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Spinoza and Mechanical Infinities

The Mechanically Bound Infinite

I want to respond to Corry Shores’ wonderful incorporation of my Spinoza Foci  research into his philosophical project (which has a declaimed Deleuzian/Bergsonian direction). It feels good to have one’s own ideas put in the service of another’s productive thoughts. You come to realize something more about what you were thinking. And to wade back through one’s arguments re-ordered is something like coming to your own house in a dream.

This being said, Corry’s reading of my material thrills, for he is, at least in evidentary fashion, one of the first persons to actually read it all closely. And the way that he fits it in with his own appreciation for Spinoza’s concepts of Infinity certainly open up new possibility for the Spinoza-as-lens-grinder, Spinoza-as-microscope-maker, Spinoza-as-technician interpretations of his thinking.

There is much to take up here, but I would like to begin at least with the way in which certain parallels Corry draws that change the way that I see what Spin0za was saying (or more exactly, what Spinoza was thinking of, and perhaps associating on), when talking about infinities. Key, as always, is coming to understand just what Spinoza had in mind when drawing his Bound Infinities diagram:

Corry points out in his analysis/summation of Letter 12, grafting from Gueroult’s commentary, that in order to understand the epistemic point (the status of mathematical figures, and what they can describe), one has to see that what Spinoza as in mind in writing to Meyer is a very similiar diagram found in his Principles of Cartesian Philosophy, of which Meyer was the active editor. There the diagram is not so Euclidean, but rather is mechanical, or, hydro-dynamical:

The diagram illustrates water moving at a constant rate (a “fixed ratio” one might say), but due to the nature of the tube it must be moving at point B, four time faster than at AC, and a full differential of speeds between. There you can see that any section of the intervening space between the two circles composed of “inequalities of distance”  in the Letter 12 diagram (AB/CD) is not really meant as an abstraction of lines and points as it would seem at first blush (the imaginary of mathematics), but rather real, mechanical differentials of speed and material change. The well-known passage

As, for instance, in the case of two circles, non-concentric, whereof one encloses the other, no number can express the inequalities of distance which exist between the two circles, nor all the variations which matter in motion in the intervening space may undergo. This conclusion is not based on the excessive size of the intervening space. However small a portion of it we take, the inequalities of this small portion will surpass all numerical expression. Nor, again, is the conclusion based on the fact, as in other cases, that we do not know the maximum and the minimum of the said space. It springs simply from the fact, that the nature of the space between two non-concentric circles cannot be expressed in number.

Letter 12

The Lathe Buried Under the Euclidean Figure

But, and this is where Corry Shores alerted me to something I did not formerly see, the relationship between the two diagrams is even further brought forth when we consider Spinoza’s daily preoccupation with lens-grinding and instrument making. It has been my intuition, in particular, that Spinoza’s work at the grinding lathe which required hours of patient and attentive toil, MUST have had a causal effect upon his conceptualizations; and the internal dynamics of the lathe (which fundamentally involve the frictioned interactions of two spherical forms under pressure – not to mention the knowing human eye and hand), must have been expressed by (or at least served as an experiential confirmation of) his resultant philosophy. If there was this heretofore under-evaluated structuring of his thought, it would see that it would make itself most known in his Natural Philosophy areas of concern, that is to say, where he most particularly engaged Descartes’s mechanics (and most explicitly where he refused aspects of his optics, in letters 39 and 40). And as we understand from Spinoza’s philosophy, Natural Philosophy and metaphysics necessarily coincide.

What Shores shows me is that Spinoza’s Bound infinities diagram (letter 12), his very conception of the circle, is intimately and “genetically”  linked to the kinds of motions that produce them. It is with great likelihood that Spinoza is thinking of his off-center circles, not only in terms of the hydrodynamics that circulate around them, but also in terms of Descartes’ tangents of Centrifugal force.

There is a tendency in Spinoza to conflate diagrams, and I cannot tell if this is unconscious (and thus a flaw in his reasoning process) or if he in his consummatephilosophy feels that all of these circular diagrams are describing the very same thing simply on different orders of description. But the connection between a tangential tendency to motion conception of the circle (which Corry makes beautifully explicit in terms of optics) and Spinoza’s consideration of bound Infinities in the letter 12 (which remains implicit in Corry’s organization of thoughts), unfolds the very picture of what Spinozahas in mind when he imagines two circles off-center to each other. Spinoza is thinking of is lens-grinding blank, and the spinning grinding form.

One can see the fundamental dynamic of the lathe from Van Gutschoven’s 1663 letter to Christiaan Huygens, illustrating techniques for grinding and polishing small lenses,

And it is my presumption that Spinoza worked at a Springpole lathe, much like one used by Hevelius, Spinoza’s Grinding Lathe: An Extended Hypothesis, the dynamics of which are shown here:

In any case, when one considers Spinoza’s Bound Infinity diagram, under the auspices of tangential motion tendencies, and the hydrodynamic model of concentric motions, I believe one cannot help but also see that the inner circle BC which is off-center from the first, is representationallythe lens-blank, and the larger circle AD, is potentially the grinding form. And the reason why Spinoza is so interested in the differenitals of speed (and inequalities of distance) between two, is that daily, in his hand he felt the lived, craftsman consequence of these off-center disequilibria. To put it one way sympathetic to Corry’s thinking, one could feel them analogically, with the hand, though one could not know them digitally, with math. The human body’s material (extensional) engagements with those differentials (that ratio, to those ratios), is what produced the near perfectly spherical lens; and the Intellect intuitionally – and not mathematically – understands the relationship, in a clear and distinct fashion, a fashion aided by mathematics and figure illustration, which are products of the imagination.

What is compelling about this view is that what at first stands as a cold, abstract figure of simply Euclidean relationships, suddenly takes on a certain flesh when considering Spinoza’s own physical experiences at lens-grinding. Coming to the fore in such a juxtaposition is not only a richer understanding of the associations that helped produce it, but also the very nature of Spinoza’s objection to the sufficiency of mathematical knowledge itself. For him the magnitudes of size, speed and intensity that are buried between any two limits are not just abstract divisions of line and figure, or number to number. They are felt  differentials of real material force and powers of interaction, in which, of which, the body itself necessarily participates. The infinities within (and determinatively outside of) any bound limits, are mechanical, analogical, felt and rational.

Corry raises some very interesting relationship question between the Spinoza Bound Infinities Diagram and the Diagram of the Ideal Eye from letter 39. They are things I might have to think on. The image of the ideal eye is most interesting because it represents (as it did for Descartes) a difficult body/world shore that duplicates itself in the experiential/mathematical dichotomy. Much as our reading of the duplicity of the Bound Infinity Diagram which shows mathematical knowledge to be a product of the imaginary, the diagram of the ideal eye, also exposes a vital nexus point between maths, world and experience.

From Mechanics to Optics (to Perception)

It should be worthy to note that Spinoza’s take on the impossibility of maths to distinguish any of the bound infinities (aside from imposing the bounds themselves), bears some homology to Spinoza’s pragmatic dismissal of the problem of spherical aberration which drove Descartes to champion the hyperbolic lens. When one considers Spinoza’s ideal eye and sees the focusing of pencils of light upon the back at the retina (focusingswhich as drawn do not include the spherical aberration which Spinoza was well-aware of), one understands Spinoza’s appreciation of the approximate nature of perceptual and even mathematical knowledge. This is to say, as these rays gather in soft focus near the back of the eye (an effect over-stated, as Spinoza found it to be via Hudde’s Specilla circularia), we encounter once again that infinite grade of differential relations, something to be traced mathematically, but resultantlyexperienced under the pragmatic effects of the body itself. “The eye is not so perfectly constructed” Spinoza says, knowing as well that even if it were a perfect sphere there as yet would be gradations of focus from the continumof rays of light so refracted by the circular lens. What Spinoza has in mind, one strongly suspects, and that I have argued at length, is that the Intellect, with its comprehensive rational in-struction from the whole, ultimately Substance/God, in intuitional and almost anagogic fashion, is the very best instrument for grasping and acting through the nature of Nature, something that neither bodily perception, or mathematical analysis may grasp. Indeed, as Corry Shores suggests in his piece, it is the very continuum of expressional variability of Substance (real infinities within infinities) which defies the sufficiency of mathematical description, but it is the holistic, rational cohesion of expression which defies experiential clusterings of the imagination: the two, mathematics and imaginary perception, forming a related pair.

In the end I suspect that there is much more to mine from the interelationship between Spinoza’s various circular diagrams, in particular these three: that of the relationship of the modes to Substance (EIIps), that of the the hydrodynamics of circulating water (PCP, implicit in the Letter 12 diagram of Bound Infinites), and the Ideal eye (letter 39), each of these to be seen in the light of the fundamental dynamics of the lens-grinding lathe to which Spinoza applied himself for so many years, and at which he achieved European renown expertise.

 

 

The Infinities Beneath the Microscope

I would like to leave, if only for Corry Shores’ consideration, one more element to this story about Real Infinities (and I have mentioned it in passing before on my blog). There is an extraordinary historical invocation of something very much like Spinoza’s Bound Infinities in the annals of anatomical debates that were occurring in last decade of Spinoza’s life. I would like to treat this in a separate post and analysis, but it is enough to say that with the coming of the microscope what was revealed about the nature of the human body actually produced more confusion than understandings in what it revealed, at least for several decades. Only recently was even the basic fact of the circulation of blood in the body, something we take for granted, grasped. And in the 1670s the overall structure or system of human anatomy was quite contested, contradictory evidence from the microscope being called in support one theory or another. Among these debators was Theodore Kerckring, who was weighing in against the theory that the human body was primarily a system of “glands” (and not ducts). Kerckring’s  connection to Spinoza is most interesting, much of it brought to light in Wim Klever’s inferential and quite compelling treatment of the relationship of Van den Enden  and Spinoza. In any case Kerckring  is in possession of a microscope made by Spinoza (the only record of its kind), and by virtue of its powers of clarity he is exploring the structure of ducts and lymph nodes. Yet he has skepticism for what is found in the still oft-clouded microscope glass leads him to muse about the very nature of perception and magnification, after he tells of the swarming of tiny animals he has seen covering the viscera of the cadaver, (what might be the first human sighting of bacteria). He writes of the way in which even if we see things clearly, unless we understand all the relationships between things, from the greatest breadth to the smallest, we simply cannot fully know what is happening, if it is destruction or preservation:

On this account by my wondrous instrument’s clear power I detected something seen that is even more wondrous: the intestines plainly, the liver, and other organs of the viscera to swarm with infinitely minute animalcules, which whether by their perpetual motion they corrupt or preserve one would be in doubt, for something is considered to flourish and shine as a home while it is lived in, just the same, a habitation is exhausted by continuous cultivation. Marvelous is nature in her arts, and more marvelous still is Nature’s Lord, how as he brought forth bodies, thus to the infinite itself one after another by magnitude they having withdrawn so that no intellect is able to follow whether it is, which it is, or where is the end of their magnitude; thus if in diminishments you would descend, never will you discover where you would be able to stand.

Spicilegium Anatomicum 1670

Several things are going on here (and in the surrounding context), but what seems most striking given our topic, we once again get a glimpse into the material, and indeed historical matterings of what bound, mechanical infinities might be. (As a point of reference, at the time of Kerckring’s  publishing Spinoza had just moved to the Hague and published his Theological-Political Treatise, having taken a respite from his Ethics approximately half done, and he will have died seven years later.) Kerckring  in a remarkable sense of historical conflation looks on real retreating infinities with Spinoza’s own microscope, and exacts much of the same ultimate skepticism toward human scientific knowledge, as per these infinities, as Spinoza  does in his letter to Meyer. This does not mean that we cannot know things through observation, or that imaginary products are not of use to us, but only that there is ultimately for Spinoza and Kerckring  a higher, rational power of interpretation, the comprehensiveness of what abounds. Neither measurement or calculation is disqualified, in fact Spinoza in his letters and experiments and instrument making showed himself to be quite attentive to each. It is rather that the very nature of human engagement requires both attention to the bodily interaction with devices and the measured thing, and also a sensitivity to anagogic, rational clarity, something found in the very unbroken nature of Substance’s Infinity. What Kerckring’s description does is perform the very consequence of conception in scientific observation itself, almost in Spinoza’s stead (expressing very simililar  sentiments as Spinoza does in Letter 32 to Oldenburg on lymph and blood, and the figure of the worm in blood,

Let us imagine, with your permission, a little worm, living in the blood¹, able to distinguish by sight the particles of blood, lymph, &c., and to reflect on the manner in which each particle, on meeting with another particle, either is repulsed, or communicates a portion of its own motion. This little worm would live in the blood, in the same way as we live in a part of the universe, and would consider each particle of blood, not as a part, but as a whole. He would be unable to determine, how all the parts are modified by the general nature of blood, and are compelled by it to adapt themselves, so as to stand in a fixed relation to one another.

There is great conceptual proximity in these two descriptions, suggesting I imagine that Spinoza used his microscopes as well, for observation, not to mention that Kerckring and Spinoza come from a kind of school of thought on scientific observation of human anatomy, perhaps inspired by or orchestrated by Van den Enden, as argued by Klever. Just the same, at the very least, Kerckring  presents greater context of just what kinds of retreating infinities Spinoza  had in mind in his letter 12 diagram, not simply a differential of motions, but also a differential of microscopic magnitudes, each of which were an expression of an ultimate destruction/preservation analysis, something that falls to the very nature of what is body is. Spinoza not only ground lenses, but also made both telescopes and microscopes, gazing through each at the world, this at a time when the microcosmic and macrocosmic, nested infinities were just presenting themselves to human beings. And as such his critique of scientific observation and mathematical calculation preserves a valuable potentiality for our (postish) modern distancings and embrace of the sciences.

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.

Govert Bidloo’s 1698 Reference to a Spinoza Microscope

Dutch Republic Stadtholder and King of England, William III

No Second Spinoza Scope

For those that have been following my thought process and research, for a brief moment I believed we may have found another user of a Spinoza microscope, Govert Bidloo in a 1698 open letter to van Leeuwenhoek on the nature of the flatworm parasite F. hepatica. Unfortunately in looking at the text of the letter yesterday I found it only to be a thorough-going reference to Theodor Kerckring’s own use of a Spinoza microscope in his 1670 Specilegium anatomicum, thus far the only first hand account of observations made with an instrument fashioned by Spinoza’s hand.

But the citation is not without merit. As I pointed out in a previous post, in addition to being professor of Medicine and Anatomy at Leiden University, Bidloo was apparently a republican pamphleteer at the time of great social unrest, and the year before his friend Eric Walten had died in prison as a result of the vehiment side taken in the the Berkker controversy, under the force of the vague charge of being a dangerous Spinozist. In this context, the reference to Spinoza’s microscope in a scentific discourse looking to elucidate the source of diseases of the body seems to be something more than coincidence. Spinoza’s lens, and Kerckring’s observations through it, is positioned by Bidloo between two perceived kinds of diagnostic failure.

Bidloo’s Letter: The Importance of Invading Animalcules and Worms

Here is a lengthy excerpt from Bidloo’s published letter, a passage which follows a record of past observations of possible disease causing worms and animalcules (remember, the distinct etiological sources of human disease are largely unknown at this point in history). The catalogue [only the tail of of which is included here] presents numerous body parts and their reported invaders, the body becoming more and more invested, and it is at the end of this that Kerckring is now cited:

Worms in the legs, the scrotum, and a tumor and bladder full of fulls are mentioned by the Misc. Cur., Years 3 and 4, Obs. 173, and the Year 7, Obs. 16.

In scabies and varioles they are described by Borellus [l.c.], Obs. 72.

In pustules, varioles, and the whole of the body: Rhodius [l.c.], Obsc. 64, Part 3.

A wholly wormy man (alas! that only this disease were somewhat rare!) is reported by the Danes in their [Acta Hafn.[ Part 3, Obs. 11.

Severe symptoms caused by mites are reported by Hildanus [l.c.], Obs. 96, as well as by Benetus [l.c.] in his last Obs., Part 35: “a constant production of worms from infancy to great age. Observations about aged worms of different forms, big and small worms, and other animalcles in all parts of the body are to be found. The dispute, or rather the argument will now have to concern the question of whether these animalcules, which are admitted to be found in the parts of living human bodies, can or cannot be causes of diseases and their symptoms, the more so because, amongst others, TH. KERCKRING, a man who has gained a great reputation in anatomy and medicine, doubts it, when on p. 177 in his [Specilegium anatomicum] Obs. 93 he tries to demonstrate the uncertainty of the opinion that is formed about things in anatomy by means and with the aid of magnifying glasses. He deduces this uncertainty: 1. from the smallness of the sharp centers of the field of view; 2. from the change of color; 3. from the alternate inspection of several parts so that what now seems to be separate in reality is united, nay, united physically. But after having highly commended a certain magnifying glass and its maker, B. Spinoza, he adds these words: by means of this my admirable instrument I saw very wonderful things, viz. that the intestines, the liver, and all the tissue of the other intestines are filled with an infinite number of tiny animalcules; however, a person who considers that a house which is inhabited is clean and bright, but nevertheless wears away through the constant maintenance of those who inhabit it, will tend to doubt whether these animalcules spoil or maintain these parts through their continuous movement.

Although I am not aware what great acceptance, credence, and confidence the unfounded reputations of experience, example, and reports of so-called happenings and so on have received and kept not only among the common people, but unfortunately also among some prominent persons, I will not now oppose or cite any authors who deny or affirm that diseases and their symptoms are caused by worms and other animalcules in the human body. For, to express my opinion both frankly and respectfully, I think that any experience, observation, and example will never by applicable, unless at best somewhere in general, in particular. (translation and notes by J. Jansen, 1972, 53-55)

Animalcules and the Body Politic

But in tension to the full spirit of Kerckring’s reservations about microscopy, and after his own Cartesian warning as to any individual diagnosis achieved through direct observation or experience, Bidloo goes on to express extreme caution to those commonly connecting disease to the states of the blood and bile, instead of thinking about the kinds of damage that can be done the transportation systems of the fluids of the body by animalcules and worms. “Over the former more words, and of the latter, more solid proofs can be produced” (60). Bidloo believes that much of the quackery of blood and bile diagnoses, can be relieved by the direct understanding of the kinds of damage tiny animals can do to the ducts and tissues of the human body, something he imagines the microscope to have revealed the body to be rife with. By his account, animalcules proliferate, bite into organs, pierce and insinuate ducts, ferment the “saps”, and cast their excrement, eggs and young all about. It is the Cartesian dream of understanding the micro-causations of the body, projected upon a image of a body teeming with invaders. (How tempting it must have been for Dutch anatomists to read the heath of the body as dependent upon an essential mechanism of ducts and their transportation of fluids, once the nature of the blood’s circulation was revealed [Harvey 1616, 1628], as the land itself was a canal-rich economy, filled with lucretive waterways in every direction.) 

Put aside by Bidloo is Kerckring’s equanimity of observation though, the inability to tell if the swarms of animals are the sign that the body’s home is florishing in the glow of vivacity, or is being spoiled and overrun by inhabitation. Kerckring’s wider view of the possible symbioses of an organism, in keeping perhaps with Spinoza’s whollistic conception of the interdependency of an expressive mechanism, for Bidloo falls to the sure evidence of minute and proliferate causes of bio-destruction: parasites corroding the canals of the body. This makes an interestingly thought-picture for the personal physician to William III, King of England and Dutch Republic Stadtholder, a man in favor republican values in criticism of the Reformed Chuch. One may suppose that Reason and close observation will guide us into discovering the plethora of worms and animalcules in society, those infesting and injuring the transportation systems and organs of healthy conduct. In citing Spinoza’s lens, and Kerckring’s vision of the teeming animalcules and worms, Bidloo evokes a complex of reason and invasion, a political eco-vision in which the proverbial Scylla (the chicanery of vaguely-diagnosing, self-serving “experts”) is torqued against the threatening Charybdis (a chaos of rabble and infestation), given over to the steerage of social health. Importantly, Spinoza’s lens is juxtaposed, (symptomatically), as a kind of clear crystal manifestion of the narrows through which the two can be negotiated.

 

Govert Bidloo, A Spinoza Microscopist?

[Addendum, September 10th: in looking at the full text of the letter referenced below, indeed Bidlow did NOT use a Spinoza microscope, but was only referencing Kerckring’s use as well as his observations on the limitations of the microscope. I keep the post up though, to preserve the thought process of a deadend of research, for whatever that may be worth, as well as for the value of Bidloo’s citation of Spinoza at a near near the death of his friend Eric Walten: Govert Bidloo’s 1698 Refference to a Spinoza Microscope ]

Physician to the King and Another Spinoza Microscope?

[The arguments below I present prospectively, waiting for a confirmation of the source]

I stumbled upon some evidence that there is a second Spinoza microscope in the historical record, and it is my hope that this glass may bring to view more of the details for which I have been straining. Thus far, the only first hand report we have is from Spinoza’s fellow Latin student, and possible van den Enden disciple, Theodore Kerckring, who in his Spicilegium anatomicum  (1670), describes how with Spinoza’s glass he had seen a “infinitely minute animalcules” teeming upon the viscera. This description is to be questioned, firstly, because Kerckring himself warns us a few sentences before, that all observations of microscopes have to be doubted; but also because Kerckring reported elsewhere some microscopic observations which plainly come from the imposition of fantasy upon sight.

In this case the account may be more sobering and exact, though I have yet been able to actually assess the content of the claim. The report comes apparently from Govert Bidloo, and man of fairly high standing, and apparently connections to Spinozist political movements of his day. In 1694 Bidloo was appointed professor of anatomy and medicine at the university of Leiden, a post to which he was not able to well-attend due to also becoming the personal physician to stadholder William III, who would die in his arms in 1702. If indeed Govert Bidloo did use and favor a Spinoza microscope, he was a well-connected anatomist and physician, and public champion of microscopic investigation.

Collaboration with van Leeuwenhoek: Parasitic Protozoon

The fact of Bidloo’s use of a Spinoza microscope is at this point circumspect, as for the moment I have only a summary of the mention of praise for a Spinoza microscope-glass (vergrootglass), in a memoir-letter written to the famed microscopist Antony van Leeuwenhoek, subsequently published in the same year, 1698. I do not read Dutch, so I had to rely upon the summation of a website owner to understand its content.

“Passage from a letter of Govard Bidloo (Henrik van Kroonevelt Ed., 1698, page 27) a memoir to Antonie van Leeuwenhoek, about the animals which are sometimes found in the liver of sheep, on the etiology of diseases (the Plague) and referring to remarks of scientists abroad on his work, and quoting the quality of the Magnifying glass made by Benedict de Spinoza.”

This is found here. The citation given, aside from the letter itself, is not traceable. Perhaps it is a television production: [52] “Cells of Spinoza”: Tetsuro Onuma, Representative of Yone Production Co.Ltd. (2002).

The phase “quoting the quality of the Magnifying glass” I assume probably means “citing the quality”. Because the context is missing for me, there is no way to affirm what I would suspect, that Bidloo is writing to van Leeuwenhoek about his observations of small parasites and their eggs, as found in the liver of sheep, and it is by virtue of the excellence of Spinoza’s glass that his observations are assured. This is somewhat also how Kerckring references his Spinoza microscope.

Historical Context For Bidloo’s Letter to Van Leeuwenhoek 

Two decades before Bidloo presented his findings to van Leeuwenhoek, in 1674 van Leeuwenhoek was startling the world as he peeled away the curtain of the microscopic, revealing to a new level of exact description and illustration, a world of minute animals and structures. Under his tiny, spherical lenses the first bacteria and protozoans were coming to life, and he began letting the world know about in through letters written to leading scientists in London. And in October ’74, he wrote to the Royal Society about his discoveries of “globules” and “corpuscles” in the bile of domesticated animals, the first Sporozoa and parasitic protozoon. It would be as an expansion upon these observations that Bidloo would conduct his own microscopic examnations. I quote here from Dobell’s excellent book in van Leeuwenhoek to give a sense of the early material and Bidloo’s connection to it, first from the letter, and then from Dobell’s commentary:

…in the bile of suckling lambs there are very little globules, and some, though very few, bright particles. which are a bit bigger; besides irregular particles, of divers figures, and also composed of globules clumped together.

The bile of yearling sheep I find to be like that of suckling lambs, only with this difference, that in this bile there are also oval corpuscles of the bigness and figure of those I remarked in ox-bile. (Letter 7 to the Royal Society, October 19th 1674).

I think there can be no doubt that the “oval corpuscles” – called eijronde deeltgensin the original – which Leeuwenhoek discovered in the gall-bladder of one of his “three old rabbits,” were the oocysts of the coccidian Eimeria stiedae; while the comparable structures which he found in the bile of sheep and oxen were, equally certainly, the eggs of trematodes [Dobbell notes: Fasciola hepatica- the worm itself -was well known to L.; for the Dutch anatomist Bidloo (1649-1713) dedicated a little memoir to him, in 1698, in which it was described and figured. If my interpretations be correct, the foregoing extract records the first observations ever made upon the Sporozoa or upon any parasitic protozoon (200)

Antony van Leeuwenhoek and his ‘Little Animals’

Eggs and the Source of Disease

It is regarding these Fasiola hepatica that Bidloo is writing to van Leeuwenhoek in 1698, apparently part of a collaboration of observations between the two microscopists. This is how Frank Egerton sums up the correspondence in his article for the Bulletin for the Ecological Society of America : 

Leeuwenhoek examined flatworms (flukes) from the livers of diseased sheep under a microscope and suspected that the sheep got the worms from drinking rainwater that collected in fields (21 February 1679, Leeuwenhoek 1939-1999, II:417-419). He pursued the subject no further until 1698, when he and Professor of Medicine Goderfridus Govard Bidloo (1649-1713) of Leiden University (van der Pas 1978) discussed liver flukes in sheep. Boththen wrote up their observations for publication, with Leeuwenhoek sending his to the Royal Society and Bidloo sending his to Leeuwenhoek, who had them published in Delft. Bidloo sent with his letter an overly precise drawing of a fluke, which shows two eyes, a heart, a circulatory system, and intestines that existed only in his imagination. Nevertheless, Bidloo did recognize the eggs and concluded correctly that the species is hermaphroditic. He also generalized from his observations that these worms seem to cause disease in sheep and that worms probably also cause disease in humans (Bidloo 1698, 1972). Leeuwenhoek went out and attempted to find fluke eggs in fields and ditches, where they might have been deposited in sheep feces (2 January 1700, 1939-1999, ?), but he had no way to identify them if he had found them. The fluke life cycle is so complex that it was not fully understood until the mid-1800s (Reinhard 1957). (53)

“A History of the Ecological Sciences, Part 19″

Indeed, the lifecycle of F. hepatica is quite complex, as it relies upon a symbiont aquatic snail, something no microscope would reveal to these men, but it is good to note that Bidloo’s microscope and analysis did properly identify the eggs of F. hepatica, something which may give clue to the magnification of his glass. It would appear that the two men were operating under at least remotely similar powers of glass, and at this point van Leeuwenhoek had achieved magnification really beyond compare for the century.  

Bidloo's illustration of the flatworm F. hepatica

The size of the eggs in question may be in order. They come in the thousands, so together are visible to the naked eye, but the eggs themselves are microscopic, measuring approximately 130-160 µm, or 130/1000th of a millimeter:

According to their optical appearance and approximate measurements, we isolated about 1,300-1,500 ‘large’ eggs from a fairly large quantity of sheep faeces. Of these, 300 were measured and their average size was found to be 154 (143-180) x84 (75-102) µm. Fasciola eggs of normal size found in the faeces of the same sheep measured 129 (107-162)x 71 (61-79) µm.

“Unusually Large Eggs of a Fasciola hepatica Strain” (1982) D. Duwel

As I have not read Bidloo’s account, I as yet cannot tell if his glass resolved such detail, but van Leeuwenhoek’s description of “oval corpuscles” must have. And we should keep our mind open to this possibilities.

If we are to speculate, having identified what Bidloo saw and concluded, and assumed that he used a Spinoza made glass, what was the nature of Spinoza’s “vergrootglas”? Literally, this word means “magnifying glass”, something distinct from the word for microscope. It is the same word used to describe the instruments sold from Spinoza’s estate at auction on November 4th, 1677. (It is even conceivable that this was one of those instruments.) A vergrootglas could be anything from a swivel-armed spectacle glass used for dissection and study, to the very powerful simple, single-lens microscopes that Swammerdam and van Leeuwenhoek used. Aside from the more famous Leiden anatomists who used a simple microscope, we are told that Bidloo’s successor to the university position, Boerhaave, used a lens as small as a grain of sand (Ruestow 95). But the story is unclear. Bidloo was a student and friend to Ruysch, a fellow student and associate of Kerckring from ’61 onwards, who used magnification quite sparingly, and would have had no need of such an intense and difficult lens.

Devils and Parasites

There is another interesting point of about Bidloo’s biography which makes his 1698 reference to Spinoza’s lens more than a point of curiosity. It is twenty-one years after Spinoza’s death, but something more than simply the persistence of the efficacy of Spinoza’ instrument forces his name into consciousness. Bidloo, the physician of William III, was apparently a political activist of a sort, a champion of republican values. And just the year before his rather vociferousfriend Eric Walden had died in prison, perhaps by suicide following a series of failed suits for his freedom, under the general accusation of being a Spinozist-atheist. Walten’s escalating pamphleted attacks against the Dutch Reformed Church, in defense of Bathasar Berkker’s “The World Bewitch’d”, were fierce and reminiscent of Spinoza’s friend Koerbagh, who also died as a political prisoner. Berkker had maddened the religious in his Cartesian-like argument that because their could be not causal interaction between Spirit and Matter, devils and angels could have no effect on this world. This denial of both the miraculous and the diabolical enraged the pious, and when Walten wrote on Berkker’s behalf, the ire came to be directed towards him, eventually with legal consequence. This connection between Bidloo and Walten I find, thinly, but indicatively here:   

In 1688 he took up the cause of William III against James II and showed himself to be a staunch defender of popular sovereignty and the elective nature of monarchy. Next, he turned to the question of the civil rights of governments over the church, and two local disputes, one concerning the privileges of the regents of Amsterdam, and other Rotterdam tax upheavals. [note, after “regents of Amsterdam”: It is unclear which pamphlets in this particular row were written by Walten and which by his friends Govert Bidloo and Romeijn de Hooghe, the famous engraver. See Knuttle, “Ericus Walten”, p. 359-383.] (44)

“Eric Walten (1663-1697): An Early Enlightenment Radical In the Dutch Republic”, by Wiep van Bunge, in Disguised and Overt Spinozism In and Around 1770

Whether Govert Bidloo used Spinoza’s microscope in his observations on the hepatica or not, I cannot say for certain now, but his reference in the published memoir, in the context of his observations on parasites of the body and a suspicion that they lead to human illness no doubt reflected to some degree the events that of the years previous, and the sourness of the death of Walten in prison. What comes to mind is Spinoza’s reflection to Oldenburg so many years before, that we are like a worm in the blood, how our perceptions are only most often local to what jostles us, itself a reflection on Kircher’s microscopic discovery of worms in the blood of plague victims. (Some thoughts here:  A Worm in Cheese ). One must remember that this was not only a time of political and religious upheaval, but also a time of plague. The clearness of Spinoza’s glass no doubt, in the minds of his admirers, expressed the clarity with which the political body must be examined. Bidloo’s study of the bile of sheep, in search of parasites with Spinoza’s glass either in hand or in mind, surely struck him as fitting.


Simple or Compound: Spinoza’s Microscopes

Smaller Objective Lenses Produce Finer Representations

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

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

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

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

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

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

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

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

The Microscope in the Dutch Republic, Edward G. Ruestow

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

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

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

“Huygens’ Design of the Simple Microscope”

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

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

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

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

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

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

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

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

“Seventeenth Century Italian Compound Microscopes” Silvio A. Bedini

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

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

The Simple Microscope in the Hands of Van Leeuwenhoek and Huygens

Spinoza’s Microscopology: a prospective comparison of context

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

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

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

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

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

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

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).

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.

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.

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