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Tag Archives: Christiaan Huygens

Evidence toward the nature of Spinoza’s Lathe(s)

Writing an email today to an interested party I found myself running over the evidence that Spinoza used either a hand driven lens-grinding lathe, or one of the springpole variety, such as the Hevelius lathe (Selenographia, 1647). It seemed best to briefly summarize them hear, as though the evidence is scant, it is not non-existent. I have already written briefly on these two lathes here: Spinoza’s Grinding Lathe: An Extended Hypothesis ; Spinoza’s “Spring Pole” Lathe: Experience to Metaphysics and Back

1. The auction of Spinoza’s estate held nine months after his death (4 Nov 1677), accounts for more than one “mill” (mollens). If such mollens are taken to be grinding lathes, it shows that he had more than one, likely for more than one purpose (telescope/microscope; grinding/polishing). It is also very possible that the estate had already lost a number of its items by the time of the auction.

2. Spinoza is generally assumed to have been tubercular. While in remission the disease may not inhibit the stenuousness of activity, when manifest any grinding lathe that would greatly reduce exertion would seem almost necessary. A springpole lathe frees the hands, and allows the larger leg muscles to bear the burden.

3. There is some evidence that Spinoza did work on larger telescope objective lenses, ones that would require heavier iron grinding forms, less conducive to a hand-driven lathe. For instance, Huygens writes his brother in reference to calculations Spinoza had done for a 40 ft. lens (in collaboration with J. Hudde), and ten years after Spinoza’s death, Constantijn Huygens writes of using a 42 ft. Spinoza grinding/polishing form (I have not checked the primary source on this yet, OC IX p. 732) which worked so well that he did not have to lift the lens from the glass to check it for blemishes even after an hour straight of use (suggesting a fixed-glass, hands free devise).

4.Christiaan Huygens at several points in his letters to his brother refers to Spinoza’s championing of small spherical lenses for microscopes. If these are not unground spherical bead-drop lenses, then these would be the kind that required very precise grinding and polishing. One can certainly imagine that hand-driven grinding lathes would be more suitable for this kind of work.

This rough sketch seems to suggest a combination of grinding and polishing lathes were used. Spinoza in his criticism of Huygens’ semi-automated grinding lathes, and artisan concern for basic tried techniques, does strongly advise that whatever Spinoza’s lathe designs, they were of a simple, efficient design. He did not appreciate speculative mechanical experimentation, at least not for its own sake. One imagines that his springpole- and/or hand- lathe was of a tried and true fundamental design, though from Huygens’s comments on Spinoza’s polishing techniques, it does appear that he possessed distinctive techniques which were either discovered by himself as a inventive craftsman, or were from a source not commonly available to others.

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.

Spinoza: Not As Abused As Is Said

Two Kinds of Disparagment Found In the Huygens Letters

I am looking at the references to Spinoza made by Christiaan Huygens, coming to them with the expectation that they would reveal a general disparagement of the man, either in terms of his optical knowledge, or in terms of his person, for these letters have been characterized as proof of a certain diminishment Spinoza had suffered in the minds of those who came to know him.

I quote below two sources that typify this kind of conclusion.

It is however the letters which Christiaan Huygens wrote to his brother Constantijn between 9 September and 11 May 1668, which provide us with the clearest evidence that by then, those engaged on actual research into dioptrics had begun to take a somewhat patronizing attitude to Spinoza’s theorizing on the subject. They make it perfectly clear that although Huygens valued “our Israelite’s” practical skill in producing first-rate lenses, he thought it very unlikely that he was capable of adding anything of value to the understanding of optical phenomena (97)

Spinoza’s Algebraic Calculation of the Rainbow & Calculation of Chances, by Michael John Petry  

Over time, he earned praise from some notable experts for his expertise in lens and instrument construction. Huygens, writing to his brother from Paris in 1667 (when Spinoza was living in Voorburg) noted that “the [lenses] that the Jew of Voorburghas in his microscopes have an admirable polish.” A month later, still using the somewhat contemptuous epithetet – occasionally replaced in his letters by “our Israelite” – he wrote that “the Jew of Voorburg finishes [achevoit] his little lenses by means of the instrument and this renders them very excellent (183) 

Spinoza: A Life, by Steven Nadler

The Optical Israelite

While Petry finds in these letters clear evidence for an accumulation of doubt as to Spinoza’s capacities as an optical thinker, the relegation of him to simply that of an excellent craftsman, Nadler acknowledging that although Spinoza’s instrument achievements were much respected, strongly suggests that he was seen merely as a “Jew”, or perjoratively as “our Israelite”. The picture that is left by these writers and others is that somehow Spinoza was seen in a poor intellectual and ethnic light by the Huygnses.

In looking at these letters, this simply does not seem to be the case. Firstly, Nadler’s implied characterization that in these letters Spinoza is ONLY the Jew or Israelite does not hold. He is also “Le Sieur Spinoza” , “Sir Spinoza” (September 9, 1667, May 11 1668), and just “Spinoza” several times. He is also addressed in combination of “Spinoza et Monsieur Hudde” (Semptember 23, 1667); whether this is a sign of his diminishment in contrast to Mr. Hudde, or one of familiarity is hard to weigh. In fact it is hard to measure the full texture of the Jewish nomenclatures, some of which Nadler finds distinctly “contemptuous”. There very well may be social contempt in these, but the title “the Jew of Voorborg” may be a title Spinoza had somehow informally gained in circles, and not simply one of Christiaan’s invention, and though “our Israelite” may strike our eyes in a jarring fashion, it is difficult to parse out the affection from the diminishment, if indeed there is such. (To understand what Huygens means by “our Israelite” one for instance may have to anachronistically ask, Is Spinoza diminishing others when he refers to the “Brazilian” in his waking dream, as an “Ethiopian” [Ep. 17].)  Because of these telescopic difficulties across centuries, at the very least I want to present the picture of the Huygenes social relationship to Spinoza as more complex and varied than what I assumed by reading the tale of these references without looking at them. And I wish to open the possibility that there was more social respect there, against the tremendous currents of the prejudice of the times, than otherwise would be assumed possible in a less nuanced reading, a respect that Spinoza had personally earned across social barriers.

Petry’s point I am unclear on, for in the letters Spinoza’s optical (vs. craft) acumen does not seem to be in question. There seems to me to be clear evidence rather that Spinoza rather had collaborated with the well-respected mathematician Johannes Hudde on calculations for a 40 ft. lens (Sept 23, 1667), and that these calculations had perhaps influenced Huygens’ own calculations for even longer lenses. Perhaps Petry has in mind Huygens’ thoughts in his May 11, 1668 letter, where Huygens discusses his new eyepiece with Constantijn. Spinoza certainly had no knowledge of the optics of this eyepiece, or its principles, but if I am reading Huygens correctly, this is his proposed solution to spherical aberration using only spherical lenses (against a hyperbolic solution). Not only would Spinoza have no knowledge of these principles, neither would any other man in Europe, Johannes Hudde included. I am unsure if we could say that this was a “patronizing attitude”. I am certainly open to evidence to the contrary.

Others have suggested Christiaan’s warnings to Constantijn should keep quiet about his invented lenses, and not reveal them to Spinoza, proves that he regarded Spinoza to be a “competitor” in lens-making. I find this an odd, or perhaps incomplete conclusion. Christiaan’s invention simply was not ready to be made public, and he knew Spinoza to be at times in close contact with Oldenburg, the secretary of the Royal Society of London. Spinoza had kept Oldenburg abreast of the details of Huygens’s progress. There is a sense though in which Spinoza may have been a competitor to Christiaan. The Huygens brothers may have had an intimate relationship to lens-grinding, and there are signs that Constantijn grew cold to Christiaan’s instructions when Christiaan had gone to Paris. The lenses ground during the time of their separation are thought by Anne van Helden to have been entirely farmed out to craftsmen. If though Constantijn continued his conversations about optics and lenses with his neighbor Spinoza, having lost his brother partner to fame in Paris, indeed Spinoza may have represented, however slightly, an emotional threat to Christiaan. It seems, by several accounts, that Spinoza was an engaging man to talk with. Any disparagement we may find in these letters from Christiaan, insofar as we find it, I think should be understood within this context as well, that the brothers were extremely close on the subject and practice of lens-grinding.

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

Huygens’s Comments On Spinoza’s Theory of the Microscope to His Brother

[Opening Comment: I post below an extensive excerpt from a significant letter by the hand of Christiaan Huygens. It is has been cited by biographers for two main reasons. For one, the initial sentence is stated as evidence for Huygens’ regard for apparently an argument or demonstration that Spinoza had put to him in Voorburg, one possibly with some conjunction with Johannes Hudde:

“It is true that experience confirms what is said by Spinoza, namely that small objectives in the microscope represent the objects much finer than the large ones.”

What is not mentioned is that this is the first sentence of a letter devoted to its theme of a compromise with Spinoza (and Hudde) over the issue of small lenses and greater magnfication). Far from being a sidenoteof the letter, Huygens has Spinoza’s argument in the forefront of his mind.

What is also considered significant about this letter (and others like it) is the way that Spinoza is addressed. Here, at the end, not by his name, but as being called “the Israelite”, (and elsewhere as “the Jew”). This is meant in the eyes of many interpreters to signify the distance that Huygens kept between himself and Spinoza, implying that he is merely “the Jew” or “the Israelite” in letters. Indeed there were likely uncrossable social status barriers between the two, but the impression left by some that Spinoza was merely “the Israelite” is not deserved, for the very letter opens with his name and his overarching position.

Other than these two much-traveled points, grafted from the letter, and others related to it, what I find most suggestive is that Spinoza’s position seems to be one shared with Johannes Hudde (they are paired at the end of the selection), and Huygens has responded to Spinoza’s point by with a compound microscope construction of a unique design, whose compromise magnification is measured at 30x. This leaves open the question as to whether Spinoza’s argument was for simple or complex microscopes (or both), but gives us a baseline from which to assesss the magnification achieved by Spinoza’s instruments, for they must be significantly greater than 30x. 

For those unfamiliar, Christiaan Huygens, was one of the most incandescent scientific minds of the 17th century (he invented the pendulum clock and discovered the rings of Saturn in the same year!). It is thought that Spinoza and he spent some significant time together in discussion between at least 1664 and the summer of ‘1665, as they were neighbors in the town of Voorburg until Christiaan left for Paris in the summer of ’66. At the time of the writing of this letter Huygens had already become the Secretary to the newly formed Royal Academy of the Sciences of France, and he write to his brother Constantijn Jr., who remained a neighbor to Spinoza. Constantijn was Christiaan’s partner in lens-grinding and instrument making, something that seemed to be a bond between them.

Christiaan Huygens
Huygens’ Letter to Constantijn  
Letter No. 1638

Christiaan Huygens à Constantyn Huygens, frère.
A Paris ce 11 Maj 1668

Il est vray que l’experience confirme ce que dit Spinosa que les petits objectifs au microscope representent plus distinctement les objects que les grands, avec des ouventures proportionelles, et sans doute la raison s’en peut donner, quoyque le Sieur Spinosa ni moy ne la scachions pas encore, mais aussi de l’autre costè il est certain qu’on distingue plus de profondeur aux objects quand l’objectif est moins convexe. de forte qu’il faut tenir le milieu entre l’un et l’autre pour avoir des microscopes qui sassent uneffect agreeable, mais si on ne cherche qu’a grosser beaucoup il faut des petites lentilles. I’ay essayè vostre derniere proportion avec vos objectifs et deux oculaires joints l’un contre l’autre qui font un bon effect sinon que les points paroissent trop, et bien plus que lors qu’on n’emploie qu’un oculaire seul de 2 pouces, et la raison y est toute evidente, puis que l’un est de 3 pouces et l’autre de 2 ½. Il vaudroit donc mieux que l’un fut de 4 ou 5 pouces du premier, parse qu’ainsi les points de l’un ni de l’autre ne paroistront pas.

Nostre anciene maniere avoit les deux oculaires si pres de l’oeil que cela empeschoit les points d’estre veus, a quoy contribuoit encore beaucoup l’ouuerture de l’objectif un peu grande. car estant petite et la multiplication forte, il est malaise que les points de l’oculaire pres de l’oeil ne paroissent, et le meilleur remede est de faire d’une matiere qui n’aye que fort peu de points. I’ay dans mon microscope un petit oculaire de 6 lignes, qui est de telle matiere, et aussi blanche que du crystal de roche; avec cela elle est fort bonne et souffe pour le moins aussi grande ouuerture que vostre petite que je vous renvoie. Je retiens l’autre pour faire des essays et vous en remercie. le poly est fort bon.

Voicy les mesure de la vraye Campanine, avec la quelle j’ay estè comparer la miene, qui a cause de la grande ouverture que j’avois donnè a l’objecif estoit beaucoup plus Claire, mais en recompense un peu moins distincte que l’autre, qui en effect est un peu somber, mais, pourtant tres excellente. J’ay du depuis ester cy mon ouverture, mais cela fait paroistre les points des oculaires qui en sont assez chargez.

L’ouverture chez l’Abbè Charles est cellecy. [insert the figure of a circle, approx. 1.25 cm in diameter]

Le diaphragme tel [insert the figure of a circle, perhaps a touch less in diameter]

Du trou de l’oeil au premier oculaire [insert the figure of a line segment, approx. 2.5 cm]
Du premier au second oculaire.
[insert the figure of a line segment, approx. 6.5 cm]
Du second oculaire au troisieme.
[insert the figure of a line segment, approx. 6.75 cm]

Je prens tousjours du milieu de l’epaisseur des verres.
Les 3 oculaires ont chacun leur distance de foier d’ 1 pouce 10 lignes.
L’objectif est de 2 pieds 5 pouces.
Toute la longueur de la lunette 3 pieds 3 pouces, qui est moindre de 4 pouces que la meine. tout est mesure de Rhynlande.
Pour ce qui est de ma nouuelle methode de composer un petit cave avec un objectif, le ne trouve pas qu’il y ait de vos petites formes qui vous puissent servir. mais pour un verre planoconvexe de 2 pieds 8 pouces comme vous en saites, il saut un oculaire don’t l’une des superficies soit travillee dans un creux comme cettuicy [insert figure of a small concave-plano lens] dont le demidiametre soit 289/1000 d’un pouce, et l’autre sur une boule don’t le demidiametre soit 187/1000 d’un pouce, [insert figure of a circle approx. .6 cm in diameter] qui est telle, de forte que vostre lentille creuse sera de cette forme [insert a concave-convex figure, with two small protruding notches near the axis], et il faut tourner le costè convexe vers l’oeil. Cette lunette grossira 30 fois, er pour cela il faut travailler l’objectif un peu grand, a fin de luy donner grande ouverture. Le costè convexe doit estre en dehors. Ce composè, suivant la demonstration, doibt faire autant que les verre hyperboliques, parce que le concave corrige les defauts de l’objectif qui vienent de la figure spherique, c’est pourquoy je ne puis pas determiner l’ouverture de l’objectif qui peut ester pourra ester 3 ou 4 sois plus grande qu’a l’ordinaire, mais si nous la pouvons seulement faire double ce fera beaucoup gaignè et la clartè sera assez grande pour la multiplication de 30. L’oculaire ne doibt avoir qu’une petite ouverture et qui soit prise justement au milieu. Il n’est pas necessaire de vous recommander le secret. et quand mesme l’invention ne reussiroit pas je ne voudrois pas que vous en dissiez rien l’Israelite, a fin que par luy, Hudden ou d’autres ne penetrassent dans cette speculation qui a encore d’autres utilitez.

Pour autheur de dioptrique je n’en vois pas encore de meileur que Kepler, dont il y a un exemplaire dans la bibliotheque de mon Pere, outre celuy que j’ay emportè, qui est reliè avec d’autres traitez. demandez moy ce que vous n’y comprendrez pas, et ce que vous voulez scavoir d’avantage, et je vous esclairci…


[I post this letter for two reasons. Firstly, its body should be made easily available to others researching, or even thinking about Spinoza and his place amid 17th century sciences. It is an informed, first-hand response to a theoretical position that Spinoza held. Secondly, and unfortunately, because my French is nearly non-existent, aided by software and careful thought.

It is my hope that someone would be moved so as to accurately translate the text into English (or another language for that matter), which we may be able to post as an effective and accurate on-line source. Perhaps even the donation of a paragraph or so by individuals, so that this would be translated by community would be interesting. My email is 

It should be noted, the measurements of the figures to be inserted are only thumbed approximations meant only for visualization, and not for fact. ]

Simple or Compound: Spinoza’s Microscopes

Smaller Objective Lenses Produce Finer Representations

A very suggestive clue to the kinds of microscopes Spinoza may have produced is Christiaan Huygens’ admission to his brother Constantijn in a May 11 1667 letter that Spinoza was right in one regard, that smaller objective lenses do produce finer images. This has been cited by Wim Klever to be a sign of Huygens making a concession to Spinoza in a fairly substantial question of lensed magnification:

After some disagreement he had to confess in the end that Spinoza was right: “It is true that experience confirms what is said by Spinoza, namely that the small objectives in the microscope represent the objects much finer than the large ones” [OC4, 140, May 11, 1668]

Cambridge Companion to Spinoza, Wim Klever, “Spinoza’s Life and Works” (33)

And this is how I have read the citation as well, not having access to the original context. But some questions arise. Does this admission allow us to conclude that Spinoza was specifically making compounded microscopes, the kind that Huygens favored? Or are “objective” lenses to be understood to be lenses both of single and compound microscopes. What makes this interesting is that if we accept the easiest path, and assume that Huygens is talking about compound microscopes, then there may be some evidence that clouds our understanding of what Huygens would mean.

Edward Ruestow tells us that be believes that Christiaan Huygens in his 1654 beginnings already had experience constructing microscopes using the smallest lenses possible. If so, Spinoza’s claim regarding compound microscopes would not be new to him (or his brother). Ruestow puts the Huygens account in the context of the larger question of the powers of small objective lenses:

It was not obvious in the early seventeenth century that the smaller the lens – or more precisely, the smaller the radius of its surface curvature – the greater its power of magnification, but smaller and more sharply curved lenses were soon being ground as microscope objectives, at first apparently because, with their shorter focal lengths, they allowed the instrument to be brought closer to the object being observed. The curvature of a small cherry ascribed by Peirsec to the objective of Drebbel’s microscope was already a considerable departure from a spectacle lens…

Whatever the intial reason for resorting to smaller objective lenses, however, it was not such as to produce a continuing effort to reduce their size still further. (A lens, after all, could come too close to the object for convenience.) In 1654 a youthful Christiaan Huygens, already making his own first microscopes or preparing to do so, appears to have ordered a lens as sharply curved as a local lens maker could grind it, and it may indeed have been a planoconvex objective lens with which he worked that year whose curvature, with a radius of roughly 8mm, was still to that of Drebbel’s (i.e. to the curvature one might ascribe to a small cherry). Fourteen years later, however, Christiaan was inclined to lenses with a focal distance of roughly an inch, and he pointedly rejected small lenses as objectives – primarily it seems, because of their shallow depth of focus…In 1680 members of the Royal Society were admiring a biconvex lens no more than one-twentieth of an inch in diameter, and Christiaan Huygens, now with a very altered outlook, would write that the perfection of the compound microscope (of two lenses) was to be sought in the smallness of its objective lens. He claimed at the end of his life that the magnification such instruments could achieve was limited only by how small those lenses could be made and used [note: On the other hand, he also recognized that there was an absolute limit for the size of any aperture, beyond which the image become confused.] (13)

[Ruestow footnotes that the 1654 microscope described as constructed by Christiaan above, is thought by J. van Zuylen is rather the Drebbel microscope purchased by Christiaan’s father, Constantijn Sr.]

The Microscope in the Dutch Republic, Edward G. Ruestow

Not only is Huygens’s turn around described, no doubt fueled by his own famed success with the single lens, simple microscope, just after Spinoza’s death, but also Ruestow suggests that Huygens indeed already knew what Spinoza’s claimed, that smaller objectives indeed do make larger magnifications, his objection being not that the magnification is inferior, but simply that the depth of field makes observation problematic. It is unclear if Ruestow’s reading of the 1654 for is correct, so we cannot say for certain that Huygens had this experience with smaller objectives, but it is interesting that Ruestow cites the same year as his concession to Spinoza, (1668, “fourteen years later” without direct citation), as the year when Huygens makes clear what his objection to smaller objectives is. This raises the question: Is the “confession” in context part of an admission of the obvious between Christiaan and his brother, something of the order, “As Spinoza says objectives represent objects with greater detail, but the depth of field is awful? (Again, because I do not have the text I cannot check this.) 

Or, does Ruestow make a mistake? Is it not letters written 14 years, but only 11 years later, when Huygens in his debate with Johannes Hudde seems to have readily accepted the possibility of greater magnification, but makes his preference in terms of depth of field. As Marian Fournier sums: 

Hudde discussed the merits of these lense with Huygens [OC5, April 5, 10 and 17 1665: 308-9, 318, 330-1], who declined their use. He particularly deplored their very limited lack of depth of field. He found it inconvenient that with such a small lens one could not see the upper and underside of an object, a hair for instance, at the same time. The compound microscope had, because of the much smaller magnification, greater defintion so that the objects were visible in their entirety and therefore the compound instrument was more expedient in Huygens’ view (579) 

“Huygens’ Design of the Simple Microscope”

It is important that Hudde is not only championing smaller objectives, he is attempting to persuade Huygens that the very small bead-lenses of simple microscopes are best. Hudde had this technique of microscopy from as early as 1663, perhaps as early as 1657, and he taught it to Swammerdam. In the context of these letters, apparently written just as Huygens and Spinoza are getting to know each other in Voorburg, Huygens’ 1668 brotherly admission reads either as a distinct point in regards to compound microscopes, or signifies a larger concession in terms of his debate with Hudde. There are some indications that Hudde and Spinoza would have known each other in 1661, as they both figure as highly influential to Leiden Cartesians in Borch’s Diary. And Spinoza was a maker of microscopes, as Hudde was an enthusiast of the instrument even then. It makes good that there would have been some cross-pollination in the thinking of both instrument maker’s techniques in those days, but of this we cannot be sure. 

Against the notion that Spinoza has argued for simple microscope smaller objectives with Huygens is perhaps the compound microscopes achieved by the Italian Divini. Divini, in following Kepler’s Dioptice, realizes a compound microscope whose ever descreasing size of the objective increases its magnification. I believe that there is good evidence that Spinoza was a close reader of Kepler’s (see my interpretation of Spinoza’s optical letters: Deciphering Spinoza’s Optical Letters ). If Spinoza was making compound lenses, and he had argued with Huygens that the smaller the objective the better, it seems that it would have been the kind of microscope described below, following the reasoning of Kepler, which he would have made. 

First, Silvio Bedini sets out the principle of Divini’s construction: 

Divini was an optical instrument-maker who established himself in Rome in about 1646 and eventually achieved note as a maker of lenses and telescopes. In a work on optics published in Bologna in 1660 by Conte Carlo Antonio Manzini, the author describes a microscope which Divini had constructed in 1648, based on Proposition 37 of the Dioptrice of Johann Kepler. This was a compound instrument which utilized a convex lens for both the eye-piece and as the objective was reduced so were the magnification and the perfection of the instrument increased (386).

Then he typifies a class of microscope of which Divini was known to have constructed with this line of analysis:

One form consisted of a combination of four tubes, made of cardboard covered with paper. Each tube was slightly larger than the previous one, and slid over the former. An external collar at the lower end of each tube served as a stop to the next tube. The ocular lens was enclosed in a metal or wooden diaphragm attached to the uppermost end of the largest tube. The object-lens was likewise enclosed in a wooden or metal cell and attached to the bottom of the lowermost or smallest tube. The rims of the external collars were marked with the digits I, II, and III, in either Roman or Arabic digits, which served as keys to the magnification of the various lengths as noted on each of the tubes. The lowermost of the tubes slid within the metal socket ring of the support and served as an adjustment between the object-lens and the object. The instrument was supported on a tripod made of wood or metal. It consisted of a socket-ring to which three flat feet were attached (384).

 And lastly he presents an example of this type, which he calls Type A:

(Pictured left, a 1668 microscope attributed to Divini):The socket-ring and feet are flat and made of tin, and the cardboard body tubes are covered with grey paper, with the digits 1, 2, and 3 inscribed on the collar tubes. The lowermost tube slides with the socket-ring for adjustment of the distance between the object-lens attached to the nose-piece in a metal cell, and the object. The ocular lens is enclosed in a metal holder at the upper end of the body tube. It consists of two plano-convex lenses with the convex surfaces in contact. The original instrument had a magnification of 41 to 143 diameters. The instrument measured 16 1/2 inches in height when fully extended and the diameter of the largest body tube was 1 1/2 inches. A replica of this instrument, accurate in every detail, was made by John Mayall, Jr., of London in 1888 (385-386).

“Seventeenth Century Italian Compound Microscopes” Silvio A. Bedini

 This 16 1/2 inch compound microscope indeed may not have been the type that Huygens’ comment allows us to conclude that Spinoza built, but it does follow a Keplerian reasoning which employed the plano-convex lenses that Spinoza favored in telescopes, one that imposed the imparitive of smaller and smaller objective lenses. It is more my suspicion that Spinoza had in mind simple microscopes, but we cannot rule out the compound scope, or even that he was thinking about both.

Futher, Spinoza’s favor of spherical lenses and his ideal notion that such spheres provide a peripheral focus of rays (found in letters 39 and 49), seems to be in keeping with the extreme refraction in smaller objectives in microscopes, although he attributes this advantage to telescopes. More than in telescopes, the spherical advantage in conglobed, simple lensed microscopes, would seem to make much less of the prominent question of spherical aberration. But in the case of either compounds or simples, the increase curvature, and minuteness of the object lens would fit more closely with Spinoza’s arguments about magnification, and Descartes’ failure to treat it in terms other than the distance of the crossing of rays.

Spinoza’s Brilliant Neighbor, The Huygens Estate: Hofwijck

Christiaan Huygens drawing of Hofwijck, where Spinoza would have visited

To add to the picture of the quiet Huygens family estate at Voorburg we have a drawing of it by the hand of Christiaan Huygens himself (undated).

This brings a certain vividness to any imagined visit by Spinoza in the summer of 1665 [thought about here: What Spinoza and Huygens Would Have Seen that Summer Night ]. It would be likely that at one of these top floor windows Huygens would have placed his telescope, and through which he and Spinoza would have gazed at Saturn. An interesting sidenote: Spinoza is said by Colerus to have drawn portraits of some quality (and he lived in the house of a master painter), so in this the two men may have shared some small interest.

Huygens’s Collaboration with Instrument Makers

Evidence Towards Huygens’s tendency to appropriate or minimize the design contributions of others

In considering the remote possibility that the rapid improvements that Christiaan Huygens made in the single lens microscope in the years 1677 and 1678 may have reflected the designs of Spinoza’s own microscopes likely purchased by the brothers, [discussed here: Did the Huygenses “buy” Spinoza’s lens polishing technique?; Traces of Spinoza’s Microscope ] one has to consider Huygens’ history of collaboration with the designs of others. J. H. Leopold in his “Christiaan Huygens and his instrument makers” discusses a suggestive falling out between Christiaan Huygens and the renowned clockmaker of Paris, Isaac Thuret. It is one that may shed some light upon Huygens’ tendency to “perfect” or minimize the contributions of others. The disagreement occurs in 1675, two years before Huygens’ synthesis of a new single lens microscope, ending a collaborative relationship that began as early as 1667. As Leopold tells it:

What happened, briefly is the following. In January 1675 Huygens invented a spiral balance spring; an invention which was as vital to portable timekeepers as the pendulum had been for stationary clocks. He promptly went to Thuret to have a model made, in order to apply for a patent. Thuret made the model, but after Huygens left he made another one for himself, with the aid of which he managed to apply for a patent before Huygens did. Huygens was furious about this breach of confidence, and no doubt Thuret did behave very badly though one should remember that we have only Huygens’ version of the matter, and there were a number of important people in Paris who thought that Thuret’s behavior was not quite so unforgivable. And indeed, without distracting in any way from the importance of Huygens’ invention, perhaps this is something to be said for Thuret. When one looks at the first sketches Huygens made of his invention it is clear that the first two (figure 2) differ in a number of details from the next (figure 3): there is a dumb-bell balance, and the spring sits in a small box between the plates where it will be in the way of the ‘scape wheel. In the subsequent sketch, which dates from a few days later, these details have been corrected. It seems possible that on other occasions, too, Thuret had put Huygens’ ideas into a more workmanlike shape, and it must have irked him to be constantly in Huygens’ shadow…The reason Huygens gave for his anger is interesting: he said that over the years he had come to regard Thuret as a friend (228).

While this is certainly at the surface a story of the appropriation of Huygens’ brilliance by another, it shows the fluidity of invention, and the likelihood that Huygens’ abstract and mathematical mechanizing thought process regarded the details of a device less significant than his overall idea of it. Further, we have seen that in his 1678 dealings with Hartsoeker over the microscope that the minimization of the ideas of others, whether malevolent or not, was a tendency in Huygens’ character. What this means for the possible appropriation of any design ideas he may have gained from the purchase of Spinoza’s estate and any instruments included there is hard to say, other than that it would probably be with some ease that he would add the ideas of a recently deceased friend and instrument maker. Further, Leopold’s article generally shows Huygens to be disconnected from the history of the device he turns his inventive mind to, unfocused on the actual mechanism and problem solving focus that a craftsman’s view gives, making the problem solving ideas of others perhaps necessary to both the priming-of-the-pump and the materialization of his remarkable mechanistic intution.

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

The Simple Microscope in the Hands of Van Leeuwenhoek and Huygens

Spinoza’s Microscopology: a prospective comparison of context

It strikes me that there is a subtle, yet important contrast between the single lens microscope that Christiaan Huygens ended up offering by the Fall of 1678 and the design which was consistently used by Van Leeuwenhoek, a contrast that points up a branching out of conception of the relationship between instrument and observation, one that perhaps help position Spinoza’s own view of lens use. 

At the end of 1678 the Huygens, Rømer, Hartsoeker microscope resulted in this design:

Its “strength” is that it was that it was equipted with a revolving wheel, into which six different preparations could be placed, enabling a kind of frame by frame, one might even say, nearly cinematic comparison specimens which could be flipped before a small grain of a lens. This designed was very quickly put into widened production by the instrument maker Herbert Butterfield. When compared to Van Leeuwenhoek’s essential model, there is a notable difference:

For Van Leeuwenhoek the specimen is placed fixed, suspended [atop the pictured needle], in the most elementary of relations. Further, in his use of the microscope Van Leeuwenhoek seemed to express a very different idea of the relationship of the device to what is seen. For instance, of the 26 samples that were sent to the Royal Society upon his death, they consisted of a pairing: each microscope came with a matched specimen which was placed ready to view. The device was not conceived apart from the staging of the observed. (And these devices were for Van Leeuwenhoek private, personal, not conceived to be widely reproduced.)

This contrast is a small point, but I think that the kind of looking that Van Leeuwenhoek was famous for, the intensified examination and preparation of the moment of witness, came out of his conception of device and specimen. And Huygens’s incredibly rapid development and “improvement” of this device, marks a difference in the act of looking, a mechanized and rotational expression of specimen interface, one where the device stands as a kind of medium between the facts of the world (and not a particular event) and an investigating mind. I make no judgment of course between these two conceptions, other than to say that their contrast perhaps provides a backdrop upon which Spinoza’s conception of lensed observation may be made more clear. He looked somewhat obliquely at Huygens’ complex machinery of automated ends (again, Letter 32), perhaps sensing that the means of witnessing color and shape help establish the quality of what is seen. The Huygens “enhancement” of the Van Leeuwenhoek design, the speeding up of the relation between the witness of one specimen and another, and they bodily experience of an intricate, mechanized interface with various phenomena, marks out a significant difference. 

These thoughts are a continuation from an originary thought begun here: Van Leeuwenhoek’s View of Technology