The Lathe Mind: What Spinoza Meant by “Individual”

What is a Lathe?

I have begun my study of the lens-grinding practices of Spinoza, and how they may have helped structure his non-Cartesian conception of Representation, and metaphysics. I will not be reporting the preponderance of my discoveries here, saving them for an article in process, but already efforts are paying off. Very little has been written on Spinoza’s lens-grinding, and almost no scholarly study has been conducted as to these connections, so this is, as far as I can tell, conceptually virgin ground in Spinoza studies.

For those who do not have a vivid conception of what lathe work is, and the basic dynamics involved, posted above is a youtube video which shows a foot-powered lathe that is not in principle distinct from the lathe that Spinoza must have used (as of yet, I cannot ascertain if it was likely to be hand or foot powered). As one can see, the rotational power of the lathe provides a concentric force for shaping material evenly, and spherically. Most broadly, it is assumed that Spinoza as a lens-grinder would by hand hold the lens blank against a rotating metal “pan” patina, which previously had been shaped into a mould form. A variable grit recipe of abrasives is placed in the pan during grinding, to aid in the shaping, and then polishing, of the lens.

Here is the eariliest illustration of lens-lathing, from a 17th century work of optics (woodcut from Manzini):

Pictured is a torino in aria, a “turner in air” device, so named because the lens had to be held high, above the eyes (there is of course a rhetoric of ascension). If it is unclear, the right hand turns a crank, which sets a vertical belt in motion, which itself turns a horizontal axis above, at whose end is a hemispherical pan, into which the left hand inserts a glass blank, itself cemented to a handle for easy grasping. This early Italian model was most likely modified by the time of Spinoza’s practice, so that the lens was held lower down, at a table or a bench. Its basic mechanics were the same.

A Reconsideration of Spinoza’s Definition of an Individual

But, for a moment, let us consider how just this motion of grinding a hand-held object against a rotating and grinding circular surface imparts to us additional information for how Spinoza conceived his various propositions, and intended them to be understood. (For it is often that a picture of the world and its relations, is that which guides our claims and descriptions).

What I have in mind, is Spinoza’s very interesting definition of what a “body” is. It is a definition I have often thought that I have understood, and even have used in my own arguments. But somehow here, with the dynamics of this technical process shedding their light upon Spinoza’s metaphysics, this Defintion comes to life in a new way:

Definition: When some bodies of the same or a differing magnitude apart from what remains [ a reliquis ] are so controled that reciprically [ invicem ] they may press against [each other], or if they with the same or diverse speeds by degrees are moved so that their motions through some fixed rule [ certa quadam ratione] reciprically they communicate; those bodies, reciprically, are united we say, and they all at once [simul ] one body or Individual compose, which through this bodily union is distinguished apart from what remains [ a reliquis ].

-Ethics II, Lemma 3, Axiom 2″, Defintion

I include Curley’s, largely taken to be precise, translation of the same passage, for interpretive comparison, most notable is his inconsistent translation of the phrase “a reliquis“; in the first half of the definition is left under-translated as an agent “other bodies”, and then in the latter half, as an ablative of separation. The notions of “remainder” [ reliquis ] and “alternate turns” or recipricality [ invictem ] when seen in view of a mechanical process can have greater meaning:

Definition: When a number of bodies, whether of the same or different size, are so constrained by other bodies that they lie upon one another, or if they so move, whether with the same degree or different degrees of speed, that they communicate their motions to each other in a certain fixed manner, we shall say that those bodies are united with one another and that they all together compose one body or Individual, which is distinguished from the others by the union of bodies.

-Ethics II, Lemma 3, Axiom 2″, Defintion

DEFINITIO. Cum corpora aliquot eiusdem aut diversae magnitudinis a reliquis ita coercentur, ut invicem incumbant, vel si eodem aut diversis celeritatis gradibus moventur, ut motus suos invicem certa quadam ratione communicent, illa corpora invicem unita dicemus, et omnia simul unum corpus, sive individuum componere, quod a reliquis per hanc corporum unionem distinguitur.

Aside from the particularities of translation, this has always been a spectacular definition of what an Individual is, for it freed up our concept of what it means to combine and act as a whole. Thereby, any ratio of speeds and communicated motions, such that it preserves itself, suddenly becomes a “body”. The entire world opens up to such transitions, of concrete things coming into a fixity of ratios and passing out, such that the boundaries of bodies, and their definitions, becomes fluid and I think cybernetic. For instance, my car and myself, as I drive it, fall under this notion of an “Individual” making Spinoza applicable to the post-industrial times.

But when we picture this definition of communicated motions and fixed manners in the specificity of a lens-grind lathe, something more comes about. To the human eye, as it turns the finishing pan strikes one as quite distinct from the lens on which it acts. It is spinning and the lens is relatively fixed. But the two in their communication of their motional states in a fixed manner – the idea of the mathematical calculation, the rule which determined the shape of the pan – come together. Two objects have been brought into a particular relation, under a rule. Here the differential of the degree of speed, under a constraint, allows the ratio of their fixity – a certain stillness, an eternity – to be partaken of, which makes of the two, one thing, a composite. We can leave aside for the purposes of a simplicity of illustration the sensate figure of the human craftsman who is fixing the lens, yet turning the lathe, a figure which necessarily must be worked into the cybernetic model of a communication of speeds and parts. But between the two parts of the patina andvitrum a combinational process creates a single Individual, one which perhaps lies key to how Spinoza imagined his Ethics to be read and used. The rest of this passage on bodies and ratios and fluids also benefits from just this technical reading as well.