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Spinoza’s “Spring Pole” Lathe: Experience to Metaphysics and Back

Spinoza’s Practiced Knowing

I mentioned in my recent post on the likely design of Spinoza’s grinding lathe that the dynamics of the Hevelius’ spring pole lathe may be tied to Spinoza’s ideas of Substance and the modes, such that one would be able to see how the epistemo-kinetic experiences Spinoza had during his many hours, days and years of lens grinding on such a lathe may have bore influence upon his metaphysical conceptions.

Here I want to take up this intuition, and perform the appropriate visualizations that would allow us, if for a moment, to picture what Spinoza’s body went through in communications with his device. In this way we might place ourselves, materially and affectively, in a relationship to his ideas, such that reading them alone in text would not allow (even if this goes against what one could argue is Spinoza’s rationalist program of understanding). That is, in short, one hopes to understand through body and affect what ideas Spinoza thought at the most abstract of levels, through their causal origins; for we can follow what Spinoza wrote, “experience can determine our mind to think…of certain essences of things” (Ep. 10), and assume that a similiarity of experiences may determine us to think of a similarity of essences. If we attain the experiences Spinoza underwent which determined him to think of certain essences (in his terms), this I believe can provide clarification to the same thoughts reached through his geometric pedogogy alone. 

The Horizontal and the Vertical: An Initial Philosophical Platform

Further below is an illustration of the tension dynamic of a spring pole lathe, as taken from Hevelius (second diagram). But first in order to follow my thinking here I want to insert a most revealing point made by Gatens and Lloyd in their critique of Hegel’s critique of Spinoza. As they point out, Hegel, while in great praise of Spinoza, felt that he did not embrace the full reality of the “negation”, Hegel’s personal contribution to the progress of philosophy and mankind. Spinoza’s description from Hegel’s point of view simply collapses into an acosmism, an undifferentitated whole of Substance, leaving no specific reality for either rocks, lakes or most importantly Man. In examining Hegel’s objection, Gatens and Lloyd introduce the vectoral notion of verticality and horizontality. It is suggested that Hegel’s problem is that he is only thinking of the “vertical” relationship of the modes to Substance, their individual, expressive relationship to the Totalizing whole. I quote at length here from the two authors because it is a very good paragraph, as they make an extremely important point:

Hegel’s critique of Spinoza thus focuses on the relation between individual mode and Substance. His complaint is that Spinoza cannot coherently articulate that relation without collapsing the infinite mode back into Substance; Substance remains undetermined, undifferentiated, while the individual mode is merely negative. But this is to miss the other dimension of Spinoza’s treatment of the finite modes -their mutual interaction, in which the determining force of Substance is mediated through the whole interconnected network of modes. Hegel’s critique of Spinoza is oriented, as it were, to the vertical relation between Substance and individual mode, rather than to the horizontal relation in which finite modes act on and are acted on by one another. Here, along the horizontal axis of finite modes, the claim that determination involves negation can be seen not as a repudiation of finite individuals but as an insight into their interdependence (71)

- Moira Gatens and Genevieve Lloyd, Collective Imaginings, chapter 3 “Re-imagining Responsibility”

Gatens and Lloyd are making clear the a key emphasis Spinoza places on modal expressions, as real, when included in our own constructive and immanent projects of freedom. I would graph out the differentiation that they find in Spinoza in this way:

I would parenthetically add to Gatens and Lloyd’s point that the reason why Hegel is thinking solely about the verticality of the modes is that the binary of individual/God, (or individual/world) is one of the primary schemas of the intersubjective investigations and inculcations of European Christianity. The salvation of the soul, through its relationship to an all-encompassing God, (via various institutional mediations), was the essential dogmatic concern, and this lengthy heritage necessarily brings the philosophical focus back to this binary difficulty: how does the individual soul return to God. Hegel, because he sees man at the apex of history, primarily must read the problematic in terms of a vertical dynamic, the individual vs. the whole. But Spinoza, because he is not burdened by the primacy of man or his reflective powers, allows another dimension of analysis which Hegel cannot see: that of the horizontal. The institutional mediations of the State, Church, Family and their imaginary relationswhich simply interpose themselves as aids to an essential verticality, are by Spinoza exploded out to the ultimate horizontal limit: the infinite expression of the modes. And the imaginary status of their mediating ideas become proliferate and constitutive vectors of power, degrees of freedom, across the field of Being (if one could put it that way without too much obfuscation).

Heveliuss Selenographia (1647) Spring Pole, Foot Pedal Lathe, illustrated

Spinoza’s Lathe

I want to return to the assumed spring pole, foot pedal lathe (pictured above), to get a much more concrete, affective sense of the vertical and the horizontal in Spinoza, and how the practices of Spinoza’a lens grinding may have helped construct his metaphysical conceptions. One must recall that Spinoza spent hours upon hours at such work lens work. To grind, polish and re-polish a lens could take several days, much of it in non-stop and highly repetitive, one might even say meditative, action (Auzout in 1664 records a time of 15 days for a single objective lens). So let our attention be called to the internal dynamics depicted above, found in focus of the dotted yellow frame. Here one should picture Spinoza seated or standing at length, his foot rhythmically pushing down a vertical tension from the spring pole at the ceiling. The vertical rising and falling motion forms a kinetic warp which not only works to orient the body spatially to the height of the room, connecting consciousness from the floor boards to the ceiling, but also creates and punctuated temporality, a timed ratio to the work. Transverse to this warp is the weft of horizontal action. The oscillations of the grinding form are pulled across the body by the push and pull connectionsof the foot the ceiling pole, and distinctly lateral to the focus of concentration. Again and again for hours these up-down, left-right actions literally weave a room of fluctuating conscious attentions, in which the craftsman necessarily embraces the lived experiences of the space, aware that whatever precise spotlight of focus he may have, it is merely a part of much larger, wider degrees of perception. Against Hegel’s fear of an individual’s collapse into the undifferentiated, the agentized craftsman becomes the draw-string of every quarter of the room, a focal point of at least two vectors action, from which and to which he is a differentiated, yet interconnected and expressive part. The melding of the craftsman and his tool is more than a metaphor. It is an experiential and metaphysical certainty.

Within this dotted frame of loomed space, at its center is a rotating circle. It whips at varying speeds in response to both the intensities of the leg, and the limits of the spring pole above, in a concentric motion. It is no secret that Spinoza had great love for the circle as a diagramed exemplar of the relationship between the modes and Substance (Ethics 2p8s, pictured below), but also as an ideal of vision and the actions of optical focus (Letter 39 to Jelles, March 3rd 1667). Here, for hours on end Spinoza would stare determinitively as a rotating circular form which remained both fixed (stable in its ratio), and changing, expressing in both the consummation of the vectors of the room’s actions. One cannot help but think that such concentrated attention upon the spinning form would leave at least a conceptual imprint upon the philosophical craftsman, especially as he considered the modal expressions to be causal interactions immanent to the whole, just as internal rectangles can be considered immanent to the properties of a circle (his diagram below). It is most suggestive to see that the rotating circular form becomes a bed of friction and idea, producing realized changes in the material of glass held in Spinoza’s sensing hand.

from Ethics 2p8s
The Turning Lap

To carry our instructive analogizing further, one must look closer at the actions immediate to Spinoza’s attention as he worked his glass into the required shape.

In the scalloped metal form likely an abrasive would be applied to aid in the grinding, the light blue arrow above represents the hand’s actions upon the circular rotation. The horizontal and vertical tensions are vortexed into an oscillating circularity. There a recipe of frictions and intelligenced experiences interact to bring about an ideal result. What Antonio Negri calls the “concrete…unique terrain of reality, [the] fruit of the paradoxical determination [a metaphysical dilation of unity and multiplicity]” (The Savage Anomaly, 127), the modal “surface of the sea”, occurs here, in the turning scalloped dish, a product of the cybernetic expressions of a room, a mechanism, and man, in which the craftsman’s hand performs a living shore of perceptual action.

The Sublime Tool

If this notional leap from mechanism to conceptual metaphysics seems too great, too fantastic, I believe that this is because we do not have a strong enough sense of the bodily, affective, imaginary foundational means of immanent abstract thought, something that Spinoza’s own metaphysics works to make more clear. Further I believe we must adjust ourselves from thinking of Spinoza merely in terms of propositions and proofs, though the rhetorical form of his work certainly at first or even second glance invites us to think of him in this way. Richard Sennett for instance in his recent pragmatic and near-poetic book, The Craftsman (2008), perhaps gives us a bridge for thinking about craft and abstraction as part of one constitutive process. He invites us to understand how human progress and freedom comes by thinking through one’s tools, how tools help frame our questions and solutions. In fact this is very much how Spinoza has conceived of abstract thinking itself, as he followed Descartes’ analogy found in the 8th rule of the Regulae : just as how a blacksmith’s tools had to be originally made by simpler tools themselves, so too simple tools of the intellect are needed to make other, more complex tools of the intellect (On the Emendation of the Intellect ). In a certain sense, one needs something that hammers in order to make a hammer:

The matter stands on the same footing as the making of material tools, which might be argued about in a similar way. For, in order to work iron, a hammer is needed, and the hammer cannot be forthcoming unless it has been made; but, in order to make it, there was need of another hammer and other tools, and so on to infinity. We might thus vainly endeavor to prove that men have no power of working iron. But as men at first made use of the instruments supplied by nature to accomplish very easy pieces of workmanship, laboriously and imperfectly, and then, when these were finished, wrought other things more difficult with less labor and greater perfection; and so gradually mounted from the simplest operations to the making of tools, and from the making of tools to the making of more complex tools, and fresh feats of workmanship, till they arrived at making, with small expenditure of labor, the vast number of complicated mechanisms which they now possess. So, in like manner, the intellect, by its native strength, makes for itself intellectual instruments, whereby it acquires strength for performing other intellectual operations, and from these operations gets again fresh instruments, or the power of pushing its investigations further, and thus gradually proceeds till it reaches the summit of wisdom.

But is our reading of Spinoza’s metaphysics anything more than simply a coincidence of horizontal and vertical vectors in the lens-grinding lathe, and Gatens and Lloyd’s horizontal and vertical spatialization of his metaphysics in defense against Hegel? Is this conflation merely accidentally bolstered by the analogy of ideas to be taken read tools in Spinoza’s very early work? I think there is much more to this than that, and that aside from the notion of the horizontal and the vertical there is a multiplicity of core principles that seem to stem from Spinoza’s unique, and one must say classed, artisan experiences. In particular we must understand that Spinoza, unlike Descartes, was through and through a practiced craftsman, an artisan by trade and value, who repetitious and refining practices which he took rather seriously must have influenced his guiding conceptions of Mind, Body, Idea and Power. In fact, it seems that it is a tooled notion of idea and body that I believe informs his vital definition of the power of the body, a defintion which will reconceptualize any of our instrumental approaches to material augment of the human body or mind:

Whatever so disposes the human Body that it can be affected in a great many ways, or renders it capable of affecting external Bodies in a great many ways, is useful to man; the more it renders the Body capable of being affected in a great many ways, or of affecting other Bodies, the more useful it is; on the other hand, what renders the Body less capable of these things is harmful.

- E4p38

Think on how this expressive yet instrumental numerical notion of power can be found within the most elementary experiences of tool use, as Richard Sennett tells us about the wonders of the flat-edged screwdriver:

…in its sheer variety this all-purpose tool admits all manner of unfathomed possibilities: it, too, can expand our skills if only our imagination rises to the occasion. Without hesitation, the flat-edged screwdriver can be described as sublime – the word sublime standing, as it does in philosophy and the arts, for the potentially strange. In craftwork, that sentiment focuses especially on objects very simple in form that seemingly can do anything (195)

- The Craftsman, Chapter Six “Arousing Tools”

I believe that Spinoza’s lifelong craft experiences with the lens-grinding lathe (among so many other simple tools) had a lasting effect on his conceptions of Mind and Body, and their necessary unification. The grinding lathe, with its intimate, indeed cybernetic, interweave of body, mind and material construction, its concentric use of the spinning semi-sphere, must have struck Spinoza as sublime in the sense that Sennett tells us. There is the evidence of Spinoza’s resistance to the sophisticated, semi-automated designs of his brilliant and wealthy neighbors the brothers Huygens ( EP 15/32 ) which tells us that Spinoza was quite hesitant to leave behind the interface of the machine with the understanding and felt hand. But it is more than this. It seems that the grinding lathe leaves its conceptual, kinetic trace all the way up through to the most abstract, and most radical of conceptions. In fact there is the very real sense in which we may read Spinoza’s Ethics (as it exists both in idea and extension) as a tool which can affect and be affected in the greatest number of ways. 

Picturing Work and the Work of Picturing

Once we have a vivid sense of the kinds of material engagements Spinoza had concerned himself with, his bodily practices of concentrated creation and refinement, we get a better sense of how Spinoza conceived of his own Rationalist, propositioned philosophical aims. From there we can place ourselves with the lived historical space of the man who lived at the cusp of our modernity, and feel something of the material and pragmatic focus of his articulations of freedom. Below is Spinoza’s rented room in Rijnsburg where he lived roughly from age 29 to 31 having fled the upheavals of Amsterdam, perhaps with concern for the return of his tuberculosis from remission. It is today’s Spinozahuis museum. As mentioned before the wood turners lathe depicted there is NOT the kind of lathe Spinoza would have used, but if you look to the upper center left of the photo you can see a hypothesized spring pole, the vertical vector of his practice. It is not known if Spinoza’s later rooms in the village of Voorburg, where it is thought that he did his most concentrated grinding work, were of this size, but the combination of the Rijnsburg room and Hevelius’s illustration gives us I believe some determinative sense of the internal dynamics of Spinoza’s lived experiences as a craftsman and thus as a thinker; they directs us to the material and conceptual causes that may have privileged Spinoza treatment of the Mind and Body over his predecessor, Descartes. There is much that divided these two thinkers from each other, but perhaps even more than joined them. Each was concerned with lens-grinding, optics and the improvement of the telescope, but only one of them was a practiced maker of lenses and instruments. Only one of them touched the glass.

The Rijnsburg Wood-turners Lathe, Spinozahuis

Hevelius's Spring Pole Lathe, from the Selenographia (1647)


The Rijnsburg Wood-turners Lathe, another angle

The Rijnsburg Wood-turners Lathe, another angle

Spinoza’s Grinding Lathe: An Extended Hypothesis

Johannes Hevelius, also, Johannes Hewel, Johann Hewelke, Johannes Höwelcke or Jan Heweliusz (January 28, 1611 - January 28, 1687)

A Proposed Homologue to Spinoza’s Grinding Lathe

It has been revealed by some digging into the record by Stan Verdult that indeed the lathe that occupies the Rijnsburg Spinoza museum is not of the sort Spinoza would have used (though it may give us a sense of the size of his lathe). [Written about here: The Rijnsburg Lathe: Like the Sun, not 200 Feet Away .] But if we are to come close to understanding the near-daily physical practices Spinoza had engaged in as a lens-grinder and maker of both telescopes and microscopes, we need to narrow the view to the design parameters his grinding lathe likely exhibited. I have mentioned in the past that the foot-driven lathe of Hevelius, as published in his astronomical study of the moon, Selenographia (1647), provides us perhaps of the most revealing illustration of the elements that would have been involved.

We know from Spinoza’s comments on the semi-automated designs of Christiaan Huygens whose home in Voorburghe certainly seems to have visited multiple times, that Spinoza favored a simple grinding mechanism, one in which the glass to be ground was held freely in the hand (affixed to a handle). The general disposition among mid-century savants to further automate the grinding process and remove the human element from the process as much as possible seems to have been looked on withextreme doubt by Spinoza. This does not mean that there was no automated aspects to Spinoza’s lens-lathe, for the lathe itself is a machined dynamic which transfers motions by the hand or the foot to a concentric movement put upon the glass blank. It is only that Spinoza preferred the moment-to-moment, lived craft judgments that came from an artisan’s practice through the encounter withthe machine. In this way our focus should be upon the nature of the machine/human interfaces used by Spinoza, and therefore a central question is whether Spinoza used a hand-driven or foot-driven lathe, with a view to visualizing each as vividly as possible.

Foot-driven lathes were not uncommon in the era, in fact Hevelius’ Illustration of his lathe was published when Spinoza was 15 years old, perhaps a decade before his reported lens-grinding days, and likely was not seen as an innovation then. I suggest that it is to this illustration we must turn if we are to get a clear picture of the kind of physical actions Spinoza trained his eye upon.

the lathe as it appears in Heveliuss Selenographia

the lathe as it appears in Hevelius's Selenographia

In the labeled illustration below, one can see the general action of the foot pedal transfer of power to a concentric motion, and the orientation Spinoza may have had, and the pole that may have been fixed to the ceiling of his room:

Here are various details so as to better see the composition of components:

Here one can see the transfer of the cord to a grinding form’s modular base. It would not be necessary, or even likely that this modularity would be a feature of Spinoza’s lathe, but the horizontal orientation of the grinding dish (as opposed to the vertical angle shown in designs from earlier in the century) would be the preferred design, for this would allow gravity to act as ally in abrasive control and arm fatigue. (We do not know how intermittent Spinoza’s tuberculosis was, a disease that he, by Colerus’s account, suffered from since about the age of 24, but the question of endurance could have been a singificant factor in the kind of lathe Spinoza used.)

In this close-up to the foot pedal one can see the simple nature of the drive mechanism. A foot pedal allows of course one to use the larger leg muscles, a benefit for more arduous projects; but it also informs a vertical tension from the floor to the ceiling. There is a cross dynamic between the communications of the foot to the spring pole high above, which is then read in the relative speeds and intensities by the hand pressing its material downward. The oscillations of upward and downward, a horizontal, yet fixed, stable circular whirrings do suggest a grid of complex physical actions and interface. One may be tempted to see in this cross-dynamic the metaphysics of the verticality of Substanced expression, and the horizontality of modal causations. In any case, the foot pedal lathe leaves a distinct epistemo-kinetic imprint upon the craftsman that engages it, something that surely would have informed Spinoza’s thinking about material and its formation. 

Yet on the level of information on technique, perhaps even of more interest in this close up of the Hevelius drawing is the shape of the grinding forms discs placed haphazardly on the floor. They are not the hollowed-out concave metal forms like those, let us say, Hieronymus Sirturus wrote about in his influential book on technique Telescopium, siue Ars perficiendi nouum illud Galilaei visorium instrumentum ad sydera (1618), (whose spherical perfection was created by being ground against a matching convex iron casting). They appear instead concavely beveled, on the inner slope of which a lens can be angled to be ground (if I read the illustration correctly).

One can see each of these types of grinding forms (a beveled inner edge, and the scalloped dish) in van Gutschoven’s 1663 letter to Christian Huygens which had answered Christiaan’s question as to how to grind smaller objective lenses [comments on: A Method of Grinding Small, Spherical Lenses: Spinoza ]:

Here in the van Gutschoven illustraton a narrow canal (vertically aligned) serves as the grinding surface just inside the lip.

And here is a concave finishing form, in whose center a small lens would be placed for polishing. The two illustrations above simply show that both form designs were employed, and we cannot be sure if Spinoza would have used one or the other, or both (though the degree of curvature shown above would be wholly inappropriate for telescope lenses for which only a slight curvature was needed). One might add, by Spinoza’s use of the terms “dishes” or “plates” for his metal laps, the scalloped spherical form, hollow at the center, one could presume was a main metal form that he used.

To return to the Hevelius example, if we can seriously entertained the prospect that Spinoza used a foot-pedal grinding lathe, I would want to point out the thorough and bodily engagement that grinding would have involved. Not only were the powers of close-eyed concentration, and precise fingered and armed exertions involved, but also a co-ordinated rhythm between the actions of the foot that from a distance below swiveled the grinding form back and forth, reversing itself, restrained from high above, bringing fortha total read of machine tensions which completed a lived circuit between the human body and its attentive results. Spinoza’s entire body would be in play in the workings of the glass, from head to toe. And if one superimposes the requirements of his metaphysics (his equivocal treatment of Thought and Extension, and his definitions of a body and power) upon this organization of machine, idea and flesh, one may see with growing clarity how his crafted practices informed his most abstract thinking.

This is the case found in the Hevelius example, which forms one end in the spectrum of the possible machine designs Spinoza likely used. There is of course a much simpler design, the hand-driven lathe, which Spinoza may have also worked from. The nature of this lathe can be seen in the 1660 Manzini manuscript, and the expert mock up made by the 400th Anniversary of the Telescope team:



One can see the typical concave metal dish (to the left) and the hand-drive of the form. In terms of dynamics instead of a swivel motion to the form, a repeated back and forth oscillation driven by the foot co-ordinated from high above, here the form can be spun in continuing circles in close proximity to the chest. Evidence that Spinoza used just such a design perhaps can be seen in the list of things sold from his estate in November of 1672.

and various instruments for grinding (‘en verscheidene slypgereedschap’) like mills (‘molens’, also plural!) and great and small metal dishes serving for them (‘groote en kleine metale schotels daartoe dienende’) and so on” (en so voort).

That there were multiple mills sold (not a complete list of what he owned one might assume) suggests a variety of more specialized devices, instead of one large workbench as that shown in the Hevelius example. But this is not at all a clear, or exclusive conclusion. Small hand-driven grinding lathes may have been employed for small microscope objectives (which Spinoza favored) or telescope eye-pieces, whereas a foot pedaled, spring pole machine could have been used for larger telescope glasses which could reach nearly 1/2 a foot in diameter.

In digression, there is evidence that Spinoza collaborated with the respected optical mathematician and amateur scientist Johannes Hudde on calculations for a 40 ft lens. To give a sense of it, such a lens would have been approximately 5 inches in diameter, of very slight curvature and only 5 – 8 mm thick: Huygens’s letter to his brother 23 Sept 1667:“Ie voudrois scavoir quelle grandeur d’ouuerture Spinosa et Monsieur Hudde determinent pour les 40 pieds” (See “The Lens Production of Christiaan and Constantijn Huygens” , 1998, by van Helden and van Gent, for the dimensions of similar lenses). Whether Spinoza was in the practice of grinding such lenses, which at the time would have been among the most powerful telescope lenses in Europe, we cannot know. But it seems he was involved in their calculation.

To return, if we are to imagine a hand-driven lathe’s effect upon Spinoza’s rational conception of Mind and Body relations, the form’s spinning, instead of oscillating, motion, may involve less of the entire body than a foot pedal lathe would; the head, the shoulders, the hands would form a frame of power and sensitivity, withthe shoulders acting as fulcrum points of stability and the hands as reading extensions. The cybernetic feedback between the hands, one holding the glass blank, the other whirling in circles would seem to be even more involved, more kinetically woven than that of the foot pedal lathe. The power transfer is more direct the thus the communication between hands more intimate. And one sees how the manifestations of concentric stability and change, eternity and flux, expressed in two respondent revolving discs, certainly could present itself as significant to the circle-loving craftsman as he sought to perfect his lens under physical pressure and frictions of grit.

By my view it seems most likely that Spinoza employed both kinds of lathes, the foot and the hand driven, perhaps at different points in his life, in a process of a refining of techniques. What really is at stake in this analysis I would contend is that one must be able to SEE what Spinoza did during a preponderance of his days, picture it physically, in an affective projection, to fully conceive what he thought. The machine and the human, that mind in the device and the matter of the idea understood to be in mutual conjunction.

A Method of Grinding Small, Spherical Lenses: Spinoza

Van Gutschoven’s Design for Grinding Small Lenses: Letter No. 1147

We have in a letter written to Christiaan Huygens by G. van Gutshoven, descriptions and diagrams of the essential processes for grinding small spherical lenses, as they were likely shared by most contemporaries of the age. The letter is surely a response to a request from Christiaan who may have been in need of smaller lens grinding techniques, either due to his future interest in compound eye-pieces for telescopes, or in regard to the question of the best lenses for microscopes which would later arise in discussions between himself and Johannes Hudde and Spinoza as well. In any case, van Guschoven an Antwerp mathematician, was Huygens’ initial teacher of the complete essentials of lens grinding in the first place, which he gave to him ten years before in a letter dated Feb. 10, 1653. It was by the aid of these instructions, among others,  that Huygens was able to grind one of the most powerful lenses in Europe, and discover the rings of Saturn in 1656.

This letter is dated only as 1663 by the editors of Huygens’s Oeuvres. 1663 was the year that Spinoza had moved to Voorburg, where the Huygens family kept their Hofwijck country estate. That spring Spinoza rented rooms in the home of master painter Daniel Tydeman, but a five minute walk from the Hofwijck. But Christiaanwas not yet there. He was living in Paris with his father who was attempting to curry the diplomatic favor of King Louis XIV, an effort which would result in Constantijn Sr.’s son becoming the secretary to Louis’ Royal Academy of the Sciences, in 1666.

None of this has occurred yet. Christiaan and Spinoza have not yet met (unless they crossed paths momentarily in the summer of 1663, when a traveling Christiaan took leave of Paris to go to London in the off-season). Huygens would not arrive in Holland and develop his relationship to Spinoza until after May of 1664.

What this letter reveals to us though is the basic mechanism and techniques used in the grinding of small lenses. We know that Spinoza made microscopes (and telescopes) at least since the year of 1661, and in his coming debates over techniques and optics with Christiaan he would champion much smaller, more highly curved lenses for microscopes, against Huygens’ designs of lesser magnification. One would think that from van Gutschoven’s descriptions we can receive a sense of the physical practices that preoccupied Spinoza for many of his daylight hours, specializing at times in these smaller lenses.

It should be noted that the Huygens brothers by this time are among the best lens-grinders in Europe, and Christiaan had already worked on several sophistocated semi-automated designs of grinding machines. These instructions must have been experienced as extremely rudimentary to Christiaan (or perhaps, it is from another date).

The letter has three figures, pictured below. The first of these shows a vertical grinding form that is likely of iron or copper. One can see the core movement of a lathe, as foot petal likely drove the strap that turns the shaft, spinning the form concentrically. For larger lenses the form would be hollow, holding the concavity of a curvature that one would want the glass to have. Here though, the small lens is to be ground in the “canal” near its lip:

“Now in this hollowed out canal C D you will grind glasses affixed to a handle and pressed into the canal, with the handle in the hand continuously; while grinding the glass you would turn it until all parts of the glass are equally ground.”

After this equanimity is roughly achieved, attention is turned to the “laminate” or layered strip A B, which turns so the top of it is horizontal to the turner’s bench. By van Gutschoven’sdirection, the laminate is of a soft wood, polar or willow. (Other techniques of the day call for paper.) The roughness of dimples are by hand ground away, and Tripoli, which is a chalky substance made of the remains of microscopic marine life, is added to the laminate to smooth the way.

After this, there is a third process recommended which can either be done in a concave wooden form G H, it too aided by Tripoli, pictured here:

Or, what seems to be a pillow (plombae), affixed to a lathe shaft EG:

There are several things of interest here. The date of the letter makes this description contemporaneous with Spinoza’s own practices, so one might assume a basic correspondence. The grooved canal method strikes one as similar to those a-centric grinding techniques discs used by diamond polishers which Spinoza may have come in contact with either briefly as a merchant of gems, or simply by growing up in a community where gem polishing. The process remained unchanged for several hundred years as late 19th century illustration below shows:

Like the diamond polisher, it is quite possible that Spinoza’s form was oriented horizontally, and not as van Gutschoven suggests, vertically. This was part of a gradual change in lens grinding techniques, much of it initiated by gem polishing influences. The horizontal mould simply made the glass easier to control, and the variable polishes to be administered more cleanly. For this reason, any polishing with Tripoli also occurred on a horizontal, turning wheel. The grinding forms designs that I have seen that the Huygens were using now all had a horizontally oriented lap. 

The second thing to note that in 1667 and 1668, after Christiaan had come to know Spinoza and become familiar with Spinoza’s techniques, he clearly did not still feel comfortable with the limits of van Gutschoven’s design, whenever he had received it, as he in repeated letters urged his brother about the fineness of Spinoza’s small lens polishing. Spinoza’s technique was not that of van Gutschoven. It is my feeling that he had developed, either though his associations in the community he grew up in, those influenced by the practices of gem polishing, means of polishing that were not common to the rest of Europe. Whether these be methods of grit application, the use of diamond dust, particular designs of a simple but effective lathe, one can only surmise. But it seems that Spinoza’s glasses were of a quality and luminosity that made them distinct.

Here is the Latin Text of van Gutschoven’s letter: The Text of van Gutschoven’s Letter to Huygens No. 1148


Aside from this I would want our investigative imagination to extend itself to the physical understanding of these practices, and the conceptual impression they would leave upon a thinking man who engaged in them repeatedly. This has been a theme of my thinking, that if Spinoza had been a potter we may do well to think about his metaphysics and arguments in terms of the potter’s wheel with which he was familiar. The grinding lathe is not so different from the potter’s wheel, and van Gutshoven’s diagrams give us a visual vocabulary for the kinds of effects and exertions that Spinoza produced in perfecting his craft. What in particular these diagrams allow, apart from the general understanding of the grinding lathe, is the picture of a grooved grinding practice, the canal, which varies from the greater method of placing a glass blank within a concave metal form. If indeed Spinoza used this method for his small objectives for microscopes, we can think along with him in the craft of it, and see him bent over the lip of the spinning canal.

As pictured here before, here is an example of a foot petaled lathe from the year 1647, that used by Hevelius. It may give us a dynamic sense of the physical engagement:

Here is a closer look at the Hevelius Lathe: Spinoza’s Grinding Lathe: An Extended Hypothesis

A Possible Influence of Diamond Polishing on Assited Lens-grinding


Was the horizontal grinding wheel, and the leaded-head a definitive influence upon the automatic conceptions of lens-grinding machines? Below are posted two notable examples of automatic designs, by Hooke and Hevelius, and the essential diamond-polishing design:

Hooke, first plate Micrographia (1665)

 Hooke, first plate Micrographia (1665)


Hevelius, Machina Coelestis, after page 433 (1673)
Jan Luyken, copper engraving of a diamond polisher (1690)
A diamond polisher, late 19th century
We do not have a date earlier than 1690 for the leaded-head design of diamond polishing. Whether this is a product of the the newly imported cuts (rose and Mazarin) during that century, or if the leaded-head was already natural to the design, I do not know. This juxtaposition of illustrations is just to open up the question of influence from jeweler’s wheel to lens-grinding conceptions.
What this has to do with Spinoza is that it poses the question as to the technical milieu in which Spinoza may have learned his craft, and the possible reasons for Spinoza’s resistance to assisted or automated lens-grinding machines. If diamond polishing formed any part of Spinoza’s introduction to lens-grinding, then the relationshp between the techniques of the one to the other many inform our understanding of Spinoza’s thinking.

Spinoza and Diamond Polishing?

What was Spinoza’s Relationship to the Gem and Diamond Trade

I post here a portion of a hard to find book, in the interest of establishing a baseline of information for others. Because this site has involved a variety of hypotheses on the kinds of influences Spinoza may have had, all should be sketched out as best we can. Among my thoughts as to the mystery of where Spinoza may have learned his lens-grinding craft, apart from any guild commitment, it occurs to me that he may have learned it, at least in part, through his involvement with the diamond trade. There is some evidence that Spinoza had dealings with gem dealers in the years 1655-56, in fact the scuffle and suit of Antonij Alverez shows that he and likely his family business had dealings with one of the largest Amsterdam diamond trade names, Duarte. Whether this engagement with the gem business led his curious mind into learning about the process of gem and diamond polishing from which he may have taken valuable techniques into his lens-grinding (using diamond dust as an abrasive) at this point we cannot say. All we can do is put the fact that Spinoza had unique skills, techniques and likely instruments for lens-polishing, as testified by Christiaan Huygens, and speculate if these come from an origin that would be specific to his Jewish community. These may have been techniques specific to gem polishing, a process which the Jews of Amsterdam predominately came to rule over, or they may have been specific to Jewish lens-grinding. In either case it may serve us well to lay out the facts of Jewish diamond trade during Spinoza’s young adulthood. At the very least such facts give us a broader picture of the time and place Spinoza grew up in, and one of the lathe-processes he would have at least in a cursory fashion been exposed to.

Jews of the Diamond City

The extensive quote below is from Jews of the Diamond City – Amsterdam (1988), put out by the Harry Oppenheimer Diamond Museum:

We hear of Jewish masterpolishers only from 1611 onwards. A notarial certificate from the year deals with a contract between Jewish diamond polishers who were trained by gentiles. A document dated 1615 mentions that one named Solomon Franco had finished his apprenticeship as diamond polisher with a certain craftsman named David Bolshnik. Additional sources in the first quarter of the 17th Century inform us about another dozen names belonging to Jews of Portuguese origin who were experts in diamond polishing. As a rule these craftsmen were poorer distant relatives of the merchants who imported the rough stones thus ensuring themselves employment and a decent income. For example, we know about the two famous families – Correal and Duarte de Paz – who gained their reputation as jewelers and diamond polishers in the 17th Century.

The waves of Jews who fled persecution from Germany and later the Jews who fled Poland and Lithuania after the massacres of 1648/9 lead to an influx of refugees lacking in means and profession to Amsterdam. Consequently, the social structure of the diamond industry underwent a gradual change; the Portuguese traders, the polishers and the jewelers became production managers who provided work for their Ashkenazi brethren who, to an increasing degree, constituted the working class.

In spite of the scant documentation of the period, it seems that the Portuguese Jews preferred their “Pollak” brothers over their gentile fellow-workers. It was their intention to teach them an “honorable” trade which would provide them with a reasonable income and standard of living.

Copper Etching Jan Luken (1690)

copper etching, Jan Luyken (1690)

It is interesting to consider what Jews saw in the polishing trade that made it so attractive to them. On a copper engraving by the Flemish artist Jan Luyken (1649-1712) a typical diamond polishing workshop is shown. It was a rather small room, dark and stiffling. The polisher stands near the polishing wheel and places the stone on the leaden head at the end of the polishing handle. Time and again he changes the position of the stone, each time choosing a different angle on the spinning iron wheel coated with diamond dust. The rotation of the wheel is affected by a transmission belt connected to a horizontal drive wheel.

A notarial certificate dated 1615 mentions that the Portuguese Jews employed gentile women to rotated the drive wheel; this it the first written testimony to a female work force in the diamond industry.

The Jewish polishers of Ashkenazi origin who were unable to employ gentile women had to employ their own wives and children to operate the wheel. Thus, day to day, from dawn to nightfall, the whole family labored 12 to 15 hours a day to make a living.

The diamond polishers in general, worked independently and received the raw material from the diamond traders. Their wages were determined according to a variable tariff based on the weight and quality of the rough stone, the form of the finished product and the quality of his work. However, these tariffs were also subject to supply and demand…

…Among all the occupations that flourished in the Jewish quarter of Amsterdam, such as peddling, printing, dispensing and others, the trade of “Diamond-schleifer” – Yiddish and Ladino word for diamond polisher -became “The Trade.” Every Jewish mother strived for her son to learn this trade which ensured him a secure future, a good livelihood and economic independence, but, above all, great mobility on the social scale.

To become a craftsman required a very high tuition fee (69-225 florins) collected by the master polisher. The training period to be an expert in all the stages of processing in the old fashionable shapes (heart, almond, rose-cut and brilliant), lasting from 15 months to four and a half-years.

Rough stones of good quality required only few preparatory stages before the polishing process: cleaving or sawing, (dividing the stone in two), and cutting, (rounding off the base). These operations were also taught by the master and only towards the 18th century can one observe the specialization in ancillary trades connected with the polishing (44-45), (Simona Edelman).

What We May Be Able To Glean

Aside from the thin hypothesis that Spinoza have have learned something from the diamond polishers of his community, there are significant facts in this brief piece. Unfortunately the text is not footnoted, so it is unclear what is an author’s conjecture and what has foundation. There is the idea that the Sephardic Jews had learned this trade from gentiles in the early part of the 17th century in Amsterdam. Henriëtte Boas places these to be Huguenot refugee’s from Antwerp, establishing one more Jewish and Protestant Reform attachment. (Yet I have also read that these techniques likely arose through a direct transmission with India, from whence the diamonds came.) Next we have a cost and a timetable set out for learning the trade. This gives clue to a non-guilded craft relationship, and may reflect upon lens-grinding as well. It is helpful to know that in 15 months a skill such as this one could be acquired for a fee. Interesting is the shift in labor distribution in the decade leading to Spinoza’s majority, as Ashkenazi started to form a “working class” in the diamond trade. One wonders if such an influx may have also opened the door to Spinoza learning lens-grinding in his community outside of the usual transmissions of knowledge, since economic relationships were changing. Additionally, we hear of the diamond dust and flat iron wheel, a material technique not mentioned in any of the lens-polishing techniques I have read in the period. Could it be that there is some improvement offered by this means? The leaded head in diamond grinding (pictured below), actually presents a semi-automated system of grinding that pre-dates any assisted lens-grinding of the time. Could the diamond-polisher’s example, (aided by the fact that he needed to make plane-cuts, and not spherical), have been the inspiration for some of the semi-automated ideas for lens-grinding, such as those by Christian Huygens, D’Orleans and Hooke? (And, is Spinoza’s rejection of assisted polishing related to the spherical shape itself, feeling that the hand bests can feel a spherical relation?). And lastly, the wheel is quite distinct from a lens-grinder’s wheel, in that the grinding is done at the edge, and not in a bowl form. Would this kind of wheel use have helped grind certain small sized lenses? Enough with the conjecture for the moment.

Jewish polisher, late 1800s

Jewish polisher, late 1800s

Some Personal Thoughts on a Possible Spinoza Lathe

Some discussion has been going on over at the Practical Machinist forum, where I have sought any views about the real world workings of any of the devices Spinoza may have used at grind lenses. I have come to the thought that it might very well be a rather simple device that Spinoza used, not much differnt than the one Manzini depicts for the start of the 17th century:

In response to my query someone was kind enough to relate some of his own, unique experiences with a machine not unlike the one illustrated. I post them here because they serve to vivify the elementary nature of these technical movements, in the manner of which a 20th century workman and a 17th century philosopher might share an experience of material and design effects.

Joe writes:

When I was in my 20s I worked for a couple of years at the Peerless Optical Co in Providence, Rhode Island, making lenses for glasses. While much of the work was automated to a degree there was still a little corner of the shop where very special lenses were ground. Because I was actually interested in the work, that became my department.

The lenses were ground against iron forms, called “laps” (either convex or concave) using a variety of progressively finer abrasives. The final polish was achieved by gluing a thick disc of felt to the lap and using a much finer polishing media. The lap spun in a bucket-like contraption that worked very much like a potters wheel. The lens was kept in contact with the lap by means of a hinged arm with an adjustable pin. The arm was held in place with the left hand, the pin pushing against the lens, while you added abrasive to the lap with the right hand. To secure the lens without damaging it, a small flat piece of metal with a center hole was “glued” to it using thick green pitch, exactly like the “sealing wax” used before the invention of gummed envelopes. We melted the pitch onto the lens with a bunsen burner. It was removed by chilling the whole piece, at which point the pitch would harden and fall off the glass.
Other than the motor that spun the lap, there isn’t a thing about this whole process that any 17th century mechanic would find surprising. Also, with particularly difficult lenses, I would have to forgo the hinged arm and hold the lens against the lap with my hand.

In our case, a special purpose-built machine re-cut the laps when they wore…I had a beautiful engraved set of brass gauges which I used to check them (by holding the gauge and lap up to a window) and which must have been 100 years old or more when I was using them. I can see where a lathe of some sort would be essential for making the laps, a primative lathe would suffice, but I can’t see it being used to actually make the lens itself.

The machine illustrated in the post above this one is very much like what I am describing. In fact, other than the hand operation it would be instantly recognizable to anyone who was making lenses in the manner I was. I actually made a couple of lenses for an antique telescope on this equipment…they worked perfectly.

In coincidence to this, Rijk-Jan Koppejan sent me a photograph of a reproduction of just this illustrated device, built by his team and part of their exposition on the invention of the telescope, organized around the 400th year Middelburg anniversary. There is to be a symposium of speakers in September, which I just may have to find a way of attending. He says he may be able to take new, more revealing photographs and send them. I will post them as he might.

Joe mentions that the curvature of this grinding “dish” may be too extreme, but that Manzini’s illustrator may not have thought this a significant factor (also, we cannot see the internal curavature of the reproduction). I don’t know enough about the optics of the time to comment.

He mentions as few more interesting details of his memory of lens grinding with such a lathe, in particular the method he had to use to correct the wear on the “laps” (as he calls them) – Spinoza calls them patinas or scutellae, plates or dishes – and thoughts about processes by which a spherical lens is checked for its optical quality:

I suspect that the drawback to using male/female laps against each other is that both pieces will wear. I am guessing that if the lens maker had a set of gages like I used, which are simply used to check the curve, the lap could be spun in any lathe-like machine and the surface selectively filed or ground to return it to true. As I’ve said, I held the lap and the gage up to a window and looked for a streak of light between them…a very accurate way of measuring once you have some practice and know what to look for.

…Another memory just came back…I think that the felt was attached to the lap with fish or hide glue. The lens was checked by holding it up to a light bulb with a single filiment. You held it in such a way that the light from the filiment reflected off the surface. If there were no breaks or nicks in the reflection, the lens was perfectly true. This could also be done by stretching a hair across a window and picking up the shadow. You could never see the imperfections with the naked eye..

…The lens was finished in what we called an “edger” which was nothing more than a lathe-like spindle that gripped the little metal piece glued to the lens and spun it against a grinding wheel. These were not the modern clay-based wheels but slow turning natural stone wheels that ran in water, the grinding wheel turning one way and the lens in the opposite direction. In this way the outer edge was gradually reduced in a manner perfectly concentric with the optical center. Even if the metal attachment was slightly off center on the original lump of glass, this process insured that it would be perfectly concentric when finished. You could only remove the metal piece after this was done and you could not replace it perfectly so it was a once-chance-only affair.

Althought at this point it is only a collective intution that Spinoza did not use a large, spring-pole lathe such as the one shown at the Rijnsburg, there are some facts that lead to me this thought. First is that when Huygens writes of the superior polish of Spinoza’s lenses, he describes them as “little lenses”:

“the Jew of Voorburg finishes his little lenses by means of the instrument and this renders them very excellent” (Complete Works, 6:155).

I do not have the original word from which “instrument” is translated, but at least at this point it strikes me that this is a small device. And these lenses are small. I am unsure if Huygens is talking about telescope lenses or microscope lenses, but there is the implication of very fine work. This also coincides with Spinoza’s own light criticism of Huygens’ very complex machine, in letter 32 to Oldenburg. (See some of my thoughts on this here.) It is of course possible that Spinoza had a spring-pole lathe much like the Rijnsburg and Hevelius lathes, but the contrast between his own approaches and Huygens’s seems more at home with a simpler device. There are other factors that cause me to think that this is so, but for now this is enough to discuss.


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