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The Zuggtmonic Drive: (Dark) Intelligence Without Center

An Organic Demoness Ontology

Naught Thought  raises the image of Dark Vitalism and first associates it with the Demoness Zuggtmoy of fantasy lore, suggesting that if we allow an ontology of powers that bubble up from below, from the very matter of matter, we are faced with a world primordially chaotic of its intents. Any intelligence is swarming, polyvalent but still planal, or vectored, like so much threatening mold and fungi that at most grow up from and adhere to an omni-present death process:

Park of of the work of a dark vitalism  is the sickening realization of such an image [Zuggtmoy, Queen of Fungus]. Steven Johnson’s Emergence begins with Toshiyuki Nakagaki’s work on slime molds in which he made one of the amoeba like creatures find a path through a maze towards a food. The mindless functioning of life, of life moving towards goals without any form of intelligence – creatures that function in a completely bottom up fashion (the rest).

And Eliminative Culinarism  also turns to what he calls a thantropic regression (drive) when separating out the consequences of the philosophy of Brassier, a separation that ultimately finds its dark vitalism home in Freud’s Death Drive and its umwege:

If Brassier unbinds and cosmically reinscribes Freud’s theory of thanatropic regression in order to extend the eliminativist vector all the way to the cosmic exteriority, then he must also unbind the theory of umwege beyond the organic life or bios. Because as Freud has explicitly argued and as Brassier has implicitly indicated, the thanatropic regression or the vectorial move toward the precursor exteriority is inextricable from the increasing convolution of the umwege. Here the convolution of umwegeor the increasing twist in the roundabout regression to the precursor exteriority must not be confused with the complexification of life as an opportunity for posthumanist scenarios, because it suggests the differential decomposition of all interiorities via nested deployment or intrusion of cosmic exteriority. After all, the emergence or determination of an index of interiority from a precursor exteriority does not mean the complete envelopment of that exteriority and its reintegration according to the laws of the interiorized horizon. There is always a part of enveloped exteriority that refuses to be assimilated within the index of interiority, thus extending the intrusion of the precursor exteriority into the emerged nested horizons of interiority (the rest June 11, 2009).

The Death Drive and Zuggtmoy

I want to take up this promotion of the Death Drive, and the image of the fungus Queen Zuggtmoy, so as to explore the fuller consequences of so called Dark Vitalism. Mostly I want to bring out how the figure – and we can think through  a figure – of Zuggtmoy enables us to see an edge to the Death Drive that previously had been obscured, as if the side of the well-used coin.

The approach towards zero (and by zero we must be careful, since there are heterogenies in this analogy, absolute zero…cold, quantity zero…nothing, and zero which lies between negative and positive numbers…placeholder) that under a Freudian conception typifies all the aim of the very complexities of life itself, life’s winding pattern, a maze, a rambling circuit that is simply trying to get back to the originary state: Death, Inorganic, Abiotic Stillness. This is how Freud presents it in Beyond the Pleasure Principle:

It would be in contadiction to the conservative nature of the drives if the goal of life were a state of things which had never yet been attained. On the contrary, it must be an oldstate of things, an initial state from which the living entity has at one time or another departed and to which it is striving to return by the mazings [Umwege] along which its development leads…For a long time, perhaps, living substance was thus being constantly created afresh and easily dying, till decisive external influences altered in such a way as to make ever more complicated mazings [immer komplizierteren Umwegen] before reaching its aim of death. These mazings [Umwege] to death, faithfully kept by the conservative drives, would thus present us today with the picture of the phenomena of life [F III 248]

Nick Land in his book Thirst For Annihilation presents something of the conclusion all here seem to be following, and we can readily see the fungal layer (crust), as it merely bubbles up in a roundabout way of only returning, an opposite form of simply the Christian soul returning to the arms of its Absolute and loving God. We can glimpse a kind of constitutive power of Zuggtmoy here, yet here she is merely passive, a result:

Life is ejected from the energy-blank and smeared as a crust upon chaotic zero, a mould upon death. This crust is also a maze – a complex exit back to the energy base-line – and the complexity of the maze is life trying to escape from out of itself, being nothing but escape from itself, from which it tries to escape: maze-wanderer. That is to say, life is itself the maze of its route to death; a tangle of mazings [Umwege] which trace a unilateral deviation from blank.

Death and Hegelian Reversals: Nature is Immediate, But…

Now it must be stated that an ontology of Death Drive, at least from a Freudian foundation, is one that already assumes a non-vital basis for Substance (or totality), for if Substance itself is living, a return to it would not be a death. This is a difficult thing, for in an Ontology of someone like Spinoza, indeed Substance presents a kind of zero in a near Plotinian sense, but life itself and its weavings are constituted by its very force, and one is never separated out from it (being its expression). A strict dichotomy between Life (Pleasure/Joy), and Death (nil, an inorganic realm), while not conceivable for Spinoza, for Freud seems determined by the very centricity of vision, an absolute focus upon the biological organism itself as a complete boundary (from which life is attempting escape, or at least unweave itself). I have argued elsewhere (in Conjoined Semiosis and The Problem with Spinoza’s Panpsychism) why organisms cannot form an absolute limit, the kind of which would then be dichotomized toward death. It is because Freud is organism centered in really a Hegelian sense, that he is forced to account for an apparent returning difference that is driven by the very acts of consciousness/life itself. Freud performs, in inverse, the very postulation of an illusion of a nil which is posited by Consciousness itself:

True, Nature is the immediate – but even so, as the other of Spirit, its existence is the immediate – but even so, as the other of Spirit, its existence is a relativity: and so, as the negative, is only posited, derivative [nur ein Gesetztes]…Spirit, because it is the goal of Nature, is prior to it, Nature has proceeded from Spirit [aus ihn hervorgegangen]. Spirit, therefore, itself proceeding, in the first instance, from the immediate, but then abstractly apprehending itself, wills to achieve its own liberation by fashioning [herausbildend] Nature out of itself; this action of Spirit is philosophy. (Philosophy of Nature 444)

Nature is both immediate, but then necessarily post to Spirit, come out of Spirit’s very apprehension. We can see if we undo this original preoccupation with (and centrality of) consciousness as a form of negation, we can see that Freud’s own dialectic unspools. The umwege  that Freud says are the “ever more complicated mazings” that are the complexifications of life, no longer are made against a background of death and zero, but come out of it, just as we have prime images of fungi and moulds that seemed by traditional lights to grow right out of putrescence and decay. In an ontological domain quite far from Hegelian negativity, matter itself thinks. There is nothing to return to, (but not “nothing” to return to), and the weavings of umwege organization are expressive powers of tendril-like freedoms.

[A fantasy illustration of the Fungal Queen from the gameplay world]

The One and the Many: Parmenides and Molds

It is here that I want to return to the powers of Zuggtmoy, in particular as they are manifested by the class of organisms slime mold. Naught Thought already directed us this way, pointing to Toshiyuki Nakagaki famed experiments with slime molds that seemed to demonstrate intelligence (referenced in Steven Johnson’s 2001 book Emergence). This is an intelligence I would like to think hard about because it defies some of our most common assumptions of the kind of forms intelligence must take.

Slime molds are a curious limnal organism, that not only lives between realms that seem conceptual opposed, Life and Decay, but also taxonomically between our easy and dominate ideas of independent Individual vs. controling Group, not to mention what is plant and what is animal (once thought a fungus, now Protista).

First let us engage the fascinating and seemingly conceptually contradictory lifecycle of slime molds, for they are neither individuals, nor colony, but participate in modes and versions of both. I propose that these examples serve as figures of philosophical analogy in particular for those brands of philosophy which like to juxtapose conceptual oppositions to be projected upon forms of life and the world. We are not going to be so forward as to assert that all things have the form of slime molds – though it does form an interesting counterbalance to explicit and implicitassumptions that “it” is like the human (or phenonemological consciousness, etc). What we are to hope is that the example of slime molds might help us overcome some of our more unconscious prejudices, especially when we engae in ontological imaginations.

As eluded to, Slime molds are remarkable creatures as they spend part of their lives in seemingly independent Individual states, and part of the time in collectives (some of which threaten our idea of what constitutes an Individual).

As you can see from the above, a lifecycle of a Plasmodial slime mold, in the haploid (single copy of a chromosome) form at the left the slime mold is either a spore or an individual cell; but, after syngamy, it begins to divide, not itself, but only its nucleus. It does this again and again until it has become one huge cell with thousands of nuclei, giving pause to the Platonic/Paramedian problem of the One and the Many, here the One being a coagulate of the nucleic many. In the Plasmodial stage the huge single cell creeps along in search for food until it eventually forms a sporangium, fructifying stalk, very much like a mushroom, which eventually will put forth the multitude of haploid spores.

To make this clearer, here below is the Plasmodial stage wherein all the individual amoeba-like cells have shed their cell walls, and the single form crawls across a supposedly “dead” territory. One can practically see the Fruedian encrustation of life, the umwege wending its way back toward Death. 

And here below is the spore producing stalk structure that culminates out of the great aggregate form:

And there is a second kind of slime mold (and a third not to be discussed) which begins in an amoeboid form, a single cell that instead of following a path of nuclei division and expansion, expends its life in solitary fashion until food becomes scarce, and emitting a aggregating chemical signal to be read by other isolated slime mold cells. Once a density threshold is crossed the mold cells cluster together to form one great colony which acts as a singular organism again confusing some of our more easy categories of self and group. 

Here is a concise description of the two different kind of slime mold processes of aggregation and reproduction:

All slime molds start life as a single, microscopic cell, and eventually end up as that puddle of goo. A plasmodial slime mold, like the one that researcher Toshiyuki Nakagaki coaxed through a maze (see article), constantly grows and divides. But instead of breaking itself into two new cells, it divides only its nucleus, becoming one larger cell with two nuclei. This process repeats until the plasmodium is a giant cell, like a sac of jelly, filled with thousands of nuclei. Ever so slowly, the plasmodium creeps across the forest floor, eating the tiny bacteria and yeast it finds there.

A different group, called the cellular slime molds, stay microscopic for most of their lives. They, too, live and feed in damp soil. When food gets scarce, though, these slime molds have an amazing trick for survival. Each individual sends out a chemical signal, allowing the slime mold cells to find each other. Then they aggregate, or stick together, until they have formed a giant roaming blob. This blob looks and acts like one creature, even though it is really thousands of individuals oozing along together.

Despite these differences, both kinds of slime molds complete their lives with an amazing final transformation. Either slime mold (plasmodial or cellular) keeps crawling along until it reaches a drier spot. There, it stops and metamorphoses into a sporangium: a tall, thin stalk with a sac on top, similar to a mushroom. The slime mold cells turn into stalk cells, or sac cells [about 20%], or spores [about 80%]. Finally, the cells that have become spores burst out of the top of the sporangium and are blown away by the wind. Where they land, they will start their life cycle over, invisible-and individual-once again.

from “Thinking Like a Swarm”

[above: individual to aggregate lifecycle of cellular slime molds]

In thinking about the cellar slime molds and their ability to signal to each other their respective states, one has to consider their communitarian capacities, how they are able to respond to the very threshold field of signally others, such that the way that we identify the boundary level of the organism itself must include the very semiotic field of the cAMP itself. Here  is information on a computer simulation of the cAMP (intracelluar messenger) effects between individual cells under aggregation, which offers signficant thoughts on patterns of formation, just how the chemical signal in chemotaxis expresses itself:

The slime mold aggregation is controlled by chemotaxis toward higher concentrations of cyclic adenosine monophosphate (cAMP). (cAMP is a common intracellular messenger in higher organisms.) The onset of starvation causes some cells to produce and secrete cAMP. Extracellular cAMP binds to receptors on cells and initiates two processes. The first, and faster, process activates the adenylate cyclase enzyme which causes production of cAMP. This cAMP is secreted; it can then bind to the same cell, further stimulating cAMP production, and to other cells. The second slower process leads to inhibition of adenylate cyclase. This second process stops the autocatalysis. The extracellular cAMP diffuses away and is degraded by phosphodiesterase, which is secreted by the slime mold cells. Once the level of cAMP has fallen the cells begin to regain the ability to synthesize cAMP.

And here is a Florescence microscopy film of the aggregation which distinctly allows one to see the visual rhythm:

No doubt this leaves us laymen with a sense that we are dealing with the bizzare and transmogrifying edge of animal/plant, and extra-somatic behaviors, ones that allow us to detach ourselves from common notions of when and where the body ends. Cellar slime molds in particular seem to have an intensified sense of Individual and swarm, wherein the field of organization is almost forced to include a semiotic dispersion of the signal itself, with great fineness to the pattern by which they are clustered into a new, single acting entity. If Zuggtmoy powers exist here, they seem exemplified by questions of division, dispersion, unification and semiotic binding.

The Brain without A Brain

Now I would like to turn to the more pronounced “intelligence” features that seem to have been discovered within slime molds. What seems at first blush the very least discerning of vegetable/animal matter, has shown remarkable capacities for behaviors which only “higher” animals could accomplish.

The most well-known of these were Nakagaki’s evocative tests that suggested that slime molds could solve mazes:

Toshiyuki Nakagaki of the Bio-Mimetic Control Research Centre, Nagoya, Japan, placed pieces of Physarum polycephalum in an agar gel maze comprising four possible routes. Normally, the slime spreads out its network of tube-like legs, or pseudopodia, to fill all the available space. But when two pieces of food were placed at separate exit points in the labyrinth, the organism squeezed its entire body between the two nutrients. It adopted the shortest possible route, effectively solving the puzzle.

The organism changed its shape, according to the researchers, to maximize its foraging efficiency and therefore its chances of survival. The meal of ground oat flakes led to a local increase in contraction of the organism’s tube-like structures, propelling it towards the food (from this summation).

Or here in News in Science:

The maze was created by laying a maze template down onto a plate of agar. In the first part of the experiment, pieces of slime mould Physarum polycephalum were placed throughout the 3 x 3cm maze. To grow, the slime mould throws out tube-like structures called pseudopodia, and it soon filled the entire maze.

The maze had four routes through, to get from one exit to the other. Food was placed at both exits, and after eight hours, the slime mould had shrunk back so that its ‘body’ filled only the parts of the maze that were the shortest route from one piece of food to the other.

The researchers suggest that as the parts of the plasmodium come into contact with food, they start to contract more frequently. This sends out waves to other parts of its body which tell give feedback signals as to whether to grow further or contract. Ultimately, to maximise foraging efficiency, the plasmodium contracts into one thick tube, running through the maze.

Surely the visual aspect of the maze gives us an impressional sense of “intelligence” whereas the description allows something more like a directed motility, but really, is there a difference between the two? In a certain way the slime mold has “represented” the territory space, not pictorially, but semiotically, instilled differences within itself which spell differences in the world such that a certain economy, a judicious precision, is achieved.

But slime molds seemingly are capable of more than spatial genius. They have also a primordial memory, a manner by which they can space out time in regulative and anticipatory rhythms, having learned what tends to happen. Last year Nakagaki released a paper detailing the new co-ordinated and seemingly mental capacities.

When the amoeba Physarum polycephalum [a slime mold] is subjected to a series of shocks [burst of dry air] at regular intervals, it learns the pattern and changes its behaviour in anticipation of the next one to come, according to a team of researchers in Japan. Remarkably, this memory stays in the slime mould for hours, even when the shocks themselves stop. A single renewed shock after a ‘silent’ period will leave the mould expecting another to follow in the rhythm it learned previously. Toshiyuki Nakagaki of Hokkaido University in Sapporo and his colleagues say that their findings “hint at the cellular origins of primitive intelligence” (in Biology News)

It is reasoned that propagation pathways change with experiences, and thus retain under rhythmed cycles the form of temporally governed action. The pattern without changes the pattern/paths within, such that even the dumbest of cellular life is musically oriented towards states it seems it could never proximately sense.

The Beauty Dark of Zuggtmoy

So what has this rumination over the biological and bio-mental capacities of slime molds given us in regards to the original philosophical question, other than reminding us that there are some remarkable and probably as yet undiscovered characteristics of even what we take to be the simplest forms of living things? I offer, let us reimagine the demoness as a primordial power, one iconically represented by slime mold organism over which she is thought to rule. What would Zuggtmoy’s relationship be to “death” and the Death Drive. Slime molds we know are fundamentally oriented towards decay. Ammonia presents a near universal signal for the presence of putrification such that the entire feeding action could be said to oriented towards its presence (like Jakob von Uexküll’s tick). In this way the slime mold is determinatively and semiotically oriented towards death.

But it does not feed on death. It does not decompose. In fact it feeds on bacteria which perform the decomposition of organic matter. It feeds upon the thin layer of life which itself depends upon death. In this way its preoccupation with death is merely directed toward the very life/death shoreline. One could say that Zuggtmoy lives on the radiance of Death. And this is far from a Death Instinct. (It is easy to confuse the two.)

I want to perhaps poetically concentrate upon this very thin radiance of life that exudes from decay and ultimately death. One can see it with the very ocular and stunning effect the grotesque has upon the eye, the way that objects such as those that one might find in Joel-Peter Witkin’s gallery, shimmer with an odd kind of microbial sheen, the way the eye is forced to traverse the object as if it were covered with serpentine forms or trajectories.

I suggest that there are two things going on under the conflation of the Death Drive. There is first of all a needed explanation of the supposed Repetition Compulsion, the way in which a person (organism) inordinately repeats past trauma undermining pleasure pursuits. The apparent contradiction when placed within a Hegelian like concept of negating consciousness necessarily pressed Freud to conceive of a drive with a very different kind of aim, the aim of a return to a Death State. In typical mytho-anecdotal Freudian fashion, Freud watched a small boy toss and retrieve a spool in Fort/Da binaries only to be conflated into Being and Non-Being manipulations in philosophies of (ocular) presence. Yet, do we not see an elemental mode of the Repetition Compulsion in the most recent Nakagaki experiments on slime mold? As the slime mold slows its movements in anticipation of a cyclictic gust of dry air, are we really to say that we are finding the roots of a Being/Non-Being pre-occupation? Further, are we to deny that the slime mold has no pleasure principle circulations of its own coherence amid the anticipation? And if we were to grant a capacity to actually affect the environment in such a way that the trauma could be influenced to be repeated, would such an investment really be a Death Drive, or rather the celebration of internal coherences and environmental contrapuntal interweave. The pleasures of internal coherence, even amid outcomes of pain, are Pleasure Principle pursuits, and we might agree with Spinoza that it is our direction towards such coherences which gives us our Identification with what is beyond us, for the philosopher ultimately with Substance. There is no essential contradiction between Pleasure and Repetition, though most certainly Repetitions ever are expressionally in need for their expansions, their umwege into greater complexity and less triviality.

The second thing that is happening in notions of the Death Drive is quite apart from the Fort/Da Hegelian origins of the concept. The name itself gave associative rise to death objects or conditions which then are taken to be mesmerizing, attractive, seductive to the soul, apparently again in some sort of opposition to life and pleasure. Oddly enough these gothic preoccupations actually seem to be imbued with pleasures and perverse associations. They are kind of super-charged pleasure pursuits. And somehow these ideational objects are supposed to fit in with the Fort/Da, presence and absence drive to repeat. I don’t think that this is the case at all, and I would like to turn to the figure of Zuggtmoy to illustrate it.

It is not to Death itself that we are drawn, but rather to its sheen, its coverage by infintesmal molecules of light, perhaps we want to see Leibniz’s windowless monads here, or the first phosphorescence that feed on monad window elements loosened. It is the way in which disturbances in coherence (in proportion, form, rhythm, expectation) causes us to narrow ourselves and detect the living things, the forces, that cover that rift or disintegration. Just as Zuggtmoy’s slime molds scent themselves toward the bacteria that thrive upon decay, so too there is a primordeal force which feeds on the life that feeds on death.

But we must pause for a moment to consider what Death is. Is it really a zero-place, a return to nil as we sometimes are inclined to believe? Is it not simply (and factually) the dis-in-tegration of composed elements? The return of nutrient richness back to a matrix of further involvement. (I am reluctantly inclined to the joke Mozart was to be found in his coffin after his death, erasing all his musical works.) A living preoccupation with Death is really a preoccupation with wholesale constitutive elements, things that must be returned to the biome in order for it to function. There is a sense that the way in which material Life feeds itself with growing complexity is by attending to the very abiotic shoreline, the biocline, at which elements become first incorporated into bodies. And Zuggtmoy, the blue-skined Abysmal queen of fungi and their kind, tells us that there is ever a ribboning and forceful consumption which preoccupies itself upon this singular and pervasive riverbed, which pours itself along every vector.

The First View From a Microscope: Finding the Finite

There is an interesting if not compelling anecdote from the history of Science (and philosophy) come from the time when they were perhaps just diverging. Theodore Kerckring was a physician of the mid 17th century and participant in the running dispute of the exact nature of the things of human anatomy that the newly invented microscopes were revealing. The biggest debate was whether the human body was a system of veins or glands (no one seemed to think it could be made of both), as until one had a conception of just what one was looking at through the clouded glass, one really could not be sure what it was, counter to our intution that one need only look at something to be able to roughly tell what you were seeing. In 1670 he published his “Spicilegium Anatomicum” a work of anatomical illustration, physician diagnoses, and also microscopic observation. Among these curiosities and position takings is found the only extant first hand testiment of what could be seen in a Spinoza designed microscope. Kerckring held a once intimate relationship with Spinoza, as they both were members of Van den Enden’s Latin school when young men, though Theodore was Spinoza’s senior by six years. He even married Van den Enden’s daughter Clara Maria with whom one biographical source reports Spinoza may have fallen in love. In any case, Kerckring reports that he is in the possession of a remarkably powerful microscope, designed by the great philosopher, and after he describes the granular forms it reveals, he then passes onto a most perplexing passage where in he describes the tiny animalcules that cover the exposed organs of the cadaver he is examining:

On that account, that which is by my wondrous instrument’s clear power detected, what is seen is wondrous: the intestines plainly, the liver, and other organs of the viscera, swarm with infinitely minute animalcules, which whether by their perpetual motion they corrupt, or preserve, it would be in doubt, oh, for something is considered to flourish and shine as a home while it is lived in, all the same though, a habitation is worn away by continuous cultivation. Marvelous is nature in her arts, and more marvelous still is Nature’s Lord, how he brought forth bodies, thus up to the infinite itself reciprocally in his size having withdrawn, that no understanding may be attained, if it be, if one be, or when it would be of some finite size; thus if by diminishing you would descend, never will you discover where you would be able to stand…(tentative translation).

It is not decided what Kerckring saw, but it is possible under some estimates of the magnification of Spinoza’s microscope (based on Kerckring’s other observations and capacites of the day), that these may have been the first human observation of bacteria, more than a decade before those made by the expert microscopist Van Leeuenhoek more than a decade later. But more than this, in Kerckrings speculative observation, something akin perhaps to early travel to the moon, we have nexus of the human with the miniscule of the world, the tiniest places, come from the glass of the great ontologist, Spinoza. And better his own difficulty in assessing if the small animals that cover the dead flesh were part of it maintainance or its destruction, with comparison to a home. To repeat the valued line,

…for something is considered to flourish and shine as a home while it is lived in, all the same though, a habitation is worn away by continuous cultivation.

As we contemplate the Death Instinct and the biocline shore between biotic and abiotic, it would be good to follow Kerckring first-sight inconclusion. We ultimately cannot say which processes of Life, and those of Death (though certainly which are proximately of this one life and this one death). There is an ecosystem, an economy of parts in organization that was glimpsed from the first history of it.

May we suggest that the demoness Zuggtmoy embodies the power of an alien, largely unseen aspect of our pre-occupation with Death. Not a drive to zero, but to the very sheen and radiance upon the decomposed, the falling to the inert, where bonds are loosened.

How Dark is Dark? The Zuggtmonic Drive

Naught Thought tells us that Dark Vitalism is the force of forces, something akin to the One… 

Dark vitalism, while not my own coinage, names the force of forces (or the One) not as a pure unification but the possibility of ‘isness’ itself as well as the resulting emanations, immanences, emergences and transcendences. The ontological cascade moves from the Real, to Immanence, to Sense and finally to Transcendence. Or from existence as only possibility, to the configurations of matter and energy, to the interaction of stimulus and sense, ending with the extension of ontic being via symbols, structures, technologies et cetera.

And that this vitalism is marked by its very chemical machinic nil, something that must be ajoined to the biological preoccupations of D&G…

The recently coined dark vitalism or mechanistic vitalism (dark as in nihilistic but also as attached to the chemical darkness of Schelling’s unground and mechanistic in that it is deterministic) must be articulated in response to Deleuze and Guattari.

If Zuggtmonic forces are driven by the chemical, proto-semiotic, machinic processes that serve a layer of un-brained intelligence which underwrites all “higher” forms of life, a celluar and contrapuntal, inter-rhythmed consumptive incorporation of elements and their living nexus radiance, then is this really a Nihilism at all? Is it not simply the de-centering of the human (and its emblem, consciousness) in such a way that we come to understand “individual” and “corporation” in very different terms. Pre-occupations with Death and Decay rather are turning to the incandesence that surrounds unloosening itself, the core operation of Eros.

Is it merely a revelatory coincidence that Zuggtmoy appears from the roots of Greek for yoking together (ζυγόν; LSJ) and cutting apart (τμῆμα; LSJ)? The Zuggtmonic drive is merely the machinic intelligence of dictative weaving together of initial consumption and incorporation, the feeding of Life upon the Life that feeds on Death, yoking what has been severed in a mat of constitutive grounding, in which the abiotic is sedimentally and musically re-interwove.

And lastly with this in mind, let us consider Eric Deschamps illustration of the seductive and puppeteering demoness. Is there something to say from the point of view of consciousness, the traditions that wish to think in terms of binaries and negations? What does it mean to see as Zuggtmonic a sexualized form of organic fungal-animal, self-directed in a self-organized realm, making the white bones of Centered Consciousness dance or hang? How close are we to Hegel’s greatest nightmare, that matter itself thinks. That instead of the bifurcation of reflective Male consciousness, as Irigaray tells us,

…[feminity in Hegel is] aware of no difference between itself and the maternal, or even the masculine, except that one is mediated by the abstract immediacy of the being (as) or by the rejection of one (as) being. The female lacks the operation of affirming its singular and universal link to one as self (Speculum, 224)

There is an operative consciousness of elemental contrapuntal pervasion, of female determination. Not one marked by severance and absence (however mediated) but by weave and subsumption through affective incorporation. A truly material thought. That desire, in its own realm, dances the white bones. Nicola talks of the Tiniest Diety and we questioned whether Zuggtmoy could be she.

Nietzsche has a beautiful thought about fungus that we should attend to…

382

Gardener and garden – Out of damp and gloomy days, out of solitude, out of loveless words directed at us, conclusions grow up in us like fungus, one morning they are there, we know not how, and they gaze upon us, morose and grey. Woe to the thinker who is not the gardener but only the soil of the plants that grow in him!

Daybreak

We can see where the fungal growth is relagated to an unbecoming lifeform of the worst association, but there is something brilliant here which is more than Nietzsche had in mind. Our conscious conclusion, not just our morbid ones which might pre-occupy with death, but ALL of our conscious conclusions can seem to come up out of no-where in the morning. Both our joys and our fears. And yes, though we must garden our soil, I suggest that we must also make a garden of slime molds and fungi (and not just neat English or German perfections). There is a system below, in our soil. A music in it, and our conscious thoughts spring up in radial circles, and inching surface travels that are far richer than the molar appearances that stir and consolidate us. Zuggtmoy affectively communicates to the plant and animal realm that is within us. I think that there is more to be said of her, her powers in political status and in ontological distaff, but this is a beginning.

Govert Bidloo’s 1698 Reference to a Spinoza Microscope

Dutch Republic Stadtholder and King of England, William III

No Second Spinoza Scope

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

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

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

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

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

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

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

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

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

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

Animalcules and the Body Politic

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

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

 

Govert Bidloo, A Spinoza Microscopist?

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

Physician to the King and Another Spinoza Microscope?

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

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

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

Collaboration with van Leeuwenhoek: Parasitic Protozoon

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

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

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

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

Historical Context For Bidloo’s Letter to Van Leeuwenhoek 

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

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

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

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

Antony van Leeuwenhoek and his ‘Little Animals’

Eggs and the Source of Disease

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

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

“A History of the Ecological Sciences, Part 19″

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

Bidloo's illustration of the flatworm F. hepatica

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

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

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

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

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

Devils and Parasites

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

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

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

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


Deciphering Spinoza’s Optical Letters

Line By Line

Below is my reading of Spinoza’s Optical Letters (39 and 40) as best as I have been able to extract interpretations from them. They are letters that are in general ignored, or when brushed over, taken to be evidence for Spinoza’s incompetence in optical matters. It seems that few have thought to examine in detail Spinoza’s point, or the texts he likely had in mind when formulating his opinion and drawing his diagrams. It should be said right from the start that I am at a disadvantage in this, as I have no formal knowledge of optics, either in a contemporary sense, nor in terms of 17th century theory, other than my investigation into Spinoza lens-grinding and its influence upon his metaphysics. In this research, the reading of this letter has proved integral, for it is one of the very few sources of confirmed scientific description offered by Spinoza. That being said, ALL of my facts and inferences need to be checked and double checked, due to my formal lack of familiarity with the subject. It is my hope that the forays in this commentary reading, the citations of likely texts of influence and conceptual conclusions would be the beginning of a much closer look at the matter, very likely resulting in the improvements upon, if not outright disagreement with, what is offered here.

[The Below English selections and links to the Latin text: here ]

Spinoza Answers

“I have looked at and read over what you noted regarding the Dioptica of Descartes.”

Spinoza is responding to a question we do not know, as we have lost Jelles’s letter. We can conclude from several points of correspondence that it is a section of Descartes’Dioptrics that Jelles’ question seems to have focused on, the Seventh Discourse titled “Of The Means of Perfecting Vision”. There, Descartes describes the interactions between light rays, lenses and the eye for purposes of magnification, preparing for the Eighth Discourse where he will present the importance of hyperbolic lenses for telescopes, and also onto the Ninth, “The Description of Telescopes”, where that hyperbola is put to use in a specific proposed construction.

“On the question as to why the images at the back of the eye become larger or smaller, he takes account of no other cause than the crossing of the rays proceeding from the different points of the object, according as they begin to cross one another nearer to or further from to eye…”

This is the beginning of Spinoza’s attack on Descartes’ rendition of how light refracts through lenses to form images of various sizes at the back of the eye. In the Seventh Discourse Descartes claims to have exhausted all factors that can influence the size of the image, which he numbers at three:

As to the size of images, it is to be noted that this depends solely on three things, namely, on the distance between the object and the place where the rays that it sends from its different points towards the back of the eye intersect; next on the distance between this same place and the base of the eye; and finally, on the refraction of these rays (trans. Olscamp).”

His descriptions that follow are varied. Among his either trite or fanciful augmentations he considers moving the object closer to the eye, then the impossibility of lengthening the eye itself, and lastly musing that if the refraction of the crystaline humor would spread rays more outward, then so too should magnification be achieved. This seems to be the extent to which Descartes will treat the factor of refraction in this discourse (hence perhaps Spinoza’s claim of the repression of a very important factor); but what Spinoza has cast his critical eye upon, I believe, is Descartes characterization of the solution to questions of magnification achieved by fundamentally extending of the distance of the intersection of rays:

There remains but one other means for augmenting the size of images, namely, by causing the rays that come from diverse points of the object to intersect as far as possible from the back of the eye; but this is incomparably the most important and the most significant of all. For it is the only means which can be used for inaccessable objects as well as for accessable ones, and its effect has no limitations; thus we can, by making use of it, increase the size of images indefinitely.

It is good to note that in his description of the strategies of telescope magnification, Descartes is operating under an extended analogy, that the telescope can work like a prosthetic lengthening of the human eye, causing the refraction that would regularly occur at the eye’s surface to happen much farther out, as if the retina were being placed at the end of a very long eye. This is his mechanical concept.

Descartes distance-analysis of magnification (and an assertion of the significance of the hyperbola) is then carried forth in the Ninth Discourse, where again Descartes will treat magnification in terms of the proximity to the eye of the crossing of rays, which here he will call the “burning point” of the lens. The descriptions occur both in the context of solutions to far and near sightedness as well as in proposals to the proper construction of telescopes, and generally follow this idea that one is primarily lengthening the eye. 

“…and so he does not consider the size of the angle which the rays make when they cross one another at the surface of the eye. Although this last cause would be principle (sit praecipua ) to be noted in telescopes…”

What Spinoza is pointing out is that when constructing telescopes, as he understands it, the aim is to increase the magnitude of the angle of rays upon the surface of the eye (the cornea), something not solely achievable merely through the adjustment of the distance of the “burning point” or the crossing of the rays of the lens from the eye. Attention to the angle of intersection is for Spinoza a more accurate discriminator probably because it leads to calculations of refraction which include the angle of incidence upon the lens, giving emphasis upon the varying refractive properties of different shapes and thicknesses of lenses in combination, some of which can increase magnification without lengthening the telescope. Descartes conceived of the objective and eyepiece lenses as mimicking the shape and powers of the eye’s lens(es), just further out in space. Though he states at several points that we do not know the exact shape of the human eye, under this homological view, he still sees a correspondence between his proposed hyperbolic-shaped lenses and those of the eye, likely drawing upon Kepler’s observation that the human crystalline humor was of a hyperbolic shape.

The fuller aspects of the factor of refraction – the third factor listed in Descartes three – are left out in such a distance calculation, Spinoza wants us to see. As mentioned, in the combination of lenses, depending upon their shape and powers, the required lengthening of the telescope can be shortened (Spinoza presents just this sort of argument to Hudde in Letter 36, arguing for the efficacy of convex-planolenses). One can also say that this same emphasis on the powers of refraction was also at play in Spinoza’s debate with Huygens over the kinds of objective lenses which were best for microscopes. Huygens finally had to privately admit in a letter written to his brother a year after these two letters, that Spinoza was right, smaller objective lenses with much greater powers of refraction and requiring much shorter tubes indeed made better microscopes (we do not know if Spinoza had in mind the smallest of lenses, the ground drop-lenses that Hudde, Vossius and van Leeuwenhoek used, but he may have). It should be said that Huygens’ admission goes a long way toward qualifying Spinoza’s optical competence, for Spinoza’s claim could not have simply been a blind assertion for Huygens to have taken it seriously. Descartes to his pardon is writing only three decades after the invention of the telescope, and Spinoza three decades after that. Be that as it may, Descartes’ measure is simply too imprecise a measure in Spinoza’s mind, certainly not a factor significant enough to be called “incomparably the most important and the most significant of all”.

Because Jelles’ question seems to have been about the length of telescopes that would be required to achieve magnification of details of the surface of the moon (the source of this discussed below), it is to some degree fitting for Spinoza to draw his attention away from the analysis of the distance of the “burning point”, toward the more pertinent factor of the angle of rays as they occur at the surface of the eye and calculations of refraction, but it is suspected that he wants to express something beyond Jelles’ question, for focal and telescope length indeed remained a dominant pursuit of most refractive telescope improvements. And Spinoza indeed comes to additional conclusions, aside from Descartes imprecision. Spinoza suspects that Descartes is obscuring an important factor of lens refraction by moving the point of analysis away from the angle of rays at the surface of the eye. This factors is, I believe, the question of the capacity to focus rays coming at angles oblique to the central axis of the lens, (that is, come from parts of an object off-center to the central line of gaze). Spinoza feels that Descartes is hiding a weakness in his much treasured hyperbola.

“…nonetheless, he seems deliberately to have passed over it in silence, because, I imagine, he knew of no other means of gathering rays proceeding in parallel from different points onto as many other points, and therefore he could not determine this angle mathematically.”

Descartes, in Spinoza’s view, wants to talk only of the crossing of rays closer to or farther from the surface of the eye, under a conception of physically lengthening the eye, and not the magnitude of the angle they make at the surface of the eye because he lacks the mathematical capacity to deal with calculations of refraction which involved rays coming obliquely to the lens. For simplicity’s sake, Descartes was only precise when dealing with rays coming parallel to the center axis of the lens, and so are cleanly refracted to a central point of focus, and it is this analysis that grants the hyperbola its essential value. In considering this reason Spinoza likely has in mind Descartes’ admission of the difficulty of calculation when describing the best shapes of lenses for clear vision. As well as the admitted problem of complexity, Descartes also addresses the merely approximate capacties of the hyperbola to focus oblique rays.

[regarding the focusing of rays that come off-center from the main axis]…and second, that through their means the rays which come from other points of the object, such as E, E, enter into the eye in approximately the same manner as F, F [E and F representing extreme ends of an object viewed under lenses which adjust for far and near sightedness]. And note that I say here only, “approximately” not “as much as possible.” For aside from the fact that it would be difficult to determine through Geometry, among an infinity of shapes which can be used for the same purpose, those which are exactly the most suitable, this would be utterly useless; for since the eye itself does not cause all the rays coming from diverse points to converge in exactly as many other diverse points, because of this the lenses would doubtless not be the best suited to render the vision quite distinct, and it is impossible in this matter to choose otherwise than approximately, because the precise shape of the eye cannot be known to us. – Seventh Discourse

This is an important passage for several reasons, but first because it comes the closest to the question of the focus of rays para-axial to the center. Again, one must keep in mind that Descartes is thinking about trying to make lenses of a shape that are exact to the shape (or powers) of the eye. Here he is thinking about ever more exotic geometrical shapes which may achieve this, and insists upon the fruitlessness of such a pursuit; it is significant that in contrast to this, Spinoza imagines rather a very simple solution to the question of aberration: the acceptance of spherical aberration and the embrace of the advantage of spherical omni-axial focus. The quoted passage directly precedes Descartes’ summation of the three factors in magnification, with which I began my citations. And I will return to the latter parts of this passage later when we investigate Spinoza’s critique of the hyperbola and the eye. (Note: Aside from this direct reference to Descartes on the issue of calculation, perhaps Spinoza considers also James Gregory, who had some difficulty calculating paraxial rays for his hyperbolae and parabolae in his Optica Promota, though writing an entire treatise devoted to their value.)

Nonetheless, Spinoza suspects that Descartes has shifted the analysis of magnification not simply because it is not amenable to calculation, but more so because, had Descartes engaged the proper investigation, he would have had to face an essential advantage of spherical lense, lessening to some degree his hyperbolic panacea to the problems of the telescope. Again, we will leave aside for the moment Descartes’ justification of this approximation on the basis of the human eye and Nature.

Soft Focus: Spherical Aberration

“Perhaps he was silent so as not to give any preference to the circle above other figures which he introduced; for there is not doubt that in this matter the circle surpasses all other figures that can be discovered.”

Spinoza goes on to expound for Jelles the virtues of the simple circle, as it expresses itself in spherical lenses. One has to keep in mind that since the publishing of Descartes’ Dioptrics  (1637), there had been a near obsessional pursuit of the grinding of hyperbolic lenses, a lens of such necessary precision that no human hand was able to achieve it. The hyperbolic lens promised – falsely, but for reasons no one would understand until Newton’s discovery of the spectrum character of light in 1672 – a solution to the problem of spherical aberration. Spherical aberration is simply the soft focus of parallel rays that occurs when refracted by a spherical lens. Kepler in his Paralipomena provides a diagram which illustrates this property:

As one can see, rays that are incident to the edges of the lens (α, β) cross higher up from the point of focus, which lies upon the axis (ω). It was thought that this deviation was a severe limitation on the powers of magnification. With the clearing away of the bluish, obscuring ring that haloed all telescopic vision, the hope was for new, immensely powerful telescopes. And it was to this mad chase for the hyperbola that Spinoza was opposed, on several levels, one of which was the idea that spherical lense shapes actually had a theoretical advantage over hyperbolics: the capacity to focus rays along an infinity of axis:

diagram letter 39

“[referring to the above] For because a circle is everywhere the same, it has the same properties everywhere. If, for example, circle ABCD should have the property that all rays coming from direction A and parallel to axis AB are refracted at its surface in such a way that they thereafter all meet at point B; and also all rays coming from point C and parallel to axis CD are refracted at its surface so that they all meet together at point D…,”

This is a very important point in the letter, for I believe it has been misread by some. At the same time that Spinoza seems to be asserting something painfully obvious in terms of the geometry of a circle, he, at first blush, in bringing this geometry to real lenses appears to be making a serious blunder. And, as I hope to show later, beneath both of these facts there is a subtle and deeper phenomenal-epistemic philosophical point being made, one that echoes through to the roots of Cartesian, and perhaps even Western, metaphysics. Let me treat the first two in turns, and then the third in parts.

The first point is obvious. As we can see from the diagram Spinoza provides, each of the refractive relationships of rays parallel to one axis are symmetical to the same relationships of other parallel rays to another axis. The trick comes in Spinoza’s second sentence, where he seems to be asserting an optical property of actual spherical lenses. As one email correspondent to me concluded, (paraphrased) “Spinoza thinks that the focal point of such a lens lies on the diameter, and this only occurs in rare cases.” The index of refraction of glass simply is not 2 in most cases. Spinoza seems to be making an enormous optical blunder in leaving the refractive index of the glass out, opening himself to a modern objection that he simply does not know the significance of the all important Law of Refraction, put forth by Descartes. This is a similiar prima facie reading done by Alan Gabbey in his widely read essay “Spinoza’s natural science and methodology”, found in The Cambridge Companion to Spinoza,

One’s immediate suspicions of error is readily confirmed by a straight forward application of Descartes Law of refraction. For the circle to have to the dioptrical property Spinoza claims, the refractive index of the glass would have to be a function of the angle of incidence, a condition of which there is not the slightest hint in the letter…[he is] apparently unaware of the importance the “[other] figures”…that Descartes had constructed (154).

The problem with these readings, among many, is that Spinoza is not at all asserting that there exists such a lens which would have this refractive property (Gabbey’s concerns about Spinoza’s awareness of the Law of Refraction should be answered by looking his familiarity with Johannes Huddes “Specilla circularia”, in letter 36, which will be taken up later). I have corrected a weakness in the prominent English translation of the text which helps to bring out the distinction I am making. If one looks at the sentence closely, Spinoza is presenting an if-then assertion (he uses the subjective in the intitial clause). IF, and only if, a circular lens can be said to have the focusing property along axis AB, THEN it would have the same property along axis CD. To repeat, he is not asserting such a property in real glass and therefore he remits any refractive index reference because it is not germane to his point; he is only at this point emphasizing the property of an infinity of axes of focus, and he is using a hypothetical sphere for several reasons.

The first reason I suspect is that he is trying to draw out the remarkable resonance of spherical forms, making his diagram evocative of notions of completeness and internal consistency. This is of course not an optical concern, but we have to consider it as an influence. We have a similiar looking diagram presented by Spinoza in the Ethics, showing an argued relationship between Substance and the modes that express it. As Spinoza writes:

diagram from the Ethics 2, prop 8, scholia

The nature of a circle is such that if any number of straight lines intersect within it, the rectangles formed by their segments will be equal to one another; thus, infinite equal rectangles are contained in a circle. Yet none of these rectangles can be said to exist, except in so far as the circle exists; nor can the idea of any of these rectangles be said to exist, except in so far as they are comprehended in the idea of the circle.” E2p8s

There is perhaps much speculation to be made as to Spinoza’s feelings about the the interweave of causes that express themselves in modes and the apparitions of focus generated by hypothetical spherical lenses (are modal expressions seen in some way like a confluence of rays?), but at this point I only want to point out Spinoza’s affinity for the sphere, and thus this one possible reason for using a full sphere to illustrate an optical property of spherical lenses. (Remember, this is just an informal letter written to a friend, and not meant as a treatise.)

The second reason is that Spinoza very likely is thinking of a real sphere, that is, the “aqueous globe” that Kepler used to investigate refraction in his Paralipomena, a work in which he was the first to articulate with mathematical precision the dynamics of spherical aberration (before there was a telescope, in 1604), and also was the first to suggest the hyperbola as the resolving figure for such aberration. Here is Kepler’s diagram of his sphere through which he gazed at various distances, illustrating his Proposition 14: “Problem: In an aqueous globe, to determine the places of intersection of any radiations parallel to an axis”.

Keplers diagram from proposition 14

Kepler's diagram from proposition 14

Thus, Spinoza’s use of a sphere in his diagram has at least two readings that have heretofore not been noticed. The first is that his description is operating at solely the hypothetical level, asserting the abstract properties of spherical symmetry, but secondly, he is referencing, or at least has in mind, a primary historical optical text, in all likelihood the text which spurred Descartes’ enthusiasm for the hyperbola in the first place (likely read by Descartes around 1620). It is precisely in this parallel fashion, between the geometrical and the manifest, that Spinoza seems to work his optical understanding.

The third reason that Spinoza is using a full sphere to illustrate his principle of omni-axial refraction is that Descartes’ treatise deals not only with lenses, but also with the human (and ox) eye. And this eye in diagrams is represented as a sphere. I will return to this point a little later, because as he encounters Descartes, he is making an argument, however loosely, against not only his optics, but his essential concepts of clear perception. By taking up a full sphere in his objection, he also poses a relation to Descartes schemas of the eye.

Aside from Descartes’ pseudo-spherical diagram of the eye, we have to consider as an additional influence Hooke’s spherical depiction of the eye with two pencils of rays focused along different axes, used to illustrate the reception of color (pictured below left). The reason why I mention this diagram is not only because it bears some resemblance to Spinoza’s, but also because Hooke’s extraordinary Micrographia might have been the source of Jelles’ question, as I will soon address, and so may have been a text Spinoza thought of in his answer, though we are not sure if he ever read it, or even looked at it, as it was in published in English. Christiaan Huygens owned a copy of it and it was the subject of a conversation between the two. If Spionoza indeed visited the Hofwijck several times, it is hard to believe that he would not have looked closely at this page of diagrams.

figure 5, Robert Hookes Micrographia

 

 

figure 5, Robert Hooke's Micrographia

“…this is something that could be affirmed of no other figure, although the hyperbola and the ellipse have infinite diameters.”

Spinoza here declares the exclusivity of a property that only spheres and their portions possess. It is hard to tell exactly at what level Spinoza is making his objection. Is it entirely at the theoretical level of optics that Spinoza believes hyperbolic lenses to be impaired, such that even if people could manufacture them with ease, they still wouldn’t be desired. If so, he would be guilty of a fairly fundamental blindness to potential advantages in telescope construction that such a lens would grant, rather universally understood. If indeed he was an accomplished builder of telescopes – and we have some evidence that he may have been – this would be a difficult thing to reconcile, forcing us to adopt an estimation of a much more craftsman level understanding of his trade. But it is possible that Spinoza is asserting a combine critique of hyperbolic lenses, one that takes into account the difficulty in making them. There are signs that spherical aberration after Descartes was taken to be a much greater problem than it calculably was, and Spinoza brings out a drawback to hyperbolic focus that adds one more demerit to an already impossible-to-make lens. Thus, as a pragmatic instrument maker he may not be assessing such lenses only in the abstract, but in reality. It may be that Spinoza sees the ideal of the hyperbolic lenses as simply unnecessary, given the serviceability of spheres, and the perceived advantage of oblique focus. This question needs to be answered at the level of optical soundness alone, but such an answer has to take in account the great variety of understandings in Spinoza’s day and age, even among those that supposedly “got it right”. For instance, such an elementary and widely accepted phenomena as “spherical aberration” was neither defined, nor labeled in the same way, by any two thinkers; nor were its empirical effects on lensed vision grasped. We often project our understanding backwards upon those that seem most proximate to our truths. Spinoza’s opinions on aberration seem to reside exactly in that fog of optical understandings that were just beginning to clear.

Man on the Moon

“So the case is as you describe; that is, if no account is taken of anything except the focal lenth of the eye or of the telescope, we should be obliged to manufacture very long telescopes before we could see objects on the moon as distinctly as those on earth.”

Here we possibly get a sense of Jelles’ question. It must have come from a reflection upon Descartes’ comments on crossing of rays at various distances from the eye, posed as a question to whether we might be able to view the Moon with such clarity as we see things here – remember, Descartes’ promised infinite powers of magnification. I mentioned already that Jelles’ question may have come in reference to Hooke’s work. We must first overcome the problem of language of course, for I do know that Jelles read English, though it is possible that he read a personal translation of a passage, as Huygens had translated a passage for Hudde. But given these barriers, I believe there is enough correspondence to make a hypothesis that is not too extravagant: Jelles had recently read a portion of Hooke’s Micrographia. The reason that I suspect this, is that the Micrographia published with extraordinarily vivid plates of magnified insects and materials, concludes with a speculative/visual account of what may be on the moon, seen through his 30-foot telescope (and a suggested 60 ft. telescope), coupled with a close up illustration of a moon’s “Vale” crater, he writes of an earthly lunar realm:

Hookes Vale

…for through these it appears a very spacious Vale, incompassed with a ridge of Hills, not very high in comparison of many other in the Moon, nor yet very steep…and from several appearances of it, seems to be some fruitful place, that is, to have its surface all covered over with some kinds of vegatable substances; for in all portions of the light on it, it seems to give a fainter reflection then the more barren tops of the incompassing Hills, and those a much fainter then divers other cragged, chalky, or rocky Mountains of the Moon. So that I am not unapt to think that the Vale may have Vegetables analogus to our Grass, Shrubs, and Trees; and most of these incompassing Hills may be covered with so thin a vegetable Coat, as we may observe the Hills with us to be, such as the Short Sheep pasture which covers the Hills of Salisbury Plains.

As one can see from this marvelous, evocative passage, the suggestion that the moon’s vales are pastorially covered with rich meadows, calling up even flocks of sheep before the mind, one can easily see that Jelles has something like this in mind when he asks what it would take to see objects on the moon, as we can see objects on the Earth. One might speculate that, having read such a passage, Jelles had a spiritual or theological concern in mind and excitment over the possibility of other people on the moon, but this would be perhaps only wistful supposition on our part. But it is too much to suppose that it was likely Hooke’s description of the moon Jelles was thinking of when he wrote his question to Spinoza, for not only are the details of an Earth-like moon present, but also Hooke’s urging of the reader to use a more power and much longer telescope than he used. Spinoza is responding directly to this aspect of telescope length.

(An alternate thought may be that Jelles had come upon Hevelius’s Selenographia, sive, Lunae descriptio 1647, filled with richly engraved plates of the moon’s surface. It did not have the same fanciful description of moon meadows, and was not circulated with the acclaim of Hooke’s Micrographia, but it did name features of the moon after Earth landmarks, giving it an Alps, a Caucasus and an Island of Sicily.)

If we allow this supposition of a posed question on Jelles’s part, we might be able to construct something of Spinoza’s thinking in his response. It would seem, in our mind’s-eye, that Jelles had read Hooke’s description of the moon and his urge for a longer telescope and set about checking Descartes’ Dioptrics if it were the case that we really would have to build an extraordinarily long telescope to see the details that Hooke invoked (indeed Huygens built a 123 ft. arial telescope; and Hevelius one of 150 ft., pictured below).

Hevelius 150 ft. arial telescope

Hevelius' 150 ft. arial telescope

Following this evolution of the question, it would seem that Jelles came to Descartes’ treatment of magnification in the Seventh (and related) Discourses, one that defined the power of magnification by the all important distance of the crossing of rays from the surface of the eye, treating the telescope as an extended eye. If indeed Jelles was not familiar with optical theory he may have taken this increase of distance for an explanation why telescopes had to be so very long to see the moon with desired detail. It would seem natural for Jelles to pose this question to Spinoza, who not only was regarded as the expert on Descartes in the Collegiant group, but also was a grinder of lenses and a designer of telescopes.

If this hypothetical narrative of the question is correct, Spinoza responded in a slightly misdirected way, taking the opportunity to vent an objection to Descartes thinking which did not have acute bearing upon Jelles’s question. For Descartes’ description of a “burning point” distance and Spinoza’s emphasis on the angle of incidence of rays oblique to the center axis, makes no major difference in the conclusion that Jelles came to, that indeed it would take a very long telescope to do what Jelles imagined, and Spinoza admits as much, above. Yet, when Spinoza qualifies his answer “if no account is taken of anything except the focal lenth of the eye or of the telescope” he is pointing to, one imagines, factors of refraction, for instance in compound telescopes and lenses of different combinations, which do not obviate the contemporary need for very long telescopes, but may affect the length.

Aside from this admission, Spinoza has taken the opportunity to express his displeasure over a perceived Cartesian obscurance, one that has lead to an over-enthused pursuit of an impossible lens, and as we have seen, in this context Spinoza puts forward his own esteem for the spherical lens, and the sphere in general. But this is no triffling matter, for out of Spinoza’s close-cropped critique of Descartes’ Dioptrics run several working metaphors between vision and knowledge, and a history of thinking about the optics of the hyperbola that originates in Kepler (made manifest, I contend, in a full-blown metaphysics in Descartes). Though Spinoza’s objection is small, it touches a fracture in thinking about the Body and Perception, a deep-running crack which might not have direct factual bearing on optical theory, but does have bearing on its founding conceptions. As I have already suggested, we have to keep in mind here that though we are used to thinking of a field of science as a closed set of tested truths oriented to that discipline, at this point in history, just when the (metaphysically) mechanical conception of the world was taking hold, it is not easy, or even advisable, to separate out optical theories from much broader categories of thought, such as metaphysics and the rhetorics of philosophy. For example, how one imagined light to move (was it a firery corpuscula, or like waves in a pond?), refract and focus was in part an expression of one’s overall world picture of how causes and effects related, and of what bodies and motions were composed: and such theories ever involved concepts of perception.

“But as I have said, the chief consideration is the size of the angle made by the rays issuing from different points when they cross one another at the surface of the eye. And this angle also becomes greater or less as the foci of the glasses fitted in the telescope differ to a greater or lesser degree.”

Spinoza reiterates his point that it is the intersecting angles of incidence at the surface of the eye which determined the size of the image seen through a telescope. He finally connects the factor of the angle of incidence and intersection to the foci of lenses themselves. It is tempting to think that Spinoza in his mention of lenses is also thinking of compound forms such as the three-lens eyepiece invented by Rheita in 1645, or as he was already familiar through visits to Christiaan Huygens’s home in 1665, proposed resolutions of spherical aberration by a complex of spherical lenses. Such combinations would be based upon angle of incident calculations.

“If you wish to see the demonstration of this I am ready to send it to you whenever you wish.”

 

Spinoza will send this evidence in his next letter (pictured at bottom).

Letter 40 “…I now proceed to answer your other letter dated 9 March, in which you ask for a further explanation of what I wrote in my previous letter concerning the figure of a circle. This you will easily be able to understand if you will please note that all the rays that are supposed to fall in parallel on the anterior of the glass of the telescope are not really parallel because they all come from one and the same point.”

Jelles has apparently had some difficulty with understanding Spinoza’s explanation. It is interesting because this confusion on Jelles’ part has actually been taken as evidence that Spinoza not only is impaired in his understanding of optics (this may be the case, but Jelles’ confusion, I don’t believe, is worthy of being evidence of it), but that those close to Spinoza around this time became aware that Spinoza’s optical knowledge was superficial at best, something not to be questioned too deeply.

As Michael John Petry writes:

“There is evidence that after 1666 Spinoza’s ideas on theoretical optics were less sought after by his friends and acquaintences…Even JarigJelleswasquiteevidently dissatisfied with the way in which Spinoza explained the apparent anomaly in Descartes’ Dioptrics” (Spinoza’s Algebraic Calculation of the Rainbow & Calculation of Chances, 96)

Petry cites other evidence which needs to be addressed (primarily Huygens’ letters), but a close reading of the nature of Jelles implied question does not seem to support in any way the notion that Spinoza’s optical knowledge had been exposed as a fraud of some sort. Alan Gabbey as well, who maintains serious doubts about Spinoza’s optical proficiency, seems to focus on Spinoza’s need to explain himself to Jelles as a sign that he is somewhat confused:

In his next letter…to Jelles, who has asked for a clarification, Spinoza explained that light rays from a relatively distant object are in fact only approximately parallel, since they arrive as “cones of rays” from different points on the object. Yet he maintained the same property of the cirlce in the case of ray cones, apparently unaware of the importance of the “[other] figures” [the famous "Ovals of Descartes"] (154).

It seems quite clear that Spinoza was aware of the “importance” of these figures, at least he was aware of Hudde’s and Huygens’ attempt to minimize that importance. But Gabbey here seems to suggest that Spinoza is evading a point of confusion by simply changing descriptions, instead of parallel rays of light, Spinoza now uses “cones of rays”. For these reasons of suspicion it is better to go slow here.

The question that Jelles raised apparently has to do with the reading of Spinoza’s circular diagram and its focus of two pencils of light rays, for Spinoza imagines that if Jelles understands these pencils as cones of rays his confusion will be cleared up. To take the simplest tact, it may very well be that Jelles, upon seeing Spinoza’s diagram, turned back to Descartes’ text in order to apply it, and found there a diagram which was quite different. What Jelles may have seen was Descartes’ figure 14 from the Fifth Discourse (pictured below, left), or really any of his diagrams which depict the interaction of rays with the eye:

figure 14 from the Fifth Discourse of the Dioptrics

figure 14 from the Fifth Discourse of the Dioptrics

One can see how in this context Jelles may have been confused by Spinoza’s diagram of the focus of two pencils of rays, and even by the accusation that Descartes is being somehow imprecise, for the illustration seems to depict rays as something like cones of rays, not rays flowing parallel to an axis, as they are in Spinoza’s drawing. Aside from this plain confusion, Jelles’ question may have dealt with some other more detailed aspect, for instance, a question about the importance of a lens’s ability to focus rays oblique to its center. If so, Spinoza would require not only that Jelles understand that rays come in cones, but also have a fuller sense of how those rays refract upon the eye, perhaps provided by the diagram that will follow. In either case, rather than understand Spinoza’s change in descriptive terminology as an attempt to dodge his incomprehension, Spinoza simply appears to be guiding Jelles in the reconsilation of both kinds of diagrams, or preparing ground for a more complete explanation.

Note: Regarding the analytical descriptions of a pencil of parallel of rays or “cones of rays” there is no standing confusion between them. They exhibit two different ways of analyzing the refractive properties of light. But there is more than this, the use of the phrase “cones of rays” by Spinoza gives a clue to what texts he has in mind in his answer. The orgin of this phrase for Spinoza likely comes from Kepler’s Paralipomena  (1604), in a very significant passage. As mentioned, Kepler has already provided a description of the phenomena of spherical aberration (shown in diagrams including the one I first cited here), and forwarded the hyperbola as a figure that would solve this difficulty. Further, he has claimed that the crystalline humor of the human eye has a hyperbolic shape. Here Kepler describes how light, having proceded from each point of an object in a cone of rays (truly radiating in a sphere), intersects the eye’s lens at varying degrees of clarity. The cone that radiates directly along the axis of the lens is the most accurately refracted:

All the lines of the direct cone [a cone whose axis is the same as the axis of the cornea and crystalline] are approximately perpendicular to the crystalline, none of those of the oblique cones are, The direct cone is cut equally by the anterior surface of the crystalline; the oblique cones are are cut very unequally, because where the anterior surface of the crystalline is more inclined [aspherical], it cuts the oblique cone more deeply. The direct cone cuts the hyberbolic surface of the crystalline, or the boss, circularly and equally; the oblique cone cuts its unequally. All the rays of the direct cone are gathered together at one point in the retina, which is the chief thing in the process; the lines of the oblique cones cannot quite be gathered together, because of the causes previously mentioned here, as a result, the picture is more confused. The direct cone aims the middle ray at center of the retina; the oblique cones aim the rays to the side…(Paralipomena 174)

This passage has multiple points of importance, in part because I suspect that it is the orgin passage of Descartes’ enthusiasm for the hyperbola, but also, as I will show later, for a naturalized justification for hyperbolic vision, something which will play to Spinoza’s optical critique. But at this point it is just sufficient to register the citation as a reference point for Spinoza’s phrase. We have already pointed out that Spinoza may have Kepler’s aquaeous globe in mind for his intial diagram, so there is something distinctly Keplerian in Spinoza’s approach.

Another reference point for Spinoza’s phrase is James Gregory’s 1663 Optical Promota, a treatise written without the aid of Descartes’ Dioptrics, but which all the same proposed parabolic and hyperbolic solutions to refraction aberrations and proposed reflective mirror telescopes to avoid the problem altogether. This text we know Spinoza had in his personal library, and he seems to be reasoning from it in part. Gregory regularly uses both “pencils of rays” and “cones of rays” as modes of analysis.

As a point of reference for us, he offers these defintions to begin his work:

6. Parallel rays are those which are always equally distant each to the other amonst themselves.

7. Diverging rays are those which concur in a point when produced in both directions: those rays produced in the opposite direction to the motion from the ray-bearing cone – the apex of the cone is the point of concurrence of the rays.

8. Converging rays are those rays are those which concur in a point in the direction of the motion when produced in both directions; these rays are called a pencil, and the point of concurrence the apex of the pencil…

10. An image before the eye [i.e. a real image], arises from the apices of the light bearing cones from single radiating points of matter brought together in a single surface.

Pencils of parallel rays feature in many of the diagrams, within the understanding that rays proceed as cones. So seems to me that Spinoza is operating with both Kepler and Gregory in mind as he answers Jelles’ question.

“But they are considered to be so because the object is so far from us that the aperture of the telescope, in comparison with its distance, can be considered as no more than a point.”

Spinoza follows Gregory’s Fourth Postulate: “The rays coming from remote visible objects are considered parallel.”

“Moreover, it is certain that, in order to see an entire object, we need not only rays coming from a single point but also all the other rays that come from all the other points.”

Spinoza may be still addressing the nature of Jelles’ request for clarification. He follows the reasoning of Gregory’s Tenth defintion (above). Whether the rays be treated as parallel pencils, or cones does not make a strict difference to Spinoza’s point, though understanding that they are coming to the lense as cones does something to express their spherical nature (one must recall that Kepler asserted that light radiates as a sphere as it can, and even that Hooke proposed that it moves in waves; Spinoza’s attachment to the sphere may be in regards to this). It is the lens’ capacity to gather together these rays come from diverse points of the object, and not just rays parallel to its central axis, that Spinoza emphasizes. In other words, though considered no more than a point, it is a point that must gather rays from a variety of angles.

“And therefore it is also necessary that, on passing through the glass, they should come together in as many other foci.”

It should be noted that Spinoza is talking about glass lenses here, and not the eye’s lens. Spinoza has taken his ideal model of a spherical refraction from the first letter, and has applied it to actual lenses (there is no requirement to the index of refraction of the glass). As Spinoza envisions it, because a glass has to focus rays coming obliquely, the foci along those alternate axes are significant factors in clarity.

Seeing More, or Seeing Narrowly

“And although the eye is not so exactly constructed that all the rays coming from different points of an object come together in just so many foci at the back of the eye, yet it is certain that the figures that can bring this about are to be preferred above all others.”

This is the big sentence, the one that opens up the place from which Spinoza is coming from. What does Spinoza mean “the eye is not so exactly constructed”? How odd. Descartes’ comments on optics indeed are often made in the service of correcting far- and near-sightedness, so there is context for a notion of the “inexactness” of the eye, and for his own uses Descartes picks up on the notion that the eye is limited or flawed: …”in as much as Nature has not given us the means…”, “I still have to warn you as to the faults of the eye”. But this is not what Spinoza has in mind. What I believe Spinoza is thinking about is the hidden heritage behind a naturalizing justification of hyperbolic vision itself. This is not strictly an optical point, as we have come to understand optical theory, but an analogical point. And this distinction organizes itself around the failure that a hyperbolic lens to handle rays oblique to its axis, with clarity, and whether this failure is something to be concerned with.

Keplers drawing the hyperbolic crystalline humor, 167

Kepler's drawing the hyperbolic crystalline humor, 167

Kepler begins the justification. The passage continues on from the conclusion of the one cited above, which ended with an explanation of why the image of the eye is blurred at its borders,

All the rays of the direct cone are gathered together at one point in the retina, which is the chief thing in the process; the lines of the oblique cones cannot quite be gathered together, because of the causes previously mentioned here, as a result, the picture is more confused. The direct cone aims the middle ray at center of the retina; the oblique cones aim the rays to the side…

so the sides of the retina use their measure of sense not for its own sake, but whatever they can do they carry over to the perfection of the direct vision. That is we see an object perfectly when at last we perceive it with all the surroundings of the hemisphere. On this account, oblique vision is least satisfying to the soul, but only invites one to turn the eyes thither so that they may be seen directly (174).

This is a striking passage in that we know the history of the hyperbolic lens, and Descartes’ fascination with it. Due to the hyperbolically shaped crystalline humor (as Kepler reasons it), the image at the border, projected at the edges of the retina, is said to be more confused due to the inability of the lens to focus oblique rays. This is what Spinoza has in mind when he says that the eye is not so exactly constructed. But there is more to this passage. Not only is the image more confused, but Kepler goes so far was to qualify this confused quality as an explanation for why the soul is dissatisfied with oblique vision. At the margins of blurred vision, according to Kepler, the sides of the retina do not “sense” for their own sake, but for the sake of central axis perfection, in effect serving the center. Kepler has provided the hyperbola as the solution for spherical aberration, but has also couched that shape within a larger context of human perception and the nature of what experience satisfies the soul or not.

This theme of the hyperbola’s justifcation through Nature continues. I will leap forward to Gregory’s Optica Promota, a writer who, as I have said, had no access to Descartes’ treatise but did read Kepler closely. At the end of a thorough and brilliant work on the value of hyperbolic and parabolic forms for use in telescopes, Gregory as well evokes Kepler’s notion of the weakness of the hyperbola, along with its naturalization. This is how he ends his Optica :

But against hyperbolic lenses, it is only objected that nothing will be able to be most clearly seen, except a visible point arising on the axis of the instrument. But this weakness [ infirmitas ] (if it would be worthwhile to call it that) is sufficiently manifested in the eye itself, though not to be impuning Nature, for whom nothing is in vain, but how much all things most appropriately she carries out [ peragit]. Nevertheless, withconicallenses and mirrors not granted, it shall be rather with spherical portions used in place of spheriods and paraboloids in catoptrics; as with hyperboloids in dioptrics, in which portions of spheres are less appropriate.

With these we go to the stars – His itur ad astra

Just as Kepler justifies hyperbolic vision by appeal to the eye’s own weakness, redeemed by the roles of the retina and the satisfactions of the soul, so here too Nature herself is the justification of central axis priority. This is a curious naturalization, given that so much of optics addresses the failings or the limitations of Nature. Such a self-contradiction deserves attention, especially with a focus upon the foundations of valuations that make one adjustment to Nature desired, and another not. But here I would like to continue the line of justifications of the hyperbola through the construction of the eye that Spinoza likely has in mind.

Descartes, if you recall from a passage cited above, also justifies the shape of the hyperbolic lens through appeal to the shape of the human eye. After he admits that the foci of rays that come obliquely to the axis of the hyperbola can only approximate a point of focus,

…for since the eye itself does not cause all the rays coming from diverse points to converge in exactly as many other diverse points, because of this the lenses would doubtless not be the best suited to render the vision quite distinct, and it is impossible in this matter to choose otherwise than approximately, because the precise shape of the eye cannot be known to us…

Descartes has not strictly forwarded Kepler’s claim that the crystalline humor has a hyperbolic shape, perhaps because his own anatomical investigations caused him to doubt the accuracy of this, but he maintains Kepler’s reasoning to some degree. While Descartes has long let go of any notion that spherical lenses may be preferred due to their omni-axial focus, he shrugs off the necessity for anything more than approximate foci along these oblique axes. The reason he provides for this is unclear. Either it is proposed that because the eye does not focus oblique rays, the benefits of any lens that does so would simply be lost – yet, if this were the reason, it would not result in the conclusion that such shapes are not best for precise vision, for they would be no worse than his hyperbola; or, he means to say that hyperbolic lenses are simply preferred because their weaknesses are natural weaknesses of the eye, with Nature not to be improved upon. This is emphasized in conclusion of the passage:

…Moreover we will always have to take care, when we thus place some body before our eyes, that we imitate Nature as much as possible, in all things that we see she has observed in constructing them; and that we lose none of the advantages that she has given us, unless it be to gain another more important one. – Seventh Discourse

There is additional evidence for the naturalized justification of the hyperbolic “weakness” (notice the question of valuation in the phrase “important one”). Firstly, when he proposes his notion that the telescope is simply an extension of the eye, Descartes imagines that all the refraction would occur in one lens, thus, “…there will be no more refraction at the entrance of that eye” (120). In this analogical conception of the extended length of the eye Descartes imagines his hyperbola as supplimenting and even supplanting the eye’s refractions. Secondly, when Descartes addresses the possibility that seeing at the borders may be an improvement of vision, he denies this, by virtue of how Nature has endowed our sight. Seeing more is not seeing better.

There is only one other condition which is desirable on the part of the exterior organs, which is that they cause us to perceive as many objects as possible at the same time. And it is to be noted that this condition is not in any way requisite for the improvement for seeing better, but only for the convenience of seeing more; and it should be noted that it is impossible to see more than one object distinctly at the same time, so that this convenience, of seeing many others confusedly, at the same time, is principally useful only in order to ascertain toward what direction we must subsequently turn our eyes in order to look at the one among them which we will wish to consider better. And for this, Nature has so provided that it is impossible for art to add anything to it. - Seventh Discourse

What Kepler has stated as simply the role of the borders of the retina to serve the perfection of the center, Descartes has made an occasion to assert the virtue of the human Will (a cornerstone of his metaphysics, and a cornerstone which Spinoza rejects, which makes the two philosophers quite opposed in their philosophy of ideal perception). For Kepler the edges serve the center, as is shown in the satisfactions of the soul. For Descartes the width of blurred vision becomes only a field upon which the Will manifests itself in making judgements of good and bad. Not only is the hyperbola’s condensed vision naturalized, it is key to how the Individual Will functions. Nature herself has foreclosed the possibility of improving the capacity to see more in a better way. Spinoza’s philsophy of mind’s-eye perception is based on the principle that one sees clearly as one sees more – more at once. (It is interesting that immediately following this assertion Descartes uses the examples of sailors and hunters who are able to improve on Nature’s provisions, but only in the direction of further sharpening their eyes to a more narrow focus. Descartes valuation is both implicit and naturalized.)

It suffices to say that in this long digression what Spinoza means by “the eye is not so exactly constructed” is that the non-spherical shapes of the eye (and our tendencies of vision that come from it) provides a focus that is not optimal. Spinoza here likely conflates his metaphysics and his optics, as perhaps does Descartes. His critique, right down to the root of centralized conceptions of a naturalization of hyperbolic vision, opens to Post-modern and Post-structuralist critiques of marginalization and philosophies of Presence, locating his objection not in the glorification of the human eye, but in the understanding of its limitations. Descartes’ philosophy of “clear and distinct” and its parasitic conceptions of Human Will are cut at in a very essential way. But the question remains, is there an optical advantage to spherical lenses, as they exhibit the flexibility of omni-axial foci? The obvious objection to hyperbolics is that they proved impossible to grind, either by hand, or in the kinds of automated machines that Descartes proposed. As a practiced lens-grinder Spinoza better than most would surely know this. But aside from this serious detraction Spinoza finds one more, and it is one that Kepler, Descartes and Gregory all admit, as they justify it not in optical terms, but in terms of naturalized conceptions of the eye and perception. Perhaps we can assume that Spinoza, out of his love for the sphere, coupled with the Keplerian sense of the spherical radiation of light, the practical considerations of lens grinding, and a epistemological conception of Comprensive Vision, saw in the admitted weakness of the hyperbola (and the eye) something that outweighed the moderate weakness of spherical aberration. In a sense, Spinoza may have seen spherical aberration in terms of his acceptance that almost all of our ideas are Inadequate Ideas. [More of this line of thought written about here: A Diversity of Sight: Descartes vs. Spinoza ]

“Now since a definite segment of a circle can bring it about that all the rays coming from one point are (using the language of Mechanics) brought together at another point on its diameter, it will also bring together all the other rays which come from other points of the object, at so many other points.”

A modified version of the letter 39 diagram, showing what Spinoza believed to be the failings of the hyperbola

A modified version of the letter 39 diagram, showing what Spinoza believed to be the failings of the hyperbola

Spinoza repeats his insistence upon the virtues of spherical lenses. As the modified diagram here shows, the capacity to refract rays along an infinity of axes is in Spinoza’s mind an ideal which hyperbolic forms cannot achieve. He does not accept the notion that an assumed narrow focus of human vision, nor the supposed shape of the crystalline humor (Kepler) determines that “hyperbolic abberation” is negligable to what should be most esteemed. This insistance upon the importance of the sphere calls to mind James Gregory’s description of refraction on sphere of the “densest medium” presented in his first proposition of the Optica:

If truly, everything is examined carefully, then it will seem – on account of the aforementioned reasons -that all the rays, either parallel or non-parallel, which are incident on the circular surface of the densest medium for refraction, are concurrent in the centre of the circle. Now we ask: how does this come about? The answer is: – Well, however a line is drawn incident on the circle, (provided they are co-planar) an axis can be drawn parallel to it and without doubt the circle can be considered a kind of ellipse so that any diameter can be called the axis, from which it appears that the special line sought is the axis of a conic section. - Optica Promota

figures 1 and 2 from the Optima Promota

figures 1 and 2 from the Optima Promota

One feels that there seems something of this ideal conception of the densest medium floating behind Spinoza’s conception of the spherical lens. Material glass somehow manifests for Spinoza, in its particularities of modal expression, these geometric powers of unified focus, and peripheral focus is a part of what Spinoza conceives of as ideal clarity.

“the language of mechanics”

But there is another very important clue in this section of the letter: the phrase “using the language of Mechanics”); for now I believe we get direct reference to Johannes Hudde’s optical treatise “Specilla circularia” (1655), an essential text for understanding Spinoza’s approach to spherical aberration.

Rienk Vermij and Eisso Atzema provided a most valuable, but perhaps sometimes overlooked insight into the 17th century reaction to Descartes resolution to spherical aberration in their article “Specilla circularia: an Unknown Work by Johannes Hudde”. They present Hudde’s small tract (it is not quite nine typed journal pages) which offers a mathematical treatment of the problem of spherical aberration. Interestingly, as it was published anonymously, Hudde’s teacher at Leiden, Van Schooten, actually thought that the work belonged to his star student Christiaan Huygens. Presumably this was because of the closeness it bore to Huygens’ 1653 calculations of aberration, and he wrote him to say as much, and he likely sent him a copy of it as Christiaan requested. Hudde’s approach is a kind of applied mathematics to problems he considered to be pragmatic mechanical issues. In a sense he simply took spherical aberration to be a fact of life when using lenses, and thought it best to precisely measure the phenomena so as to work with it effectively. The hyperbolic quest was likely in his mind a kind of abstract unicorn chasing. He wanted a mechanical solution which he could treat mathematically, hence his ultimate distinction between a “mathematical point” of focus and a “mechanical point”. As Vermij and Atzema write describing this distinction and its use in analysis:

At the basis of Hudde’s solution to the problem is his distinction between mathematical exactness and mechanical exactness. Whereas the first is exactness according the laws of mathematics, the second is exactness as far as can be verified by practical means. After having made this distinction, Hudde claims that parallel incident rays that are refracted in a sphere unite into a mechanically exact point (“puntum mechanicum”). In order to substantiate his claim Huddethen proceeds to the explicit determination of the position of a number of rays after refraction.

Restricting his investigation to the plane, Huddeconsiderstherefraction of seven parallel rays by explicitly computingthepoint of intersection of these rays with the diameter of the circle parallel to the incident rays for given indices of refraction. The closer these rays get to the diameter, the closer these points get to one another until they finally merge into one point. Today, we would call this point the focal point of the circle; Hudde does not use this term.

Returning to spheres, Hudde erects a plane perpendicular to the diameter introduced above and considers the disc illuminated by the rays close to this diameter. He refers to this disc as the “focal plane”. On the basis of the same rays he used earlier, Hudde concludes that the radius of the focal plane is very small compared to the distance of the rays to the diameter. Therefore this disc could be considered as one, mechanically exact point. In other words, parallel rays refracted in a sphere unite into one point (111-112).

From this description one can immediately see a conceptual influence upon Spinoza’s initial diagram of spherical foci, and far from it being the case that Spinoza knew nothing about spherical aberration and the Law of refraction, instead, it would seem that he was working within Hudde’s understanding of a point of focus as “mechanical”. We know that Spinoza had read and reasoned with Hudde’s tract, as he writes to Hudde about its calculations, and proposes his own argument for the superiority of the convex-plano lens. And the reference to “the language of mechanics” seems surely derived straight from Hudde’s thinking. What these considerations suggest is that Spinoza’s objection to the hyperbola to some degree came from his agreement with Hudde that spherical aberration was not a profound problem. As it turns out, given the diameters of telescope apertures that were being used, this was in fact generally correct. Spinoza joined Hudde in thinking that the approximation of the point of focus was the working point of mechanical operations, and the aim of shrinking it down to a mathematical exactness was not worth pursuing (perhaps with some homology in thought to Descartes’ own dismissal of the approximations of focus of rays oblique to the axis of the hyperbola).

F. J. Dijksterhuis summarizes the import of Hudde’s tract, in the context of Descartes’ findings in this way:

The main goal of Specilla circularia was to demonstrate that there was no point in striving after the manufacture of Descartes’ asphericallenses. In practice one legitimately makes do with spherical lenses, because spherical aberrations are sufficiently small. (Lenses and Waves. Diss. 72)

Spinoza has a connection to the other main attempt to resolve the difficulty of aberration from focus using only spherical lenses, that which was conducted by Christiaan Huygens. Spinoza in the summer of 1665 seemed to have visited Huygens’ nearby estate several times, just as Huygens was working on developing a theory of spherical aberration and devising a strategy for counteracting it which did not include hyperbolas. In that summer as Spinoza got to know Huygens, he was busy calculating the the precise measure of the phenomena. In 1653 he had already made calculations on the effects in a convex-plano lens, an effort he now renewed under a new idea: that the combination of defects in glasses may cancel them out, as he wrote:

Until this day it is believed that spherical surfaces are…less apt for this use [of making telescopes]. Nobody has suspected that the defects of convex lenses can be corrected by means of concave lenses. (OC13-1, 318-319).

What followed was a mathematical finding which not only gave Huygens the least aberrant proportions of a convex-plano lens, but also the confirmation of its proper orientation. In addition he found the same for convex-convex lenses. In August of that summer Huygens wrote in celebration:

In the optimal lens the radius of the convex objective side is to the radius of the convex interior side as 1 to 6. EUPHKA. 6 Aug. 1665.

During this time the secretary of the Royal Society was writing Spinoza, trying to get updates on the much anticipated work of Spinoza’s illustrious neighbor (he was about to become the founding Secretary for the Académie Royale des Sciences for Louis XIV. Spinoza writes to Oldenburg:

When I asked Huygens about his Dioptricsandabout another treatise dealing with Parhelia he replied that he was still seeking the answer to a problem in Dioptrics, and that soon as he found the solution he would set that book to print together with his treatise on Parhelia. However for my part I believe he is more concerned withhisjourneytoto France (he is getting ready to to live in France as soon as his father has returned) than with anything else. The problem which he says he is trying to solve in the Dioptrics is as follows: It is possible to arrange the lenses in telescopes in such a way that the deficiency in the one will correct the deficiency of the other and thus bring it about that all parallel rays passing through the objective rays will reach the eye as if they converged on a mathematical point. As yet this seems to me impossible. Further, throughout his Dioptrics, as I have both seen and gathered from him (unless I am mistaken), he treats only spherical figures.

This letter is dated October 7, 1665, two months after Huygens had scribed his Eureka optimalization of the lens shape. Significantly, Huygen found that lenses of this optimal shape actually were not the best for his project of combining lens weaknesses (302-303), rather lenses with greater “weaknesses” were better combined. Several facts can be gleaned from Spinoza’s letter, and perhaps a few others guessed at. Spinoza had both looked at and discussed with Huygens his contemporary work. So the sometimes guarded Huygens was not shy about the details of his project with Spinoza. It may well have been Huygens’ treatment of the convex-plano lens here that caused Spinoza to write to Hudde less than a year later with his own calculations in argument for the superiority of the convex-plano lens, using Hudde’s own Specilla as a model. (Hudde seemed quite interested in Spinoza’s proofs of the unity of God, and the correspondence seems to have begun as early as late 1665.) What cannot be lost is that with a joint awareness of both Hudde’s and Huygens’ attempts to resolve spherical aberration, Spinoza was in a very tight loop of contemporary optical solutions to the problem. Not only is his scientific comprehension trusted by both Huygens and Oldenburg at this point, but perhaps also by Hudde.

What is striking though is Spinoza’s pessimism toward Huygens’ project. Given Spinoza’s optical embrace of spherical lenses (in the letters 39 and 40 we are studying), what would lead Spinoza to such a view he qualifies as “As yet this seems to me impossible.” Is this due to a familiarity with Huygens’ mathematics, and thus comes from his own notable objections? Has Huygens actually shared the frustrations of his experiments? Or is he doubtful because Spinoza has only a vague notion of what Huygens is doing? He seems to deny the very possibility of achieving a mathematical point of focus, though his mind remains tentatively open. His added on thought, Further, throughout his Dioptrics, as I have both seen and gathered from him (unless I am mistaken), he treats only spherical figures” , is also curious. He seems privy to the central idea that Huygens is using spherical lenses to achieve this – what other figure would it be? – but it is possible that Spinoza here qualifies his doubt as a general doubt about sphericals which he only believes Huygens is using in his calculations, showing only a cursory knowledge. Perhaps it is only an addendum of information for Oldenburg.

Huygens indeed would soon find such a solution to aberration writing,

“With concave and convex spherical lenses, to make telescopes that are better than the one made according to what we know now, and that emulate the perfection of those that are made withellipticor hyperbolic lenses” (OC13, 318-319).

I am unsure if he had come to this solution before he left for Paris in mid 1666, or if he would even have shared this discovery with Spinoza, but he also came to the same pessimistic conclusion as Spinoza held, at least for Keplerian telescopes, for his design only worked for those of the Gallelian designs which had fairly low powers of magnification. By combining convex lenses the aberration was only increased. This would be the case until February of 1669, when Huygens finally came up with right combinations of lenses.

“For from any point on an object a line can be drawn passing through the center of a circle, although for that purpose the aperture of the telescope must be made much smaller that it would otherwise be made if there were no need of more than one focus, as you may easily see.”

Again Spinoza returns to his initial point, now putting it in context of real telescopes. Such telescopes required the stopping down of the aperture, something that reduced the impact of spherical aberration; but restricting the aperture reduced the amount of light entering the tube, hence making the image less distinct. I am unsure what Spinoza refers to in “as you may easily see”, for neither of his diagrams seem to distinctly address this aspect. Perhaps Spinoza has in mind two diagrams of the eye that Descartes provides, contrasting the angles of rays entering the eye with a narrow and a wide pupil aperture. Was this a diagram which Jelles had mentioned in his response (below, left)?

Descartes diagram 17 of the eye, Sixth Discourse

 

 

Descartes' diagram 17 of the eye, Sixth Discourse

“What I here say of the circle cannot be said of the ellipse or the hyperbola, and far less of other more complex figures, since from one single point of the object only one line can be drawn passing through both the foci. This what I intended to say in my first letter regarding this matter.”

I am unsure what Spinoza means by “both the foci”, but it appears that he asserts again that because there is only one axis of either hyperbolics or ellipse available to any rays of light arriving for refraction, and that spherical lenses, again, have the advantage that rays come from any particular point of an object then can be focused to a single “mechanical point” along an available axis. Under Spinoza’s conception, this is an advantage that cannot be ignored.

Below I post Spinoza’s last diagram to which he refers with his final remarks. I place it beside Descartes diagram to which it most likely refers. This may be the most telling aspect of Spinoza’s letter, for we have to identify just what Spinoza is making clear as distinct from what Descartes was asserting.

Descartes’ diagram is a variation of as similar diagram which illustrated his prototype idea of forming a single lens made of an objective lens and a tube of water which was imagined to be placed directly upon the eye, making a long prosthetic lens, physically extending the eye. In this version he proposes that because such a watery tube is difficult to use, the tube may be filled with one large glass lens, with surfaces A and B acting as the anterior and posterior surfaces. And yet again acknowledging that the making of such a lens is unlikely, the same diagram is meant to serve as a model of an elementary telescope:

…because there would again be some inconvenience…we will be able to leave the whole inside of this tube empty, and merely place, at its two ends, two lenses which have the same effect as I have just said that the two surfaces GHI and KLMshouldcause. And on this alone is founded the entire invention of these telescopes composed of two lenses placed in the two ends of the tube, which gave me occasion to write this Treatise. – Eighth Discourse

Spinoza’s diagram from Letter 40

 

 

 

Descartes diagram 30, Seventh Discourse

“From the attached diagram you will be able to see the proof that the angle formed at the surface of the eye by rays coming from different points becomes greater or less according to the difference of the foci is greater or less.”

There are several ways to look at Spinoza’s diagram, but it is best to take note of where it diverges from Descartes’ (for Jelles would have had the latter to compare it to). The virtual image of the arrow appearing to be much closer to the eye is eliminated, presumably because the appearance of magnification is not in Spinoza’s point. The refraction of the centerpoint of the arrow remains, and is put in relation to refractions of rays coming from the extreme ends of the arrow. The refractions within the eye have been completely collapsed into an odd, artfully drawn eye, (the touch of lid and lashes actually seem to speak to Colerus’ claim that Spinoza was quite a draftsman, drawing life-like portraits of himself and visitors). Behind this collapse of the eye perhaps we could conclude either a lack of effort to portray his version of refractions into the mechanisms of the eye, or even a failure of understanding, but since this is just a letter to a friend, it probably marks Spinoza’s urge just to get a single optical point of across, and he took more pleasure in drawing an eye than he did tracing out his lines of focus. An additional piece of curiousness, which may be a sign of a very casual approach is that the last arrow in the succession, which to my eye appears to be one supposed to be in the imagination of the mind, Spinoza fails to properly reverse again so that it faces the same direction as the “real” one, although perhaps this is an indication that Spinoza thought of the image as somehow arrived within the nervous system at a point, on its way to be inverted by the imagination (though in the Ethics he scoffs at Descartes’ pituitary concept of projective perception). There is of course the possiblity that I am misreading the diagram, and the the final arrow somehow represents the image as it lies on the retina at the back of the eye. At any rate, it is a confusing addition and one wonders if it is just a part of Spinoza’s musings.

As best I can read, below is an altered version of the diagram designed to emphasize the differences between Descartes’ drawing the Spinoza’s:

The first thing to be addressed, which is not labeled here, is what C is. There is the possibility that it is a crude approximation of the crystalline humor, acknowledged as a refractive surface. If so, the upper arc of the eye and the figure C would form some kind of compound refractive mechanism approximate to what Descartes shows in his eye, here compressed and only signified. But I strongly suspect that C is the pupil of the eye, as the aperture of the telescope has been recently has been referred to in terms of its effect on the requirements of refraction, and in Descartes text there is a definite relationship between the telescope aperture and the pupil of the eye (it has also been proposed to me that C is the eyepiece of the telescope).

The primary difference though is the additional emphasis on the cones of rays that come from either end of the object to be seen (here shaded light blue and magenta). This really seems the entire point of Spinoza’s assertion, that spherical lenses are needed for the non-aberrant focus of oblique cones for a object to be seen clearly. In addition to this, the angle that these rays make at the surface of the eye (indicated) points to Spinoza’s original objection to Descartes incomplete description of what is the most significant factor the construction of a telescope.

What remains is to fully assess this conception of refraction that Spinoza holds. While it is made in the context of historic discussions of the blurred nature of the borders of an image’s perception, it is also true that such an oblique focusing must occur, however slightly, at any point exactly off from the center axis of a hyperbolic lens. It may well be that Spinoza is balancing this aberration of focus in hyperbolic lenses with the found-to-be overstated aberration of spherical focus. Given his comprehensive conception of clear mental vision -seeing more is seeing better – and its attendant critique of the Cartesian Will, given his love for the sphere, perhaps aided by a spherical conception of the propagation light come from Kepler, with Spinoza being much sensitized to the absolute impracticality of ground hyperbolic glasses through his own experiences of glass grinding, it may have been quite natural for Spinoza to hold this optical opinion…though it is beyond my understanding to say definitively so. 

“So, after sending you my cordial greetings, it remains only for me to say that I am, etc.”

This is a curious ending for such a wonderful letter. Perhaps we can assume that once again the editors of his Opera suppressed important personal details.

 

These English selections and links to the Latin text: here

The Simple Microscope in the Hands of Van Leeuwenhoek and Huygens

Spinoza’s Microscopology: a prospective comparison of context

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

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

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

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

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

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

Huygens Appropriation Further Notes and Complications

More Notes on Huygens’s New Microscope

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

Christiaan Huygens first design

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

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

Feb 21 1677 – Spinoza dies in The Hague.

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

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

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

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

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

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

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

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

Christiaan Huygenss third design 29 August

Christiaan Huygens's third design 2.9.78

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

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

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

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

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

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

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

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

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

How The Clouded Glass Sphere Becomes Opened up to Light

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

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

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

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

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

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

and various instruments for grinding (‘en verscheidene slypgereedschap’) like mills (‘molens’, also plural!) and great and small metal dishes serving for them (‘groote en kleine metale schotels daartoe dienende’) and so on” (en so voort).

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

Next I noticed his search for a polishing agent:

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

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

 

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

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

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

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

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

 

 

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.

Jan Hendriksz Glazemaker…the Glazier

Jan Hendriksz Glazemaker was born in 1619 or 20, married in 1651, and buried Dec 5 1682.

Assumed to be the translator of Spinoza’s works into Dutch, on the strength of the evidence from Duijkerius’ Philopater novel, Glazemaker is seen to be a thorough participant in the Van den Enden and Jan Rieuwertsz circle of Cartesian-Collegiant politicists. Nadler counts him, taking him as part of the Mennonite Amsterdam community, a likely friend of Jelles from youth. It should be noted as a very shallow but perhaps significant resource that, as per his adopted name, he worked as a glazier before becoming a professional translator. As a glazier, and part of a glazier family (after his step father Wijbrandt Reijndersz), he was familiar with techniques of glass making (if peripherally), sources for very good glass, and possibly spectacle makers.

(There is a history that connects the glass used for lens-grinding to the glass used for windows and mirrors. Rolf Willach in his “Development of Lens Grinding and Polishing…” reports that at least in the early part of the century, the glass used was window glass cut into circles, and deduces that three telescopes from the first decades of the 1600s used Venetian mirrors to grind into their plano-convex shape.)

Though a negligable lead in the quest for Spinoza’s early lens-grinding knowledge, because Hudde’s technique of microscope lenses was a glass-beading technique, and by one report Van Leeuwenhoek was inspired to learn lens-crafting from watching a fair glass-blower, it is something to mark.

 

A list of some of Glazemaker’s translations and their dates [Spinoza leaves Amsterdam mid 1661]

De deugdelijke vrou (1643)
Joh. Barclai, D’Argenis (1643)
Toonneel der werreltsche veranderingen (1645)
Romainsche Historien van Titus Luvius, sedert de bouwing van Romen tot aan d’ondergang van ‘t Macadonische Rijk. (1646)
Nikolous Coeffeteau, Romanische historien (1649)
D. Erasmus, Onderwijs tot de ware godgeleertheit (1651)
Homerus, De Iliaden (1654)
Descartes, Redenering om ‘t beleed, om zijn reden wel te beleiden ende waarheit in de wetenschappen te zoeken (1656)
Descartes, Meditationes de prima philosophia: of bedenkingen van d’eerste wijsbegeerte (1656-1657)
Descartes, Principia philosophiae: of beginselen der wijsbegeerte (1657)
Descartes, Proeven der wijsbegeerte (1659)
J. Lily, De vermaakelijke Historie, Zee- en Land-Reyze van Euphues (1668 )

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