Infinitely Narrow: How Spinoza Corrects Descartes’ Lenses

Corry Shores has another nice post up in his series on my study of Spinoza’s optical theories and practices. He is the only person, as far as I know, who has made an attempt to read through the whole of my study and it is with great appreciation to find my thoughts reflected there. Here, 6: Seeing Differences between Descartes and Spinoza. Some Observations on Spinoza’s Sight. [The Kvond Spinoza’s Foci Summary Series], he points out a power conceptual, and pictorial difference between Descartes and Spinoza. In my understanding it is hard to over estimate just how pervasive Descartes’ optical metaphor for consciousness and methodology for clarity became, in particular when it was grafted onto by Idealist notions of fundamental intentionality, self-hood, and subject/object duality. Spinoza’s correction to the hyperbolic lens, the lens that Descartes felt would unlock all the powers of clear, nearly unlimited vision to man, stands at a fundamental cross-roads in the history of philosophy, noting the turn-out where modernity could not branched off from the Idealism it followed.

This contrast between the narrowly clear and self-evident, and the broad spectrum, comprehensive intuition of a whole makes an interesting contact point to a discussion Carl Dyke and I have been having over at his blog, on the Infinity Standard (something he regards as an unhealthy societal influence), Existential infinity. Descartes envisioned an infinity as well, an infinite power developed upon the tunnel vision of narrow band precision of clarity, ultimately founded upon the notion of the “self” as indubitable. While Spinoza wanted to say of lenses, of eyes, and ultimately of consciousness, whenever we are perceiving something clearly it is always because we are already perceiving the vista of what lies beyond it. There is no narrow clarity that supersedes and establishes the role of the margin. In fact, as is the case in criticisms of philosophies of Presence, it is always the margin, the ground, that allows the narrow, bright center to have importance, or even substance at all. As I have mentioned before, recent concerns about objects and their centrality are grown out of the image of clear centrality itself, something that comes out of Descartes’ optics, and as I tried to show, Kepler before him.

We do not realize how much our folk and philosophical conception of consciousness and the world is governed by a metaphor of tunnel vision.

A related post: The Hole at the “Center of Vision”

Seeing Machines and Modes of Slavery

The Human Machine

Corry Shores puts up a wonderful response to some of my optical research on Spinoza, drawing on some threads and putting them together in a way that I just had not yet: Seeing Machines. There he picks out what for me are several vital issues that are found in not only Spinoza’s, but also Descartes’ preoccupation with optical matters, both theoretical and practical, and really touches the primary concern. How do these modes of production (ideas, machines) reflect, express and criticize the very rise of instrumentality and really Capitalized labor (and merchant class related freedoms) in which they arose?

Consider how Descartes proposed his own notions of a transcendent God and free will. His sharp division between mind and body was essential for his project. Spinoza, however, reconciled the two [by means of his parallelism]. He was not so narrowly focused on abstract rational conceptions. He did not just design lenses for seeing things with greater focus. As well, he ground and polished them with his own hands. Ideas and their material instantiations cannot be divorced. In fact, kvond writes, “a calculation, for Spinoza, must be seen as an act, the mathematical point, as a relation and expression, and an instantiation, a persistence.” We do not just see, we see from a certain conceptual perspective. [Descartes saw the world mechanically. This perspective might view slaves as machines and not people.] Kvond puts it that we are always seeing-with.

In my view this connection is exactly right. Descartes’ preoccupation with the narrow focus of optical (and mental) clarity, and the attendant vision of machinic Instrumentality, is precisely related, ultimately, to the question of human slavery. It is no mere metaphor that Spinoza uses in his Ethics when he devotes his fourth part to the subject matter of “Human Slavery”. He is speaking of the emotions, but for Spinoza ideational over-focus was material over-focus. Emotional Slavery expressed itself in physical slavery. And he is not only thinking of individuals. It would seem out of place to give Descartes responsibility for 17th century slavery (why not, so much else gets laid at his feet!), but there are valid, thematic, if not arguments, parallels to be drawn between Descartes’ pursuit of a machinic world vision (paired from Mind), his attempt build automated devices that would not be stained by human hand interference, the attempt to mentally isolate clarity in terms of a point of focus, and the general colonial trend towards labor efficiency that would eventually replace indentured servitude (practical slavery) with outright slavery itself (the evaporation of the “human” in the name of production). I see in the very “object” oriented, optical preoccupation with central clarity – the hallmark of much, if not all of Idealism that followed – the conceptual cornerstone for Instrumentality itself, the mode of thought that regards a clarity and sureness of an intentional part as the grounds for what human beings should know, and what they do.

Additionally, it is precisely how we eroticize the boundary (that which lies outside our view of clarity, the “object” of our orientation), that fuels – both literally and imaginarily – our very Instrumentalities.

This is no mere theoretical question, but a large scale question of concept and human action. Much, if not all of the value of philosophy is that at the widest level in a certain register, what hu/man is capable of thinking becomes reconfigured, and I cannot help thinking that the preoccupations with optics and lenses that distinguished many of the great, newly affluent minds of the mid-17th century, bears a conceptual connection to the real human and institutional relationships that constituted the nature of their wealth. Optics, Instrument and slavery are not divorced, or at least Spinoza would refuse to divorce them. Corry did not realize it, but in the time of my optical study of Spinoza I also found compelling the likelihood that Spinoza, and the Spinoza family had at the very least tangential ties to the slave trade enhanced sugar buisness, leaving me with the suspicion that slavery and its connection to commerce lead in part to Spinoza’s decision to leave the occupation of family merchant behind, and devote himself both to philosophy and lenses.

Most of these are conjectural sketches, but because it seems that no one in Spinoza scholarship has much brought up the matter, they perhaps form a sketch of what is worth thinking about: Spinoza the Merchant, Caliban and the Prophetic Imagination, The London Question, Spinoza and the Ethiopian, The Sephardim and the Slave Trade, Spinoza Family Sugar Trade Timetable, Gabriel Spinoza and Barbados.

In this way it is possible perhaps to address the knot of questions behind recent talk about Ontology and Politics. The relationship between the two is I think best expressed by Spinoza’s political expression of ontologies, achieved through the erasure of the human/natural-world divide, descriptively turning Man into a force of nature, which is likely what it always was. But, as Corry helps me remember, this is not just a conceptual position, but also a part of the very intimacy philosophy bears to its time.

What is “Passing through Infinities”?

Corry Shores has another beautiful, traveling meditation and analysis of some thoughts that I raised (I certainly enjoy seeing my thoughts reflected in that mirror, as I discover things that I must have been thinking however dimly, or should be thinking). Here he takes on the trope of “passing through infinities” that I found in von Kleist’s “On the Marionette Theatre”  and the appeal I made to Leibniz’s triangle. He does such an excellent job of explicating Kleist’s story, I recommend his post if only for this. There is a certain openness and journeying that marks Corry’s analysis of things, as he works his way forward, a real pleasure. And Corry does a wonderful job of bringing out the illustration of the concave mirror, and the reversal/vanishing of the image that occurs as the object approaches the focal point (passing onto Deleuze and Bergson). Again, Spinoza’s optics, his experiences with the building of telescopes (and perhaps likely use of mirrors and/or camera obscuras), is something no one has considered when weighing the meanings of Spinoza’s take on infinities. What Corry brings out, though not explicitly, is that Spinoza’s own position upon infinities was itself shaped by his work with lenses and mirrors.

Transverse Condensation

But I want to think to myself about what it means for us to “pass through an infinity” as Kleist claims that a conscious person must in order to attain grace. What I strongly suspect is that this is what Spinoza has in mind when he talks of the three tiers of knowledge, with emphasis on the latter two of these: the imaginary, the rational and the intuitional. Intuitional knowledge is that which is produced when rule-following, rational description is suddenly acceded, surpassed with a kind of accelerated leap of clarity, a clarity which is necessarily comprehensive and not apparitional: Spinoza uses the example of how we can do mathematics without having to move consciously through all our steps. As we journey down into the details of anything in the world, including ourselves, any rational ordering of “what is” not only employs imaginary separation of things from all else (their causes included), but there is a certain density that is achieved in any contemplation wherein one crosses through to the other side, having absorbed the orderings of our body. The confusions and conflations that mark out our imaginary engagements, bringing together under a certain mode of intensity, are first separated out into rational descriptions of causation, but then these delimitations are transcended. The world itself is not transcended. Only our imaginary/rational structurings of it are. And in this way Spinoza’s “intuition” bears a certain condensive similarity to “imagination” such that the two work to prepare and then exonerate the rational which lies inbetween.

I want to say that it is not enough to be analogical here, or more loosely, metaphorical. It is not that we cross through infinities like passing through the focal point of a curved mirror, or like a line crossing over another. Instead infinities are literally gathered up in bounded limitations, and pursued together along certain lines of traverse, and that then these infinities are passed through, onto the other side so to speak, unto a certain comprehensiveness, the kind of comprehensiveness that Spinoza (contrary to Decartes) urges us to start with.

Spinoza and Optics and Pirates

I see now that Corry Shores has put up a reading, and mutual expression of some of my work on Spionza and Optics, “Spinoza’s Foci for Deleuze’s Attraction”. I have to say that I have not read it yet (for sometimes I savor/reserve the first reading of a text for a generous moment, for when you first enter into a thought-space associations and inference trails occur that are highly valuable, and may not occur again), but by all cursory scans, it is the very first close reading of my research, and I can’t wait to see what he says. Read it before I do.

An Analog/Digital Philosophical Repository

Corry Shores emails me a link to a wonderful directory for the philosophical dicussion of the Analog/Digital distinction, with a particular Deleuzian flavor.

Here.

He also mentions that this weekend he is set to begin a project concerning Analog and Digital consciousness, and has just recently posted an abridged copy of his paper:

Posthumanism and Pixels, Condensed Version

As I told to him, and to others below, my interest in the Analog/Digital distinction was primarily in concern over Hoffmeyer’s biosemiotic use of the two in his life-defining concept of Code Duality, something I have found problematic (a criticism I have not written yet).

I look forward to Corry’s work. It sounds exciting. There is from Corry even the suggestion that his project may find some correspondence points to my research on Spinoza and optics, which would be intriguing.

Spinoza’s Optical Letters: Redux

As some know, primarily last summer I spent my time researching and theorizing on Spinoza’s lensgrinding and optical concepts, a largely underdeveloped field in Spinoza studies. The greater portions of my findings are listed here on this site under the sub-heading Spinoza’s Foci. A spearpoint of this research was uncovering the substantive arguments and conceptions that lay behind Spinoza’s rejection of Descartes’ optics, as found in his two letters 39 and 40, letters that have be nearly completely ignored by commentators on Spinoza, or if address, addressed in what seems a delinquent, or dismissive fashion. Spinoza is mostly thought to not know what he is talking about. On the other hand, Spinoza’s objections if carefully examined reveal both technically an alternate position on the problem of “spherical aberration,” but more deeply, a radically distinct conception of what vision is, in particular how it works as an insufficient analogy for consciousness. While Descartes wanted to emphasize the power of the central clarity powers of hyperbolic vision (both in the human eye, and in his proposed lenses), Spinoza understood vision and conciousness both as holistic events, ones best approached with the pragamatic appreciation of our limitations. I provide very little philosophical extrapolation here, though the implications are vast, perhaps running through down to the root of Idealism and Phenomenology. This epistolary commentary also does not touch on such other important factors such as the kind of lathe Spinoza likely used, nor much on his likely technique, and kinds of instruments he made and calculated for, which form a significant secondary branch of my research. Yet as these letters remain nearly the only first hand statement Spinoza made on optical matters, they are the anchorage point for anything else that is likely to be asserted.

For the convience of interested readers I here post a Word document version of my line-by-line explication of these rarely read and rather under-interpreted letters. I realized that the previous weblog versions were very difficult to read and browse through, hopefully something this version will correct. The two entries that can be found in this document are: Deciphering Spinoza’s Optical Letters and  Spinoza: Letter 40 and Letter 39. These are both the English translation of the two letters by Spinoza, and then my explication. This version is not footnoted (though there are citations), and it retains some of the idiocyncratic paragraphing and color coding. It is a 14,000 word document (48 pages), though Spinoza’s letters are only 900 words or so.

[click download]: Deciphering Spinoza’s Optical Letters Line by Line

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.

A Look Back for a Moment, The Hole of Spinoza’s Vision

Right now I’m busy composing my Cabinet article, a result of this width of research I have done. Part of this process is looking back at my various conclusive essays to see where I have gotten. There is one that really struck me as a signficant reduction of the kinds of philosophical conclusions that can be drawn from my study of Spinoza’s optical endeavours, in particular pointing out how deeply he diverged from Descartes who preceded him. I repost it here for anyone else’s pleasure, for I read it again this morning and was really moved by its import (sometimes it is like that, one forgets what one wrote):

here: “The Hole at the Center of Vision”

Comments are of course appreciated kvdi@earthlink.net

 

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 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.

The 1661 Technique of “Glass Drops”, a Possible Link to Bead Lens Microscopes

Robert Hooke published a very brief account of the technique for the making of bead lenses, by melting little threads of glass until they balled up. Such minute glass balls could then be ground into spherical lenses which required very short focal lengths, but in the hands of a master such as van Leeuwenhoek, produced tremendous magnification and clarity. This is what Hooke wrote in his Micrographia (1665):

And hence it is, that if you take a very clear a broken Venice Glas, and in a Lamp draw it out into very small hairs or threads, then holding the ends of these threads in the flame, till they melt and run into a small round Globul, or drop, which will hang at the end of a thread; and further if you stick several of these upon the end of a stick with a little sealing Wax, so that the threads stand upwards, and then on a Whetstone first grind off a good part of them, and afterward on a smooth Metal plate, with a little Tripoly, rub them till they come to be very smooth; if one of these be fixt with a little soft Wax against a small needle hole, prick’d through a thin plate of Bras, Lead, Pewter, or any other Metal, and an Object placed very near, be look’d at through it, it will both magnifie and make some Objects more distinct then any of the great Microscopes. But because these, though exceedingly easily made, are yet very troublesome to be us’d, because of their smallness, and the nearness of the Object; therefore to prevent both these, and yet have only two Refractions, I provided me a tube of Bras…

When tracking down the possible techniques in microscope construction Spinoza may have pursued, it seems that such tiny spherical lenses may have a possible design that Spinoza used. In support of this a Spinoza correspondent and, it seems, collaborator, Johannes Hudde had practiced the single lens, bead technique as early as 1663, and was an advocate to the technique to Moncoyns and then Huygens. It would seem certainly that Spinoza had heard of it, and because of its ease, one may surmise that he at least tried it out. And given Spinoza’s championing of smaller objective lenses for microscopes in his informal debates with Huygens, one would think that he had some experimental success.

As far as I can tell little is known of how this technique came to Western Europe, one supposed from Italy. Robert Hooke had it by 1664 and Hudde and Vossius had something like it in 1663. A piece in this development may though have been published in 1662, in an English translation of selections of Antonio Neri’s L’Arte Vetraria, The Art of Glass. (Interestingly Spinoza died with a 1668 edition of Neri’s book.) Published in the 1662 English edition is an account of the Royal Society experiments with "Glass Drops", a technique brought to Charles II after the Restoration by the excentric and sometimes brilliant German prince Rupert who became a member of Charles’s privy council.

As one can see from the below, the method of forming drops straight from the pot to be cooled in various liquids was NOT the one used by Robert Hooke a couple of years later, but one can perhaps consider that the production of these very fine threads at the end of small dollops of glass may be related to the development of the single lens thread-melting technique (perhaps in conjunction with other sources). I post below a transcription of the original text as a resource for the study of the development of the bead lens technique. I have not read further accounts of this testing, nor have I invested the time to look at other Royal Society experiments during this time.

An Account of the Glass Drops.

Here Drops were first brought into England by his Highness Prince Rupert out of Germany and shewed to his Majesty, who communicated them to His Society at Gresham College. A Committee was appointed by the Society, who gave this following Account of them, as ’tis Registred in the Book appointed for that purpose, and thence transcribed by their permission, and there published. The which I the rather desired, that this might be a pattern for experiments to be made in any kinde whatsoever, as being done with exceeding exactness.

This account was given to the Society by Sir Robert Morray. MDCLXI.

A B the thread, B C the body, B the neck, A the point or end of the thread.

They are made of Green-glass well-refined; til the Metall (as they call it) be well refined, they do not at all succeed, but crack and break, soon after they are drop’t into the water.

The best way of making them, is to take up some of the Metall out of the pot upon the end of an Iron rod, and immediately let it drop into cool water, and there lye till it cool.

If the Metall be too hot when it drops into the water, the Glass drop certainly frosts and cracks all over, and falls to pieces in the water.

Every one that Cracks not in the water, and lies in it, till it be quite cold, is sure to be good.

The most expert Workmen, know not the just temper of the heat, that is the requisite, and therefore cannot promise before hand to make one that shall prove good, and many of them miscarry in the making, sometimes two or three or more for one that hits.

Some of them frost, but the body falls not into pieces; others break into pieces before the red heat be quite over, and with a small noise; other soon after the red heat is over, and with a great noise; some neither break nor crack, till they seem to be quite cold; other keep whole whilest they are in the water, and fly to pieces of themselves with a smart noise as soon as they are taken out of the water; some an hour after, others keep whole some days or weeks, and then break without being touched.

If one of them be snatched out of the water whilst it is red hot, the small part of the neck, and so much of the thred or string it hangs by, as has been in the water, will upon breaking fall into small parts, but not the Body, although it have as large cavities in it, as those that fly in pieces.

If one of them be cooled in the air, hanging at a thread, or on the ground, it becomes like other Glass, in all respects, as solidity, &c.

When a Glass drop falls into the water, it makes a little hissing noise, the body of it continues red a pretty while, and and [sic] there proceed from it many eruptions like sparkles, that crack, and make it leap up and move, and many bubbles do arise from it in the water, every where about it, till it cool: but if the water be ten or twelve Inches deep, these bubles diminish so in the ascending, that they vanish before they attain the superficies of the water; where nothing is to be observed, but a little thin steam.

The outside of the Glass drop is close and smooth like other Glass, but within it is spungious, and full of Cavities or Blebs.

The figure of it is roundish at the bottom for the most part, not unlike a pear pearl, it terminates in a long neck, so that never any of them are straight, and most of them are Crooked and bowed into small folds and wreaths from the beginning of the neck till it end in a small point.

Almost all those that are made in water have a little protuberance or knob a little above the largest part of the body, and most commonly placed on the side towards which the neck ends, although sometimes it be upon that side that lies uppermost in the vessel where it is made.

If a Glass drop be let to fall into water scalding hot, it will be sure to crack and break in the water either before the red heat be over, or soon after.

In Sallet Oyl they do not miscarry so frequently as in cold water.

In oyl they produce a greater number of bubbles, and larger ones, and they bubble in oyl longer than in water.

Thsoe that are made in oyl have not so many, nor so large blebs in them, as those made in water, and divers of them are smooth all over, adn want those little knobs that the others have.

Some part of the neck of those that are made in oyl, & that part of the small thread that is quenched in it cool’d, breaks like common Glass. But if the neck be broken neer the body, and the body held close in ones hand, it will crack and break all over: but flies not into so small parts, not with so smart a force and noise as those made in water, and the pieces will hold together till they be parted: and then there appears long freaks or rays upon them, pointing towards the center or middle of the body, and thwarting the little blebs or cavities of it, whereof the number is not so great, nor the size to large as in those made in water; if the Glass drops be dropt into vineger, they frost and crack, so as they are sure to fall to pieces before they be cold, the noise of falling in is more hissing than in water, but the bubbles not so remarkable.

In milk they make no noise, nor any bubbles that can be perceived, adn never miss to frost and crack, adn fall in pieces before they be cold.

In spirit of wine they bubble more than in any of the other liquors, and while they remain entire, tumble too and fro, and are more agitated than in other liquors, and never fail to crack adn fall in pieces.

By that time five or six are dropt into the spirit of wine, it will be set on flame: but receive, no particular taste from them.

In water wherein Nitre or Sal Armoniack hath been dissolved, they succeed no better than in vineger.

In oyl of Turpentine one of them broke as in the spirit of wine, but the second set it on fire, so as it could no more be used.

In Quick-silver, being forced to sink with a stick, it grew flat and rouch on the upper side: but the experiment could not be perfected, because it could not be kept under till it cool’d.

In an experiment made in a Cylindrical Glass, like a beaker filled with cold water of seven or eight onely one suceeded, the rest all cracking and breaking into pieces, onely some of the company, who taking the Glass in their hand, assoon as the drop was let fall into it, observed that at the first falling in, and for some time after, whilst the red heat lasted, red sparks were shot forth from the drops into the water, and that at the instant of the eruption of those particles, and of the bubbles which manifestly break out of it into the water, it not only cracks and sometimes with considerable noise, but the body moves and leaps, as well of those that remain whole in the water, as those that break.

A blow with a small happer, or other hard tool will not break one of the Glass Drops made in water, if it be touched no where but on the body.

Break of the tip of it, and it will fly immediately into very minuted parts with a smart force adn noise, and these parts will easily crumble into a coarse dust.

If it be broken, so that the sparks of it may have liberty to fly every way, they will disperse themselves in an orb with violence like a little Granado.

Some being rubed upon a dry tyle, fly into pieces by that time the bottom is a little flatted others not till half the rub’d off. One being rub’d till about half was ground away, and then layed aside, did a little while after fly in pieces without being touched. Another rub’d almost to the very neck on a stone with water and Emery did not fly at all.

If one of them be broken in ones hand under water, it strikes the hand more smartly, and with a more brisk noise than in the air: yeah, though it be held near the superficies none of the small parts will fly out of it but all fall down without dispersing as they do in the Air. One of them borken in Master Boyles Engine, when the Receiver is well Evacuated will fly in pieces as in the open air.

Anneal one of them in the fire, and it will become like ordinary Glass, onely the spring of it is so weakned, that it will not bend so much without breaking as before.

A Glass drop being fastned into a cement all but a part of the neck and then the tip of it broken off it made a pretty smart noise but not so great as those use to do that are broken in the hand, and though it clearly appears ot be all shiver’d within, and the colours turned grayish, the outside remained smooth, though cracked, and being taken in pieces, the parts of it rise in flakes, some Conical in shape, and so crack all over that it easily crumbled to dust.

One fastned in a ball of cement some half an Inch in thickness, upon the breaking off the tip of it, it broke the ball in pieces like a Granado.

Two or three of them sent to a Lapidary to peirce them thorow, as they do Pearls, no sooner had the tool entred into them, but they flew in pieces as the use to do when the tip of them is broken off.

Title Page For the 1662 English Translation of Antonio Neri's The Art of Glass