Frames /sing


Category Archives: Spinoza’s Foci

Infinitely Narrow: How Spinoza Corrects Descartes’ Lenses

Corry Shores has another nice post up in his series on my study of Spinoza’s optical theories and practices. He is the only person, as far as I know, who has made an attempt to read through the whole of my study and it is with great appreciation to find my thoughts reflected there. Here, 6: Seeing Differences between Descartes and Spinoza. Some Observations on Spinoza’s Sight. [The Kvond Spinoza’s Foci Summary Series], he points out a power conceptual, and pictorial difference between Descartes and Spinoza. In my understanding it is hard to over estimate just how pervasive Descartes’ optical metaphor for consciousness and methodology for clarity became, in particular when it was grafted onto by Idealist notions of fundamental intentionality, self-hood, and subject/object duality. Spinoza’s correction to the hyperbolic lens, the lens that Descartes felt would unlock all the powers of clear, nearly unlimited vision to man, stands at a fundamental cross-roads in the history of philosophy, noting the turn-out where modernity could not branched off from the Idealism it followed.

This contrast between the narrowly clear and self-evident, and the broad spectrum, comprehensive intuition of a whole makes an interesting contact point to a discussion Carl Dyke and I have been having over at his blog, on the Infinity Standard (something he regards as an unhealthy societal influence), Existential infinity. Descartes envisioned an infinity as well, an infinite power developed upon the tunnel vision of narrow band precision of clarity, ultimately founded upon the notion of the “self” as indubitable. While Spinoza wanted to say of lenses, of eyes, and ultimately of consciousness, whenever we are perceiving something clearly it is always because we are already perceiving the vista of what lies beyond it. There is no narrow clarity that supersedes and establishes the role of the margin. In fact, as is the case in criticisms of philosophies of Presence, it is always the margin, the ground, that allows the narrow, bright center to have importance, or even substance at all. As I have mentioned before, recent concerns about objects and their centrality are grown out of the image of clear centrality itself, something that comes out of Descartes’ optics, and as I tried to show, Kepler before him.

We do not realize how much our folk and philosophical conception of consciousness and the world is governed by a metaphor of tunnel vision.

A related post: The Hole at the “Center of Vision”

Spinoza and Optics and Pirates

I see now that Corry Shores has put up a reading, and mutual expression of some of my work on Spionza and Optics, “Spinoza’s Foci for Deleuze’s Attraction”. I have to say that I have not read it yet (for sometimes I savor/reserve the first reading of a text for a generous moment, for when you first enter into a thought-space associations and inference trails occur that are highly valuable, and may not occur again), but by all cursory scans, it is the very first close reading of my research, and I can’t wait to see what he says. Read it before I do.

Spinoza’s Optical Letters: Redux

As some know, primarily last summer I spent my time researching and theorizing on Spinoza’s lensgrinding and optical concepts, a largely underdeveloped field in Spinoza studies. The greater portions of my findings are listed here on this site under the sub-heading Spinoza’s Foci. A spearpoint of this research was uncovering the substantive arguments and conceptions that lay behind Spinoza’s rejection of Descartes’ optics, as found in his two letters 39 and 40, letters that have be nearly completely ignored by commentators on Spinoza, or if address, addressed in what seems a delinquent, or dismissive fashion. Spinoza is mostly thought to not know what he is talking about. On the other hand, Spinoza’s objections if carefully examined reveal both technically an alternate position on the problem of “spherical aberration,” but more deeply, a radically distinct conception of what vision is, in particular how it works as an insufficient analogy for consciousness. While Descartes wanted to emphasize the power of the central clarity powers of hyperbolic vision (both in the human eye, and in his proposed lenses), Spinoza understood vision and conciousness both as holistic events, ones best approached with the pragamatic appreciation of our limitations. I provide very little philosophical extrapolation here, though the implications are vast, perhaps running through down to the root of Idealism and Phenomenology. This epistolary commentary also does not touch on such other important factors such as the kind of lathe Spinoza likely used, nor much on his likely technique, and kinds of instruments he made and calculated for, which form a significant secondary branch of my research. Yet as these letters remain nearly the only first hand statement Spinoza made on optical matters, they are the anchorage point for anything else that is likely to be asserted.

For the convience of interested readers I here post a Word document version of my line-by-line explication of these rarely read and rather under-interpreted letters. I realized that the previous weblog versions were very difficult to read and browse through, hopefully something this version will correct. The two entries that can be found in this document are: Deciphering Spinoza’s Optical Letters and  Spinoza: Letter 40 and Letter 39. These are both the English translation of the two letters by Spinoza, and then my explication. This version is not footnoted (though there are citations), and it retains some of the idiocyncratic paragraphing and color coding. It is a 14,000 word document (48 pages), though Spinoza’s letters are only 900 words or so.

[click download]: Deciphering Spinoza’s Optical Letters Line by Line

Evidence toward the nature of Spinoza’s Lathe(s)

Writing an email today to an interested party I found myself running over the evidence that Spinoza used either a hand driven lens-grinding lathe, or one of the springpole variety, such as the Hevelius lathe (Selenographia, 1647). It seemed best to briefly summarize them hear, as though the evidence is scant, it is not non-existent. I have already written briefly on these two lathes here: Spinoza’s Grinding Lathe: An Extended Hypothesis ; Spinoza’s “Spring Pole” Lathe: Experience to Metaphysics and Back

1. The auction of Spinoza’s estate held nine months after his death (4 Nov 1677), accounts for more than one “mill” (mollens). If such mollens are taken to be grinding lathes, it shows that he had more than one, likely for more than one purpose (telescope/microscope; grinding/polishing). It is also very possible that the estate had already lost a number of its items by the time of the auction.

2. Spinoza is generally assumed to have been tubercular. While in remission the disease may not inhibit the stenuousness of activity, when manifest any grinding lathe that would greatly reduce exertion would seem almost necessary. A springpole lathe frees the hands, and allows the larger leg muscles to bear the burden.

3. There is some evidence that Spinoza did work on larger telescope objective lenses, ones that would require heavier iron grinding forms, less conducive to a hand-driven lathe. For instance, Huygens writes his brother in reference to calculations Spinoza had done for a 40 ft. lens (in collaboration with J. Hudde), and ten years after Spinoza’s death, Constantijn Huygens writes of using a 42 ft. Spinoza grinding/polishing form (I have not checked the primary source on this yet, OC IX p. 732) which worked so well that he did not have to lift the lens from the glass to check it for blemishes even after an hour straight of use (suggesting a fixed-glass, hands free devise).

4.Christiaan Huygens at several points in his letters to his brother refers to Spinoza’s championing of small spherical lenses for microscopes. If these are not unground spherical bead-drop lenses, then these would be the kind that required very precise grinding and polishing. One can certainly imagine that hand-driven grinding lathes would be more suitable for this kind of work.

This rough sketch seems to suggest a combination of grinding and polishing lathes were used. Spinoza in his criticism of Huygens’ semi-automated grinding lathes, and artisan concern for basic tried techniques, does strongly advise that whatever Spinoza’s lathe designs, they were of a simple, efficient design. He did not appreciate speculative mechanical experimentation, at least not for its own sake. One imagines that his springpole- and/or hand- lathe was of a tried and true fundamental design, though from Huygens’s comments on Spinoza’s polishing techniques, it does appear that he possessed distinctive techniques which were either discovered by himself as a inventive craftsman, or were from a source not commonly available to others.

A Look Back for a Moment, The Hole of Spinoza’s Vision

Right now I’m busy composing my Cabinet article, a result of this width of research I have done. Part of this process is looking back at my various conclusive essays to see where I have gotten. There is one that really struck me as a signficant reduction of the kinds of philosophical conclusions that can be drawn from my study of Spinoza’s optical endeavours, in particular pointing out how deeply he diverged from Descartes who preceded him. I repost it here for anyone else’s pleasure, for I read it again this morning and was really moved by its import (sometimes it is like that, one forgets what one wrote):

here: “The Hole at the Center of Vision”

Comments are of course appreciated


Spinoza’s Circle and the Interior

Some Ruminations on Spinoza’s “Simplest” Thought

A single figure keeps returning to me as I contemplate Spinoza’s optical concepts and metaphysics, in view of the prevailing Cartesian science of the age, that elementary figure that Spinoza provides to help explain how he conceives of the reality of the modes, even the modes of ideas for non-existent things, in relationship to the ultimate reality of Substance, God or Nature. As Spinoza explains, the figure stands for something that has not parallel, not example, because it is a fundamental relationship which is unique and totalizing.

Ethics part 2, prop 8 schol. — 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. Let us grant that, from this infinite number of rectangles, two only exist. The ideas of these two not only exist, in so far as they are contained in the idea of the circle, but also as they involve the existence of those rectangles; wherefore they are distinguished from the remaining ideas of the remaining rectangles. (Elwes trans)

This has always been a convenient image for the explanation how the modes dependently are an expression of the totality which is all of what there is. One practically sees how the modes, while causally interacting with each other to produce current states of being, immanently rely upon a larger comprehesivity. And if one wants to even leave off from the narrowness of Spinoza’s explicit thought, the chords D and E could be read as vectors which produce an intersecting point (unlabeled), the modal expression of two lines of force, a point of focus, this seems at least arguable when considering much of the rest of Spinoza’s view.

But two other realizations come to me as well. The first is that the rectilinearitythat Spinoza presents within the borders of the circle very well may for Spinoza have represented the linear analyses of motion provided by Descartes. Part of the challenge presented to Spinoza, as he tried to heal a perceived breech between Body and Soul, Thought and Extension, was how to bridge mathematical descriptions with affective realities. In a certain sense the rectilinearity with the circle of Substance for Spinoza represents the ideational crispness of mathematical description understood as a partial, yet sufficient expression of substance. The mathematics is to some degree subsumed. Just as Huygens and others struggled to assume the advantages of the Perspectiva  tradition in optics, yet still fully explain the properties of light’s propagation (which Huygens would show to be that of a wave or a pulse), Spinoza too sought to preserve the mechanized sureties of Descartes mathematizations, yet with a view that could account for the affective propagations living bodies (as early as Kepler’s Paralipomena light is described as an “affectus”).

Secondly though is the realization that the circle does not only represent Substance as a whole, but also any conatus expression of Body (defined by Spinoza as a preservation of a ratio of motion and rest over time). The circle above can also be read as the recursive coherence of a body, and the internal causal relationships of which it is composed, immanent to its essence. 

In other words, a body, in the ordinary as well as in the Cartesian sense, preserves its physical integrity in just the same way the whole universe preserves it: they differ only with regard to the degree of probability that each can ‘survive’ externally caused modifications. Only the unique individual of level-ω can be modified in infinite ways without giving up its identity.

The Physics of Spinoza’s Ethics, David Lachterman

What level-ω is in Lachterman’s nicely conceived reduction is the last border of an entire body. Level-2 is the most elementary kind of body for Spinoza, a hypothetical composition of what one supposes is at least two of the most simple bodies “corpora simplicissima”. The human body, and all such bodies we regularly recognize as such are what Lachterman regards as level-k bodies (2 < k < ω). Following these descriptions, the circle above from the Ethics could be read not only as the schema of the level-ω Body, but also of any typical level-k Body. It is only the degree of power, freedom and being that preserves such a circle (ratio) that distinguishes it from the ultimate whole. Spinoza world can be seen as one of circles within such circles. The modal causal interactions are immanent expressions not only the totality of Substance or Nature, but also are expressions of the ratio of motion and rest of which a said body (level-k) is composed. The existential modality of ideas and extensions which is interior to the circle (level-k) can be read as contingent to the essence of that Body taken as a whole, as it is determined to exist.

While it is fair and best to understand the diagram exactly in the way that Spinoza meant it, I think it is important to realize that in a figure such as this, representing something for which Spinoza says there is no parallel, the image is likely overdetermined by several other Spinoza concerns and conceptions. The circle and its interior floats through Spinoza’s thinking process (additionally). The diagram can be read across at least these two layers: the affective subsumption of Cartesian mathematicization of Nature in terms of propogating, interacting bodies; and, the immanence of constituent modes of bodies under gradations of Being and power. And I would end that the suggestive recursivity of this body (level-k) opens itself perhaps to Autopoietic descriptions, at least for those bodies considered to be alive, and Autopoiesis itself to Spinozist re-description.

Spinoza’s “Spring Pole” Lathe: Experience to Metaphysics and Back

Spinoza’s Practiced Knowing

I mentioned in my recent post on the likely design of Spinoza’s grinding lathe that the dynamics of the Hevelius’ spring pole lathe may be tied to Spinoza’s ideas of Substance and the modes, such that one would be able to see how the epistemo-kinetic experiences Spinoza had during his many hours, days and years of lens grinding on such a lathe may have bore influence upon his metaphysical conceptions.

Here I want to take up this intuition, and perform the appropriate visualizations that would allow us, if for a moment, to picture what Spinoza’s body went through in communications with his device. In this way we might place ourselves, materially and affectively, in a relationship to his ideas, such that reading them alone in text would not allow (even if this goes against what one could argue is Spinoza’s rationalist program of understanding). That is, in short, one hopes to understand through body and affect what ideas Spinoza thought at the most abstract of levels, through their causal origins; for we can follow what Spinoza wrote, “experience can determine our mind to think…of certain essences of things” (Ep. 10), and assume that a similiarity of experiences may determine us to think of a similarity of essences. If we attain the experiences Spinoza underwent which determined him to think of certain essences (in his terms), this I believe can provide clarification to the same thoughts reached through his geometric pedogogy alone. 

The Horizontal and the Vertical: An Initial Philosophical Platform

Further below is an illustration of the tension dynamic of a spring pole lathe, as taken from Hevelius (second diagram). But first in order to follow my thinking here I want to insert a most revealing point made by Gatens and Lloyd in their critique of Hegel’s critique of Spinoza. As they point out, Hegel, while in great praise of Spinoza, felt that he did not embrace the full reality of the “negation”, Hegel’s personal contribution to the progress of philosophy and mankind. Spinoza’s description from Hegel’s point of view simply collapses into an acosmism, an undifferentitated whole of Substance, leaving no specific reality for either rocks, lakes or most importantly Man. In examining Hegel’s objection, Gatens and Lloyd introduce the vectoral notion of verticality and horizontality. It is suggested that Hegel’s problem is that he is only thinking of the “vertical” relationship of the modes to Substance, their individual, expressive relationship to the Totalizing whole. I quote at length here from the two authors because it is a very good paragraph, as they make an extremely important point:

Hegel’s critique of Spinoza thus focuses on the relation between individual mode and Substance. His complaint is that Spinoza cannot coherently articulate that relation without collapsing the infinite mode back into Substance; Substance remains undetermined, undifferentiated, while the individual mode is merely negative. But this is to miss the other dimension of Spinoza’s treatment of the finite modes -their mutual interaction, in which the determining force of Substance is mediated through the whole interconnected network of modes. Hegel’s critique of Spinoza is oriented, as it were, to the vertical relation between Substance and individual mode, rather than to the horizontal relation in which finite modes act on and are acted on by one another. Here, along the horizontal axis of finite modes, the claim that determination involves negation can be seen not as a repudiation of finite individuals but as an insight into their interdependence (71)

- Moira Gatens and Genevieve Lloyd, Collective Imaginings, chapter 3 “Re-imagining Responsibility”

Gatens and Lloyd are making clear the a key emphasis Spinoza places on modal expressions, as real, when included in our own constructive and immanent projects of freedom. I would graph out the differentiation that they find in Spinoza in this way:

I would parenthetically add to Gatens and Lloyd’s point that the reason why Hegel is thinking solely about the verticality of the modes is that the binary of individual/God, (or individual/world) is one of the primary schemas of the intersubjective investigations and inculcations of European Christianity. The salvation of the soul, through its relationship to an all-encompassing God, (via various institutional mediations), was the essential dogmatic concern, and this lengthy heritage necessarily brings the philosophical focus back to this binary difficulty: how does the individual soul return to God. Hegel, because he sees man at the apex of history, primarily must read the problematic in terms of a vertical dynamic, the individual vs. the whole. But Spinoza, because he is not burdened by the primacy of man or his reflective powers, allows another dimension of analysis which Hegel cannot see: that of the horizontal. The institutional mediations of the State, Church, Family and their imaginary relationswhich simply interpose themselves as aids to an essential verticality, are by Spinoza exploded out to the ultimate horizontal limit: the infinite expression of the modes. And the imaginary status of their mediating ideas become proliferate and constitutive vectors of power, degrees of freedom, across the field of Being (if one could put it that way without too much obfuscation).

Heveliuss Selenographia (1647) Spring Pole, Foot Pedal Lathe, illustrated

Spinoza’s Lathe

I want to return to the assumed spring pole, foot pedal lathe (pictured above), to get a much more concrete, affective sense of the vertical and the horizontal in Spinoza, and how the practices of Spinoza’a lens grinding may have helped construct his metaphysical conceptions. One must recall that Spinoza spent hours upon hours at such work lens work. To grind, polish and re-polish a lens could take several days, much of it in non-stop and highly repetitive, one might even say meditative, action (Auzout in 1664 records a time of 15 days for a single objective lens). So let our attention be called to the internal dynamics depicted above, found in focus of the dotted yellow frame. Here one should picture Spinoza seated or standing at length, his foot rhythmically pushing down a vertical tension from the spring pole at the ceiling. The vertical rising and falling motion forms a kinetic warp which not only works to orient the body spatially to the height of the room, connecting consciousness from the floor boards to the ceiling, but also creates and punctuated temporality, a timed ratio to the work. Transverse to this warp is the weft of horizontal action. The oscillations of the grinding form are pulled across the body by the push and pull connectionsof the foot the ceiling pole, and distinctly lateral to the focus of concentration. Again and again for hours these up-down, left-right actions literally weave a room of fluctuating conscious attentions, in which the craftsman necessarily embraces the lived experiences of the space, aware that whatever precise spotlight of focus he may have, it is merely a part of much larger, wider degrees of perception. Against Hegel’s fear of an individual’s collapse into the undifferentiated, the agentized craftsman becomes the draw-string of every quarter of the room, a focal point of at least two vectors action, from which and to which he is a differentiated, yet interconnected and expressive part. The melding of the craftsman and his tool is more than a metaphor. It is an experiential and metaphysical certainty.

Within this dotted frame of loomed space, at its center is a rotating circle. It whips at varying speeds in response to both the intensities of the leg, and the limits of the spring pole above, in a concentric motion. It is no secret that Spinoza had great love for the circle as a diagramed exemplar of the relationship between the modes and Substance (Ethics 2p8s, pictured below), but also as an ideal of vision and the actions of optical focus (Letter 39 to Jelles, March 3rd 1667). Here, for hours on end Spinoza would stare determinitively as a rotating circular form which remained both fixed (stable in its ratio), and changing, expressing in both the consummation of the vectors of the room’s actions. One cannot help but think that such concentrated attention upon the spinning form would leave at least a conceptual imprint upon the philosophical craftsman, especially as he considered the modal expressions to be causal interactions immanent to the whole, just as internal rectangles can be considered immanent to the properties of a circle (his diagram below). It is most suggestive to see that the rotating circular form becomes a bed of friction and idea, producing realized changes in the material of glass held in Spinoza’s sensing hand.

from Ethics 2p8s
The Turning Lap

To carry our instructive analogizing further, one must look closer at the actions immediate to Spinoza’s attention as he worked his glass into the required shape.

In the scalloped metal form likely an abrasive would be applied to aid in the grinding, the light blue arrow above represents the hand’s actions upon the circular rotation. The horizontal and vertical tensions are vortexed into an oscillating circularity. There a recipe of frictions and intelligenced experiences interact to bring about an ideal result. What Antonio Negri calls the “concrete…unique terrain of reality, [the] fruit of the paradoxical determination [a metaphysical dilation of unity and multiplicity]” (The Savage Anomaly, 127), the modal “surface of the sea”, occurs here, in the turning scalloped dish, a product of the cybernetic expressions of a room, a mechanism, and man, in which the craftsman’s hand performs a living shore of perceptual action.

The Sublime Tool

If this notional leap from mechanism to conceptual metaphysics seems too great, too fantastic, I believe that this is because we do not have a strong enough sense of the bodily, affective, imaginary foundational means of immanent abstract thought, something that Spinoza’s own metaphysics works to make more clear. Further I believe we must adjust ourselves from thinking of Spinoza merely in terms of propositions and proofs, though the rhetorical form of his work certainly at first or even second glance invites us to think of him in this way. Richard Sennett for instance in his recent pragmatic and near-poetic book, The Craftsman (2008), perhaps gives us a bridge for thinking about craft and abstraction as part of one constitutive process. He invites us to understand how human progress and freedom comes by thinking through one’s tools, how tools help frame our questions and solutions. In fact this is very much how Spinoza has conceived of abstract thinking itself, as he followed Descartes’ analogy found in the 8th rule of the Regulae : just as how a blacksmith’s tools had to be originally made by simpler tools themselves, so too simple tools of the intellect are needed to make other, more complex tools of the intellect (On the Emendation of the Intellect ). In a certain sense, one needs something that hammers in order to make a hammer:

The matter stands on the same footing as the making of material tools, which might be argued about in a similar way. For, in order to work iron, a hammer is needed, and the hammer cannot be forthcoming unless it has been made; but, in order to make it, there was need of another hammer and other tools, and so on to infinity. We might thus vainly endeavor to prove that men have no power of working iron. But as men at first made use of the instruments supplied by nature to accomplish very easy pieces of workmanship, laboriously and imperfectly, and then, when these were finished, wrought other things more difficult with less labor and greater perfection; and so gradually mounted from the simplest operations to the making of tools, and from the making of tools to the making of more complex tools, and fresh feats of workmanship, till they arrived at making, with small expenditure of labor, the vast number of complicated mechanisms which they now possess. So, in like manner, the intellect, by its native strength, makes for itself intellectual instruments, whereby it acquires strength for performing other intellectual operations, and from these operations gets again fresh instruments, or the power of pushing its investigations further, and thus gradually proceeds till it reaches the summit of wisdom.

But is our reading of Spinoza’s metaphysics anything more than simply a coincidence of horizontal and vertical vectors in the lens-grinding lathe, and Gatens and Lloyd’s horizontal and vertical spatialization of his metaphysics in defense against Hegel? Is this conflation merely accidentally bolstered by the analogy of ideas to be taken read tools in Spinoza’s very early work? I think there is much more to this than that, and that aside from the notion of the horizontal and the vertical there is a multiplicity of core principles that seem to stem from Spinoza’s unique, and one must say classed, artisan experiences. In particular we must understand that Spinoza, unlike Descartes, was through and through a practiced craftsman, an artisan by trade and value, who repetitious and refining practices which he took rather seriously must have influenced his guiding conceptions of Mind, Body, Idea and Power. In fact, it seems that it is a tooled notion of idea and body that I believe informs his vital definition of the power of the body, a defintion which will reconceptualize any of our instrumental approaches to material augment of the human body or mind:

Whatever so disposes the human Body that it can be affected in a great many ways, or renders it capable of affecting external Bodies in a great many ways, is useful to man; the more it renders the Body capable of being affected in a great many ways, or of affecting other Bodies, the more useful it is; on the other hand, what renders the Body less capable of these things is harmful.

- E4p38

Think on how this expressive yet instrumental numerical notion of power can be found within the most elementary experiences of tool use, as Richard Sennett tells us about the wonders of the flat-edged screwdriver:

…in its sheer variety this all-purpose tool admits all manner of unfathomed possibilities: it, too, can expand our skills if only our imagination rises to the occasion. Without hesitation, the flat-edged screwdriver can be described as sublime – the word sublime standing, as it does in philosophy and the arts, for the potentially strange. In craftwork, that sentiment focuses especially on objects very simple in form that seemingly can do anything (195)

- The Craftsman, Chapter Six “Arousing Tools”

I believe that Spinoza’s lifelong craft experiences with the lens-grinding lathe (among so many other simple tools) had a lasting effect on his conceptions of Mind and Body, and their necessary unification. The grinding lathe, with its intimate, indeed cybernetic, interweave of body, mind and material construction, its concentric use of the spinning semi-sphere, must have struck Spinoza as sublime in the sense that Sennett tells us. There is the evidence of Spinoza’s resistance to the sophisticated, semi-automated designs of his brilliant and wealthy neighbors the brothers Huygens ( EP 15/32 ) which tells us that Spinoza was quite hesitant to leave behind the interface of the machine with the understanding and felt hand. But it is more than this. It seems that the grinding lathe leaves its conceptual, kinetic trace all the way up through to the most abstract, and most radical of conceptions. In fact there is the very real sense in which we may read Spinoza’s Ethics (as it exists both in idea and extension) as a tool which can affect and be affected in the greatest number of ways. 

Picturing Work and the Work of Picturing

Once we have a vivid sense of the kinds of material engagements Spinoza had concerned himself with, his bodily practices of concentrated creation and refinement, we get a better sense of how Spinoza conceived of his own Rationalist, propositioned philosophical aims. From there we can place ourselves with the lived historical space of the man who lived at the cusp of our modernity, and feel something of the material and pragmatic focus of his articulations of freedom. Below is Spinoza’s rented room in Rijnsburg where he lived roughly from age 29 to 31 having fled the upheavals of Amsterdam, perhaps with concern for the return of his tuberculosis from remission. It is today’s Spinozahuis museum. As mentioned before the wood turners lathe depicted there is NOT the kind of lathe Spinoza would have used, but if you look to the upper center left of the photo you can see a hypothesized spring pole, the vertical vector of his practice. It is not known if Spinoza’s later rooms in the village of Voorburg, where it is thought that he did his most concentrated grinding work, were of this size, but the combination of the Rijnsburg room and Hevelius’s illustration gives us I believe some determinative sense of the internal dynamics of Spinoza’s lived experiences as a craftsman and thus as a thinker; they directs us to the material and conceptual causes that may have privileged Spinoza treatment of the Mind and Body over his predecessor, Descartes. There is much that divided these two thinkers from each other, but perhaps even more than joined them. Each was concerned with lens-grinding, optics and the improvement of the telescope, but only one of them was a practiced maker of lenses and instruments. Only one of them touched the glass.

The Rijnsburg Wood-turners Lathe, Spinozahuis

Hevelius's Spring Pole Lathe, from the Selenographia (1647)


The Rijnsburg Wood-turners Lathe, another angle

The Rijnsburg Wood-turners Lathe, another angle

Why Spinoza? A Historical, Sociological Argument

Why Study Spinoza? …

The question may arise when considering the work of a philosopher, why should we study him, particularly for those outside of the discipline of philosophy. In the case of Spinoza there are some who have suggested that his importance has lain in his proximity to Descartes both in time and in concept. Under this idea, at least philosophically, we have been living in a largely Cartesian age, one that descends from Descartes’ fundamental dichotomy of Substances – Mind and Body – and has been attempting to heal the respective gap between subject and object ever since. This has been reflected in two main offspring-lines passing through the intermediary bridge of Frege/Brentano, those that wrestled with the problems of reference in the Analytic School, and those that articulated philosophies of Presence in the Continental School. These differences are seen to reflect, or express, large-scale sociological facts, the manner in which we in the West conceptualized and utilized objects of industry, and conditioned ourselves in our bodies in a detached and extra-mental way. In this lineage of thought and action Spinoza can be seen to stand, conceptually, as the path not taken. If we were to allow an analogy from biology, Spinoza’s thinking, born in the generation just after Descartes, represents a species of thought which for a variety of reasons did not come to proliferate here. Spinoza’s is a continent of life unto itself whose capacities for coherence and analysis express powers that Descartes’ and his descendants do not.

Related to this conceptual importance of Spinoza is the quality of the time in which he lived. Spinoza lived at the cusp of modernity. In Amsterdam, as an ostracized member of a marginalized group of Jewish merchants and religious believers, Spinoza witnessed and debated some of the most remarkable human leaps in social growth in the history of the West. During the decades of Spinoza’s life the fledgling Dutch Republic posed experiments in early capitalism, democracy and social tolerance (attended by the shadows and dangers of each), such that the core of his thinking can be regarded as something of a stem-cell of modern capitalist and democratic logic, one that, when examined, may provide us with a grammar of analysis for our own times insofar as they have been long delayed in the development of what remarkably was given birth in mid-17th century Holland. Within this notion of Spinoza as a divergent line of conceptual branching are the hopes and possibilities for what is possible to think, and in thinking, do. While Descartes’ division between Mind and Body may have served the human West well for several centuries, Spinoza’s unification of the two, formulated radically as a correction to Descartes, may provide an even more significant capacity, given our place and time. In short, we may be ready for Spinoza.

human stem cell

human stem cell

Spinoza’s Grinding Lathe: An Extended Hypothesis

Johannes Hevelius, also, Johannes Hewel, Johann Hewelke, Johannes Höwelcke or Jan Heweliusz (January 28, 1611 - January 28, 1687)

A Proposed Homologue to Spinoza’s Grinding Lathe

It has been revealed by some digging into the record by Stan Verdult that indeed the lathe that occupies the Rijnsburg Spinoza museum is not of the sort Spinoza would have used (though it may give us a sense of the size of his lathe). [Written about here: The Rijnsburg Lathe: Like the Sun, not 200 Feet Away .] But if we are to come close to understanding the near-daily physical practices Spinoza had engaged in as a lens-grinder and maker of both telescopes and microscopes, we need to narrow the view to the design parameters his grinding lathe likely exhibited. I have mentioned in the past that the foot-driven lathe of Hevelius, as published in his astronomical study of the moon, Selenographia (1647), provides us perhaps of the most revealing illustration of the elements that would have been involved.

We know from Spinoza’s comments on the semi-automated designs of Christiaan Huygens whose home in Voorburghe certainly seems to have visited multiple times, that Spinoza favored a simple grinding mechanism, one in which the glass to be ground was held freely in the hand (affixed to a handle). The general disposition among mid-century savants to further automate the grinding process and remove the human element from the process as much as possible seems to have been looked on withextreme doubt by Spinoza. This does not mean that there was no automated aspects to Spinoza’s lens-lathe, for the lathe itself is a machined dynamic which transfers motions by the hand or the foot to a concentric movement put upon the glass blank. It is only that Spinoza preferred the moment-to-moment, lived craft judgments that came from an artisan’s practice through the encounter withthe machine. In this way our focus should be upon the nature of the machine/human interfaces used by Spinoza, and therefore a central question is whether Spinoza used a hand-driven or foot-driven lathe, with a view to visualizing each as vividly as possible.

Foot-driven lathes were not uncommon in the era, in fact Hevelius’ Illustration of his lathe was published when Spinoza was 15 years old, perhaps a decade before his reported lens-grinding days, and likely was not seen as an innovation then. I suggest that it is to this illustration we must turn if we are to get a clear picture of the kind of physical actions Spinoza trained his eye upon.

the lathe as it appears in Heveliuss Selenographia

the lathe as it appears in Hevelius's Selenographia

In the labeled illustration below, one can see the general action of the foot pedal transfer of power to a concentric motion, and the orientation Spinoza may have had, and the pole that may have been fixed to the ceiling of his room:

Here are various details so as to better see the composition of components:

Here one can see the transfer of the cord to a grinding form’s modular base. It would not be necessary, or even likely that this modularity would be a feature of Spinoza’s lathe, but the horizontal orientation of the grinding dish (as opposed to the vertical angle shown in designs from earlier in the century) would be the preferred design, for this would allow gravity to act as ally in abrasive control and arm fatigue. (We do not know how intermittent Spinoza’s tuberculosis was, a disease that he, by Colerus’s account, suffered from since about the age of 24, but the question of endurance could have been a singificant factor in the kind of lathe Spinoza used.)

In this close-up to the foot pedal one can see the simple nature of the drive mechanism. A foot pedal allows of course one to use the larger leg muscles, a benefit for more arduous projects; but it also informs a vertical tension from the floor to the ceiling. There is a cross dynamic between the communications of the foot to the spring pole high above, which is then read in the relative speeds and intensities by the hand pressing its material downward. The oscillations of upward and downward, a horizontal, yet fixed, stable circular whirrings do suggest a grid of complex physical actions and interface. One may be tempted to see in this cross-dynamic the metaphysics of the verticality of Substanced expression, and the horizontality of modal causations. In any case, the foot pedal lathe leaves a distinct epistemo-kinetic imprint upon the craftsman that engages it, something that surely would have informed Spinoza’s thinking about material and its formation. 

Yet on the level of information on technique, perhaps even of more interest in this close up of the Hevelius drawing is the shape of the grinding forms discs placed haphazardly on the floor. They are not the hollowed-out concave metal forms like those, let us say, Hieronymus Sirturus wrote about in his influential book on technique Telescopium, siue Ars perficiendi nouum illud Galilaei visorium instrumentum ad sydera (1618), (whose spherical perfection was created by being ground against a matching convex iron casting). They appear instead concavely beveled, on the inner slope of which a lens can be angled to be ground (if I read the illustration correctly).

One can see each of these types of grinding forms (a beveled inner edge, and the scalloped dish) in van Gutschoven’s 1663 letter to Christian Huygens which had answered Christiaan’s question as to how to grind smaller objective lenses [comments on: A Method of Grinding Small, Spherical Lenses: Spinoza ]:

Here in the van Gutschoven illustraton a narrow canal (vertically aligned) serves as the grinding surface just inside the lip.

And here is a concave finishing form, in whose center a small lens would be placed for polishing. The two illustrations above simply show that both form designs were employed, and we cannot be sure if Spinoza would have used one or the other, or both (though the degree of curvature shown above would be wholly inappropriate for telescope lenses for which only a slight curvature was needed). One might add, by Spinoza’s use of the terms “dishes” or “plates” for his metal laps, the scalloped spherical form, hollow at the center, one could presume was a main metal form that he used.

To return to the Hevelius example, if we can seriously entertained the prospect that Spinoza used a foot-pedal grinding lathe, I would want to point out the thorough and bodily engagement that grinding would have involved. Not only were the powers of close-eyed concentration, and precise fingered and armed exertions involved, but also a co-ordinated rhythm between the actions of the foot that from a distance below swiveled the grinding form back and forth, reversing itself, restrained from high above, bringing fortha total read of machine tensions which completed a lived circuit between the human body and its attentive results. Spinoza’s entire body would be in play in the workings of the glass, from head to toe. And if one superimposes the requirements of his metaphysics (his equivocal treatment of Thought and Extension, and his definitions of a body and power) upon this organization of machine, idea and flesh, one may see with growing clarity how his crafted practices informed his most abstract thinking.

This is the case found in the Hevelius example, which forms one end in the spectrum of the possible machine designs Spinoza likely used. There is of course a much simpler design, the hand-driven lathe, which Spinoza may have also worked from. The nature of this lathe can be seen in the 1660 Manzini manuscript, and the expert mock up made by the 400th Anniversary of the Telescope team:



One can see the typical concave metal dish (to the left) and the hand-drive of the form. In terms of dynamics instead of a swivel motion to the form, a repeated back and forth oscillation driven by the foot co-ordinated from high above, here the form can be spun in continuing circles in close proximity to the chest. Evidence that Spinoza used just such a design perhaps can be seen in the list of things sold from his estate in November of 1672.

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).

That there were multiple mills sold (not a complete list of what he owned one might assume) suggests a variety of more specialized devices, instead of one large workbench as that shown in the Hevelius example. But this is not at all a clear, or exclusive conclusion. Small hand-driven grinding lathes may have been employed for small microscope objectives (which Spinoza favored) or telescope eye-pieces, whereas a foot pedaled, spring pole machine could have been used for larger telescope glasses which could reach nearly 1/2 a foot in diameter.

In digression, there is evidence that Spinoza collaborated with the respected optical mathematician and amateur scientist Johannes Hudde on calculations for a 40 ft lens. To give a sense of it, such a lens would have been approximately 5 inches in diameter, of very slight curvature and only 5 – 8 mm thick: Huygens’s letter to his brother 23 Sept 1667:“Ie voudrois scavoir quelle grandeur d’ouuerture Spinosa et Monsieur Hudde determinent pour les 40 pieds” (See “The Lens Production of Christiaan and Constantijn Huygens” , 1998, by van Helden and van Gent, for the dimensions of similar lenses). Whether Spinoza was in the practice of grinding such lenses, which at the time would have been among the most powerful telescope lenses in Europe, we cannot know. But it seems he was involved in their calculation.

To return, if we are to imagine a hand-driven lathe’s effect upon Spinoza’s rational conception of Mind and Body relations, the form’s spinning, instead of oscillating, motion, may involve less of the entire body than a foot pedal lathe would; the head, the shoulders, the hands would form a frame of power and sensitivity, withthe shoulders acting as fulcrum points of stability and the hands as reading extensions. The cybernetic feedback between the hands, one holding the glass blank, the other whirling in circles would seem to be even more involved, more kinetically woven than that of the foot pedal lathe. The power transfer is more direct the thus the communication between hands more intimate. And one sees how the manifestations of concentric stability and change, eternity and flux, expressed in two respondent revolving discs, certainly could present itself as significant to the circle-loving craftsman as he sought to perfect his lens under physical pressure and frictions of grit.

By my view it seems most likely that Spinoza employed both kinds of lathes, the foot and the hand driven, perhaps at different points in his life, in a process of a refining of techniques. What really is at stake in this analysis I would contend is that one must be able to SEE what Spinoza did during a preponderance of his days, picture it physically, in an affective projection, to fully conceive what he thought. The machine and the human, that mind in the device and the matter of the idea understood to be in mutual conjunction.


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