Frames /sing


Tag Archives: Wim Klever

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.

The “Corporeal Equation” of 1:3: What Makes A Body for Spinoza?

If a Body Catch a Body Comin’ Through the Rye

I have always been fascinated by Spinoza’s defintion of a body as found in the Second Part of the Ethics. Not because it reflected some proto-physics, but because it allowed a radical revisioning of what defined boundaries between persons, and between persons and things. What seems implicit in such a definition is that something of a cybernetic recusivity surrounds and defines any isolated “part” of the Universe, yet, a recursivity that only comes clear by taking a perspective. One understands that really for Spinoza the entire Universe composes a single such body.

Here is Spinoza’s famous Ethics  defintion, and an even more elementary and bold one from his much earlier Short Treatise on God, Man and His Well-Being (KV)

Ethics: When a number of bodies of the same or different magnitude form close contact with one another through the pressure of other bodies upon them, or if they are moving at the same or different rates of speed so as to preserve an unvarying relation of movement among themselves, these bodies are said to be united with one another and all together to form one body or individual thing, which is distinguished from other things through this union of bodies (E2p13a2d)

KV: Every particular corporeal thing [lichaamelijk ding] is nothing other than a certain ratio [zeekere proportie] of motion and rest.

Yet, such a vision for Spinoza is more than an instructive imaginary relation, it indeed is a proto-physics, a concrete real which must be accepted as such. There is a certain sense in which Spinoza’s conception of a body must be reconciled with the “facts” of contempory physics if we are to geta stronger impression of the truth of his metaphysics and psychology. As Spinoza wrote to Blyenbergh, “Ethics, … as everyone knows, ought to be based on metaphysics and physics” (Ep 38). At a general level, in Spinoza’s own terms, if his physics is radically wrong this may pose serious doubts as to his Ethics (an entirely rationalist reading of his philosophy notwithstanding). And concordantly, one might assume, new information in physics could have a rippling effect across his philosophy and Ethics.

It is not my aim here to explore these wider meta-questions, but rather to for a moment pause upon a change in my own thinking. I had always taken Spinoza’s above defintions just as I explained, fantastic frameworks for revisioning the world as it common-sensically and historically has come down to us, intellectual opportunities for instance to see the connections between bodies in a Batesonian or an Autopoietic sense. This still remains. But I came to realize that when Spinoza is thinking about a “certain ratio” (as Shirley translates) or a “fixed manner” (Curley), he is thinking of something quite quantifiable, something numeric. I had of course loosely thought that this was the case, but until recently I had never strictly thought about it.

Spinoza’s Objection

There is an interesting, rather provocative point in Spinoza’s letters to Oldenburg, as he is reporting back to this Secretary of the Royal Society on the progress of his brilliant neighbor Christiaan Huygens. It seems apparent from what Spinoza reports that he has had intermittent, but somewhat substantive discussions on not only optics and lens-grinding, but also on physics. Huygens, by what history tells, had corrected Descartes’ rules of motion, and done so through experiment. Huygens was quite interested in the rules of motion for he had invented the pendulum clock way back in 1656 (the same year he had discovered the rings and a moon of Saturn), and for a decade was focused on improving it. Spinoza reports back to Oldenburg Huygens’ disagreement with Descartes, but tantalizingly also speaks of his own disagreement, in particular, with the sixth rule of motion:

Spinoza: “It is quite a long time since he [Huygens] began to boast that his calculations had shown that the rules of motion and the laws of nature are very different from those given by Descartes, and that those of Descartes are almost all wrong…I know that about a year ago he told me that all his discoveries made by calculation regarding motion he had since found verified by experiment in England. This I can hardly believe, and I think that regarding the sixth rule of Motion in Descartes, both he and Descartes are quite in error.” (Letter 30A)

Oldenburg: “When you speak of Huygens’ Treatise on Motion, you imply that Descartes’ Rules of motion are nearly all wrong. I do not have to hand the little book which you published some time ago on ‘Descartes’ Principia demonstrated in geometrical fashion’. I cannot remember whether you there point out that error, or whether you followed Descartes closely to gratify others.” (Letter 31)

Spinoza: “As to what you say about my hinting that the Cartesian Rules of motion are nearly all wrong, if I remember correctly I said that Mr. Huygens thinks so, and I did not assert that any of the Rules were wrong accept the sixth, regarding which I said I thought that Mr. Huygens too was in error.” (Letter 32)

Many commentators have not been able to make much headway when interpreting Spinoza’s objection to Descartes sixth rule of motion, for at the very least, it seems woven to his other rules, and the objection should have spread far wider than this, as in the case with Huygens. Alan Gabbey (The Cambridge Companion ) for instance simply finds it nonsensical. And Lachterman in “The Physics of Spinoza’s Ethics”, really almost avoids the issue altogether. (Wim Klever has taken the question directly on in “Spinoza and Huyges: A Diversified Relationship Between Two Physicists”, tying it to a Cartesian difficulty in explaining cohension, while Rivaud finds what seems to be an untenable conceptual connection between speed and essence in his “La physique de Spinoza”.)

I certainly am not one here to solve the question, but it did get me thinking about how Spinoza conceived of a body, and what a “certain ratio” meant to him.

Descartes’ Sixth Rule of Motion and Spinoza’s Defintion of a Body in the Short Treatise

Below is the sixth rule of motion to which Spinoza found objection. It essentially describes what would ideally happen if two bodies of the same size, one in motion and one at rest, struck. Descartes suggests that if the moving body had four (4) degrees of speed before impact, after impact the ratio would be 1:3, with the body at rest taking on one (1) degree of speed, the bodies rebounding:

Descartes:51. Sixth rule.
Sixthly, if body C at rest were most accurately equal to body B moved toward it, it would be partly impelled by B and would partly repel it in the contrary direction. That is, if B were to approach C with four degrees of speed, it would communicate to C one degree and with the three remaining would be reflected in the opposite direction.

Huygens reportedly showed through experiments at the Royal Society that instead all the degrees of speed would be imparted to the body at rest, and the intially moving body would then be stopped, and it was to this, as well as to Descartes’ rule that Spinoza expressed an unspecified objection. But this is not the ultimate point here for me. I was rather struck by an early note on Spinoza’s defintion of a body found in the Short Treatise , which proposes the same ratio of 1:3 that Descartes used to illustrate his sixth rule, here below stated as the ratio of motion to rest, and not as “degrees of speed”:

Spinoza: Short Treatise, notes to the Preface to Part II:

12. As soon, then, as a body has and retains this proportion [a proportion of rest and motion which our body has], say e.g., of 1 to 3, then that soul and that body will be like ours now are, being indeed constantly subject to change, but none so great that it will exceed the limits of 1 to 3; though as much as it changes, so much does the soul always change….

…14. But when other bodies act so violently upon ours that the proportion of motion [to rest] cannot remain 1 to 3, that means death, and the annihilation of the Soul, since this is only an Idea, Knowledge, etc., of this body having this proportion of motion and rest.

What is striking to me is that such an elementary numerical value for the definition of a body would occur to Spinoza in this context. Alan Gabbey wants us to point out that this ratio of 1:3 is found in editorial notes, and my not even be of Spinoza’s hand, though I am unsure if Spinoza would have allowed such a strong example to slip through if it was alien to his thinking. Provocative is that the context for this proposed illustration of a “corporeal equation” (as Matheron has named it), of 1 to 3, is that it is the human body that is being discussed and not abstract solids such as those Descartes discusses in his physics. Even if Spinoza does not imagine that the human body might actually retain such an elementary 1:3 ratio of motion to rest, somewhere in his conception of the human body there is an affinity to such an simple math. One for instance would not be describing a super computer whose mark would be its complexity, and turn to such a number. It would appear that at least figuratively Spinoza at the time of the Short Treatise  thought of the human body as elementarily composed such that its conatus expressed a homeostasis that was comprehesible and simple. The numerical value of 1 to 3 held perhaps a rhetorical attraction.

By the time of Spinoza’s geometrical treatment of Descartes’ philosophy, the proposed illustrative values that Descartes included in his rules for motion are no longer there. Spinoza generalizes them apart from any particular equation. One could see in this perhaps already a distancing from some of Descartes’ assertions, and Oldenburg tells Spinoza that he looked over Spinoza’s exposition of Descartes to see signs of his disagreement, finding none.

What the sixth rule Meant for Spinoza

For my part, if we take Descartes’ sixth rule at face value, and imagine the interaction between two bodies of the same size, one at rest, one in motion, we get a glimpse into the kind of change Spinoza thinks makes a body. For once the supposed transfer of a degree of speed occurs, the two bodies are now in communication. As long as they are not interacted with by other bodies their ratio will remain 1:3, and they would be considered an “individual”. And if one of those bodies interacted with another body so as to change its speed, immediately one realizes that if the idea of a single body is to be preserved the definition of parts needs to be expanded so that the ratio is to be expanded across a host of interactions. One sees how the definition of a body as a body is entirely contingent upon how you calculate.

Wim Klever finds in Spinoza’s 1665 objection to Descartes’ sixth rule (made almost 4 years after the writing of the Short Treatise ) a testament to Spinoza’s thorough-going commitment to a physics of immanence. This could be. But one could also imagine the case that Spinoza had been caught up in a conversation with Huygens at the Hofwijck estate and was entirely caught off guard by Huygens’ sweeping dismissal of Cartesian physics, which up to that point had been a touchstone for most scientific thinking in Europe. Spinoza’s objection to the sixth rule may have only been a reaction, one that prudently and instinctively placed himself between Descartes and Huygens, on a single point, a point he could not elaborate on.

But what was it about Huygens’ correction to Descartes which may have also given Spinoza pause, especially if Descartes’ rule for the transfer of motion between two equal bodies, one moving, one at rest helped frame Spinoza’s general notion of what makes a body? Would it not be that there was a complete tranfer of motion from one to the other, that one stopped and the other started? Because Spinoza envisioned bodies moving together in community, and integrated communication of impinging interactions that could be analyzed either in terms of their recursive cohensions (for instance how the human body can be studied solely in terms of its own internal events, as one might say, immanent to their essence), or in terms of extrinsic interactions which “through the pressure of other bodies” cause these internal events, the intuitional notion that a body in motion would deliver all of its motion to another body at rest, and not be rebounded simply defied the over all picture of what Spinoza imagined was happening.

I suggest that somewhere in the genealogy of Spinoza’s thought about what defines a body he found Descartes sixth rule quite suggestive. The idea that two bodies which do not seem to be in communication, one moving, one unmoving, (an essential perceptual differential which allows us to distinguish one thing from another in the world), suddenly can appear in communication from the change they bring about in each other in collision, now departing at a ratio of speeds, helped Spinoza psychologically and causally define the concrete yet contingent composition of an individual. The corporeal equation of 1 to 3 standing in for the possibility of mathematical determination which could conceptually unite any two parts in a single body, given the right analysis.

But when Spinoza encountered Huygens’ thorough dispatch of Cartesian mechanics we can suspect that Spinoza came in contact with his own theoretical disatisfactions with Descartes. As we know, Spinoza was part of a small cadre of mathematicians and thinkers which found dissatisfaction with Descartes idealized optics, something that no doubt formed part of his discussions with fellow-lense grinding and instrument maker Christiaan Huygens. And too, Spinoza likely felt that though Descartes’ mechanics provided an excellent causal framework for rational explanations of the world, his determinations lacked experimental ground. It would seem to me that Spinoza’s objection to the sixth rule of motion poses something of a revelation into the indeterminancy of Spinoza’s physics. The sixth rule may have played a constructive role in his imagination of what a body must be, but in particular in view of Huygens’ confirmed rejection of the rule, it became simply insufficient. Spinoza’s physical conception of a body stands poised between a Cartesian rational framework of causal interaction and mechanism, which proves lacking in specifics, and the coming Newtonian mechanics of force. However, in such a fissure, one does have to place Spinoza’s notion of immanence.

Autopoiesis Comes?

Signficantly, and something which should not be missed, is that the definition from axiom 2 of proposition 13 of Part 2 above is not the only conclusive one that Spinoza provides in the Ethics. Lemma 4 under axiom 3 actually provides a view of the body which does not require that the parts themselves remain in a fixed ratio to each other. Rather, it is only the ratio itself that must be preserved:

If from a body, or an individual thing composed of a number of bodies, certain bodies are separated, and at the same time a like number of other bodies of the same nature take their place, the individual thing will retain its nature as before, without any change in its form [forma].

This allows us to see that by the time of his writing of the Ethics, Spinoza’s notion of ratio, the aim of his mechanics, is far from what Newton would develop. The causal histories traceable through interactions between bodies certainly were signficantly important for Spinoza, but it was the preservation of a mode of interaction which really concerned Spinoza’s focus. That all the bodies that compose and individual could conceivably be replaced, without that individual being considered as changed (as for instance we know of nearly every cell of the human body), is something that Newtonian physics would not enumerate. It is within this conception of preservation that I think Spinoza’s mechanical conceptions have to be framed, in the entirety of an effect between bodies, the cohesiveness of the modal expression.

One need only turn to something like Autopoietic theory (both those of life by Maturana and Varela, and suggestively of social forms by Luhmann) to see a lineage given from Spinoza’s Lemma 4 description:

The defintion of a living thing understood to be a self-producing machine:  “An autopoietic machine is a machine organized (defined as a unity) as a network of processes of production (transformation and destruction) of components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in space in which they (the components) exist by specifying the topological domain of its realization as such a network.” (Maturana, Varela, 1980, p. 78)

On the difference between “organization” and “structure”:  “…[I]n a toilet the organization of the system of water-level regulation consists in the relations between an apparatus capable of detecting the water level and another apparatus capable of stopping the inflow of water. The toilet unit embodies a mixed system of plastic and metal comprising a float and a bypass valve. This specific structure, however, could be modified by replacing the plastic with wood, without changing the fact that there would still be a toilet organization.”
(Maturana & Varela, 1987, p. 47)

Where Lies Spinoza’s Physics?

Spinoza’s immanent connection between physics and metaphysics in a turn toward a decisive ethics, is one in which any outright mechanics must be understood beyond simply A causes B, and the appropriately precise mathematical calculation of what results. If Spinoza’s physics (and even its relationship to Descartes who preceded him, and Newton who followed him) is to be understood, it is this recursive relationship between parts that has to be grasped, the way in which parts in communication can be analyzed in two ways, along a differential of events internal to a horizon, and events external to that horizon, interior and exterior, even with a view to the conceived totality. It seems that it is this replaceable nature of body-parts in composite that qualifies Spinoza’s physics as interpretively distinct, and what allows it to place within the domain of cause not only questions of material interaction, but also psychology and belief, and ultimately social values of good and bad. 

What it seems that Spinoza was most concerned with in his assessment of a physics is the kinds of concrete reactions which ground our selective ability to usefully distinguish one thing from another, a usefulness that ever trades on the community of rational explanations with share with others. The result of this physics is an ultimate ground upon which we can and do build our own mutual body of social wholes, our own physics of decisions and distinctions. Physics both ground and distinguish us for Spinoza, always suggesting an anatomy of joined, contiguous parts; it is an anatomy that guides the effortless butcher’s knife that ideally, knowingly, seldom would need sharpening.

Spinoza and Tuberculosis: His Disease and Devotion

[Tuberculosis can be a difficult disease to diagnosis. The following is working under the assumption that the diagnosis of “phthisis” for Spinoza’s long-running pulmonary problems is best understood as the disease tuberculosis.]

The Influence of Disease

It is interesting that of all the influential facts we seem to have about Spinoza’s life, his tuberculosis may be neglected only as much as his lens-grinding has been. Very little of how debilitating this disease can be, nor its chronic nature seems to be considered when framing a picture of Spinoza’s motivations for life decisions. At most his tuberculosis, called in biographies “phthisis” (its name derived from Greek) gives us a remote picture of a man made weak and coughing at times. Then there is the oft repeated, unsupported, yet romantically satisfying thought that he died not only of his TB, but also from inhalations of glass dust from his lens-grinding. The facts of the disease seldom seem to enter into the explanations for Spinoza’s decisions and life turns.

Spinoza’s early biographer Colerus tells us that Spinoza had been suffering from tuberculosis for more than 20 years when Spinoza died at the age of 44, in February of 1677:

Spinosa was a Man of a very weak Constitution, unhealthy and lean, and had been troubled with a Pthysick above twenty years, which oblig’d him to keep a strict course of Dyet, and to be extreamly sober in his Meat and Drink. Nevertheless, his Landlord, and the people of the House did not believe that he was so near his end, even a little while before he died, and they had not the least thought of it.

If we track backwards, this would place the first bout with tuberculosis very close to the date of his father’s death (March 28, 1654), and his taking over of the family firm (September 1654). Spinoza’s step mother, Esther, died only five months before his father did (October 14, 1653), after a year of serious illness, itself a year after Spinoza’s own sister Miriam had died. Tuberculosis is a highly contagious disease when symptomatic, (if living 24-hours-a-day exposed for two months it is estimated that you have a 50% chance of being infected).

To more fully picture the condition, the symptoms of active tuberculosis include:

– A cough which may last three or more weeks and may produce discolored or bloody sputum
– Unintended weight loss
– Fatigue
– Slight fever
– Night sweats
– Chills
– Loss of appetite
– Pain with breathing or coughing (pleurisy)

That Spinoza may have contracted tuberculosis from his father (or other family members), and may himself have become symptomatic in the year 1656 or so is not something that many people have considered. (To his credit, Nadler does momentarily bring up the idea that Spinoza may have suffered from the same thing that killed his step-mother (Spinoza: A Life, 155); why he notes the step-mother and not his father I do not know. These are years that we have very little historical record of, and a struggle with the illness may very well be a reason for this (the highest risk for developing of the disease is in the first two years after infection). When Spinoza applied for orphan status in March of ’56 (two years after his father died), and when the cherem is read against him in July of the same year, removing him from the community, having failed to pay the family firm’s imposta tax, he may indeed already have been tubercular, and perhaps even seriously so. This would make his excommunication something of a quarantine, not only of ideas, but also in a vividness of metaphor, of body and illness. A cutting off of an already diseased limb. We really need not go that far, though it should be considered. We have had such a variety of motivations projected onto Spinoza and his situation at this time, from Jonathan Israel’s thought that Spinoza was during this period attempting to be excommunicated by being outrageous simply to climb out from the burden of onerous debts, to Wim Klever’s notion that Spinoza at this point was so invested in his political and spiritual education with Van den Enden, long broken from the community, the excommunication was but a trifle. Either of these may be so, but if Spinoza had by now become symptomatic, his illness certainly would have played into his inability to run the firm to profit, or more significantly, his desire to no longer conduct that kind of vigorous business or to remain in the community 0f his youth. No matter the thesis for his excommunication and his change of attitude towards the values in life, the facts of an onset of a lethal diseased that might have killed many of his family members certainly would play an informing role.

Chekhov’s Example

Tuberculosis does not always head in a straight line, by my understanding. It can be recurrent. Chekov, for instance, who like Spinoza also suffered from the disease over a twenty-year period. A first onset expressed itself in an initial bout of fevers in December of 1883, and then three days of coughing up blood a year later in December of 1884. It was not until six years after these, from the strain of trans-Siberian travel, that again the disease seemed to surface, much more forcefully. Chekhov, like Spinoza, died in his 44th year, at the peak of his intellectual and creative powers. [Citing “Chekhov’s Chronic Tuberculosis” (1963), by Brian R. Clarke]. This is how one medical information website describes the nature of the disease’s chronic mechanism:

In addition, TB can spread to other parts of the body. The body’s immune (defense) system, however, can fight off the infection and stop the bacteria from spreading. The immune system does so ultimately by forming scar tissue around the TB bacteria and isolating it from the rest of the body. Tuberculosis that occurs after initial exposure to the bacteria is often referred to as primary TB. If the body is able to form scar tissue (fibrosis) around the TB bacteria, then the infection is contained in an inactive state. Such an individual typically has no symptoms and cannot spread TB to other people. The scar tissue and lymph nodes may eventually harden, like stone, due to the process of calcification of the scars (deposition of calcium from the bloodstream in the scar tissue). These scars often appear on x-rays and imaging studies like round marbles and are referred to as a granuloma. If these scars do not show any evidence of calcium on x-ray, they can be difficult to distinguish from cancer.

Sometimes, however, the body’s immune system becomes weakened, and the TB bacteria break through the scar tissue and can cause active disease, referred to as reactivation tuberculosis or secondary TB. For example, the immune system can be weakened by old age, the development of another infection or a cancer, or certain medications such as cortisone, anticancer drugs, or certain medications used to treat arthritis or inflammatory bowel disease. The breakthrough of bacteria can result in a recurrence of the pneumonia and a spread of TB to other locations in the body. The kidneys, bone, and lining of the brain and spinal cord (meninges) are the most common sites affected by the spread of TB beyond the lungs.

“experience had taught me”

At the very least, if Spinoza was showing symptoms of the disease as early as 1656, as Colerus’ very rough estimate would place them, Spinoza’s life decisions to not pursue wealth, but rather a life of philosophy, must be cast in a slightly different psychological light. Spinoza writes of his change of mind in The Emendation of the Intellect:

After experience had taught me that all the usual surroundings of social life are vain and futile; seeing that none of the objects of my fears contained in themselves anything either good or bad, except in so far as the mind is affected by them, I finally resolved to inquire whether there might be some real good having power to communicate itself, which would affect the mind singly, to the exclusion of all else; whether, in fact, there might be anything of which the discovery and attainment would enable me to enjoy continuous, supreme, and unending happiness.

I say “I finally resolved,” for at first sight it seemed unwise willingly to lose hold on what was sure for the sake of something then uncertain. I could see the benefits which are acquired through fame and riches, and that I should be obliged to abandon the quest of such objects, if I seriously devoted myself to the search for something different and new. I perceived that if true happiness chanced to be placed in the former I should necessarily miss it; while if, on the other hand, it were not so placed, and I gave them my whole attention, I should equally fail (Elwes translation).

This is thought to have been Spinoza’s earliest philosophical text, before the Short Treatise, Shirley placing its composition between the years 1657 and 1660. What, we may ask, was this “experience” that has taught Spinoza the futility of social life, the uncertainty of “fame and riches”. Are these generic experiences that all of us would have, or perhaps the particularities of watching his father die in tubercular fashion, after a life of substantial monetary and honorific gain? Or, more jarringly, was it the onset of the same disease, the same coughing up of blood, that he had seen his father and his step-mother succumb to? This would certainly have a life-turning effect. Spinoza continues in the opening of the Emendation, actually referencing the analogy of fatal illness and remedy as the very mode of his decision making:

For I saw that my situation was one of great peril and I was obliged to seek a remedy with all my might, however uncertain it might be, like a sick man suffering from a fatal malady, who, foreseeing certain death unless a remedy is forthcoming, is forced to seek it, for therein lies all his hope (Shirley translation).

Is this just a proximate reference, or is Spinoza speaking literally of his own onset of illness?

We see no evidence for debilitation in April of ’55 in the record of Spinoza’s subpoena and physical confrontation with the Alvares brothers. He is struck so hard his hat comes off, something which might afford a reference to physical weakness, but none is mentioned. In fact, from the vague description it seems that only the hat seems worse for wear, leaving the impression of a firm man. And in ’58, from Fra Tomás’ 1659 report to the Spanish Inquisition, we find Spinoza to have a handsome face “de buena cara” with light, clear, but perhaps pale skin, blanco. This would seem to put him in good health. The only thing I would mention is that in this report there is great contrast given between his very dark hair and eyes, and the paleness of his skin. Prado, in whose company Spinoza is in, has a “brownish” complexion on the other hand. While he may have been in good health at the time, the paleness of his skin may have been due to some convalescence. In 1659 he is described by another informant for the Inquisition as having a “well-formed body, thin, long black hair, a small moustache of the same color, a beautiful face”.

Yet as we have seen from the example of Chekhov, an attack of tuberculosis does not necessarily leave one debilitated for life. The body’s immune system can indeed isolate the infection, and return one to health, even robust health, only to be susceptible to the disease later, at times of great stress or weakness. Assuming that his disease was that of tuberculosis, one cannot conclude that Spinoza’s health was never robust, as some have thought.

The Beginnings of “Isolation” and a Conserve of Roses

A great deal of investigative imagination and analysis has gone into the question as to why Spinoza left Amsterdam for the much more quiet Rijnsburg in 1661. Gullan-Whur suspects that something had frightened Spinoza in a way that the excommunication had not, perhaps something to do with the Spanish Inquisition. Perhaps an increasing pressure from Dutch authorities and Jewish reaction made it unsafe for Spinoza to continue his Amsterdam life, some feel. And there is the account of a knife attack outside the theatre, if it is to be believed. Alternately, some think that he went to Rijnsburg to be closer to the Collegiant movement. Spinoza’s very good, generous friend Jarig Jelles bought a large new house on the Herengracht in Amsterdam in 1660, but Spinoza did not move in. First he moved to near  “near ” Ouderkerk, and then to Rijnsburg near Leiden’s university. Why? It is mentioned that his move towards isolation was so that he could be away from distractions from friends, so that he could concentrate on his work, and this is no doubt true. But is it too much to notice that his withdrawal from friends and the air of the city may have been really a question of health? Was it not that tuberculosis struck him again, and it is was in full view of his mortality, and even questions of contagiousness, a theoretical need for fresh air, that brought him to concentrated isolation?

By September 1661 he writes to Oldenburg that his Short Treatise, (one may say his most overtly spiritual work) is still a work in progress. There is no hint of his illness in their correspondence. In the winter of ’62/’63 he has the company of Johannes Caesarius, who is living with him, helping him in a none-too-satisfactory fashion with the geometrical treatment of Descartes’ philosophy. Gullan-Whur reads Caesarius to be Jan Casier, a student of Van den Enden’s school, now a young, Dutch Reformed ordinand (1642-77). As a collaborative biographical note of perhaps significant correspondence during this period, Adriaan Koerbagh, Spinoza’s friend and comrade in spirit of the same age, had received his doctor of medicine from nearby Leiden University in 1659, with a dissertation on the causes of Tuberculosis, Disputio medica unauguralis de Phthisi. In 1661, the year that Spinoza moved to Rijnsburg, Koerbagh became a Doctor of Law, again at nearby Leiden, and in Koerbagh’s later political trial he admits that he had discussed philosophical matters with Spinoza numerous times in the years 1661-63. Having conducted a study of the causes of tuberculosis, one wonders if Koerbagh had ever seen Spinoza as a patient. Or if Adriaan himself had tuberculosis which weakened him (as he would died only within a few months of being sentenced to prison and hard labor in 1669). Along this thin line of argument, is it a coincidence that a conserve of roses is the only conserve mentioned in Koerbagh’s Bloemhof  (1668). The suppressed Bloemhof  was a 672 page dictionary of terms written by Adriaan and his brother, meant to demystify the use of foreign phrases and technical jargon, putting into the vernacular the verbal obfuscations by which eclesiastical, medical and legal “experts” carried out much of its authority over the common man. In June 1665 it is for a conserve of roses that Spinoza says he is waiting (Letter 28), writing to the physician Johan Bouwmeester who was an intimate of Adriaan Koerbagh. Spinoza had visited his friends in Amsterdam earlier in the year, and during his visit to the city he seems to have suffered a recurrence of his tuberculosis:

At the same time I also expected some of the conserve of roses which you promised, although now for a long time felt better. On leaving there, I opened a vein once, but the fever did not abate (although I was somewhat more active even before the bloodletting because of the change of air, I think). But I suffered two or three times with tertian fever, though by good diet I have at last rid myself of it and sent it packing. Where it went I know not, but I don’t want it back.

At this time Spinoza has just moved from Rijnsburg to Voorborg near the Hague. Likely having finished first drafts of parts I and II of a then tripart Ethica, he makes a break and begins his work on the Politico-Theological Treatise. Spinoza distinctly associates the “air” of Amsterdam with the onset of his illness. It would appear likely that this causal belief was consistent in his life, and thus part of his reason for moving out of Amsterdam in the first place. One can also ask, something I’ve not seen considered, was the renewed attack of his disease in some way linked to the much discussed break from the Ethics, and his turn to political issues of the day?

Voorburg, Not So Quiet

At this point I would like to take up some of the psychological criticism aimed at Spinoza by his biographer Gullan-Whur. In making her assessment of a certain flaw in Spinoza’s self-perception she provides us with a rather telling description of the house Spinoza moved into in Voorburg. She points out that although Spinoza, in her opinion, plays the role of the isolated sage, being crankily troubled by intrusions, he moved into one of the most bustling, connected locations in all of Voorburg:

Voorburg was a rural village, but Benedictus had not chosen to live in a peaceful part of it, for the Kerkstraat houses, huddled on a terrace and generally having only a gable loft above their ground floors, were flanked by the market place and a boat-servicing harbour beside the Vliet. Yet, whole this lodging was feverishly cacophonous compared with sleepy Katwijkerlaan, he never complained…nothing was easier that getting to any Dutch city from Voorburg. The philosopher could leave home almost at the ringing of the horse-boy’s bell to catch the trekschuit. Voorburg being on the way to everywhere (the canal system joined the River Schie at Delft, and continued south to Rotterdam and Dordrecht), he should have foreseen a continuous flow of callers (154-155)

She goes onto conclude that Spinoza himself does not own up to his own emotional needs for company, caught up in the production of his own image. I might suggest that Gullan-Whur has severely misread Spinoza’s contradictory needs for isolation and for contact. This essentially is the mindset of the chronically, if sporatically, ill. Rather than this being a profound conflict of conscience, or the inability for Spinoza to understand his own needs, Spinoza’s tuberculosis and his philosophical/scientific endeavours required both isolation and contact. Indeed I would suggest that it was likely the disease that forced Spinoza to reconsider his life, and it was this ever-present relationship to his own body and mortality that made his rationalist philosophy most concerned with the freedoms of the body. Gullan-Whur’s example of reading the man is actually instructive for all interpretations which ignore his physical histories. In fact Iwould think that all of Spinoza’s metaphysical positions on the body should benefit from being seen in the light of  a possible continual threat and experience of tuberculosis. 


It is persuasive to infer, and least as persuasive as any other reasoning I have encountered, that Spinoza’s father and step-mother indeed died of tuberculosis, and that Spinoza had contracted the illness from them. On average, people have a 50 % chance of becoming infected with tuberculosis if they are in close contact eight hours a day for six months. If Colerus’s estimate is right that Spinoza had struggled with the disease for more than twenty years, this would put his first attack right at the decisive years of the late 50s, as Spinoza was forming his new political and theological relationships with Van den Enden and Prado, leaving behind the family business. (By stating this length as more than 20 years, Colerus at the very least seems to want to place the illness before Spinoza’s milestone move from Amsterdam.) This encounter with a disease that may have killed his father and step-mother surely would have shaped the decisions Spinoza was making. And the resultant dedication to philosophy, science and selective isolation should not be considered outside of this persistent awareness of both his disease and the effects it may have had on others. All the complexities of influence that we can convincingly conjure up may very well pale to the experience of the fatal fever and cough a year after you watched your father and step-mother, and perhaps even sister, pass under similar conditions. It is agreed that this is a time of plagues, and the death of family members and close friends, certainly by 1664 was not uncommon. This does not mitigate the personal effect the disease would have had upon Spinoza in the determinative years of 1655-1658, not to mention the consequences of managing the disease over a lifetime.

Why the timing and substance of the disease has not been well considered by biographers and interpreters of Spinoza’s life, I do not quite understand, except for the recognizable need to comprehend the man in terms of much vaster, more abstract historical and intellectual factors.

Spinoza’s Ethics, A Polished Lens

Polishing Lenses and Propositions

I want to set out some basic thoughts on a guiding intuition of my research on Spinoza’s optical experiences and products. This is the notion that perhaps Spinoza conceived of his Ethics, and the entire network of cross-referenced, mutually inferring propositions, demonstrations and scholia, to be something like a lens, polished to the improvement of our mind; and by virtue of his metaphysical parallelism, to the improvement of our body, giving those who use it, greater capacity to act. The analogy that is at work here is a hopefully satisfying and sophisticated elaboration of “he polishes lenses, he polishes propositions”, a thought given birth in Borges’ poem on the philosopher.

If we are to embrace this analogy in a literal sense so as to gain access to the ways Spinoza’s lens-grinding may have affected his approach to his metaphysics, drawing a conceptual connection between the attentive, precise, manual craftsmanship he engaged in during the day, and that studious argumentation he produced at night: the idea of the “eyes of the mind” is one that we should be take careful note of. 

I shall not treat the more philosophically suggestive of his uses from the second part of the Ethics here, where he warns against what he seemed to find as a Cartesian temptation, to “fall into pictures”:

We must investigate, I say, whether there is any other affirmation or negation in the Mind except that which the idea involves, insofar as it is an idea…so that our thought does not fall into pictures. For by ideas I understand, not the images that are formed at the back of the eye (and if you like, at the middle of the brain), but concepts of Thought [or the objective Being of a thing, insofar as it exists only in Thought]

Ethics, 2p48s.

This is a passage that is important, and deserves a separate treatment, though I have approached it elsewhere, (not sufficiently) :A Diversity of Sight: Descartes vs. Spinoza , Spinoza: The Body of Ideas as Lens . Here though I want to instead look at Spinoza’s use of the phrase in the Fifth Part, where he addresses the problematic claim that through the mind we know that we are eternal. I do not want to focus at all the subject of the eternity of mind, but rather his use of the phrase, and his way of illuminating what he means by it. I quote the passage below, with two of its most successful translations, along with my own:

At nihilominus sentimus experimurque, nos aeternos esse. Nam mens non minus res illas sentit, quas intelligendo concipit, quam quas in memoria habet. Mentis enim oculi, quibus res videt observatque, sunt ipsae demonstrationes…

Ethics V P23s

Still, we sense and experience ourselves to be eternal. For the mind no less senses those things that through thinking it grasps, than those it has through memory. For the mind’s eyes, by which it sees and observes things, are demonstrations themselves…(Mine)

…still, we feel and know by experience we are eternal. For the Mind feels those things that it conceives in understanding no less than those it has in memory. For the eyes of the mind, which sees and observes things, are the demonstrations themselves…(Curley)

Nevertheless, we feel and experience that we are eternal. For the mind senses those things that it conceives by its understanding just as much as those which it has in its memory. Logical proofs are the eyes of the mind, whereby it sees and observes things…(Shirley)

We can see what appears to be an analogy, the mind’s eyes are demonstrations, or as some translate, logical proofs. I think it is important to understand that because of Spinoza’s parallelism (again, the principle that anything that occurs mentally, in the exact same order and connection occurs in extension), we have to consider anything, including thoughts and arguments, along with their material counterparts. Understanding that the demonstrations and proofs of the Ethics are not just ideas, but also, as text are also material expressions of Substance, our relationship to them is not just that of a mind to an idea, but also our body to the body, a material assemblage. If we are to think consistently along with Spinoza, the mind’s eyes literally become the demonstrations of the Ethics, such that our minds and body come into material and ideational combination with their reality. In this understanding, we literally “see through” the text of the Ethics. It is not just prosthetic, but cybernetic to our capacity to act, giving us greater freedom, as a body.

Spinoza via Wittgenstein?

This passage from Spinoza was highlighted by Wim Klever in his essay “Anti-Falsificationism: Spinoza’s Theory of Experience and Experiments” found in Spinoza: Issues and Directions : the Proceedings of the Chicago Spinoza Conference(1986). There he puts it into relation to two Wittgenstein citations, which help make clear the way in which we can “see through” proofs or demonstrations:

“Because of the proof our view will be changed… Our view will be remodeled… The proof guides our experiences, so to speak, in distinct canals [ in bestimmte Kanäle ].” – Remarks on the Foundations of Mathematics III (30-31).

“In another mind-space – one might say – the Thing [ das Ding ] appears differently.” Remarks on the Philosophy of Psychology (98).

There is an experiential sensing with the mind, an actual perception, in the process of thinking, and argumental proofs not only are means by which the mind senses, their material existence are the organs of the mind, as we combine with them. And if we follow Wittgenstein’s lead, through our thinking [Spinoza’s  intelligendo ] we sense res, things and situations. The proofs and propositions of the Ethics can be considered as material combinations which enhance our powers of action, through their conditioning of our experiences.

As I have pointed out elsewhere, Deciphering Spinoza’s Optical Letters , Descartes, in his Dioptrics, conceived of the telescope as a literal extension of the physical extension of the eye. His hyperbolic model of the ideal lens was meant to accomplish the same refractions that normally occur at the surface of the eye, just further out, so that “…there will be no more refraction at the entrance of that eye” (120) (as he says of his prototype, water-filled model of a telescope). And, as I have pointed out in the same article, because Spinoza wants to understand seeing as a “mind’s eye” event, Spinoza’s ideal lens was a more panoptical design, one that focused rays equally, comprehensively, coming from all directions: based on the powers of the sphere.

I suggest that Spinoza’s Ethics, in its symmetrically of internal reference, was thought by Spinoza to be something of a physical-mental extension of the mind, a rationally polished refraction of all the kinds of causal relations a human being could undergo, meant to bring those events into rough focus so that in that clarity, we may have a greater power to act. Just as Descartes’ imagined his hyperbolic telescope to be attuned to the narrow focus of a frontally discerning Will, extending the eye out into space, so Spinoza, more grandly, pictured the Ethics literally to be the eyes of the mind, propositions and demonstrations being panoptical perfections, to the degree that humanly we, or he, could make them. These “eyes” were vectors of power.

Spinozas letter 39 diagram, with Descartes hyperbola projected upon it, to show the contrast in ideal visions

Spinoza's letter 39 diagram, with Descartes' hyperbola projected upon it, to show the contrast in ideal visions

This has been a rough outline of the general idea I am putting forth, founded on the essential Spinozist assurance that whatever occurs mentally, occurs physically, and Spinoza’s pan-directional ambitions in his thinking of optics.

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.

A 1940 Review of Theodore Kerckring’s “Spicilegium Anatomicum”

Spinoza’s Microscopist

I post here a link to a 1940 Canadian Medical Association Journal review of Theodore Kerckring’s “Spicilegium Anatomicum”, a work which contains specific reference to observations made with a Spinoza made microscope. Kerckring was a fellow student of Spinoza’s at van den Enden’s Latin school, and then studied anatomy at the University of Leiden when Spinoza was nearby at Rijnsburg, and was likely part of a Cartesian circle which both J. Hudde and Spinoza held some influence over. Wim Klever argues that he was a loyal follower of van den Enden, who he takes also to be Spinoza’s major philosophical influence. Kercking would marry van den Enden’s daughter.


by Albert G. Nicholls
To give context, here is an annotated, modern translation of Marcello Malpighi’s De Polypo Cordis, to which Kerckring is likely responding in his counter to the assertion that “polyps of the heart” develop in life. Kerckring corrects that what has been observed are post-mortum coagulations of blood. Aside from the issue of heart polyps, it was Malpighi’s microscope-aided, revolutionary observations of the fine organization of organ tissue in terms of “cells” which overturned the long-held view that organs such as the spleen, lungs or liver were simply colagulations (parenchyma) or a “confused lumps”, and Malpighi had responded directly to criticism : “De Polypo Cordis” (1666)

Line of Argument

The line of reasoning I will be following in this evidence might be called questions about the philsophy of seeing, as the dificulties of applying the microscope to anatomy attest, “seeing” is not a simple matter of “looking”. In order to assess how Spinoza concieved of the powers of the microscopes he built, one must take into view what micro-vision meant for those attempting it, in particular for those of a Cartesian conception of the world. Kerckring’s text gives a portal into the ambiguities of lensed vision, and the trust of observation.

Spinoza’s Lens-Grinding Equipment


Door to the Hofwijck Estate where Spinoza likely strode

Door to the Hofwijck Estate where Spinoza likely strode


Spinoza Purchases Lens Grinding Laps

With these I may have ended, in truth, but because for me new dishes for glasses being polished may be fashioned, such is the spirit, your council in this matter I would be eager to hear. I do not see what we may profit in ‘turning’ convex-concave glasses…

…A further reason why convex-concave glasses are less satisfactory, apart from the fact that they require twice the labour and expense, is that the rays, being not all directed to one and the same point, never fall perpendicular on the concave surface. – Letter 36, June 1666

This is what Spinoza writes to mathematician and microscopist Johannes Hudde, part of a correspondence that had begun before the end of the previous year, a correspondence which may have had its impetus in another lettered exchange: the on-going discussions on probability and actuary models between Hudde and Christiaan Huygens of that same year. Spinoza was getting to know his neighbor Huygens, and ends up writing to Hudde, someone he may have known since Rijnsburg and Leiden in the early 60’s.

The value of this letter for those investigating any potential lens-grinding practices Spinoza may have had is that here Spinoza cues that he had his metal shapes or laps made for him, at least at this time in the summer of 1666. The context of these remarks is Spinoza’s argument for the superiority of convex-plano lenses, using the same mathematical analysis of refraction that Hudde uses in his brief “Specilla circularia” (1655). Huygens, the previous summer, had personally calculated to a new degree of precision the phenomena of spherical aberration using convex-plano lenses (something Spinoza may have been privy to), and as Huygens has just left for Paris in April, Spinoza asks Hudde for both practical and theoretical optical advice.

I only wish to present to this context information about the kinds of workmen the Huygens brothers used over the years for their own telescopic lens-grinding projects:

View from the Huygens Estate, the Hofwijck

View from the Huygens Estate, the Hofwijck


Christiaan Huygens’ Marbler and Chimney-Sweep

There is no doubt that at first their work consisted solely in grinding and polishing the glass. Even the metal shapes, on which the lenses were ground, were obtained from the outside. Their first ones were of iron (in 1656 Caspar Kalthof supplied one of these, [OC1, 380-81]), later they used copper shapes but for many years they did not make any themselves. In 1662 Christiaan still stated quite emphatically that he had never bothered with making shapes, although he did correct and finish them (OC4 53), and in 1666 in Paris he had a copper shape supplied to him (OC6, 87). But by 1668 we hear that Constantijn makes small shapes (for eyepieces) himself, on a lathe (OC6, 209), and it would appear that later he learned to make larger ones as well, for the instructions for making Telescope-lens (written in 1685 by the two brothers together) contains  detailed instructions about this part of the work (OC21, 251).

“Christiaan Huygens and his instrument makers” (1979), J. H. Leopold


It is not entirely clear if the brothers made their own eyepieces around 1660, but they did not do so later on. Occasionally their correspondence contains references to local craftsman who prepared glass or ground eyepieces; the brothers focused on the delicate work of grinding object lenses.

In 1667 and 1668, Constantijn employed Cornelis Langedelf for polishing glass and grinding eyepieces, and in 1683 this same man delivered the tubes for one of Constantijn’s telescopes. From 1682 the brothers preferred the services of Dirk van der Hoeven, who lived nearby in The Hague. At the same time the brothers also did business with a marbler van der Burgh, who supplied them with grinding laps and glass. The relationships the brothers had with these two craftsmen were not identical. In the case of van der Hoeven – he was often simply referred to as Dirk or the chimney-sweeper – it was only his labour was hired. The brothers supplied the materials and tools, including the grinding laps. Van der Burgh, on the other hand, had a workshop of his own, and the Huygens[es] were were not his only clients. Moreover, one might expect this marbler to have been a more skillful grinder than his chimney-sweeping fellow citizen. So, it was probably was not the routine preparatory work that Constantijn asked of van der Burgh in April 1686, when he sent him two pieces of glass to be flattened 15.

“The Lens Production by Christiaan and Constantijn Huygens” (1999), Anne C. van Helden and Rob H. van Gent

What seems evident from both the Helden and Gent account, and the interpretation of Leopold is that it was not uncommon at all to hire-out for the production of the metal laps in which lenses would be ground. It seems clear from Spinoza’s letter 32 to Oldenburg in November of 1665 that the Huygenses were at least in the possession of a lathe that not only could grind lenses, but also laps or pans, for it is regarding this very (semi-automated) turning of the pans that Spinoza had his greatest doubts:

The said Huygens has been a totally occupied man, and so he is, with polishing glass dioptrics; to that end a workshop he has outfitted, and in it he is able to “turn” pans – as is said, it’s certainly polished – 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. [See: Spinoza’s Comments on Huygens’s Progress .]

Whether anything good came of this Huygens lathe we cannot know. What is significant though in this combination of evidence, is that Spinoza seems to have made use of someone like the marbler Dirk van der Hoeven, at The Hague, just as the Huygens did, but also that Spinoza maintained a priority using the free had to either polish these purchased laps, or to polish lenses in them. That a chimney-sweep and a marbler would both be hired by someone as wealthy as the Huygens family, suggests a rather wide-spread and eclectic economic foundation for the procurement of these services and other related grinding services, something that did not require a specialist.

It is interesting to place Spinoza somewhere between the handyman Chimney-sweep and the savant Christiaan Huygens. Perhaps, if we take a more refined glance back through history, he seems to be between holding the straight-forward lathe experience of marbler-turner van der Hoeven and the specialized knowledge of Christiaan’s brother Constantijn, who spared no expense in carrying out Christiaan’s designs and theories.

As I have mentioned several times on this weblog, the picture is a bit more complicated than that. Christiaan Huygens had to bow to Spinoza’s assertion that the smaller objective lens makes a better microscope, and marveled at the polish that Spinoza was able to achieve in his microscopes, a polish achieved by “by means of the instrument” in a method that Christiaan did not seem to know. The speciality of knowledge did not restrict itself to just microscopes, but to telescope lenses as well. It is reasonable that the Huygenses purchased telescopes, microscopes and lathes from the Spinoza estate upon his death, and there does seem to have been something special about Spinoza’s laps (one’s he likely polished), as Constantijn used one in 1687, ten years after Spinoza’s death:

[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. XI, p. 732, footnote). [cited by Wim Klever]

Spinoza, it would seem, used a man like van der Hoeven, but held at least to some particular degree both theoretical and craft advantages over Christiaan Huygens.

Approaching Huygens

Approaching Huygens

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.

Pythagorian Spinoza?

Leibniz’s Summation

Of some significance, here I post a summation of Spinoza’s philosophy, as passed through the mouth of a loyal friend, Tschirnhaus, and as relayed to Leibniz in 1675, originally published in English by Wim Klever. It draws out some curious Klever might say esoteric aspects of Spinoza’s thinking. Most distinct about it is the notion that Spinoza held a Pythagorian idea of a transmigration of the Mind. Besides the obvious distortions that can be brought about through one man telling another man what someone else believes, there remains the possibility that the account is somehow intentionally colored in details, either to couch Spinoza, or to put him in a personally favorable light:

As Klever relates:

“In spite of Spinoza’s warning that Tschirnhaus should be reluctant in communicating what he had received for private use, we know that Tschirnhaus nonetheless revealed many secrets to the inquisitive Leibniz. This appears from a note written by Leibniz which he must have made shortly after a meeting. I think it worthwhile to quote this note here in full because it enables us to see how Spinoza’s doctrine was perceived, understood, and explained by his friends and followers in or around 1675. A second reason is that this note which is not known by many scholars and iis not yet available otherwise in English contains several interesting points which cannot be found elsewhere and is also for that reason relevant:

Sir Tischirnhaus told me many things about the handwritten book of Spinoza. There is a merchant in Amsterdam, called Gerrit Gilles [Jarig Jelles] I think who supports Spinoza. Spinoza’s book will be about God, mind, happiness or the idea of the perfect man, the recovery of the mind and the recovery of the body. He asserts the demonstration of a number of things about God. The he alone is free. He supposes that freedom exists when the action or determination originates not from an external impact, but only from the nature of the actor. In this sense he justly ascribes freedom to God alone.

According to him the mind itself is in a certain sense a part of God. He thinks that there is a sense in all things to the degrees of their existence. God is defined by him as an absolutely infinite Being, which contains all perfections, i.e. affirmations or realities or what may be conceived. Likewise only God would be substance or a Being which exists in itself, or which can be understood by itself; all creatures are nothing else other than modes. Man is free insofar as he is not determined by any external things. But because this is never the case, man is not free at all, though he participates more in freedom than the bodies.

The mind would be nothing but the idea of the body. He thinks that the unity of the bodies is caused by a certain pressure. Most people’s philosophy starts with creatures, Des Cartes started with the mind, he [Spinoza] starts with God. Extension does not imply divisibility as was unduly supposed by Descartes; although he supposed to see this also clearly, he fell into the error that the mind acts on the body or is acted upon by the body.

He thinks that we will forget most things when we die and retain only those things that we know with the kind of knowledge that he calls intuitive, of which of which only a few are conscious. Because knowledge is either sensual, imaginative, or intuitive. He believes a sort of Pythagorical transmigration, namely that the mind goes from body to body. He says that Christ is the very best philosopher. He thinks that apart from thought and extension there are an infinity of other positive attributes, but that in all of them there is thought like here in extension. How they are constituted cannot be conceived by us but every one is infinite like space here (“Spinoza’s life and works” Cambridge Companion to Spinoza, 46-47)


I posted below some rough thoughts I had some time ago, and their related Spinoza texts. Klever’s evidence of a kind of at least percieved Pythagorian transmigration adds an esoteric meaning to Spinoza’s mathematization. And while I cannot conceive how such a transformation could be understood within the propositions of the Ethics [on what account is the preservation of identity maintained], it does give conceptual context for some of the more difficult to interpret passages on this issue.

Notable as well is the summation’s deviation from Spinoza’s theory of the three knowledges as found in the Ethics. Here, the trinity of “imaginary, rational, intuitive” has become “sensual, imaginary, intuitive”. Assuming an accurate translation of the passage, this may give some clue to the differences of Spinoza’s treatment of the Imaginary and Order (spoken about here, in Spinoza’s Two Concepts of Order). Professor Della Rocca in correspondence had affirmed his belief that Spinoza is somewhat inconsistent in his treatment of “order” in the various parts of the Ethics. What is suggested by the Leibniz summation, perhaps, is that even the rational, propositional conception of true and free in Spinoza is still imaginary; this may be linked to Spinoza’s variation on whether we can or cannot ever have wholly Adequate Ideas.