to their agitation), they would go out to occupy the place of the highest.’
- 18.
Let us reiterate that the reconstruction that follows here skims over all the complexities of textual interpretation mooted above at the beginning of this section, including some presumably non-Whiggish appeals to clarifications in the utterances of the Principleseleven years later. For a recounting of a more analytical initial unfolding of these textual findings, see Appendix 2.
- 19.
My notion of ‘surface envelope’ is a good example of a term of interpretative art belonging to my hermeneutical categories 2, 3 and 5, discussed earlier in Sect. 10.2.1. To see the reasons for its introduction, refer to Appendix 2.
- 20.
The second element, recall, is quite small compared to the pieces of third element, something Descartes goes out of his way to claim, in first describing the elements, as we saw above in Note 13: ‘Its parts (third element) I judge to be as much larger and to move as much less swiftly in comparison with those of the second as those of the second in comparison with those of the third.’ We are about to see one important reason why he has done this.
- 21.
In Le MondeDescartes did this somewhat confusedly, improving his explication of massiveness and its role considerably in the Principles. On the emergence of massiveness or solidity as a key concept in de-coding Le Monde, based in part on its more clear deployment in the corresponding sections of the Principles, see Appendix 2. In short, I am reconstructing the underlying model in Le Monde, using a crisp hermeneutics of ‘solidity’ as aggregate volume to surface ratio and meshing that concept with my analysis of the size/speed distribution of the boulesin the vortex. By using the graphical representations of these ideas, mediated by my interpretive construct of ‘surface envelopes’, the resulting decoding of the underlying model emerges. Note that in this process of reading, the verbal descriptions of the size/speed ratios come directly from the text, as does the concept of solidity—more clearly expressed in the Principlesthan in Le Monde, to be sure. The verbal descriptions are clarified and amplified graphically. The ‘least Cartesian’ notion used in this interpretation is that of ‘surface envelopes’, but even it has textual warrant in the overall direction of the theory, and in Descartes’ various descriptions of the centrifugal tendency of planets (and comets) and the resistances they encounter at various levels of the vortex.
- 22.
This articulates the simple notion of centrifugal tendency as a function of size (quantity of matter) and force of motion only. In this mature application of the dynamics to a ‘real’ fluid vortex, it is clear that centrifugal tendency is a function of size, force of motion and ‘solidity’ (or massiveness), the latter taken in relation to the solidity of the relevant, resisting surface envelope.
- 23.
It must be reiterated that the systematic conclusions reached here constitute a charitable reading of the relevant passages in Le Monde, supplemented carefully by the somewhat more clear and cogent presentation in the Principles. As Appendix 2 shows, this reading depends to a large degree on using the discussion in the Principlesto clarify and complete a reductio ad absurdumargument (concerning these various force relations) which is poorly and incompletely presented in Le Monde, but quite clear in the Principles.
- 24.
There is of course much more to say about this theory of comets. First of all, it makes some concrete empirical predictions, which could have stood unrefuted for at least a generation after 1633; to wit, comets do not come closer to stars than a layer K; they are ‘more massive’ than planets, they move in spiral paths oscillating out of and into solar systems. In addition, in dealing with the phenomena of comets’ tails, Descartes had to attribute odd optical properties to the K layer as part of his overall theory of cosmological optics—raising thereby issues quite telling about the origin and import of his theorizing, as we shall see in Sect. 10.8.
- 25.
The term ‘falling’ is chosen quite deliberately. In the previous argument about the placement of planetary orbits, a planet ‘too high up’ in the vortex for its particular solidity is extruded sun-ward, falling (and spiraling) down in the vortex to find its proper orbital distance. Below in Sect. 10.5we shall see that Descartes’ theory of local fall, and theory of the orbital motion of the moon, when taken in their simplest and most charitable acceptations, both also make use of this notion of falling in a vortex until a proper orbital level is found (assuming no other circumstances prevent completion of the process, as they do in local fall of heavy terrestrial bodies near the surface of the Earth). Ultimately, however, the interpretation of these two theories becomes more fraught, requiring additional interpretative attention, as we shall learn in Sect. 10.6.
- 26.
- 27.
- 28.
In early August 1628 Beeckman obtained a copy of Kepler’s Astronomia nova. It is typical of Beeckman that his initial notes relate to the broader issue of mechanical explanation raised by the general tenor of Kepler’s approach. In Chapter 36 of the Astronomia novaKepler remarked that he erred in his Ad Vitellionem Paralipomenain postulating the weakening of the force of light with increasing distance from the source in order to account for the decrease in illumination over distance. He now saw that nothing is lost by the light. As much light moves from the source to a distant sphere of illumination as to a nearby one; but, since the larger, more distant sphere has more parts, the illumination offered by an equal quantity of light decreases. Beeckman leapt at the opportunity provided by this confession. He noted that Kepler would have been better advised to embrace a corpuscular view of light. In that case he could more easily have understood that the force of light does not decrease, but that as the light moves from the source equal quantities of light corpuscles must illumine spheres of increasing surface area. Beeckman chided Kepler for not seeing what ‘obviously’ must be granted—that light is corporeal: ‘Truly Kepler was not able to know these things by a first intention and only when driven by necessity, because he falsely thinks that there is no distance between the particles, but merely what (scholastic philosophers) term simple extension,although they do not understand it themselves and foolishly avoid the assertion, which however must be made sometime or other, that light is a body […stulte vitantes dicere (quod tamen aliquando faciendum erit) lumen esse corpus.]’ (Beeckman (1939–1953) iii p.74).
Beeckman immediately drove home his point by applying it to the issue of the causes of celestial motion. For Beeckman this was the key problem raised by Kepler’s enunciation of the elliptical orbit of Mars. He himself, Beeckman ironically suggested, had often pondered the celestial motions in a manner little different from Kepler, ‘If I obtain some leisure and sometime or other free myself from this most burdensome office which is most unsuited to meditations, I shall discuss these things more accurately than Kepler, not only on account of the principle mentioned above which he refused to understand; namely that light is corporeal; but also because he did not know what is very true; that all things once moved, always move, unless they are impeded.’ (Ibid.) Certainly, Beeckman seems to be saying, Kepler saw the problem of explaining the celestial motions, and he invoked some immaterial celestial powers, forces or emanations to that end. But, despite his great astronomical acumen, Kepler did not realize that light and other celestial emanations must be corporeal in order to be able to affect material bodies, and, moreover, he did not know that circular motion needs no explanation because it falls directly under Beeckman’s general law of inertia.
- 29.
Beeckman (1939–1953) iii pp.74–5. ‘Let the rays of the sun which are reflected by the earth have a force of attracting the moon and let the earth itself have a force of repelling the moon. . . I say that the sun’s rays reflected by the earth retain their force much longer than the rays of the earth itself, because the sun’s rays come to the moon from a more remote place and the distance between the earth and the moon is very small compared to the distance between the sun and the earth. Therefore, the solar rays have just as much force near the moon where it now is as they would have if the moon were near the earth; but the earth has much more force near itself than near the moon, because the distance between the earth and the moon is very much greater than the distance from the earth’s surface to the tops of its mountains. Thus, the earth strongly repels the moon when it is near the earth. The repelling force vanishes little by little as the earth-moon distance increases, and the repelling force of the earth is overcome at some point by the attractive force of the solar rays reflected by the earth. In this manner, the moon can never move further away from the earth nor approach it more closely.’
- 30.
One problem is that Beeckman realized that the unreflected rays of the sun would attract the moon to it. Beeckman (1939–1953) iii 75. Soon after Descartes’ visit in October 1628 Beeckman returned to the problem and offered a solution based on a ‘reduplication’ of rays trapped between the Earth and the moon (ibid. p.100).
- 31.
Beeckman (1939–1953) iii. p.100.
- 32.
ibid. Two interesting issues arise in relation to Beeckman’s model here: [1] Did Beeckman imagine this extended to a multi solar system universe of Cartesian type, or was he thinking only of a unique solar system and a chorus of fixed stars? We do not know for certain, but it is indeed hard to see how any given star can both be in the attracting chorus and be a local repellor of its own planets. [2] Note Beeckman’s emphasis on the magnitude and rarity (density) of a planet. Beeckman was always acutely interested in how the volume to surface ratios of bodies, especially corpuscles, affected their mechanical interactions. The similarity in this respect to Descartes’ later vortex celestial mechanics is obvious.
- 33.
ibid. p.101. ‘Or, if it seems more plausible to avoid using an external agency in removing and attracting the planets to the sun or the moon to the earth, let us imagine that all magnetic virtues attract, but that there are many [sorts of particles], such as heat, light, etc. simultaneously flowing out [of the sun and earth] which repel. Moreover, let us conceive that the attractive force extends to a greater distance, so that the force of the heat particles taken at an equal distance is less. Thus the moon is driven away from the earth as long as the heat and other bodies flowing from the earth overcome the magnetic virtue; but, when they grow weak, the magnetic virtue still remains. Therefore, the moon is dragged to that place in which the forces are equal.’ It is clear that Beeckman entertains a corporeal theory of magnetism, cf ibid. p.102. For Beeckman’s corpuscular-mechanical theory of magnetism see also Beeckman (1939–1953) i 36, 101–2, 309; ii 119–20, 229, 339; iii 17, 76.
- 34.
Beeckman (1939–1953) iii p.103. Perhaps because he was displeased with the rather vague discussion of the magnetism as essentially involving attraction, implicated in the previous model, Beeckman was now in effect recurring to an account of magnetism he had used as early as 1615 in order to explicate the magnetic action of the fixed stars upon the solar system: Back in 1615, and more usually throughout his work, Beeckman had reduced apparent magnetic attraction to a differential repulsive action arising when magnetic effluvia drive air or aether out from between the lodestone and the piece of iron, thus allowing the pressure of air or aether on the remaining surfaces of the lodestone and iron to push the two together. Here in this final account of ‘celestial’ mechanics, there is a partial mobilization of a similar style of explanation. When the fixed stars send a flow of (magnetic) effluvia through the solar system, there will be more solar emanations immediately within the orbit of a given planet than immediately beyond it, and more celestial ‘magnetic’ effluvia outside the planet’s orbit than within it. Solar heat/light effluvia push out, but celestial magnetic effluvia push in, and orbital equilibrium is achieved. As Beeckman continued toward the end of this sequence of speculations, he also speculated about countervailing forces arising from impact of corpuscular emanations to explain, amongst other things, the eccentricity of orbits and precession of the equinoxes. ibid. pp.102, 108.
- 35.
van Berkel (2000).
- 36.
van Berkel (2000) and Sect. 8.3.3 above.
- 37.
Stevin, had of course preferred pure Archimedean statics and so had rejected the dynamical approach to statics and mechanics characteristic of the pseudo-Aristotelian tradition of the Mechanical Problems. In Stevin’s view systems in static equilibrium cannot be explained by considering the arcs through which bodies would move if they ceased to be in equilibrium, as in virtual or real displacements. You cannot deduce equilibrium conditions from the supposition that motion has or would occur—that is absurd, since if motion occurs the forces are not in equilibrium. This led Stevin to deny that the study of motion, that is, natural philosophy, could be pursued in a rigorous mathematical manner. (Stevin, ‘Appendix to the Art of Weighing’in Stevin (1955–1966) vol. 1, 507–9; and ‘The Practice of Weighing, “‘To the Reader’”, ibid.vol. 1,. 297.) How ironic, then, that Descartes sought natural philosophical capital, by recourse not to the Mechanical Problemsbut to the purely statical, purely mathematical, equilibrium science of Stevin. He did this first in the hydrostatics manuscript of 1619 (see above Chap. 2, and Gaukroger and Schuster 2002540, 545–9) and now in his mature work, his vortex mechanics was also at its core a science of equilibrium, not a science of motion and displacement.
- 38.
Gaukroger (2000)
- 39.
In fact, one might go a step further and suggest the following: Our interpretative diagrams, Figs. 10.2, 10.3, 10.4, display the type of ‘figuring up’ that characterized Descartes’ physico–mathematics, and which, had he supplied them himself, might have aided comprehension of his physics for the last 350 years. Cf. above note 12, and Chap. 3, notes 51 and 105.
- 40.
In sum, therefore: Charitable [1] reading deals with our interpretation of the vortex mechanics, as well as the theory of fall, lunar motion and tides, taken in their first order, most simple acceptations. Charitable[2] reading is open to the deeper complexities in the accounts of local fall, the motion of the moon, cosmological optics and comets’ tails, but it is still charitable in looking for the physico-mathematical genealogy and conceptual keys to Descartes’ texts.
- 41.
AT.XI.70; SG 45; MSM. 119.
- 42.
AT.XI.71–2; SG 45–46; MSM.119–121.
- 43.
AT xi pp.64–83
- 44.
AT xi pp.72–3, SG 47; MSM 123.
- 45.
Aiton (1959) 27 links Descartes’ ideas on the corpuscular nature of gravity to Gilbert’s De magnete. The role of Beeckman as a channel for these ideas and source of new ones of a related nature should be kept in mind, especially in light of what we now know about Beeckman’s recent ‘celestial mechanical’ speculations, based on Sect. 10.3above.
- 46.
AT xi 73; MSM 125; SG 47
- 47.
AT xi 73–4; MSM 125; SG 47
- 48.
This finding has very important consequences indeed for how one thinks about the status within the vortex mechanics of the phenomena of local fall (as well as planetary and cometary fall and rise). As we have seen, vortical mechanics focuses on explaining orbital equilibrium, as we have learned to define it above in Sect. 10.2.3. And, as we have argued in Sect. 10.4, the orbital spiraling down and up are ‘predicted’ and loosely explained in general terms by the theory, but no clear physico-mathematical description can be given of such a process, compared to the clear definition of the state of orbital equilibrium. This difference is reflective of deep tectonic alignments in the aims and evolution of Descartes’ physico-mathematics ‘turning-toward-corpuscular-mechanism’. We now see that local fall is also this sort of ‘slippage’ phenomenon, holding just when no orbital equilibrium has been effected—the moon, as we shall shortly see, would be an example of a ‘terrestrial’ body which has found orbital equilibrium in the vortex of the Earth! Therefore, on Cartesian vortex mechanical principles, local fall will not become an object of exact physico-mathematical study—a conceptual result that would hardly surprise the Descartes of 1633 and which would have finally made sense to him about his abortive physico-mathematical assault on local fall in 1619. To summarize in aphoristic terms: bodies in local fall are trivial, sub-scientific instances of the operations of the vortex mechanics; the moon is a planet– or comet–esque object illustrating the fine points of the vortex ‘equilibrium mechanics’.
- 49.
We place scare quotes around the term ‘in orbit’ for the following reason: As we shall find out when we examine the theory of the moon in more detail in Sect. 10.6, Descartes probably thought of the moon as a ‘comet-like’ object, in that it was so ‘solid’ that it was indeed ‘too solid to find a stable orbit inside the Earth’s vortex’. Hence, in all probability, he meant that it was only held in orbit at the outer boundary of the Earth’s vortex, by the strong resistance to centrifugal translation found at the boundary between the Earth’s vortex and the encompassing solar vortex In any case, the moon is an example of a very ‘solid’ terrestrial body that, rather than continuing to fall toward the Earth, has ‘risen’, that is, centrifugally translated upward to the limits of the local vortex.
- 50.
- 51.
AT.XI.81; SG 52; MSM.141.
- 52.
Ibid.
- 53.
AT.XI. 82–3; SG 52–3; MSM 141–143
- 54.
AT.XI. 82; SG 53; MSM 143.
- 55.
Cf. Galileo (1953) 441. Galileo alludes to shorter voyages in the Mediterranean from east to west than from west to east. He attributes this to a prevailing east wind caused by the lag of the air behind the diurnal rotation of the Earth. Burton, in the ‘Digression of Air’ in the Anatomy of Melancholy(Burton 1628 [1927], 409) asks why ‘…from Moabar to Madagascar in that Indian Ocean the merchants come in three weeks as Scaliger discusseth, they return scarce in three months, with the same or like winds: the continual current is from East to West.’ Bacon, in De Fluxu et defluxu Maris(1857–1874, vol v. 449) attributes the tides to the continental disruption of a permanent westward current derived from the diurnal motion of the heavens. Descartes’ model in Le Mondemakes no allowance for such continental disruption and treats the oceans in idealized terms (much like the Aristotelian ‘sphere of water’) as continuous, for the purpose of allowing the ‘tidal bulges’ to translate around the globe, as the model requires. As Biro (2009) has shown, in the Principles of PhilosophyDescartes later addresses the tensions between his idealized ocean model and the state of geographical knowledge in his time. See below, Chap. 11on this and other adjustments made in the Principlesto difficulties in Le Monde.
- 56.
AT.XI. 83; MSM. 143; SG 53.
- 57.
Kepler attributes the tides to the moon’s attraction of waters directly under it (Kepler 1938ff, III, 26)
- 58.
I am not advocating here history as mere literature or entertainment. Rather I believe that Descartes had intentions and conceptual structures reconstructable on the basis of textual and contextual evidence. My conceit is meant to motivate and focus proper historical scholarship on Le Mondeand related texts, not to displace those texts or dissolve disciplined historical inquiry into more or less amusing creative writing. What ‘Descartes’ says here is also arguably a good heuristic guide to what to look for in post-Newtonian Cartesians. This conceit derives from the same tactics of role play mentioned above at Note 6.
- 59.
AT.XI. 76–77; MSM 129–133; SG 49–50.
- 60.
- 61.
Note, of course, that in this connection the medium is the terrestrial substance ‘air’ not the interstitial boulesof second element.
- 62.
Recalling his words: ‘Now, it is evident that, since this stone contains in it much more of the matter of the earth than a quantity of air of equal extent (and in recompense contains that much less of the matter of the heaven), and since also its terrestrial parts are less agitated by the matter of the heaven than those of this air, the stone should not have the force to rise above that quantity of air, but, on the contrary, the quantity of air should have the force to make the stone fall downward.’ AT XI 76–7.
- 63.
Cf. Descartes’ remarks cited earlier: ‘That is to say, just as one side of a balance can be raised or lowered only if the other side does exactly the contrary at the same instant, and, just as the heavier always raises the lighter so too the stone R, for example, is so opposed to the quantity (exactly equal in size) of air above it....that that air would necessarily have to descend to the extent that the stone rose. And, in the same way, it is also so opposed to another, like quantity of air below it,…that the stone must descend when this air rises.’ (AT XI 76) And, ‘…so you see that each part of terrestrial bodies is pressed toward T, not indifferently by the whole matter surrounding it, but only by a quantity of this matter exactly equal to the size of the part; that quantity, being underneath the part, can take its place in the case that the part falls.’ (AT XI 77)
- 64.
See Sects. 3.3 and 3.5.
- 65.
An additional pressure contributing to Descartes’ perseveration on volume relations, and hence inclining him toward a implied hydrostatical account of fall comes, of course, from his doctrine of matter-extension, since given volumes of matter-extension (terrestrial bodies) cannot fall or move at all, unless equal volumes of matter-extension (under various elemental forms) also move to replace them. It was his aero-statics, first outlined to Reneri whilst Le Mondewas being composed, that first betrayed this fault line of conceptual articulation. Cf. Sect. 8.2.3.3.
- 66.
In addition this forestalls objections made against the rotation of the Earth on the basis of the failure of bodies to fall to the west of the spot vertically under their point of release. It is standard cosmological Copernican fare.
- 67.
AT.XI.78; SG 50; MSM.135.
- 68.
AT XI 79; SG 51; MSM 135–137.
- 69.
- 70.
Or alternatively it is an object of comet-like high solidity, and would translate out of the Earth’s orbit if not constantly kept in check by the outer boundary of the latter with the encompassing solar vortex. We will learn more about the solidity of the moon and Earth in the present section.
- 71.
AT.XI. 69–70; SG 45; MSM 119.
- 72.
AT.XI. 71–2; SG 45–46; MSM 119–121.
- 73.
What is meant is that in this option the total force of motion would be taken to be some function of the quantity of matter, speed and density (ease of passage through the medium).
- 74.
AT.XI. 68–69, 71; SG 44–46 MSM 117–121 Both loci imply that the moon and Earth should have equal centrifugal tendencies, and hence orbital placement in the solar vortex (leaving the complication of the moon’s motion in the terrestrial vortex aside for the moment). They do this by alluding to the orbiting objects having as much ‘agitation’ or ‘force’ as the matter of the heavens by which they are being moved.
- 75.
As he had in the celestial mechanics of Le Mondeproper, see Appendix 2.
- 76.
Principia Philosophiaepart III para CXLIX. .....cum (Luna) non minorem habeat vim agitationis quam Terra, in eadem sphaera circa Solem debeat versari; et cum mole sit minor, aequalem habens vim agitationis, celerius debeat ferri.
- 77.
AT.XI. 84; SG 54; MSM 147.
- 78.
Cf. Sect. 4.2 and Fig. 4.1 therein—Descartes’ analysis of the stone rotating in the sling.
- 79.
AT.XI. 86; SG 55; MSM.151.
- 80.
Or, at least seem to contribute; later Descartes argues that even in the absence of the sun, the vortex would produce the same cone of light. AT.XI.88, which should also be compared with AT.XI.109–10.
- 81.
AT.XI. 87–8; SG 55–6; MSM.151–3.
- 82.
Cf. passage cited in previous note, especially final sentence. The surface of the sun becomes per force, a privileged surface, in the same sense that these appeared in the hydrostatics manuscript of 1619, as discussed in Sect. 3.3.2, and again below. On this issue see the incisive article by Alan Shapiro (1974) especially pp.254–57, 265.
- 83.
AT.XI.88; SG 56; MSM 153–155
- 84.
Ibid. 96–7; SG 61–62; MSM. 169–171
- 85.
Principia part III para. LXII; Miller and Miller p.116 (the term in brackets of course enters the Miller and Miller translation from the 1647 French edition of the Principles). Principiapart III para. LXII. ‘Praeterea notandum est, non modo globulos omnes qui sunt in linea recta SE, se invicem premere versus E; sed etiam unumquemque ex ipsis, premi ab omnibus aliis, qui continentur inter lineas rectas ab illo ad circumferentiam BCD ductas, et ipsam tengentes. Ita exempli causa globulus F, premitur ab omnibus aliis, qui sunt intra lineas BF et DF, sive in spatio triangulari BFD; non autem sic a reliquis, adeo ut si locus F esset vacuus, uno et eodem temporis momento, globuli omnes in spatio BFD contenti, accederent quantum possent ad illum replendum, non autem ulli alii. Nam quemadmodum videmus eandem vim gravitatis, quae lapidem in libero aere cadentem recta ducit ad centrum terrae, illum etiam oblique eo deferre, cum impeditur eius motus rectus a plani alicuius declivitate; ita non dubium est quin eadem vis, qua globuli omnes in spatio BFD contenti, recedere conantur a centro S, secundum lineas rectas ab illo centro eductas, sufficiat ad ipsos etiam inde removendos, per lineas a centro isto declinantes.’
- 86.
Gaukroger, in his edition and translation of Le Monde, (SG, xxxvi) writes of the standard editions deriving from Clerselier’s: ‘The illustrations are not Descartes’ own, although those in the Treatise on Lightare undoubtedly based on sketches, no longer extant, by Descartes....Clerselier commissioned his own illustrations, which I have reproduced here, and these are slightly different from those of the first editions (of Le Mondeand the Traité de l’homme).’
- 87.
AT.XI. 89–90; SG 57; MSM.155–7 (emphases added).
- 88.
AT. XI. 90–1; SG 57–58; MSM 157–61.
- 89.
AT XI 89; SG 57; MSM 155.
- 90.
See Sect. 3.3.
- 91.
AT.XI. 93, 94; SG 59, 60; MSM 163, 165.
- 92.
Figure 10.19has the balls marked ‘40’ pressing laterally against each other and preventing further fall, so that Descartes can address and ‘resolve’ the seeming problem for his theory of light that this situation would present. He writes, ‘At this point you will perhaps say to me that it appear from (Fig. 10.19) that the two balls numbered 40 and 40, after having descended a little, come to touch one another, which is why they stop without being able to descent further. In exactly the same way, the parts of the second element that must advance toward E (Fig. 10.12) will stop before having completely filled the whole space we have assumed to be there. But I reply to this that their being able to advance toward E at all is sufficient to establish perfectly what I have said, namely that since the whole space that is there is already filled by some body…the parts press continually on that body and strive against it as if to chase it out of its place.’ (AT X 94–5. SG 60–61; MSM 165–7.)
- 93.
In respect of the production of light, that is, not in relation to production of orbital rotation and settling to orbital equilibrium and establishment of orbital distance from the sun.
- 94.
AT.XI.104; SG 67; MSM.183.
- 95.
A slightly different interpretation is also possible: that the previous Chapter 14 may represent the beginning of the matching process. Chapter 14, with its corpuscular-mechanical explanations of the properties of light, adds little to what we already know as a result of our studies in this book. (See Gaukroger (1995, pp.258–60) for a good overview.) If it does begin the process of matching appearances, the stakes in that process are much raised in Chapter 15, with the turn to explaining fundamental astronomical/cosmological matters of fact.
- 96.
AT.XI. 104–9; SG 67–70; MSM 183–197. Thus Descartes makes brief allusion to the novaeof 1572 and 1604, explaining them as due to the shifting and bending of intervortical boundaries, which can produce multiple images of a single star, or, so he claims, a star’s sudden appearance or disappearance. In Chap. 12we shall see that he presents a very different model for explaining novae(as well as the recently discovered phenomenon of variable stars) as part of a radical, new strategy of system building and system binding in the Principles.
- 97.
The problem is termed timely not because it was hotly debated at this stage in the early 1630s, but just because there was so little attention to comets in the period between the Galileo fomented controversy in 1618, and the work of the Accademia del Cimento and others in the 1660s. Descartes is boldly attacking an inviting, open and at present little studied issue.
- 98.
AT.XI.110; SG 70–1; MSM 199–203.
- 99.
Point X has been added to Clerselier’s figure for ease of discussion
- 100.
AT.XI. 116–7; SG 74–5; MSM 209–211.
- 101.
Descartes’ text says DAF. The Gaukroger and Mahoney and translations therefore follow this. But Clerselier’s figure lacks an ‘F’. It is reasonable to assume that F is meant to be at the intersection of the Earth’s orbit and line refracted ray GS.
- 102.
AT.XI. 117–8; SG 75; MSM 213.
- 103.
- 104.
- 105.
In the Principia, as we shall see in Chap. 12, Descartes pursued a much improved version of this sort of strategy of empirical grip and systematic scope.
- 106.
The conceit arose out of Gaukroger’s reflection on Gaukroger (2000), as well as issues arising in the composition of our joint study, Gaukroger and Schuster (2002). I have accordingly entitled the present chapter, as well as Schuster (2005) and previous conference and seminar presentations of this argument, ‘Waterworld’, in homage to Gaukroger’s striking and amusing term.
References
Works of Descartes and Their Abbreviations
AT = Oeuvres de Descartes(revised edition, 12 vols.), edited by C. Adam and P. Tannery (Paris, 1964–76). References are by volume number (in roman) and page number (in Arabic).
SG = The World and Other Writings, edited and translated by Stephen Gaukroger (Cambridge,1998).
MM = René Descartes, The Principles of Philosophy, translated by V. R. Miller and R. P. Miller (Dordrecht, 1991)
MSM = Rene Descartes, Le Monde, ou Traité de la lumière, translated by Michael S. Mahoney (New York, 1979).
CSM(K) = The Philosophical Writings Of Descartes, 3 vols., translated by John Cottingham, Robert Stoothoff, and Dugald Murdoch, and (for vol. 3) Anthony Kenny, (Cambridge, 1988) References are by volume number (in roman) and page number (in arabic).
HR = The Philosophical Works of Descartes, vol I translated by E.S. Haldane and G.R.T. Ross (Cambridge, 1968 [1st ed. 1911])
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Schuster, J. (2012). ‘Waterworld’: Descartes’ Vortical Celestial Mechanics and Cosmological Optics in Le Monde . In: Descartes-Agonistes. Studies in History and Philosophy of Science, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4746-3_10
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