Why does Spinoza not mention the pendulum clock?

At first glance, Spinoza seems to exclude the pendulum clock from his thinking and writ-ing. Moreover, he seems to mock Huygens’ clocks in Letter 30 (1665), telling Olden burg that Huygens cannot sell them because they are too expensive. Moreover, there seems to be a kind of diminishment in Spinoza’s application of the pendulum analogy. The Dutch phi-losopher applies the pendulum clock analogy solely in his proto-Ethics, the Short Treatise (ca.1660), but the clock disappears in the corresponding passage of the Ethics (1677).

More precisely, in the second chapter of the first part of the Short Treatise, Spinoza writes the following:

From all that we have said so far it is clear that we maintain that extension is an attribute of God. Nevertheless, this does not seem possible at all in a perfect being.

For since extension is divisible, the perfect being would consist of parts. But this cannot be attributed to God, because he is a simple being. Moreover, when exten-sion is divided, it is acted on; and that too cannot in any way be the case in God (who is not susceptible of being acted on, and cannot be acted on by any other being, since he is the first efficient cause of everything).

To this we reply:

1. That part and whole are not true or actual beings, but only beings of reason;

consequently, in Nature there are neither whole nor parts.

2. A thing composed of different parts must be such that each singular part can be conceived and understood without the others. For example, in a clock that is composed of many different wheels, cords, etc., I say that each wheel, cord, etc., can be conceived and understood separately, without needing [the understanding of] the whole as a whole. Similarly, with water, which consists of straight, oblong particles. Each part of it can be conceived and understood, and can exist, without the whole. But since extension is a substance, one cannot say of it that it has parts, since it cannot become smaller or larger, and no parts of it could be understood separately. For in its nature it must be infinite.

In this chapter, Spinoza discusses some of the most essential concepts of his metaphysics.

One of these subjects is the part/whole relation, which is also the main theme of Letter 32. In the citation above, the Dutch philosopher argues that – modally speaking – parts of a whole can be conceived of separately and can exist on their own. Importantly, he gives two examples to illustrate his views: the parts of water that can exist separately from the whole “water” and the parts (wheels, cords, etc.) of a pendulum clock which can be conceived of and exist separately. To this idea, Spinoza contrasts the concept of “corporeal

substance”. In contrast to the parts of a whole body of water and a pendulum clock, the corporeal substance as substance is a continuum. There are no parts that can be conceived or exist separately.

But of course in Spinoza’s metaphysics of the Ethics, all physical objects are modes of the attribute extension of the unique substance. In the corresponding part of the Ethics, in E1p15, Spinoza no longer sets up a contrast between water and the clock to the corporeal substance. On the contrary, he treats “water” as a modus of the corporeal substance and argues that there are two ways to look at this parts/whole relation:

This will be sufficiently plain to everyone who knows how to distinguish between the intellect and the imagination – particularly if it is also noted that matter is everywhere the same, and that parts are distinguished in it only insofar as we conceive matter to be affected in different ways, so that its parts are distinguished only modally, but not really. For example, we conceive that water is divided and its parts separated from one another – insofar as it is water, but not insofar as it is corporeal substance. For insofar as it is substance, it is neither separated nor di-vided. Again, water, insofar as it is water, is generated and corrupted, but insofar as it is substance, it is neither generated nor corrupted. And with this I think I have replied to the second argument also, since it is based on the supposition that mat-ter, insofar as it is substance, is divisible, and composed of parts.

The first way is to conceive of the whole (water) as water (modally), which implies that the parts can be thought of individually and can exist separately. The second way is to conceive the same body of water as substance, which entails that it cannot exist on its own.

Amazingly, the example of the pendulum clock disappeared from Spinoza’s explanation in the corresponding passage from the Ethics. Why? In Spinoza’s metaphysics, generally speaking, there is a rejection of the Aristotelian distinction between the artificial and the natural. Natural things such as water are not more or less natural than artifacts produced by men since men are just parts of nature like all other things. As a consequence, modes such as machines designed and produced by men are no less natural than other modes like water, trees or flowers.⁴⁹ However, Spinoza is very cautious about applying artifacts as mod-els for natural phenomena. For example, he does not use the pendulum clock in the Ethics although he could have. Moreover, it is very hard to find texts where he actually makes use of this kind of analogy with man-made machines. Spinoza differs from his contemporaries Huygens, Descartes, Leibniz and Boyle, who all evidently applied the machine metaphor.

Why does Spinoza not mention the pendulum clock? It is possible to figure this out by drawing from the appendix of De Deo. The main problem that Spinoza has with artifacts is that they are designed and constructed by a creator who is distinct from his creation and who has a certain purpose (telos). For instance, Huygens and his technician constructed a pendulum clock in order to measure time and longitude at sea. In this appendix, Spinoza

49 See E3p2s.

radically rejects the idea that a human body or nature as a whole could be conceived as a man-made machine, although he had applied the analogy of the automaton (probably thinking of the pendulum clock) to explain the functioning of the human mind in chapter 85 of his The Emendation of the Intellect. He wrote already in Letter 4 (1661) that man is not created but generated: “I ask you, my friend, to consider that men are not created, but only generated, and that their bodies already existed before, though formed differently”.

In summary, Spinoza’s anti-finalism might be the most important reason why he does not explicitly mention the machine analogy in general and the pendulum clock in particular.

7. Conclusion

To summarize, the spectacular observations made by Christiaan Huygens in February 1665 concerning self-synchronizing pendulum clocks may provide a context for understanding Spinoza’s otherwise paradoxical Letter 32 to Henry Oldenburg, written in November of 1665. In this letter, Spinoza appears to imply that bodies can adapt themselves to other bodies in a non-mechanistic way, and absent the agency of an external cause – a claim that is completely contradictory with the metaphysical determinism that is an important and characteristic element of Spinoza’s philosophy.

Christiaan Huygens was the first to observe the phenomenon of synchronization in two pendulum clocks. Synchronization is a phenomenon whereby oscillators that are appropri-ately coupled together will adjust their oscillations so as to exhibit a synchronous motion that is regulated by weak impulses communicated through their mutual coupling. Thus the synchronized oscillators appear to behave as if they had spontaneously adapted them-selves [se accommodat] to each other without any corporeal contact. They appear to act as if they “feel each other” or “communicate which each other” at a distance. Consequently, despite his strongly mechanistic worldview, Huygens initially referred to this phenomenon as “the sympathy of clocks”, which seems to suggest a kind of action-at-a-distance as a re-sult of a hidden, or ‘occult’, quality inherent in the clocks.

Huygens did not hide his discovery. On the contrary, he directly notified his father and the fellows of the Royal Society. Moreover, his discovery was published only a few weeks later in the first scientific journal, the Journal des savants. Consequently, within the space of a month, the entire République des lettres was made aware of this odd phenomenon.

Therefore, it is not unreasonable to assume that Spinoza was likewise aware of Huygens’

observations, all the more so since, according to Letter 26 (1665), the Dutch philosopher visited Huygens in Voorburg during that time.

This may explain the context within which Spinoza wrote “I consider things as parts of a whole to the extent that their natures adapt themselves to one another so that they are in the closest possible agreement”. This assertion seems not only to represent a dis-continuity in his views on the nature of the relations between bodies but also – and more importantly – it seems to be inconsistent with his metaphysical determinism. However,

the paradigm of the synchronization of bodies explains that bodies can “adapt themselves”

to other bodies. Moreover, the effect is completely explainable in terms of the mechanis-tic model of the collision of bodies so that the phenomenon is entirely compatible with Spinoza’s mechanistic views as well as his concept of the causality of bodies. Moreover, this hypothesis allows us to explain why Spinoza speaks of “the laws” which adapt themselves.

It is likely that he had Huygens’ law of the pendulum in mind. By this line of reasoning, each pendulum has its own natural frequency, its own law, so to speak, which adapts itself slightly during the process of synchronization to the law of other pendulums in order to form one law, that is, one whole united by a mutual relation of motion and rest.