Frames /sing


Tag Archives: Christiaan Huygens

Some Rough Thoughts On Spinoza and Technology

The Free Hand

Christiaan Huygens's assited lens mechanism

Today, in contemplating Spinoza’s objection to Huygens’s semi-automated lens-grinding lathe (from Letter 32), and considering what it might mean for an overall Spinoza view of technology, I am struck by an immediate incongruity. Christiaan Huygens’s love of the mechanical, that is the ambition for the nearly direct implementation of the math to the material, through the correct devising of a means of transfer, seems to embody much that Spinoza would agree with. That is, both are determinative mechanists, and the proper construction of a mechanism would seem to be paramount in both thinkers view of how a lens should be ground. For one could say without too much occlusion, Spinoza thinks of the world being made up of two things: information (what he calls “Idea”), and matter (what he calls “extension”). The direct transfer of information to matter that technology seems to promise would seem to be exactly that Spinoza would favor.

But instead Spinoza baulks at the notion that the “free hand” of the craftsman should be removed from the process:

..what tho’ thusly he will have accomplished I don’t know, nor, to admit a truth, strongly do I desire to know. For me, as is said, experience has taught that with spherical pans, being polished by a free hand is safer and better than any machine (Letter 32).

One has to ask, is this just a technician’s sobriety, a conservative, “let’s see what it can do before we get too excited”? It seems not, for he really is not at all enthused to even find out. There seems a much more rooted objection, a tugging away from the simple connection between Idea (information) and Thing, that technology embodies. It is strange, because the minimization of the anthropological that Spinoza’s philosophy is most notable for comes right up against another principle, perhaps something we can call the principle of implementation. For Spinoza, because all technology is in combination with human beings, and its use a part of the human perception of the world and itself, in order for any technological process to be assessed, ALL elements of its assembled mechanism, including those of the state of the human beings involved, have to be considered. Because human beings do not form a “kingdom within a kingdom,” any device must be considered within the causal matrix of ideas and matter than make up its users and its practitioners. At least that is what I have come to believe Spinoza is thinking about, as he expresses reluctanceto remove the “free hand” from the process of crafting lenses. He is not against such a handless construction, but one senses that he is hesitant, holding in his view a greater scope of the issue at hand. For the 17th century desire to remove the craftman is not simply the desire to remove the “human error” from a process, but also is a labor calculation, suggestive of the Capitalist forms that were on the rise. The “free hand” question, is the question of interface, of communicative dialogue between the mechanism of gears and wheels and the mechanism of the human person (and community).

In a sense, what is at stake is the full consideration of interface. The impress of an idea (information) upon matter is a condition-dependent relation. One cannot simply press any kind of material into a spinning grinding mould to produce a lens. The specifics of the states of each must be appreciated. In this same sense there is a temporality, a historicity, to the transfer of ideas, one that Spinoza weighs as he wrote his first “rule for living” in the Emendation:

1. To speak to the understanding of the multitude and to engage in all those activities that do not hinder the attainment of our aim. For we can gain no little advantage from the multitude, provided that we accomodate ourselves as far as possible to their level of understanding. Furthermore, in this way they will give a more favorable hearing of truth.

His rule is to speak to the multitude, yet he will learn to not publish his Theological-Political Treatise in Dutch, keeping it from the multitude. Right away a differential comes apparent. The accomodation is really a measurement, a measurement that not only must be done with reason, but within the melieu of imaginary constructions and affective affinities. Perhaps this is why Spinoza is removed from the direct seduction of mechanical transfer. This is a finesse of his monist metaphysics. The transfer of ideas (information) to form, is never actually a transfer at all, but must be seen as an unfolding of two parallel Attributes. There is no descent into matter. Here Descartes and Spinoza radically diverge. Spinoza’s immanence becomes a line of permutation. The human element indeed has no hierarchical privilege in his Universe. It is shot through with error, but removing the human hand does not necessarily increase the power of an instrumental relation. This conceptualization of the human hand as a hand of error, of the craftsman as the ignorant purveyor unreflectant and unmodern traditions, a drag on the transcendent rise of Reason, is – I think Spinoza would say – an imaginary relation. For a machine to work properly, the free hand must always be located, and gauged.

This comes in view of past thoughts on this issue:

To Understand Spinoza’s Letter 32 to Oldenburg

Spinoza’s Comments on Huygens’s Progress


What Spinoza and Huygens Would Have Seen that Summer Night

Telescoping with Spinoza and Christiaan Huygens

The night sky July 13th 1665 near Voorburg

The night sky, 11:31 p.m. July 13th 1665 near Voorburg

 …with which they have been able to observe the eclipses of Jupiter caused by the interposition of satellites, and also a kind of shadow on Saturn as if made by a ring. – Spinoza to Oldenburg, May 1665

It is tempting to imagine that having seemingly met and discussed with some enthusiasm issues of astronomy and microscopy in late April of 1665, Spinoza may have visited often with Huygens at his country estate which was some 10 minutes walk from Spinoza’s rooms on Kerkstraat. Aside from issues of social standing, Spinoza as a maker of telescopes and microscopes, surely would have wanted to talk with Huygens on the state of the art of the day, and further, Christiaanin esteem and sharing may have wanted to share the facts of his experiences of discovery with his most compelling neighbor. But we must ask, what could Spinoza and Huygens have seen, if they had looked through a telescope together?

It is probably without doubt that Huygens had set up one of his long telescopes permanently on the estate, for though he had not made astronomical discoveries for nearly decade, issues of significance were happening in the sky. In the Winter of 1664-5 a brilliant comet had showed itself, and then another in March 27thof ’65, the last being visible to the naked eye for a month. These were occasions not only for religious fervor, and signs of the end of Times, but also windows into the structure of the universe, events to observe closely so to feed the growing theories on the nature of cosmic bodies and their travel. Plague and war was rife, and yet and imperative of knowledge was blooming. As a general note, everyone’s eyes were on the sky, and Huygens’s telescope most surely was trained there. 

from Lubinetski’s 1667 treatise Theatrum Cometicum

from Lubinetski’s 1667 treatise Theatrum Cometicum

Aside from the striking sky pyrotechnics of comets, there is further in evidence that the sky was still much on Huygens’ mind in the summer of 1665. As recently as 1660-1661 Huygens was busy defending the power and accuracy of his telescope to the accusations of fraud come from the famed Italian telescopist Divini. (Huygens had controversallydiscovered the rings of Saturn in 1656, lead to them by his discovery the moon of Saturn later to be named Titan, in 1655, which he regarded as “my moon”.) Withthe existence of the Saturn’s rings still in dispute, evidence for them resting solely on the strength of his telescope, the prestigious Prince Leopold of Tuscany had twice proposed a paragone, a face-off field test between Huygens’s telescope and Divini’s, before persons of high social status, an offer that Huygens each time refused. In this vien of concerns, Roger Hahn in “Huygens and France” suggests as quite likely that Huygens continued interest in the telescope in April of 1663 lead him to the house of Adrien Auzout in Paris, and to a group that included Pierre Petit who were working on a 80 to 100 ft. telescope under the promise of seeing Huygens’ rings of Saturn more clearly. Then, what must have been a great relief to Huygens, in April of 1664 the rising Italian telescopist Campani himself faced the arrogant and well-connected Divini in a paragone, and definitively defeated him, soon after publishing a confirmation of Huygens’s Saturn findings through the report of the shadow of the questionable rings (look closely at the wording of Spinoza’s letter 26, where this shadow is mentioned). Following this history of observation and dispute, Spinoza writes of his early meeting of Huygens in May of 1665, and their talk of issues of astronomy. He mentions in his letter their discussion of the rings of Saturn, as well as the eclipses of Jupiter. With Saturn, comets and Huygens’s telescope in the forefront of the last years of European astronomy, and fresh to their friendship, one can easily imagine Spinoza having walked the ten minutes to the Huygens estate (pictured below), as the sun was lowering into the late evening of a long summer day, in order to look through the long-contested and now vindicated device. The sky would not have completely lost the sun’s light until just after 11:30.

If we imagine the night to be something like that of July 13th, there would be no moon. The canal’s lapping could be heard perhaps from the upper story, and somehow too the breadth of the property, the rush of the breeze across the rows of orchard and bush, so symmetically laid forth. Dark shadow-lines set out in geometry, ringing faintly as if strings. Here, would not Christiaan Huygens have trained his telescope on Saturn, the home of his distantly reached sight of rings, and a moon he had discovered? How many times had he looked at it? Saturn happened to be at its zenith on this night, due South, low on the horizon as the sky blackened. Christiaan had carved into the lens withwhich he had seen Saturn’s moon and rings with a line from Ovid: Admovere oculis distantia sidera nostris : They carried distant stars to ours eyes. This would have been a remarkable moment for Spinoza as he contemplated the Infinite.

East on the ecliptic there was Jupiter. Would they not have focused then on that great planet, having discussed the discovery of its eclipses only a few months earilier? Would not the glass telescope have brought to two great, but quite distinct minds into intersecting conversation. Neighbors of such diversity, such disjunction, living a short walk from each other, stretched thin across the solar system by means of a glass and metal? Would Huygens have mentioned, tipping that lens to its precise point, that he believes that light moves in spherical waves?

The Huygens Estate at Voorburg

The Huygens Estate in Voorburg

Traces of Spinoza’s Microscope

Nicholas Bion cites Huygens’s “Dioptricks” and the Traces of Spinoza’s Microscope

Stuart Talbot sends me this citation regarding the ground or unground nature of Huygens’ microscope lenses:

Nicholas Bion (c.1650-1733) , Instrument Maker to the French King , The Construction and Principal Uses of Mathematical Instruments, Paris 1709 . transl. Edmund Stone 1758 ( reprint Astragal Press 1995 Mendham NJ USA ISBN 1-879335-60-3 ) Chap IX. p.299 says “Mr. Huygens in his little tract upon microscopes, in his Dioptricks, beginning at page 221, shews how to make the small Glafs Globes for fingle microscopes, by melting powdered Glafs in nthe flame of a Lamp, which will run into various small Globes, and making Choice of such as he found best , which he pout into small round holes, made in a very thin Copper Plate, punched with a Needle, and those he liked best he fixed therein; thus easily making several Micrsopes. The well figuring, and polishing such small Globes, being more owing to Chance than Design”

This certainly argues against Huygens’s widespread use of a ground-lens method, but perhaps not exclusively so. I thank Mr. Talbot for directing my attention to M. Fournier’s article on Huygens’ microscope.

Spinoza’s Microscope?

Interestingly Mr. Talbot in passing raised the possibility that because the Huygenses may have purchased microscopes in the Spinoza estate (they are listed as vergrootglazen in the advertisement) one has to ask whether elements of these microscope designs, as bought, were involved in Huygens’ new microscope. This is not something I had directly considered, focusing more on the possible transmission of Spinoza’s lens-grinding techniques. In thinking about this, because the distinct innovation that Christiaan is credited with is the “enclosing of the [fluid] preperation between a tiny disk of glass and mica” one has also to wonder if this, or even the double-frame aspect of construction, was something that may have been part of the Spinoza vergrootglazen

If such design traces exist, they would be found in the illustration below:

Traces of Spinozas Microscope?

Traces of Spinoza's Microscope?

 As strained a thought investigation as this may be, these are questions worth pondering. The barrel “condenser”, a restriction of the specimen’s lighting, seems to be certainly of Hartsoeker’s input (later to be reduced to a mere diaphragm in the metal piece). Van Leeuwenhoeks trademark specimen post is here made into the frame stanchion, whose proximity to the lens is controlled by the lower screw. The specimen carrier is placed to the inside of frame G, marked EE.

If indeed, as I and others suspect, the Huygenses were the purchasers at Spinoza’s estate, we have the acquisition of three kinds of microscopes by Christiaan Huygens in the 6 months prior to the sketch above:

Spinoza’s microscopes in early November 1667

Hartsoeker’s two microscopes (of wood and brass) in mid March 1668.

Musschenbroek’s microscope had been ordered as testified in a letter to his brother dated 26 March 1668.

Huygens Appropriation Further Notes and Complications

More Notes on Huygens’s New Microscope

Having now read Marian Fournier’s “Huygens’ Designs for a Simple Microscope” (1989) the extended hypothesis that Christiaan Huygens was somehow aided in his quick production of a “new microscope” by the grinding techniques that may have been found in the purchase of equipment from Spinoza’s estate, suffers complication. This is largely due to the remission of any detail as to the grinding of lenses in this rather through report. Indeed, there is text citation as to the blowing of lenses [cited is a manual OC viii, Part II, 683-4 and OC viii, 89 letter dated 30 July 1678 ]. Having not read these passages I cannot say for sure how exclusive these descriptions are, since they are taken to be refinements of the blowing techniques themselves. It is possible, at least from this distance, that such blown lenses were then ground, but as there is no existent discussion of such a process, it is hard to embrace that this formed a decisive aspect of the process. Instead it seems that Christiaan and Constantijn were absorbed with nearly every other aspect of the microscope model, trying multiple configurations of the frame, the eyepiece, diaphragm, specimen holding means, etc. This relative silence as to the lens could I suppose suggest that by June 1668 the technique of lens grinding (if assumed) was settled on, and all that remained for improvement was the apparatus.

Christiaan Huygens first design

Be that as it may, Ms. Fournier presents clearer a timetable presentation of the unfolding of the microscope’s conception and production, some of which exposes the possibility of further questions. I reprint here some of the relevant events:

Christiaan Huygens is in The Hague, returned from Paris due to illness, from June 1676 to July 1678.

Feb 21 1677 – Spinoza dies in The Hague.

Unknown date – Christiaan translates Van Leeuwenhoek’s letter to the Royal Society dated Feb 15 1677 into French.

Aug. 1677 – Van Leeuwenhoek discovers the animalcules in semen, spermatozoa. (May have informed Huygens: Fournier)

Nov. 4 1677 – The Huygenses possibly purchase the grinding dishes and other equipment from the Spinoza Estate.

Feb 1678 – Christiaan studies spermatozoa through a microscope of unknown kind, taking notes (OC viii. Part 2. 698 )

March 1678 – already in close contact, Hartsoeker sends Christiaantwo microscopes and instructions for their use. Two attributes are noted: 1). a 1 to 1½ ft tube used to restrict ambient light on the specimen, and 2). a movable glass, polished or plain, behind the object to control the beam of light (dating letters 14 and 25 March, 4 April . [Ruestow adds that Hartsoeker did not only mail these, but also at the end of March came to The Hague to show the spermatozoa of a dog in person].

26 March 1678 – Christiaan orders a single lens microscope from the renowned Van Musschenbroek workshop.

May 1678 – Christiaan completes the first drawn version of the design his microscope.

An Article on the authorship of the microscope is published in the Journal des Sçavans, crediting Harksoeker with primary credit for the control of specimen lighting, and Huygens for that of the sandwiching of the speciment between glass and mica discs.

Christiaan Huygenss third design 29 August

Christiaan Huygens's third design 2.9.78

Fournier, quite differently than Ruestow, paints Huygens in Paris as being very reluctant for the recognition of his microscope. Ruestow is quite convinced that Huygens attempted to cheat Hartsoeker of some credit. Given that Huygens was returning to Paris after a two year absence, and that the credit he probably wished was from the society members he made his presentations to, and intercoursed with daily. It seems unlikely that issues of priorty and publication are those that defined Huygens sense of identity and self-esteem.

And Fournier brings out more than any other source the ubiquity of this kind of lens scope, confirming my suspicion it was not at all the lens beading technique which Hartsoeker supplied to Huygens. In fact it seems that Huygens “recently” had visited the house of the master of the small lens, Van Leeuwenhoek (581). Given that over time Huygens’s design would move away from the distinct component that Harksoeker is credited with contributing, as Fournier reports, “the development proceeded from a very long tube to a simple perferation directly behind the object, which served to limit the amount of stray light” (589), one wonders just where Hartsoeker’s fingerprint on the device remains.

As for my chain of inferences which link the production of this microscope with the possible acquisition of the grinding equipment of Spinoza’s estate, it remains tenuous. Until I or another go over the cited material describing the production of the lenses used. Most certainly it seems that the ball-bead lenses were employed in the new design, but the experimentation with the melting method may suggest dissatisfaction with this rather quick and easy method of making lenses. Given that the rate of Huygens’ microscopic observations balloon to daily notes in June of 1678, lasting until early ’79, it may be that Huygens himself used lenses of a kind different that more ubiquitously distributed. Such a view may be supported by Ruestow’s citation of OCCH xiii 522-7, which in retrospect provides the possibility of both a bead lens and a ground lens being used (26). What is provocative is that the very thing which Huygens found disconcerting about the bead lens in April 1665, the depth of field, is that which is addressed to some degree by grinding the bead lens into a convex/convex shape, opening up the aperture, drawing out more detail. Fournier sums up Huygens’ objection to Hudde as:

He particularly deplored their very limited lack of depthof field. He foundit inconvenient that with such a small lens one could not see the upper andunderside of an object, a hair for instance, at the same time (“Huygens’ Design…” 579).

Constantijn Huygens Uses Spinoza’s Grinding Dish (1687)

In correspondence Wim Klever directs my attention to evidence that the Huygenses used Spinoza’s grinding equipment as late as 10 years after his death. The citation is here, thus translated from the OCCH:

[I] have ground a glass of 42 feet at one side in the dish of Spinoza’s clear and bright in 1 hour, without once taking it from the dish in order to inspect it, so that I had no scratches on that side ” (Oeuvres completes vol. XXII, p. 732, footnote).

If I have the details here correct, it seems either that indeed the Huygenses had purchased Spinoza’s lens grinding equipment at auction in November of 1677 and maintained the use of that equipment, or that Spinoza may have made a grinding-dish for the brothers under their specification before he died. What is revealed is that Spinoza’s skill had been directed toward not only microscope instruments, but also towards telescopes of a rather large magnitude. This lens appears to have a focal length of 42 ft. And secondly of course, here Constantijn jr., a rather experienced lens-grinder himself, seems to have marveled at the confidence in the lumininocity of the lens produced.

(This reported Spinoza lens is much shorter in focal length than three known to have been made in 1686 by Constantijn: w/ diameters 195, 210 and 230 mm, and w/ focal lengths of 122, 170 and 210 ft.; each “made from the same very poor glass – a heterogeneous and discoloured potash-rich, but essentially lead-free `forest glass’.”)


On the Issue of Clarity and Light: Van Leeuwenhoek’s Lenses

Because the grinding of a droplet-made spherical lens can increase the clarity of the glass in use, and as this reflects upon the hypothesis that Spinoza’s equipment may have rendered Christiaan Huygens’ new microscope more feasible, and considering the fact the known users of glass-bead lenses – Van Leeuwenhoek, Hudde and Hooke did grind them – we add the testament of the young Irish doctor Thomas Molyneux, who “waited” on Van Leeuwenhoek, on the behalf of the Royal Society:

…he fixes whatever object he has to look uppon, then holding it up to the light…but in one particular [after viewing many disappointingly low magnification glasses] I must needs say that they far surpass them all [several Glasses I have seen in both England and Ireland], that is in their extreme clearness, and their representing all objects so extraordinary distinctly. for I remember that we were in a dark rome with only one Window, and the sun too was then of a that [off to the window], yet the objects appeered more fair and clear, then any I have seen through Microscopes, though the sun shone full upon them, or tho they received more then ordnary LIght by help of reflectiv Specula or otherwise: so that I imagine tis chiefly, if not alone in particular, that his Glasses exceeds all others, which generally the more they magnify the more obscure they represent the Object; and his only secret I believe is making clearer Glasses, and giving them a better polish than others can do (Dobell 58).

Though this account is for a lens much latter in design than the 1677/78 microscopes under immediate consideration, Molyneux’ description seems to place great weight, even at that date, upon the importance of polish (and glass quality), allowing us to focus on the possibility that the Huygenses affection for Spinoza’s polishing techniques may have had an influence on their purchase of his remaining Estate, and a consequence upon the design of their July 1678 microscope.

Why Spinoza’s Method of Lens Polishing Might Have Been Integral

How The Clouded Glass Sphere Becomes Opened up to Light

Al Shinn has given me a link to work being done by Alvaro Amaro de Azevedo, which might explain why a hypothesized Spinoza lens polishing expertise could prove decisive in employing a single lens technique. First, Amaro de Azevedo approximated a simple, thread-melting techique thought to have been used by Van Leeuwenhoek, and achieved practical results of about x500 magnification and more, reaching those even achieved by Van Leeuwenhoek himself (x266 is I believe the highest magnification of an existing Leeuwenhoek lens, but Ruestow estimates that x500 could not have been “unusual” (14), noting that a recommended lens by Hartsoeker would “entail a magnification of x770”). Amaro de Azevedo even reached a magnification level of x1000 using soley the melted beads of glass thread, whose proximity to the specimen challenged most 17th century specimen staging capacities. If nothing more, this established the ease of dramatic single lens, beaded magnification achievement. Here his experiments are detailed.

Yet Mr. Amaro de Azevedo later learned that nearly all of existent Leeuwenhoek lenses had been ground lenses, and not simply beaded from melted glass. He set to grounding equally powerful lenses. As I have said, Johannes Hudde is reported to have ground his bead lenses (in salt), and Hooke too ground his bead lenses. It has consternated some modern analyzers of this method as to why a rather effective, tiny glass globule lens should prove insuffient? Why grind glass? The answer to this might help establish why an additional and otherwise guarded means of grinding technique might pave the way towards a more effective beaded lens.

Alvaro Amaro de Azevedo in his second round of experiments actual unveils some of the possibilities for these techniques (improvised on modern equipment), and produced results suggestive of the necessity of the additional polishing means. Here is his article, “The Challenge of Grinding Lenses for Single Lens Microscopes” (keeping a close eye upon the aspects that were feasible in the 17th century).

The first thing I notice is that the grinding abrasive required the use of mills, as Alvaro decides to use sand:

Anyone who has ever read about lens grinding techniques is aware that the main resource for succeeding is the grinding powders…I honestly have no idea where such powders could be found locally but the article mentions that Leeuwenhoek might have employed sand and graded it by levigation. So that was what I did. The sand was collected from a nearby beach and then washed thoroughly. After it had dried, the sand was put into a mill where it was crushed for one hour. The resulting flour was then suspended in water and through levigation six fractions were collected. I named them from 1 (the coarsest) to 6 (the finest).

As an simple point of correspondence, bought at the auction of Spinoza’s estate were various “mills” (molens):

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).

The plurality of mills suggests a gradation of grits produced, such as perhaps those used by Amaro de Azevedo. Whether these were of salt as Hudde is said to have used, or of sand, these mills speak to a particular technique of grinding and polishing, something that could be passed on through the equipment alone.

Next I noticed his search for a polishing agent:

For polishing purposes, I tried to find the jewelry rouge (iron oxide) but it was in vain. Then I tried to smash a hematite stone and I got a powder that was too coarse for a good polishing powder. Then I made many attempts to find a good substitute and at the end of the day I made a polishing tool that doesn’t need powder to carry on polishing.

His solution is certainly not one that Spinoza would use, though the iron oxide powder may have been something that Spinoza picked up in Amsterdam when he learned to grind glass, given the plethora of gem and diamond polishers that may have florished in his community (it was one for the few non-Guild regulated buisnesses available to Jews). Robert Hooke used “tripoli” (a diatomaceous material, getting its fineness from the remains of microscopic organisms). This was long used by Venetian spectacle makers, its use forwarded by instructional manuscripts written by Sirturus and then Rheita. Because Van Leeuwenhoek put tripoli under his microscope to examine it, it is quite likely that he used this as well.


Lastly though, as Amaro de Azevedo ground his smaller and smaller lenses, leaving behind a cut glass blank, and eventually grinding melted beads of glass themselves, as did Hooke and Hudde (and likely Van Leeuwenhoek), achieving greater and greater limits of magnfication, he comes to the vital point, illumination and focal distance:

The main advantage of ground lenses are that they can focus at longer distances compared to the same magnification from ball lenses and thus, I could capture images from already mounted slides that wasn’t possible before. I also noticed that ground lenses allow wider apertures and as consequence, the images seemed to be brighter and higher in resolution.

A modern maker of the two comparable lenses, that is, of the simple beads of glass spheres, and their tiny ground counterparts might not readily notice the distinct advantage that Amaro de Azevedo brings out here. The reason is, the quality of glass that is readily available to us simple was not makeable then. Glass, even the best of it, was bubbled, marred with striations, and considerably darker, tinged with colored. Any advantage in opening up the aperture and letting in more light was not simply a convenience, but rather probably marked the difference between being able to see a specimen or not. For instance, when Robert Hooke says that the single bead lens is simply too small, and that he fears for his eyesight, he means not only too small, but too small and too dark.

Aligned with this point was the techniques of lighting the specimen would prove most important. Ruestow infers that Hudde’s microscopic observations may have been impaired for many years for it did not occur to him to look directly at a light source, with the specimen in between, an improvement attributed to Van Leeuwenhoek (22, n.85). Is this why Hudde did not come up with any astounding discoveries despite owning the beading technique for more than decade before Van Leeuwenhoek comes upon the scene?

These three factors, rather poor occluding glass, just discovered techniques in lighting and specimen preparation, and in some cases guarded secrets in grinding and polishing techniques, all point to the difficulty of microscopic discovery, when using bead-lenses. What is suggested is that the best polishing of these tiny melted spheres would open up the aperture and clarity of an otherwise murky ball glass lens, when pushed to the greatest of magnifications. Thus the state of the technology may have demanded an adequate polishing means, one provided by the purchase of Spinoza’s equipment by the Huygenses.



Hooke’s Method of the Single Bead Lens

In suppliment to my last thoughts on the spread of the simple microscope, and the unlikelihood that Christiaan Huygens was not familar with the elemental aspects of this design (1677), here is Robert Hooke’s widely read description of just such a microscope, in Micrographia (1665), which of course Christiaan Huygens had in his possession (Spinoza’s letter 29) and translated from for the benefit of those who did not read English (for Johannes Hudde for instance):

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…

Though brief, there is certainly enough information here to experiment with and form the kind of microscope the Christiaan Huygens ended up producing.

Did the Huygenses “buy” Spinoza’s lens polishing technique?

The Meteoric Rise of Huygens’s Microscope

The following is an exercise in historical imagination, only meant to elicit what is possible from what we know. Perhaps a fiction bent towards fact.

Wim Klever has brought to my attention a detail which sheds some light upon the possible lens polishing techniques Spinoza employed. Admittedly the connective tissue for a conclusion is not there, but the inference remains.

Professor Klever tells me that in his “Insignis opticus: Spinoza in de geschiedenis van de optica” he cites Freundenthal’s publication of the advertisement of the auction of the Spinoza’s estate in the Haarlemse Courant. The advertisement was printed on November 2nd, and occurred on November 4th (almost 9 months after Spinoza’s death). It seems likely that Constantijn Huygens jr., and/or his brother the famed scientist Christiaan,  bid at and purchased what remained of Spinoza’s estate. This is how Wim Klever roughly translates some of the items:

books, manuscripts, telescopes (‘verrekyckers, mind the plural!), microscopes (‘vergrootglazen’, also plural), glasses so grinded (‘glazen soo geslepen’), 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).

It is the number of devices and equipment that is Klever’spoint. Spinoza is not a dabbler in optics. He does not grind a few spectacle glasses for the near-sighted, but rather is interested in full-blown optical instrument production. There are multiple telescopes and microscopes to be had, as well as perhaps something more important, his grinding dishes, and at least two lathes or mills not to mention other small details of his process. Certainly the bill of sale attests to a rather thorough industrial investment on Spinoza’s part, making of his optical enterprises something quite substantial, but what I am most interested in here is the timing of this auction, in the view of the events that immediately are set to follow, events which may give clue to the nature of just what it is that Constantijn Huygens purchased for his brother.

Spinoza’s death, and auction occurs right at the doorstep of a very important moment in history: the official discovery of protozoa, bacteria, and then spermatozoa by Van Leeuwenhoek in nearby Delft. And it is this discovery which will eventually catapult the single lens simple microscope into European renown. But there is, I suggest, a good chance that Spinoza had been making, using, giving to others and possibly selling this kind of microscope for a very long while (Klever translates “vergrootglazen” as “microscope” as one should, but there is another word for microscope, and this word means “glass that magnifies” perhaps more suitable for a single lens microscope.)  


First, I should point out that Christiaan Huygens had been a neighbor to Spinoza since 1663 when Spinoza moved to Voorburg, a sleepy village just outside ofThe Hague. He is a profound experimenter and scientist, having, among other remarkably brilliant things, invented the pendulum clock and discovered the rings of Saturn in the very same year of 1656. Spinoza had, most agree, become a conversational friendinthe summer of 1665, when the two of them discussed optical theory it seems with some regularity and detail. The Huygenses lived about a 5 minutes walk from Spinoza’s room at the house of master painter Daniel Tydeman, just down the road. Christiaan moved to Paris in 1666 to take the prestigious position of founding Secretary to Académie Royale des Sciences established by the Sun King Louis XIV to rival the Royal Society of London. There was no doubt extreme pressure to counter and surpass the great flow of knowledge that was collecting at the Royal Society under the supervision of Oldenburg. 

During the intervening years, as Huygens attempted to bolster his Academy, in letters written to his brother back in Voorburg he expressed interest in Spinoza’s lens polishing technique. As early as 1667, he writes Constantijn “the [lenses] that the Jew of Voorburg has in his microscopes [I don’t have the original word here] have an admirable polish” and a month later again, “the Jew of Voorburg finishes his little lenses by means of the instrument and this renders them very excellent”. Here we have an attestation to both the mystery of the quality of Spinoza’s polish, (it was a technique which Spinoza apparently kept to himself); and also there is the hint that the instrument used was meant for very fine work, on the smaller of lenses. (In general, the difficulty in acquiring a fine polish on lenses was a significant aspect of lens-crafting technique, as polishing away the pitting of the glass brought in the grinding often would change the spherical shape of the lens.) In 1668 Christiaan then writes to his brother a concession over a debate that he must have been having with Spinoza, that Spinoza is right that the smallest objective lenses make the very best microscopes.

These references by Christiaan establish that the Huygens brothers’ had interest in techniques which Spinoza was not free with, and that Spinoza was on the side of the debate that theoretically would favor the use of single lens microscopes; this, at the very least, confirms their acquisition of his equipment and lenses to be something of a notable event. If there was anything to Spinoza’s technical capabilities which resided in the equipment he used (small grinding dishes, the nature of his lathe, an abrasive recipe, a polishing material), this fact might be evidenced by a sudden change in the capacities of either brother in making microscope lenses.

And remarkably, such a change was to come.

Now the issue of timing. Here is a timetable of events that led up to Christiaan Huygens presenting a “new microscope” to the Académie Royale des Sciences, one that perhaps reflects something of Spinoza’s technique in crafting lenses.

9 Oct. 1676  Van Leeuwenhoek sends his letter regarding the discovery of protozoa and bacteria.

21 Feb. 1677  Spinoza dies at the The Hague.

22 Feb. 1677  Van Leeuwenhoek’s letter 18 to the Royal Society is read aloud, the “first ever written account of bacteria” (Dobell).

August 1677 Van Leeuwenhoek discovers the animalcules in semen, spermatozoa

4 Nov. 1677 Spinoza’s auction, the Huygenses seem to have acquired some of Spinoza’s equipment.
@ 4 Nov. 1677 Van Leewenhoek writes to the president of the Royal Society, William Brouncker, about his observation of the spermatozoa in semen. This sample was brought to him by Leiden medical student Johan Ham (who also might have had a single lens microscope).
Late 1677 Christiaan expresses interest in the Van Leeuwenhoek/Ham discovery (OCCH 8:77; and 62-3, 65).

March 1678  Hartsoeker explains to Christiaan how he makes lenses from beads of glass.

16 July 1678  Christiaan presents to the Académie Royale des Sciences the “new microscope” that differs from others in Holland and England only in the very small size of the lens.

Aug. 1678  Christiaan writes “my microscopes” have made a “great noise” in Paris.

One must know that single lens microscopes had already been in use in the Netherlands for some time before these dates. It had been used, but its capacity for magnification had not been regularly harnessed to make scientific discovery. Part of this was due to a difficulty in using it, for it must be pressed very closely to the eye, requiring great patience, and lighting techiques for the specimen in contrast had to be developed. And part of this dearth of scientific discovery was due to simply the lack of a conceptual framework for the microscopic world. This was a new world. Few as yet would even know where and why to point such a small and powerful viewing glass. Be that as it may, the microscope technique of forming tiny bead lenses from threads of melted glass was certainly known and talked about in a close scientific circle of experimenting savants (a short history of the spherical glass here). Among those notables were Spinoza’s correspondent Johannes Hudde who made them at least since 1663 when he showed his design to the French diplomat Monconys, and possibly used it as early as 1659 when he youthfully writes in a letter how he will uncover the secrets of generation through its powers. The scholar Vossius has one in 1663 which he also shows to Monconys, and in 1666 publishes the claim that the smaller the lens the stronger the magnification. And then to greatest attention Hooke describes his own bead microscope in the Micrographia in 1665 (some comments here), complaining though that it is too difficult to regularly use, fearing the loss of his eyesight.


Hooke's Fly's Eye, from the Micrographia

And of course, it is the king of all microscopists, Van Leeuwenhoek, who exclusively employed this kind of microscope, making over 500 of them almost all for his personal use (some comments here). When he began using them is of much debate. He makes a claim late in life that had had made bead microscopes as early as 1659 (so simple are they to make!), yet some scholars find him to have been directly informed by the description left by Hooke in the Micrographia. We do not hear of his use until 1774, and the nature of his microscope he keeps secret for sometime. It is Van Leeuwenhoek’s microscope – upon the reading of his 18thletterto the Royal Society, the day after Spinoza’s death – that will suddenly take center stage through its discoveries (although its nature at this time remains largely unknown). The single lens microscope is the strongest microscope in the world, but only now will Christiaan Huygens be coming to realize it.

For many years it seems Johannes Hudde had to defend his tiny spherical lenses against Huygens’ intution that larger, compound scopes would do a better job. It seems quite likely that Spinoza found himself mostly on the Hudde side of the argument, even I think it likely that it was Hudde himself, or one in his circle who disseminated the technique to him, either in Amsterdam or at Leiden. To this possibility, the famed Leiden anatomist Swammerdam attributes Van Leeuwenhoek’s technique to Hudde, as he does his own’ and Borch in his diary mentions the heavy influence of Hudde upon these Cartesians. Apart from this debate, Christiaan as a user of the compound scope as late as January 1675 to Oldenburg expresses an outright pessimism towards Van Leeuwenhoek discoveries already relayed to the Royal Society. These may be founded on his own frustrations when attempting to repeat the experiments, as he simply did not have enough magnification power, or they may even be a product of Van Leeuwenhoek’s low social standing as a mere draper in Delft (while Christiaan does not strictly know what kind of microscope Van Leeuwenhoek possesses, he may have guessed. There may be a class issue that folds into the conception of the microscope. Bead lenses are simply, too simple. They are not the shiny, gearing tubes of an upper machinery):

I should greatly like to know how much credice Mr. Leeuwenhoek’s observations obtain among you. He resolves everything into little globules; but for my own part, after vainly trying to see some of the things which he sees, I much misdoubt me whether they be not illusions of his sight…(Dobell 172)

Christiaan Huygens Makes His Turn

But back to the excitment. Something has turned Christiaan Huygens’ pessimism of the simple microscope into an enthusiasm. Most certainly some of this can be attributed to the sudden notability of Van Leeuwenhoek’s discovery of the protozoa and bacteria in marshy and boggy water. In November he will have discovered what male semen looks like under high magnification. At stake were arguments over just how Life itself was generated. (Did it arise spontaneously as it seemed to do in moulds, or was there some “mechanism” to it?) One can imagine the primacy of such a question. Secondly though, it is thought that Christiaan Huygens’s sudden leap towards the simple microscope was nearly entirely triggered and faciliated by the young microscopist Hartsoeker, who not long too before had discovered this technique for himself. The two were in correspondence and in March 1678 Hartsoeker reveals to him his secret. As Edward Ruestow narrates in his wonderful history The Microscope and the Dutch Republic:

The announcement of the discovery of spermatozoa in the fall of 1677 arouses the particular interest of Christiaan Huygens and, through the young Hartsoeker, drew him belatedly to the bead microscope…but having heard of a young man in Rotterdam whose microscopes could reveal the recently discovered spermazoa, Christiaangot in touch with Hartsoeker.

The essential account of their first contact, which is Hartsoeker’s, is tainted by its entanglement with his later claim that he had in fact been the first to discover spermatozoa. The surviving correspondence begins with a reply from Hartsoeker in March 1678 in which he explained how he made the bead with which he observed the “animalcules” found in semen. He presented Christiaan with a number of these sphericals, as well as some wood and brass devices to hold them in place, and by the endofthe month had himself come to The Hague to show Christiaan the spermatozoa of a dog. Hartsoekercontinued to correspond with Christiaan about the employment and improvement of these instruments, all of which Christiaan meanwhile shared with his brother Constantijn. The following year Constantijn spoke of Hartsoeker as “the inventor of our microscopes,” and years later Christiaan recalled Harksoeker having taught them to make little spheres that served as lenses (24-25)

This is all very convincing. Christiaan, after many years of resistance to the idea of tiny spherical lenses, debating with Hudde and possibily Spinoza, spurred on by the need for more powerful magnfication due to the discovery of protozoa, bacteria and then the most importantly, the elusive key to life, spermatozoa, collaborates with a savantish, largely unknown young man from Rotterdam who even claims that had discovered the technique himself when he was a young boy, and suddenly is applying his own rather vast device-making knowledge to craft the best microscopes in Europe, presenting them to the Paris academy, confirming Van Leeuwenhoek’s discoveries only three and a half months after having learned how to bead lenses himself. Huygens is shopping his microscope across the continent, while Van Leeuwenhoek refuses to allow anyone to look into or even see his.

But the problems with this quick reversal narrative is subtle. For one the lens-bead techique is extremely simple. Hartsoeker himself said he discovered it while toying with a thread of glass and a candle. Swarmmerdam says that he could make 40 more or less servicable bead lenses in an hour. It also, as I have said, was rather ubiquitous. To recount: Huddehadbeen in possession of it at least since 1663, was willing to depart with it for at least Swammerdam and Monconys, andin fact had discussed its advantages with Huygens in April 1665. As M. Founeir describes Huygens’ objection to Hudde:

Hudde discussed the merits of these lense with Huygens [OCV, 308-9, 318, 330-1], who declined their use. He particularly deplored their very limited lack of depthof field. He foundit 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 (“Huygens’ Design…” 579).

Vossius, Huygens’s friend seems to be in possession of it then, and it is no doubt related to the “flea glasses” that Descartes speaks of in 1637, “whose use is quite common everywhere”.  Further, of course, when Hooke describes it in brief in his 1665 Micrographia, he exposes the method to the whole English reading world. This text Huygens remarkably had in his possession very soon after its publication, one of the few copies in Europe despite the Anglo-Dutch war of that year; and we have that copy, a section of which is annotated with Huygens’ hand.  Huygens had even been so kind to actually translate some of the English for Johannes Hudde.

Further in evidence that Christiaan Huygens was well-familliar with this lens, in November 1673 Hooke demonstrates to the Royal Society “microscope with only one globule of glass, fastened to an instrument with many joints” likely made in wide production by the Dutch instrument maker Musschenbroek. And even more conclusively, Christiaan’s own father Constantijn Sr. a few months later writes of a powerful “machine microscopique” used by both Swammerdam and Leiden professor of Botany Arnold Seyn (Ruestow, 24 n.96); and we know that Swammerdam later favored a single lens scope. Given their prevalence, simplicity andthe extent of Huygens’ likely intercourse with these lenses, it could not be that Christiaan Huygens and his brother were somehow deprived, waiting to be told how to bead glass by the 22 year old [Leiden student?] Hartsoeker? It may be imagined that perhaps Hudde kept his personal means of grinding tiny lenses secret from Huygens due to some competitive antagonism and Huygens’ obstinancyover the larger, compoundlens microscope design. Perhaps. But it could not be that all of educated Europe keep it a secret from one of the foremost scientific minds of the time. Something does not sit right. Was it simply Huygens’s disinterest in such a low-depth of field, simple lens, andhis proclivities for certain other types of lens formations (compound, like his telescopes) that kept him from wanting to know? Was Hartsoeker simply the expedient when Christiaan needed to catch up quickly? The way that Edward Ruestow tells it we get the sense that it merely took the interest of Huygens, the timely injection of technique, and then the application of the Huygens’ brothers marvelous technical sense. Perhaps.

But I suggest that one piece is missing from this puzzle. It may be not until the Huygenses acquired the lens-grinding equipment and lens examples from Spinoza’s estate that they possessed the technical means of polishing these small spherical bead lenses: a talent for minute polish which Spinoza had showed early on. Could it be that this was the link, the technical means which accelerated the rapid development of the Huygens microscope from concept to actuality?

The Huygens droplet design, as it ended up in late 1678

Ruestow cites the kinds of changes that the Huygens brothers made to the Hartsoeker lens technique, such as “removing the molten globule from the thread of glass withametal wire, or, with one end of the wire moistened, picking up small fragments of glass to fuse them into globules over the flame” (25). All these seem aimed trying to make the sphere smaller and smaller, increasing its magnification. In the endChristiaan would proclaim to his French audience that his microscope is not much different than those in Holland and England, other than the size of its smaller lens, supposedly something which he alone had achieved.

He also produced a casing that was built around this tiny lens, “mounting their own beads in small squares of thin, folded brass; with the bead trapped between the opposing holes pierced with a needle through the two sides of the folded brass, those sides were pinched together with hammered pieces of wire. The microscope would go through several revisions.

As Ruestow writes of its appearance in Paris:

“on July 16th he presented to the assembly the ‘new microscope’ he had brought back withhim from Holland – one that, according the the academy minutes, was ‘extraordinarily small like a grain of sand’ and magnified incredibly…before July was out, Christiaanusedthe instrument to show the members of the academy the microscopic life Leeuwenhoek had found in pepper water, soon after publishing the first public announcement of their discovery in the Journal des Sçavans, Christiaanalsoidentified it with the discovery of the spermatozoa.” 

By August his microscope had caused the “great noise” all over Paris, so much so that John Locke at Blois had heard of it. Through the next year he had “cultivated the impression” that Van Leeuwenhoek’s observations were made with a microscope like his own. French instrument makers set to copying his invention. The response was not altogether gleeful. In London Hooke was somewhat put out that so much excitment surrounded what for him was a well-known device, one that he himself had fashioned, used and written of. And Hartsoeker, having finished his third year at the University at Leiden, all the while had been left in the shadows, not something that sat well with his rather conceitful temperment. Traveling to Paris Hartsoeker sought in some way to unmask his role in the creation of this remarkable device, exposing Huygens to be something of a plagerist. As Ruestow reports, knowing wisely Christiaan steered him from that course,

but [Christiaan] quickly took his younger compatriot under tow and wrote a brief report for him, published in the influential Journal des Sçavans, that asserted Hartsoeker’s active role in making new bead microscopes (27).

We have here evidence of Christiaan’s tendency to obscure the origins of his microscope. Yet was there more to the development than simply Hartsoeker’s revelation of the thread melting techique? Was it that in the purchase of Spinoza’s lens-polishing equipment they acquired something of the techiques long appreciated by the brothers? Does this technique prove essential to Christiaan’s implementation of a rather simple bead-glass lense? Was Hartsoekersimply solicited for the one remaining aspect of the technique that Spinoza’s equipment would not provide, that of simply melting the glass into a lens? We do know that the grinding of the already quite spherical bead was common among its users. For instance Van Leeuwenhoek ground and polished almost all of his tiny bead lenses, (and modern assayers do not quite know why). Further, Johannes Huddealsopolished his bead lenses, reportedly with salt. Was there something to Spinoza’s knowledge of small lens-crafting that facilitated Huygens’ suddenly powerful microscope design? Something even that Hartsoeker was privy to? And lastly, if Spinoza’s equipment and techniques are implimented in this sudden rise of the simple microscope, what does this say about Spinoza’s own microscope making practices.

All this fantastic story is just speculation of course

It could merely be a coincidence that, with Spinoza having died just as protozoa and bacteria were being discovered; and with his equipment coming into the hands of the brilliant Huygenses almost 9 months later, they they then just happen to be aided by a young microscopist that gives the means needed to suddenly develop a microscope that will sweep across Europe in merely a few months. Christiaan Huygens and his brother were brilliant enough for that. Perhaps Spinoza’s ginding dishes and recipes simply sat in the dust, having been acquired. But it should be noted that many years before this, the physcian Theodor Kerckring, a friend of Spinoza’s and a member of the inner, Cartesian circle, son-in-law to its central member Franciscus Van den Enden, writes of his use of Spinoza’s microscope:

“I have to my disposal a very excellent (praestantissimum) microscope, which is fabricated by that noble Benedictus Spinosa, mathematician andphilosopher…What I in this way discovered with the help of this admirable instrument…[are] endless many extremely small animalcula….”

This is found in his Spicilegium anatomicum published in 1670, seven years before Van Leeuwenhoek’s acclaimed description of the protozoa and bacteria in letter 18. It is not clear at all what “animalcula” Kerckring saw (some offer that they are post-mortum microbes, or mistaken ciliated action), but there is the possibility that these were the earliest microorganisms to be described, or at the very least, Spinoza had perfected an advanced form of the single lens, bead-microscope whose powers of magnfication approached many of those of Van Leeuwenhoek, and even that of its copist Christiaan Huygens. The timing remains. In November of 1677 the Huygenses lmay have acquired Spinoza’s lens grinding equipment, and in 8 months they have a microscope of remarkable powers.

Descartes and Spinoza: Craft and Reason and The Hand of De Beaune

Some Reflections on Letter 32

Descartes in 1640 reports to Constantijn Huygens, “You might think that I am saddened by this, but in fact I am proud that the hands of the best craftsman do not extend as far as my reasoning” (trans. Gaukroger). And as Graham Burnett translates, “Do you think I am sad? I swear to you that on the contrary, I discern, in the very failure of the hands of the best workers, just how far my reasoning has reached” (Descartes and the Hyperbolic Quest, 70).

The occasion is the wounding of the young, brilliant craftsman Florimond De Beaune on a sharp piece of glass, as he was working to accomplish the automated grinding of a lens in a hyperbolic shape on a machine approximating Descartes’ design from La Dioptrique. This at the behest of Descartes himself:

His wound to the hand was so severe that nearly a year later De Beaune could not continue with the project, a project he would not take up again. Descartes’ craftsmanless, all-turning machine could not be achieved. It is as if its “reason” had chewed up even the best of earth’s craftsman.

Compare this to Spinoza’s comment on Christiaan Huygen’s own semi-automated machine, in letter 32 to Oldenburg. (One wonders if he may even had had a now infamous injury to De Beaune in mind.) Descartes seems to write callously to Christiaan’s father in 1640 [following Gaukroger’s citation], 25 years later Spinoza writes soberly about the machine of the son:

…what tho’ thusly he will have accomplished I don’t know, nor, to admit a truth, strongly do I desire to know. For me, as is said, experience has taught that with spherical pans, being polished by a free hand is more sure [tutius] and better than any machine.

Issues of class play heavily into any attempt to synthesize the rationality of a mechanism with the physical hands [and technical expertise] of the required craftsman to build it. What comes to mind for me is the same Constantijn’s Huygens enthused reaction to the baseness of the youths Rembrandt and Lievens in 1629, when he discovered their genius. As Charles Mee relates and quotes:

Unable to have Rubens, Huygens evidently decided to make his own Rubens, and he saw the raw material in Leivens and Rembrandt. He loved the fact that this “noble pair of Leiden youths” came from such lowly parentage (a rich miller was still a miller after all): “no stronger argument can be given against nobility being a matter of blood” (Huygens himself had no noble blood). And the fact of their birth made the two young men all the more claylike, so much more likely to be shaped by a skilled hand. “When I look at the teachers these boys had, I discover that these men are barely above the good repute of common people. They were the sort that were available for a low fee; namely with the slender means of their parents” (Rembrandt’s Portrait ). 

The standing of the rising Regent riche had to position itself between any essentialist noble quality of blood, and the now stirring lower merchant and artisan classes, whose currencied freedoms in trade and mobility were testing ideological Calvinist limits. Leveraging itself as best it could on rational and natural philosophy, a philosopher-scientist-statesman was pursuing a stake in freedom and power, one that rested on the accuracy of his products. In this way it seems that Descartes’ – feigned? – glee over De Beaune’s injury, insofar as it embodied a superhuman outstripping of remedial others, manifests this political distancing to a sure degree. De Beaune was no ignorant worker, for his high knowledge of mathematics made him much more “technician” than craftsman, (in fact de Beaune had proposed the mathematical problem of inverse tangents which Descartes would not be clear on how to solve (letter, Feb 20 1639), and it was his Notes brièves and algebraic essays which would make Latin editions of Descartes Géométrie much more understandable to readers). Reason and rationality could in the abstract certainly in some sense free even the most economically and culturally base kinds (at least those with a disposition to genius), but in fact savants likely imagined that their lone feats of Reason actually distanced themselves from the “hands and limbs” on which they often relied.

Seen in this way, Spinoza’s sober view of Christiaan Huygens machine perhaps embodies something more than a pessimism of design, but rather more is a reading of the very process of liberation which technological development represented for a class of thinkers such as Leibniz or the Huygenses. The liberation of accuracy and clarity was indeed a cherished path, but perhaps because Spinoza was a Jewish merchant’s son, excommunicated, because Spinoza understood personally the position of an elite [his father had standing], within a community itself ostracized though growing with wealth, a double bind which he relinquished purposively, any clarity was necessarily a clarity which connected and liberated all that it touched. It was inconceivable to have dreamed a rationality so clear that it would distance itself from the the hands that were to manifest it. Perhaps Spinoza keeps in his mind the hand of De Beaune.