Some Observations on Spinoza’s Sight

How The Two Philosophers “See”

I feel that there are some important things to say about my recent post, A Diversity of Sight: Descartes vs. Spinoza , but I am still undecided just how deep the influence of these thoughts run. So pervasive is the metaphor of vision and light within Western metaphysics, any identification of an ocular appropriation into the field of metaphysics, and the questioning of its radical truth or application, may have far reaching interpretive effects.

What may prove the advantage of this analysis is that it promotes a simplification. Like all simplifications it is misleading to take this as the whole story, but it does help us identify a core element of disagreement between the two Natural Philosophers. The difference between Descartes and Spinoza cannot be reduced to these two diagrams, of course. But there is an essential divergence in the thinking about vision as a metaphor for thought that is expressed in them. 

Descartes' Ur Image: The Hyperbola

Spinoza's Ideal Optical Eye

The first of these, for those uninterested in the optics under question in Spinoza’s letters 39 and 40, shows the capacity of a hyperbolic lens to focus any rays that are parallel to its central axis to a point along that axis. What the hyperbola provides is a schema for thinking about vision and clarity, the analogy of imagining that a focused image of the world that is “clear and distinct” is one where all the rays of a kind are brought to a mathematical ideal, poured into a point. We are not dealing here with all the details of lenses, and how they interact with the human eye and light in the fullness of their variety, but rather with a guiding diagram of what a lens should do – focus rays of light to a center point – and what that means for the experience of vision. For this reason, it is best to understand that this image for Descartes is likely intuitive of directions for investigation, steering both his theories and empirical observations.

The second of these is from Spinoza’s Letter 39, and works as a vivid contrast to Descartes’ Hyperbola. Instead of imagined parallel rays focusing down into an ideal point in the very center of the eye (which in some ways Descartes will conflate with the free Will), for Spinoza the Ideal Eye is one that in using the properties of a circle is able to focus rays parallel to a variety of axes (in fact, an infinity of axes). Rays coming from all directions are hoped to be focused across the back of the eye. And Spinoza sees the human eye (insofar as it does not have a spherical lens), as failing to achieve this kind of vision. Ideal mental vision, instead of being modeled upon a central point of focus, Spinoza conceives of as panoptical; that is, one “sees” as best as a human mind can the cross-section of rays as they converge from every direction upon the human being.

As admitted, this is truly a vast over-simplification, for much unites these two philosophers, and the kinds of radical divergences that Spinoza makes are must more diverse than this simple diagram comparison. But really there is something suggestively profound in this contrast. For one, in that Descartes’ hyperbola inheritance may be traced to Kepler’s Paralipomena its conceptual framework should be viewed as grafted from that Neo-Platonic Ideal, opening up the question of what aporias arise under such a graft (for instance, a point of focus in a Neo-Platonic realm, does not operate with the same powers or meanings as a point of focus does within a Will-driven conception of the soul). Additionally, Spinoza’s rejection of the naturalization of the hyperbola, and the analogy of center-focused human vision, has far-reaching consequences for the reading of the place of the Self in his philosophy of power and affect. If Ideal vision occurs across a field of foci, the periphery has no less a “truth” than any center. The margin does not merely, as Kepler says, “serve” the axis – so goes the critique in so many postmodern attacks on a philosophy of Presence – hence the margin is the very place where a search for truth is made, whether it be the margin of society or a comprehensive Totality of Being.

It is my hope that these two sketches of focus, one by Descartes and one by Spinoza, can help draw out the more refined differences of both philosophers, along an analogy of sight.

A Possible Influence of Diamond Polishing on Assited Lens-grinding

 

Was the horizontal grinding wheel, and the leaded-head a definitive influence upon the automatic conceptions of lens-grinding machines? Below are posted two notable examples of automatic designs, by Hooke and Hevelius, and the essential diamond-polishing design:

 Hooke, first plate Micrographia (1665)

 

 

Hevelius, Machina Coelestis, after page 433 (1673)

 

 

 

Jan Luyken, copper engraving of a diamond polisher (1690)

 

 

 

 

 

A diamond polisher, late 19th century

 

 

 

We do not have a date earlier than 1690 for the leaded-head design of diamond polishing. Whether this is a product of the the newly imported cuts (rose and Mazarin) during that century, or if the leaded-head was already natural to the design, I do not know. This juxtaposition of illustrations is just to open up the question of influence from jeweler’s wheel to lens-grinding conceptions.

What this has to do with Spinoza is that it poses the question as to the technical milieu in which Spinoza may have learned his craft, and the possible reasons for Spinoza’s resistance to assisted or automated lens-grinding machines. If diamond polishing formed any part of Spinoza’s introduction to lens-grinding, then the relationshp between the techniques of the one to the other many inform our understanding of Spinoza’s thinking.

Spinoza and Diamond Polishing?

What was Spinoza’s Relationship to the Gem and Diamond Trade

I post here a portion of a hard to find book, in the interest of establishing a baseline of information for others. Because this site has involved a variety of hypotheses on the kinds of influences Spinoza may have had, all should be sketched out as best we can. Among my thoughts as to the mystery of where Spinoza may have learned his lens-grinding craft, apart from any guild commitment, it occurs to me that he may have learned it, at least in part, through his involvement with the diamond trade. There is some evidence that Spinoza had dealings with gem dealers in the years 1655-56, in fact the scuffle and suit of Antonij Alverez shows that he and likely his family business had dealings with one of the largest Amsterdam diamond trade names, Duarte. Whether this engagement with the gem business led his curious mind into learning about the process of gem and diamond polishing from which he may have taken valuable techniques into his lens-grinding (using diamond dust as an abrasive) at this point we cannot say. All we can do is put the fact that Spinoza had unique skills, techniques and likely instruments for lens-polishing, as testified by Christiaan Huygens, and speculate if these come from an origin that would be specific to his Jewish community. These may have been techniques specific to gem polishing, a process which the Jews of Amsterdam predominately came to rule over, or they may have been specific to Jewish lens-grinding. In either case it may serve us well to lay out the facts of Jewish diamond trade during Spinoza’s young adulthood. At the very least such facts give us a broader picture of the time and place Spinoza grew up in, and one of the lathe-processes he would have at least in a cursory fashion been exposed to.

Jews of the Diamond City

The extensive quote below is from Jews of the Diamond City – Amsterdam (1988), put out by the Harry Oppenheimer Diamond Museum:

We hear of Jewish masterpolishers only from 1611 onwards. A notarial certificate from the year deals with a contract between Jewish diamond polishers who were trained by gentiles. A document dated 1615 mentions that one named Solomon Franco had finished his apprenticeship as diamond polisher with a certain craftsman named David Bolshnik. Additional sources in the first quarter of the 17th Century inform us about another dozen names belonging to Jews of Portuguese origin who were experts in diamond polishing. As a rule these craftsmen were poorer distant relatives of the merchants who imported the rough stones thus ensuring themselves employment and a decent income. For example, we know about the two famous families – Correal and Duarte de Paz – who gained their reputation as jewelers and diamond polishers in the 17th Century.

The waves of Jews who fled persecution from Germany and later the Jews who fled Poland and Lithuania after the massacres of 1648/9 lead to an influx of refugees lacking in means and profession to Amsterdam. Consequently, the social structure of the diamond industry underwent a gradual change; the Portuguese traders, the polishers and the jewelers became production managers who provided work for their Ashkenazi brethren who, to an increasing degree, constituted the working class.

In spite of the scant documentation of the period, it seems that the Portuguese Jews preferred their “Pollak” brothers over their gentile fellow-workers. It was their intention to teach them an “honorable” trade which would provide them with a reasonable income and standard of living.

copper etching, Jan Luyken (1690)

It is interesting to consider what Jews saw in the polishing trade that made it so attractive to them. On a copper engraving by the Flemish artist Jan Luyken (1649-1712) a typical diamond polishing workshop is shown. It was a rather small room, dark and stiffling. The polisher stands near the polishing wheel and places the stone on the leaden head at the end of the polishing handle. Time and again he changes the position of the stone, each time choosing a different angle on the spinning iron wheel coated with diamond dust. The rotation of the wheel is affected by a transmission belt connected to a horizontal drive wheel.

A notarial certificate dated 1615 mentions that the Portuguese Jews employed gentile women to rotated the drive wheel; this it the first written testimony to a female work force in the diamond industry.

The Jewish polishers of Ashkenazi origin who were unable to employ gentile women had to employ their own wives and children to operate the wheel. Thus, day to day, from dawn to nightfall, the whole family labored 12 to 15 hours a day to make a living.

The diamond polishers in general, worked independently and received the raw material from the diamond traders. Their wages were determined according to a variable tariff based on the weight and quality of the rough stone, the form of the finished product and the quality of his work. However, these tariffs were also subject to supply and demand…

…Among all the occupations that flourished in the Jewish quarter of Amsterdam, such as peddling, printing, dispensing and others, the trade of “Diamond-schleifer” – Yiddish and Ladino word for diamond polisher -became “The Trade.” Every Jewish mother strived for her son to learn this trade which ensured him a secure future, a good livelihood and economic independence, but, above all, great mobility on the social scale.

To become a craftsman required a very high tuition fee (69-225 florins) collected by the master polisher. The training period to be an expert in all the stages of processing in the old fashionable shapes (heart, almond, rose-cut and brilliant), lasting from 15 months to four and a half-years.

Rough stones of good quality required only few preparatory stages before the polishing process: cleaving or sawing, (dividing the stone in two), and cutting, (rounding off the base). These operations were also taught by the master and only towards the 18th century can one observe the specialization in ancillary trades connected with the polishing (44-45), (Simona Edelman).

What We May Be Able To Glean

Aside from the thin hypothesis that Spinoza have have learned something from the diamond polishers of his community, there are significant facts in this brief piece. Unfortunately the text is not footnoted, so it is unclear what is an author’s conjecture and what has foundation. There is the idea that the Sephardic Jews had learned this trade from gentiles in the early part of the 17th century in Amsterdam. Henriëtte Boas places these to be Huguenot refugee’s from Antwerp, establishing one more Jewish and Protestant Reform attachment. (Yet I have also read that these techniques likely arose through a direct transmission with India, from whence the diamonds came.) Next we have a cost and a timetable set out for learning the trade. This gives clue to a non-guilded craft relationship, and may reflect upon lens-grinding as well. It is helpful to know that in 15 months a skill such as this one could be acquired for a fee. Interesting is the shift in labor distribution in the decade leading to Spinoza’s majority, as Ashkenazi started to form a “working class” in the diamond trade. One wonders if such an influx may have also opened the door to Spinoza learning lens-grinding in his community outside of the usual transmissions of knowledge, since economic relationships were changing. Additionally, we hear of the diamond dust and flat iron wheel, a material technique not mentioned in any of the lens-polishing techniques I have read in the period. Could it be that there is some improvement offered by this means? The leaded head in diamond grinding (pictured below), actually presents a semi-automated system of grinding that pre-dates any assisted lens-grinding of the time. Could the diamond-polisher’s example, (aided by the fact that he needed to make plane-cuts, and not spherical), have been the inspiration for some of the semi-automated ideas for lens-grinding, such as those by Christian Huygens, D’Orleans and Hooke? (And, is Spinoza’s rejection of assisted polishing related to the spherical shape itself, feeling that the hand bests can feel a spherical relation?). And lastly, the wheel is quite distinct from a lens-grinder’s wheel, in that the grinding is done at the edge, and not in a bowl form. Would this kind of wheel use have helped grind certain small sized lenses? Enough with the conjecture for the moment.

Jewish polisher, late 1800s

A Diversity of Sight: Descartes vs. Spinoza

Different Foci of “Clear and Distinct”

This may be premature in my process, but I would like to set down some simple correspondences that have arisen in my reading of Kepler’s Paralipomena to Witelo (1604), correspondences that elicit strong tidal differences between Descartes’ approach to vision – with its attendant metaphysical counterpart, the clear and distinct Idea – and Spinoza’s. That this is found in some of the historically least interesting of Spinoza texts, what has been taken by many to be Spinoza’s blundering into optical theory [ letters 39 and 40 to Jelles, full text ], is suggestive of Spinoza’s critical brilliance. For within Spinoza’s conception of optics and his close-cut rejection of Descartes reasoning seem to be important radical divergences, insofar as vision and light are understood to be more than analogous of metaphysical truths. In these letters Spinoza questions the very vision-philosophy that privileges a central-line of axis, one that fundamentally connects a viewer within to an external and opposing point: a hidden, underpinning assumption of Descartes’ mathematization of the experiential self, Will and the world. Though there is much in Descartes’ philosophy that substantially departs from the Perspectiva epistemology tradition, his enthused embrace of the powers of the hyperbola embody a grounding of the eye, (and therefore the mind), in a centralized perception and knowledge upon which Spinoza places his criticism.  

I have not encountered any analysis which shows that Descartes’ enthusiasm for the hyperbola derives directly from Kepler’s Paralipomena, yet as I am not fully familiar with the literature perhaps this is a commonplace understanding. Gaukroger, for instance, gives evidence that Descartes read this text around 1620, and allows three possible points of influence, but does not speak to the potential influence of Kepler’s offer of the hyperbola as a natural normative of vision. Yet in the process of reconstructing Spinoza’s conceptions in these two letters of objection to Cartesian optics this connection with Kepler owes be fleshed out. One will see that in the Paralipomena Kepler not only sets out the virtues of the hyperbola’s anaclastic line in terms of its resolution of spherical aberration from focus – the primary and crowning demostration of Descartes’s 8th discourse of La Dioptrique – but he also naturalizes the hyperbola, claiming that the hyperbolic shape of the posterior of the crystalline humor is the very thing that helps establish the soul’s satisfaction with centered-object viewing. In fact, the wide sweep of Descartes’ metaphysics and optics in brief seems signaled by Kepler in his treatment of the hyperbola. And, because I suspect that Spinoza has Kepler’s descriptions in mind when responding to Jelles, making an argument for the importance of a radii of axes of perception, and emphasizing the importance of the angle of incidence in the measure of magnification (see letters linked above), his alternate response to Kepler provides a valuable clue to the stake Spinoza is making against Descartes, both in philosophy and science. In short, Descartes makes a virtue out of the Kepler’s description of the hyperbola and the eye, and Spinoza makes it something of a flaw or limitation. 

Setting Forth Kepler’s Hyperbola

Kepler's illustration exploring the properties of refraction, page 106

First, perhaps it is best to set out what Kepler has to say about the hyperbola so that a comparison can be made. Initially, he embraces the figure in an attempt to assess a law of refraction, which he hopes to find through the virtue of its special properties. He will not attain the law of refraction, but what he does make clear is that the hyperbola alone possesses the capacity to focus parallel rays to a single mathematical point, or vice versa. Thus, he writes of the figure above:

What is required is to say what sort of surface it is upon which these radiations in this position coming forth from α, so that they strike just as do here the lines βλ, μγ, and so on, so that these lines are either tangents to that surface, or lines equidistant to the tangents…These, moreover, are found only in the hyperbola, not in the parabola, which tends toward a straight line parallel to the axis, not one meeting the axis, as X A here. (107-108).

Not to get lost, were are simply establishing that Kepler points out the solitary characteristic of the hyperbola which will make a lens of this shape central to Descartes’ ambitions for providing aberration-free vision through hyperbolic lenses.

The next apparence of the hyperbola in Kepler’s text occurs in chapter 5, where the geometry and anatomy of the human eye is discussed. Here Kepler presents a small, simple drawing of the “crystalline humor” which behind the cornea in the eye is the primary means of focusing light. I enlarge it here for clarity:

Kepler's drawing of the crystalline humor, page 167

Kepler writes of the shape of the humor:

 On the posterior side…[the] figure is a hyperbolic cononoid, a hyperbola rotated on its axis. For [Johannes] Jessenius thus relates, that it is not spherical as [Felix] Platter said but that it protrudes markedly, and is made oblong stretching up almost into a cone; and that on its anterior face it is of a flattened roundness…(167).

Kepler has emphasized a correction. The humor is not spherical as Platter claimed, but hyperbolic, and made nearly like a cone. It is this particularity of the eye, coupled with his earlier hyperbolic observations that will create a certain naturalization of hyperbolic vision, something that speaks to the very nature of the human soul. The aspherical effect of the crystalline humor on vision is made clear a few pages later where Kepler discusses how the various cones of light coming from each of the points of an object to be seen, interact with and refract upon the cornea and the crystalline humor. What will be shown is that the humor is biased towards the production of clarity oriented towards its central axis, and that light cones that come obliquely to this angle, will appear less clear to the human eye, as they are focused to the borders of the image:

All the lines of the direct 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 cut very unequally, because where the anterior surface of the crystalline is more inclined, 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…(174)

Kepler then takes these facts of refraction and uses them to explain the experience we have of satisfactory vision. What is most notable is that Kepler wants us to understand how the oblique “more confused” images at the borders of an image actually complete and serve the focus of vision around the central axis:

…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). 

The “surroundings of the hemisphere” invite our eye from to this or that. Oblique vision proves satisfying to the soul only to the degree that it inspires the eye to turn its hyperbolically-aided central axis across its field. The concept is that the deprivation of clarity somehow drives the soul to complete its picture. This is an important point when considering the influence of vision as a primary analogy for Cartesian metaphysics.

Kepler Completes the Synthesis of Eye and Lens

Lastly, Kepler will place the facts and inclinations of vision within the context of the powers of hyperbolic focus, and he does this in such a way that it would seem sure that when Descartes looks to solve the problem of spherical aberration he would see in the hyperbola a natural bias towards centralized focus.

Kepler's illustration of the spherical aberration of rays, page 194

After a protracted investigation of the behavior of light rays in refraction through a crystal globe filled with water, and an explanation of our visual experiences of the images and confusions that result, Kepler will conclude that the hyperbola alone resolves the need for gathering a cone of rays into a single point:

Proposition 24 – Rays converging towards some single point within a denser medium are gathered by the hyperbolic conoidalsurfacebounding the medium to one single point, closer than the former point…These two things [two requirements], however, are accomplished, not by one or another circle but by conic sections…Further, of the conic sections, only the hyperbola or some line very close to it, is the measure of refractions, as was shown in Sect. 5 of chapter 4. Indeed, this very thing was demonstrated there: that the surface making all the rays outside the denser medium parallel is a conoid that does not differ from hyperbolic (198).

Given this remarkable property, Kepler then concludes that “nature’s plan” has endorsed the priorty of the hyperbola. And it seems that there can be little doubt that Descartes worked to synthesize this priorty which his own metaphysical priorty for “clear and distinct” ideas:

Hence it is evident nature’s plan concerning the posterior surface of the crystalline humor in the eye. That is, she wished to gather all the radiation of any visible object entering the opening of the uvea [pupil] into a single point of the retina in order both that the point of the picture might be all the more evident, and that the rest of of the points of the picture might not be confused by extraneous rays whether stray or gathered together. – Chapter 5, proposition 24, corollary (199).

Spinoza: “the eye is not so exactly constructed..” (letter 40)

To pull back for a moment. If this analysis is correct, that a decisive rift in Cartesian philosophy could be seen in Spinoza’s letter to a friend discussing what at most appears to be a trivial oversight on Descartes’ part is striking. Many scholars seem to have struggled over the meaning of Spinoza’s words in these letters (39 and 40) sensing that there is an elementary blunder in Spinoza’s thinking, but, as seen in their lack of a careful examination of it, there is an inability to locate just what this blunder would be. Instead, because Spinoza has been read as solely a metaphysician, his foray into optical matters in these two letters was largely dismissed as Spinoza simply wading in too deep a water. With very few exceptions, most only assumed that Spinoza was unfamiliar with the issues at stake, and his in-concordant use of terms appeared to prove this; yet a change in scholarship is occurring. Perhaps our examination of these two letters can add to this shift of perspective.

What does Spinoza mean in his letter 40 talk about the inexactness of the human eye?:

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. And therefore it is also necessary that, on passing through the glass, they should come together in as many other foci. 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 (letter 40, full text)

We have seen from Kepler that the likely reference is to the distortions of “more confused images” at the borders of vision, in part due to the aspherical, single axis nature of the eye’s lenses. This stands in contrast to Spinoza’s diagram, which he takes to be an ideal spherical refraction: 

Spinoza's diagram of the virtue of spherical refraction, Letter 39

Spinoza is extolling the comprehensive capacities of spherical refraction, and his embrace of this concept marks out a distinct divergence from Descartes’ naturalized emdorsement of a center-focused vision.  Descartes will develop a theory of clear and distinct thinking which narrows the field of mental vision. This vision is imagined to be in concert with what Nature had planned in having given the eye its own hyperobolic lens; conversely, Spinoza will take from Descartes the notion of “clear and distinct”, but the concept of vision in which it is to be deployed is dramatically different. Spinoza emphasises the clarity of a connective, hemispherical scope; Descartes is aimed at the close focus on the surest of things.

Looking With the “Mind’s Eye”

This difference perhaps can be made more distinct by considering the use of the phrase “the Mind’s eye” by both thinkers. For instance, in his Regulae, after his very influential Rule 8 [the full text of which I post and briefly engage here ], Descartes tells us in Rule 9 how we must compare improvements in thinking by attending to how we naturally see things. Human vision provides the exemplar of how of mental vision is, and the issue is one of central focus:

Rule 9: We must concentrate our mind’s eye totally upon the most insignificant and easiest matters, and dwell upon them for long enough to acquire the habit of intuiting the truth distinctly and clearly.

…We can best learn how mental intuition is to be employed by comparing it with ordinary vision. If one tries to look at many objects at one glance, one sees none of them distinctly. Likewise, if one is inclined to attend to many things at the same time in a single act of thought, one does so with a confused mind. Yet craftsmen who engage in delicate operations, and are used to fixing their eyes on a single point, acquire through practice the ability to make perfect distinctions between things, however minute and delicate. The same is true of those who never let their thinking be distracted by many different objects at the same time, but always devote their whole attention to the simplest and easiest of matters: they become perspicacious.

– Descartes, The Regulae, Rule 9

It is not without significance that Descartes in his metaphor of close focus appeals to artisans and craftsmen to praise the powers of concentrated vision. These are not a class of persons that he would embrace in society- his attitude toward de Beaune and Ferrier is well known – but their analogous use in a hierarchy of powers is in keeping with his concept of knowledge being like an ascent of mechanized complexity, from primitive mental tools to those most intricate (Rule 8, Regulae). The same artisan trope is found again in his La Dioptrique, where the limits of the eye are by craftsmen strained and improved by the exercise of ocular muscles. I quote at length below because it is an important passage. For one, it is found at the end of the 7th Discourse which is the text that Spinoza and Jelles are commenting on in their letters, and is at the cusp of his presentation of the 8th Discourse praise of the hyperbola. Secondly, here the virtue of a dispersive vision (which Kepler describes as limited by the hyperbolic shape of the lens) is denied: seeing more is not seeing better, as is testified by experience; and thirdly, Descartes treats the possible alteration of the limits of crystalline humor and pupil’s capacities as being achievable, not in the direction that Spinoza would like (tpward a more-than-human breadth of clear vision), but in terms of an exceedingly close narrowing, achieved by trained specialists:

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.

I have still to warn you that the faults of the eye, which consist in our inability to change sufficiently the shape of the crystalline humor or size of the pupil, can bit by bit diminish or be corrected through practice: for since this crystalline humor and the membrane which contains this pupil are true muscles, their functions become easier and greater as we exercise them, just like those of other muscles of our body. And it is in this way that hunters and sailors train themselves to look at very distant objects, and engravers or other artisans who do very subtle work to look at very close ones. 

– Descartes, Seventh Discourse

In the highlighted passage Descartes repeats Kepler’s summation of the benefits of a hemisphere of vision, that it simply leads to a field of vision which helps serve our central axis: Kepler: “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 “. Yet Descartes has changed the emphasis some and placed the notion of “willing” at this central axis (a literal conflation). The widening of a view only provides the occasion for free choice, which will express itself in the turning of the single axis of the eye. (It is thus clear that Descartes and Spinoza mean different things by “the faults of the eye” and “the eye is not so exactly constructed”.)

Spinoza: “so that we must not fall into pictures”

What is compellingly consistent is that Spinoza’s own use of Descartes’ “Mind’s eye” phrasing will directly address the Cartesian issue of the freedom of the will, not to mention the pictorial conception of clarity and distinctness. The phrase is most pointedly found in his Ethics, just where the distinction between willing and understanding is by Spinoza denied (E2p48 and 49):

E2p48 – In the mind there is no absolute, or free, will, but the Mind is determined to will this or that by a cause which is also determined by another, and this again by another, as so to infinity.

Scholium – We must investigate, I say, whether there is any other affirmation or negation in the Mind except that which the idea involves, insofar as it is an idea – on this see the following Proposition [49] and also D3 – so that our thought does not fall into pictures. For by ideas I understand, not the images that are formed at the back of the eye (and, if you like, in the middle of the brain), but concepts of Thought [NS: or the objective Being of a thing insofar as it consists only in Thought]; – trans. Curley

Descartes’ notion of looking with the “Mind’s Eye” requires learning what distinctness is in terms of our experience of human vision, a lesson that requires that we focus closer and closer upon obvious things, training our eye to become more and more exact, a lesson which in turn gives us to understand the centrality of the focus of a single axis, and the use of a breadthof vision as merely the field for a freedom of choices; yet in Spinoza the human eye itself is seen as “inexact” in its singular axis of focus. And looking with the Mind’s eye is for Spinoza not so much a process of learning to see clearer and clearer pictures, (or even holding one clear idea or another in mental vision), but rather learning to look in a way quite unlike the way of the human eye, within a matrix of conceptual understandings; and this matrix is one which decenters the central axis of vision (and one could say the “self”), strives to achieve something akin to an infinity of axes of vision, (nothing more than a breadth understanding of the order of Adequate Ideas and thus the causes of the phenomena we witness, and that we affectively experience). While Descartes would say, following closely our analogous experiences of human vision, that seeing more is not seeing better, Spinoza would say that one is only seeing better if one is seeing more: hence his thought moves very, very quickly to the intuition of the Adequate Idea of God.

A Difference in Method

One grasps this if one compares Descartes’ notion of method with Spinoza’s own early Emendation notion of method, which is in response to it. The below passage is important because it follows several points which bear 8th Rule influence (a focus upon human powers, viewing knowledge building like blacksmithing, for instance). While Descartes is interested in focusing the mind on simple truths which may serve ultimately to connect one to a transcendent God, Spinoza’s method is not one of focus upon this or that truth, but upon the standard of truth itself as it immediately directs one’s attention to a maximalizationof thought: a most perfect Being. It is the distinction between one kind of perception and all others, which throws the vision wide:

That is, the most perfect method will be one which shows how the mind should be directed according to the standard of a given idea of the most perfect Being…From this one can readily understand how the mind, as it understands more things, at the same time acquires other tools which facilitate its further understanding. For, as my gathered from what has been said, there must first of all exist in us a true idea as an innate tool, and together with the understanding of this idea there would likewise be an understanding of the difference between this perception and all other perceptions. Herein consists on part of our method. And since it is self-evident that the more the mind understands Nature, the better it understands itself, it clearly follows that this part of our method will become that much more perfect as the mind understands more things, and will become then most perfect when the mind attends to, or reflects upon, the knowledge of the most perfect Being. (trans. Shirley 39)

The web of truths that “Mind’s eye” vision focuses on is a breadth of vision, governed by a comprehension of determined causes. And in a sense, this begins with God, God as a totalizing reality of Being from which we are not separate. A field of vision, which for Descartes provides an array of choices which an axis-eye then willfully judges and picks its way through, for Spinoza is an incandescent weave of causes and effects, any adequate understanding of which leads to all others. It is a spherical conception of a refraction along an infinity of axes, in which the Will plays no part.

Descartes’s Hyperbolic Doubt and Hyperbolic Lens

In considering Kepler’s introduction of hyperbolic lenses and his Nature’s single-axis plan for the eye, and then Descartes synthesis of the two, there is the happy result of support found for a contested interpretation of Descartes offered by Graham Burnett, in his book Descartes and the Hyperbolic Quest . Professor Burnett offers that Descartes’ obsessive, mechanized pursuit of the grinding of a hyperbolic lens, and his project of legitimatizing his Natural Philosophy through “hyperbolic doubt” are something more than a mere conflation of uses of the word “hyperbolic”. Burnett tells us, citing Gaukroger’sbiography, that the two may correspond to a single conception of mind, (quoting at length):

What configuration of mind of mind allows natural light to coalesce into a clear and distinct idea? The answer…is hyperbolic doubt. If once we saw, as in a glass darkly, and if at some (beatific) point we will see face to face, for the time being the best we can seem to do is to see through the right kind of glass that one that does not distort or obscure: and this just might be, at least least initially, the focusing glass of hyperbolic doubt. To play out the suggestion then: Descartes greatest scientific success lay from his perspective, in his systematic investigation of optics and the perfection of human vision those investigations promised; his optics presented an instanteous light that could be focused into clear and distinct images by means of the imposition of ahyperbolic form. Descartes’ greatest philosophical success lay, from his perspective, in a systematic investigation of the human mind and the perfection of cognitive operations those investigations promised; that the human mind received, via natural light of reason, an instanteous, clear and distinct illumination, but only by means of the interposition of another hyperbolic focusing device – the hyperbolic doubt.

I do not wish to overemphasize the signification of the parallelism, tantalizing as it is. Following Gaukroger’s reconstruction of Descartes’ psychology [Descartes, an intellectual biography ], a quite elaborate extension of the hyperbolic (lens)/hyperbolic (doubt) analogy would be possible. In Gaukroger’s reading, the imagination mediates between the pure intellect and the realm of the senses, and the experience of cognition inheres in this intermediate faculty, which represents the content of the intellect and the content of the senses both as “imagination.” Where these two map onto each other the experience is that of “perceptual cognition.” As the project of hyperbolic doubt is abundantly imaginative, and as Descartes has insisted that the natural light of reason does not stream down from God but is within our intellects, it would be possible to argue that the imagination plays the role of the focusing of the hyperbolic lens, and receives the light emanating from the intellect, which normally enters the imagination confusedly, quickly distorted by the “blinding” profusion of imagery from the senses (126-127).

Indeed, if we follow professor Burnett’s conclusion, and allow it to have a substance greater than mere lexical coincidence, we find that when armed witha knowledge of Kepler’s antecedent approach to the hyperbola such a reading begins to cohere. Descartes’ embrace of Kepler’s hyperbola of the human eye shows that “extreme doubt” and the focus of the Will that it accomplishes is for Descartes truly both a mechanism for focusing the mind upon simple truths and a naturalized legitimization of a will-centered, single axis organized perception. What professor Burnett intuited through his study of Descartes’ life-long pursuit of an automated, hyperbolic lens-grinding machine, is given traction when the genealogy of Descartes’ conception of the importance of the hyperbola is traced back to Kepler, its orgin. And this is exposed in two almost-ignored letters written by Spinoza on a subject he long had been considered deficient in, as the force of Spinoza’s attack upon both Descartes’ metaphysics andhis optics is to be considered as being of one cloth. Spinoza has Kepler in mind because Descartes had Kepler in mind. This is suggestive of the power of Spinoza’s critique, and the level at which he carried it forth. It touched not only the abstraction of Descartes’ metaphysics, but also the optical-theory origins of Descartes preoccupation, that human vision was somehow naturally hyperbolic and therefore offering a guide toward the perfection of the mind. Because our inheritance of the optical trope of human vision is so rooted in our conceptions of the world, and our acceptance of Descartes’ approach to thought and mechanism is so pervasive, Spinoza’s optical critque proves promising of a radical importance at the very least.

Lasting Questions

None of this goes any distance toward proving whether Spinoza’s critique of Descartes in letters 39 and 40 was correct in the terms he meant it by, speaking of how light and lenses behave. Clearly Spinoza was well informed about the nature of Descartes’ claim as to the importance of the hyperbola. He had read and followed Johannes Hudde’s Specilla circularia, which dismissed the importance of spherical aberration in a mathematically exact way, minimizing Descartes’ impractical solution; and he was likely familiar with ChristiaanHuygens’ own complaints about Descartes’ failures in treating telescope magnification accurately. Additionally, it seems quite likely that Spinoza was familiar with the Ur-source of Descartes’ own embrace of the hyperbola, Kepler’s Paralipomena to Witelo, since he addresses specific terms of its explanation, and the argument he presents in brief cuts to the quick of the virtues of the hyperbola presented there: the idea that the human eye’s hyperbola somehow expresses Nature’s plan which in Cartesian hands would naturalize a priorty of a single-axis, will-driven priority of focus and choice. By arguing for the “inexactness” of the eye, Spinoza is undermining a primary vision/knowledge metaphor which helps form part (but most certainly not all !) of Descartes’ metaphysics of clarity.

There are therefore a few questions that remain. For one, Kepler does not merely serve as a source for a negative critique of Descartes, insofar as he has followed Kepler. For instance Kepler’s conception of light in many ways diverges from Descartes’, and could be said to have concepts which presage Christiaan Huygens’ own wave theory, which would eclipse Descartes’ optics. It remains to be seen if Spinoza’s optical understanding stems directly from Kepler in a positive sense, that is, if Spinoza’s holds optical concepts which were superior to Descartes’ theories due to Kepler’s influence. Spinoza has used Kepler to undercut Descartes’ metaphysics, but where does Spinoza stand in terms of contemporary optics? For this to be answered, Spinoza’s praise of the versatility of an infinity of axes has to be set up against the contemporary science of telescope construction. For though Descartes’ hyperbolic lenses were nearly impossible to make at that time, in theory at least they would have offered an advantage. Spinoza’s objection is that Descartes is incomplete in his analysis of magnification, and that the capacity of a lens to handle a variety of axes is important in compound telescope magnification. Such a possible importance remains unaddressed, though all existing telescopes obviously achieved their magnification without hyperbolic lenses (and notably, Christiaan Huygens had privately solved the issue of spherical aberration using only spherical lenses in the summer of 1665, when Spinoza and he were closest).

The other question that remains is to determine the large scale consequences of Spinoza’s rejection of a naturalized, single-axis concept of hyperbolic vision, upon his own preoccupation with lens-grinding and instrument making. The grinding of a lens, after all, is exactly the kind of “craftsman” or “artisan” practice that Descartes lauded in his 9th Rule, one that lead to an acuity of vision. The purpose of a lens is most often to achieve a magnification which concentrates the vision at a local point. And this is the mode of narrow focus to which Spinoza seems to making his objection. But if we allow the analogy between craftwork and mental tools found in the works of both Descartes and Spinoza, the careful refinement of a proposition, such as those found in Spinoza’s Ethics, would be read as a kind of development of perspicuity. Permitting the Ethics to stand as our model for complex, intricate knowledge, by analogy any grinding of glass into a polished shape must be seen as part of an interlocking of all other actions, ideas and material states; for just as there is extensive cross-reference in Spinoza’s Ethics, Spinoza’s own daily preoccupation with lens-grinding and instrument building must be seen as cross-referenced to an infinity of other causes and actions, all leading to an theorized increase in freedom. As Spinoza clarified a piece of glass and made it capable of magnfication, was it that he was concerned not just withthe the lens, but how this magnification fit with other lenses, in devices, with phenomena to be discerned, and the Ideas we hold as we use them? It would seem at that this is so, but this question has to be answered more fully.

 

 

An origin of Spinoza’s “cones of rays” explanation, Letter 40

[addendum: in addition to these thoughts, the influence of a more recent source, James Gregory’s Optica Promota (1663) has to be considered]

Kepler and How Spinoza Viewed the Eye and Light

As a point of reference it is important to locate the origin of Spinoza’s phrase “cones of rays” found in his letter 40, since implicit in this phrase is likely the conception of light and refraction which would help us make sense of his objection to Descartes. This phrase has a history of what seems a bit of interpretive confusion, for instance, that expressed by Alan Gabbey in his Cambridge Companion to Spinoza article, “Spinoza’s Natural Science and Methodology”. Here professor Gabbey quotes the phrase as if it embodies the locus of Spinoza’s befuddlement:

Spinoza explained that light rays from a relatively distant object are in fact only approximently parallel, since they arrive as “cones of rays” from different points on the object. Yet he maintains the same property of the circle in the case of ray cones, apparently unaware of the importance of the “[other] figures” [the famous “Ovals of Descartes”] that Descartes had constructed in Book 2 of La Géométrie to provide a general solution to the problem of spherical aberration [Ep 40].

I have already pointed out that Spinoza indeed was not “unaware” of the “importance” of Descartes’ figures (since he was intimate with the debate over that importance), and that part of Gabbey’s difficulty may stem from a weakness in translation, or not taking into account Spinoza’s familiarity with Hudde’s Specilla circularia: here. Spinoza, all the same, is constructing an argument that seems to shift parameters. In Letter 39 he speaks of the capacity of spherical lenses to focus parallel rays to an (approximate) point of focus opposite, along an infinity of axes, and now he tells Jelles that this capacity is to be understood not for parallel rays, but for “cones of rays”, which is more accurate to what is actually occurring. Where does Spinoza get his conception of “cones of rays”?

I believe it is found in Kepler’s Paralipomena to  Witelo (1604), a work I am beginning to suspect holds some of Spinoza’s resistance to Descartes. Descartes called Kepler his “first teacher” in optics, so when there is a divergence between the two, Kepler and Descartes, one may perhaps look to Kepler as a source for other resistance to Descartes’ conclusions. (It is a mistake to assume that solely in terms of temporal advancement, all of Descartes deviations from Kepler are corrections, for in some ways Kepler held views antecedent to our better conceptions on the nature of light.) In letters 39 and 40 Spinoza is critiquing Descartes explanation of how image size is produced in telescopes, and he finds in Descartes’ explanation some delinquencies which give undue favor to the hyperbola. Where Spinoza likely draws his conception of “cones of rays” is where Kepler is discussing the manner in which images are formed in the human eye:

Now in order to approach closer to the way this picturing happens, and to prepare myself gradually for the demonstration, I say that this picturing consists of as many pairs of cones as there are points in an object seen, the pairs always being on the same base, the breadth of the crystalline humor, or making use of a small part of it, so that one of the cones is set up with its vertex at the point seen and its base at the crystalline (though it is altered somewhat by refraction in entering the cornea), the other, with the base at the crystalline, common with the former, the vertex at some point of the picture, reaches to the surface of the retina, this too undergoing refraction in departing from the crystalline. And all the outside cones come together at the opening of the uvea [pupil], at which space the intersection of the cones takes place, and right becomes left..

…[now speaking of a single cone of those cones of rays] Thus those rays which previously were spreading out in their progress through the air, are gathered together now that they have encountered in to the cornea, so much so that any great circle described by those rays upon the cornea, which in their decent touch the edges of the opening is wider than the circle of the opening of the uvea; however, these rays, all the way to the opening of the uvea, are so strongly gathered together through such a small depth of the aqueous humor, that now the edges of that opening are trimmed of by the extremes, and by that decent they have made illuminous a portion on the surface of the crystalline humor, if indeed they all have first arisen at a point at a certain and proportionate distance (which is pecular to each eye, and not just the same for all), they fall approximately perpendicularly, because of the similar convexity of the cornea and the crystalline humor. (trans. Donahoe, 170)  

Included in this reference is also the obvious fact that for an object to be seen, light from all its points must be gathered. It is part of Kepler’s picture:

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

Because Spinoza is arguing that the hyperbolic lens – designed to receive rays solely parallel to its one axis – is insufficient for the variety of angles at which light arrives, the question of parallel or coned rays does not seem germane to his argument. His emphasis in the original description seems meant to be in terms of axes, assuming a “mechanical point” of focus definition. (Whether it is ultimately germane to contemporary telescope construction is another question.)

It must be noted, though here is both a most significant implication of the cone of light having a spherical (wave?)front, something ungrasped by Descartes but captured later by Huygens, in the text that follows as Kepler closely describes this action of cones of rays in the eye, he emphasizes the “hyperbolic posterior surface of the crystalline” (171), possibly disturbing the cohesion of Spinoza’s purely spherical ideal of light refraction. If indeed Spinoza is taking Kepler’s description as his source, this gives us to consider how Spinoza might mean the inexactness of the construction of the eye (letter 40). In what way can the eye be considered imperfect, and is there a Kepler source for this notion?

Spinoza writes: “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.”

There is an antecedent to this in Keplers’ description of the action of rays as they come from cones at angles oblique to the axis of the cornea:

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 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…

…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). 

Here Kepler seems to be making the exact same point as Spinoza, with an additional hint towards the necessity of the oblique in Spinoza’s concern. The construction of the eye, in so far as its lenses are aspherical, it is retarded its capacity to handle the focus of cones of rays oblique to its single axis. This first calls our attention to the limits of human vision (in individuals and in plan), and then suggests that Spinoza’s point is one of practical application in terms of lenses: that in aiding human vision and constructing telescopes, the symmetry of spherical lenses is preferred for magnification, handling a greater variety of angles of incidence through its infinity of axes.

This does not of course establish the veracity of Spinoza’s argument, but in locating a likely origin for Spinoza’s conception, we at least place Spinoza’s argument within the context of a larger view, to be weighed with all other anti-hyperbolic (Cartesian) positions  of his day (Hudde, Huygens). As I have said, it is my sense that Spinoza derives more than this from Kepler’s account of light. More posts to follow.

Descartes’ 8th Rule: A Spinoza Touchstone

Rules For the Direction of the Mind, gives clue to Spinoza’s concept of the instrumentation of knowledge

I post here Descartes’ 8th Rule from his Regulae, as a marker to important influences upon both Spinoza’s philosophy in general – it contains the seeds of his argument for Three Knowledges, for instance – and his approach to technology, as it possesses the analogy that knowledge production is like the development of blacksmithing. This is not to mention the inclusion of possible paths to the discovery of the importance of the anaclastic, significant for the subject of Spinoza’s objection to Descartes’s claim for the importance of the hyperbolic lens. I highlight the relevant places of correspondence:

Full Text of the 8th Rule with Annotations and Highlights

Rule 8: If in the series of things to be examined we come across something which our intellect is unable to intuit sufficiently well, we must stop at that point, and refrain from the superfluous task of examining the remaining items.

The three preceding Rules prescribe and explain the order to be followed; the present Rule shows when order is absolutely necessary, and when it is merely useful. It is necessary that we examine whatever constitutes an integral step in the series through which we must pass when we proceed from relative terms to something absolute or vice versa,

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

Some Rough Thoughts On Spinoza and Technology

The Free Hand

Christiaan Huygens's assited lens mechanism

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

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

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

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

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

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

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

This comes in view of past thoughts on this issue:

To Understand Spinoza’s Letter 32 to Oldenburg

Spinoza’s Comments on Huygens’s Progress

The Rijnsburg Lathe: Like the Sun, not 200 Feet Away

Mystery Solved: Rijnsburg Lathe, a 19th Century Woodturner’s Lathe

Stan Verdult over at the excellent Spinoza site http://spinoza.blogse.nl/ has done excellent research and unearthed the origins of the Rijnsburg lathe, which for some reason the Spinozahuis seems to have been less than forward about. He has uncovered a 1984 Bulletin which tells us that H.G. van de Sande Bakhuyzen who was at that time [±1899] director of the Leiden observatory made an inquiry into the buying of the cutting lathe from a wood turning shop (houtdraaierij) at Leiden, the name (“Dusoswa”). The device had been used for a long time and was to some degree worn out. For a time it was held in the foyer of the observatory before it was taken to Rijnsburg. Without any doubt it is a product of the nineteenth century. It appears to be in mechanical form, less like any grinding lathe Spinoza may have used, and more like a woodturners lathe, used for carving [the above description is my wide paraphrase from Stan Verdult’s most generous rough translation of a portion of the article for me].

Here is an article portion, for those that read Dutch:

I post here my response to Stan Verdult’s call that the lathe should be removed. It makes such an interesting case for those that take Spinoza’s philosophy seriously. Spinoza’s central distinction between Rational and Imaginary knowledge comes into view. The useful impression that the lathe was authentic is part of a museum’s theatrical powers, the attempt to re-create many of the associations that one would have, that Spinoza must have had when walking into that room. In a sense, the “inauthentic” lathe (IS it inauthentic?) delivers many of the affects that an empty room could not. Is this a knowledge that Spinoza would favor?

My posted comment at Stan’s site:

I loved what you have said about the lathe. This is wonderful research. And I do question why the Spinoza house has not been more forthcoming about the nature of its exhibit. But if you are recommending that the lathe be removed from the Spinozahuis in September I’m not sure that that is a good idea. First of all, the lathe gives a strong sense that Spinoza himself worked at lens-grinding. It creates an impact that is important. One should only take it out if there was another that would replace it (which may not be more authentic: perhaps if it was modeled on an image from Hevelius for instance this would be an improvement, but still it would only a guess). Secondly, the lathe there has become a bit iconic. It forms a large part of the visual memory of the house for those that have been there over the years. An empty room would not do. The big problem is that it is not properly labeled. One should simply know that this is a 19th century woodturner’s lathe, just meant to give a general idea, an impression. Lathes in the 19th century had not progressed much from the lathes of the 17th century, and it seems likely that Spinoza used a lathe that was fairly simple in design. (The semi-automatizing “improvements” of savants like Christiaan Huygens were not necessarily seen as improvements by Spinoza: see Letter 32). The odd thing is that the story you have uncovered is a fascinating one. It reveals the texture of the Spinozahuis itself, its living history, the way that history is made. A museum simply does not exist “sub specie aeternitatis”. Revealing how the lathe got there, and acknowledging its role in the living history of the museum would actually direct our attention to some of the more important features about a house trying to keep the memory of Spinoza alive, that history is an effort and a narrative. The important thing is for the exhibit to be clear, and when it is not clear, accurate, I would think.

With the 400 year anniversary of the telescope coming to Middelburg in September, this would be a natural time to emphasize the Spinozahuis lathe’s history, and to organize additional information around the piece letting others become more aware of Spinoza’s commitments to optics, not a small portion of his life.

Spinoza writes of the sun, “when we look at the sun, we imagine it as about 200 feet away from us, an error that does not consist simply in this imagining, but in fact that while we imagine it in this way, we are ignorant of its true distance and the cause of this imagining. For even if we come to know that it is more than 600 diameters of the earth away from us, we nevertheless imagine it is near. For we imagine the sun so near not because we do not know its true distance, but because an affection of the body involves the essence of the sun insofar as our body is affected by the sun” (E2p35s).

The Spinozahuis imaginary presentation of a lathe in a taken-to-be authentic environment provides an interesting case of the theater of the past. We want to affectively feel what the past was like, and part of feeling that is knowing the facts of the past. Though our affective affinities the Spinozahuis lathe communicates many of those facts in a most imaginary way, the wood in its size and geometery speaks to us, and this is important. But if we are to be freed, in a Spinoza sense, our affects must be coupled with knowledge, the tracing out of that tenuous line to the past, one that might mitigate from moment to moment our imaginary composition, but will not diminish it altogether. The sun will still appear to be 200 ft away, and the sun will still rise up out of the sea, even though we know that it does not. But we will be free to know why it does these things.

What Spinoza and Huygens Would Have Seen that Summer Night

Telescoping with Spinoza and Christiaan Huygens

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

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

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

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

from Lubinetski’s 1667 treatise Theatrum Cometicum

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

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

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

The Huygens Estate in Voorburg