Frames /sing


Spinoza’s Foci – Articles on Spinoza’s Optics and Lens-Grinding

This portion of the site is a collection of research sources, conjectures, theories and analyses surrounding the question of the likely optical instruments and optical knowledge that Spinoza had, with a view to understanding how his practices and experiences informed his metaphysics, an understanding which may in turn provide valuable insight into the heritage of mechanization and instrumentation we have received since the first bold attempts to marry instrument, geometry and vision by Descartes.

Below is a categorized, and then alphebeticized listing of the history of most of these postings, to be updated from their daily course from time to time. Keep in mind that because these exist as notations taken in a process of research, prospective interpretations or hypotheses offered at one point, may not be retained at another. As a process, it must be read in process. 

The concept of the Philosopher as Lens Grinder

As Lensmaker: A Quick Overview - a brief reflection back upon the notion of Spinoza as lens-maker.

Borges and Spinoza: Ground Glass - a poem of Borges’s on Spinoza is considered. Borges was the first to direct my attention to the centrality of Spinoza’s lens-grinding in his metaphysical project.

Descartes and Spinoza: Craft and Reason and The Hand of De Beaune - an analogous comparison of Descartes’ comments on the wounding of the hand of the craftsman, and Spinoza own letter 32 claim that polishing lenses/forms with a free hand is more “sure”. Here the balance of reason and craft, in the context of social standing is touched on.

Instrumentality and Perception in the Seventeeth Century - a few thoughts on the thinking of instrumentality that characterized much of the 17th century, as it comes under a Spinozist critique, both in terms of optics and politics.

Some Observations on Spinoza’s Sight - Two primary diagrams of Descartes and Spinoza are placed side by side in order to draw very rough, but perhaps productive lines of investigation in the metaphor of vision in their thought.

The Lathe Mind: What Spinoza Meant by “Individual” - how the lathe must have informed Spinoza’s metaphysics is brought forward. This was written early on in my investigation, but it gives a strong conceptual sense of the questions that drive this research. Here the example of Spinoza’s definition of the Body is re-examined under the dynamics of what a lathe presents, suggesting a further re-evaluation of much of his metaphysics from the point of view of the idea-material-fixity-change-feedback-craftsman interfaces involved in lathe production.

A Short Note on the Notion of Spinoza as Craftsman - that Spinoza must be considered as a craftsman and not just a metaphysician is argued. Not looking that daily practices of his lens grinding, the nature of that instrument and its experiences, would be like not thinking about a potter’s wheel when attempting to understand the philosophy of put forth by a potter.

Some Rough Thoughts On Spinoza and Technology - Continuing thoughts on the possible conclusions that can be drawn from Spinoza’s criticism of Huygens’ lens-grinding machines from letter 32 to Oldenburg.

Spinoza: The Body of Ideas as Lens - the notion that the body itself may be seen as a lens, crafted through the sharpening of the adequacy of ideas is here touched on. It may be that through his continuous work on the lathe Spinoza came to understand that the prescription of the Ethics was a material imposition upon the facts of the body.

Spinoza’s Eyes of the Mind and the Grinding Form an analysis of Spinoza’s conception that the demonstrations of the Ethics are the “eyes of the mind” with a comparison to how Descartes’ use the same phrase. The analogy of the lens-grinding form is put forth as an elucidation of how Spinoza conceived his Ethics.

Van Leeuwenhoek’s View of Technology and Spinoza - prospectively, a philosophical consideration of Van Leeuwenhoek’s refusal to show others his lenses, his methodology of examination and instrument design is put in relationship to Spinoza’s own likely merchant-class approach to optics and instruments. The powers of instrumentation and issues of specimen staging are brought together.

Historical Context of Spinoza’s Work and Influences

Anti-Trinitarian Politics at the Time of Spinoza’s Collegiants - Jonathan Israel is quote to give a succinct sense of the political melieu into which Spinoza’s circle fit. The popularity of the Collegiants at the time of Spinoza’s departure of Amsterdam is noted.

Glazemaker’s translation of Descartes’ La Dioptrique (1659) - A link to Glazemaker’s translation of Descartes’ Dioptrics, and its perhaps significant date are introduced. Glazemaker’s glass knowledge and he knowledge of optical theory are put in very loose association.

How Much were Spinoza’s Lenses and Microscopes? - some historical evidence for how much Spinoza’s lenses and instruments may have earned him.

Huygens’s Lens - a photo of the lens that Huygens’ used to discover the moon and rings of Saturn in 1655. The presence of an Ovid line on the glass is noted.

Leibniz’ “optical” Response to the Theologico-Political Treatise a brief consideration of Leibniz’s Letter 45 to Spinoza, and how his “Notitia opticae promotae” served as a response to Spinoza’s TTP.

A Short History of Early Spherical Microscope Lenses - a chronology of spherical lens, simple microscope events is given, placing Spinoza in the stream of its development. The thought is that perhaps this powerful design is among those that Spinoza may have employed. Spinoza’s relationship to Kerckring is importantly given its place.

The Simple Microscope in the Hands of Van Leeuwenhoek and Huygens - A comparison between the rotary conception of the specimen viewing found in Christiaan Huygens microscope and the Van Leeuwenhoek idea of a “staged”, fixed specimen, as it reflects a different idea of device and observation.

Spinoza and Hooke’s Micrographia: The minascule made Large - the possible influence of Hooke’s Micrographiais raised, given that it was in the possession of ChristiaanHuygens when Spinoza’s friendship with him developed during the meaningful summer of 1665. Was Spinoza spurred to greater microscope use (and design) at this point?

Spinoza: Not As Abused As Is Said - the evidence for the presumed disparagement of Spinoza’s optical knowledge (and social standing) is questioned.

What Spinoza and Huygens Would Have Seen - a brief research and imagination of what Spinoza and Huygens would have seen if they looked together at the night sky on a mid-summer date, in the village of Voorburg in 1665.

Questions of Technique

A Closer Look at the Rijnsburg Lathe - Enlarged picture views of the Rijnsburg Spinozahuis lathe, and an illustration.

An Extended Hypothesis: Spinoza’s Grinding Lathe - my conclusions reached after research on the likely nature of Spinoza grinding lathe, falling between that of Hevelius’ lathe as depicted in the Selenographia, and the elementary hand lathe as shown in Manzini.

Constantijn Huygens Uses Spinoza’s Grinding Dish (1687) - evidence is cited that the Huygenses used equipment madeby Spinoza as late as 10 years after his death.

Did the Huygenses “buy” Spinoza’s lens polishing technique? - a hypothetical account of how the acquistion of Spinoza’s lens-grinding equipment might have accelerated Christiaan Huygens production of the single lens microscope.

Evidence toward the nature of Spinoza’s Lathe(s) - A brief summary of facts which may have had bearing on the kind of grinding lathes Spinoza used.

Govert Bidloo’s 1698 Refference to a Spinoza Microscope - a look at a 1698 citation of Kerckring’s observations made on and with a microscope made by Spinoza.

Hooke’s Method of the Single Bead Lens - a quotation of Hooke’s description of the single lens bead technique, as found in the Micrographia (1665).

Huygens’s Comments On Spinoza’s Theory of the Microscope to His Brother - a posting of the original French text of Huygens’s May 11 1668 letter to his brother, and some commentary on conclusions for Spinoza’s technique.

Jan Hendriksz Glazemaker…the Glazier - that fact that the Cartesian circle participant and assumed translator of Spinoza’s works had a history of glass knowledge is brought forward.

A Method of Grinding Small, Spherical Lenses: Spinoza - comments on the technique for grinding small lenses provided to the Huygenses by van Gutschoven regarding what would can conclude about Spinoza’s own practices.

Monconys’ Visit: Six Degrees of Separation for Spinoza - the importance of French diplomat Bathazar Moconys’ 1663 visit is fleshed out. This visit ties together some of the most signfiicant figures in Spinoza’s optical milieu, Hudde, Vossius, Huygens, (not to mention Vermeer at Delft) and attests to the pervasiveness of the single-lens, bead microscope design.

On the Issue of Clarity and Light: Van Leeuwenhoek’s Lenses - a 1685 quote by Thomas Molyneux is presented in support of the view that the lens polish of bead, single microscope lenses can have a determinative affect on distinctness and luminosity.

The Rijnsburg Lathe: Like the Sun, not 200 Feet Away - Finally, the mystery of authentication of the Rijnsburg Spinozahuis lathe is revealed. A question of its role in the museum is raised and discussed.

Simple or Compound: Spinoza’s Microscopes - A discussion of the conclusions that may be drawn from Christiaan Huygens’ 1668 admission that Spinoza is correct that smaller objective lenses produce finer representations of objects.

Some Personal Thoughts on a Possible Spinoza Lathe - having located a likely simple lathe design, here are posted some thoughts of someone who actually had used this kind of lathe to grind lenses. This is a first hand account of the process, giving view into some of the experiences Spinoza might have had.

Spinoza’s Comments on Huygens’s Progress -letter 32′s observations on and objections to Huygens’ lens grinding machine are examined. Significant aspects of the Latin are retranslated, making more clear Spinoza’s point of emphasis, and opening of questions about whether Spinoza had extensive experience in polishing (or grinding) metal forms.

Spinoza’s Lens-Grinding Equipment - A commentary on the likely source types for Spinoza’s grinding laps, given those used by the Huygenses, with a rough assessment of Spinoza’s place in the milieu local knowledge.

Spinoza: Two Grinding Lathes roughly from the Period - two potential designs for Spinoza’s lathe are shown. The first is hand-driven from the Manzini text, the second is spring-pole from Hevelius.

Swammerdam’s Microscope: A single lens example 1678 - a reproduction of Swammerdam’s single lens microscope is posted. Of possible importance, as he represents one of the 1661 Leiden anatomists students Spinoza may have known, and this kind of microscope (single lens) may have been one that Spinoza made.

To Understand Spinoza’s Letter 32 to Oldenburg - Various designs of Christiaan Huygens’s actual (and theoretical) lens grinding machines are shown to give better context to Spinoza’s description of, and objection to, the device he likely saw, as written about in letter 32. The issue of mechanistic complexity, the role of the craftsman, and Spinoza’s notion of liberation is broached.

Traces of Spinoza’s Microscope - Evidence is cited that Huygens primarily used melted bead lenses, and a diagram is presented from Huygens’s notebook which may represent design elements of Spinoza’s microscopes purchased at the auction of his estate.

Two more looks at the Rijnsburg Draaibank - two alternate photos of the Rijnsburg Spinozahuis lathe.

Why Spinoza’s Method of Lens Polishing Might Have Been Integral - the citation of the experimental work of Alvaro Amaro de Azevedo, with an eye to further establishing that Spinoza’s polishing techniques may have central to the leaps in microscope technology achieved in the summer of 1678.

Interpreting Spinoza’s Optical Concepts

A Conflation of Spinoza Diagrams - two diagrams used by Spinoza – one from the Ethics to illustrate the relationship of the Modes to Substance, and the other used to illustrate the supposed focusing power of spherical lenses – are put juxtaposition, with the suggestion that the latter is in some sense being thought of in terms of the former, giving priority to the circle.

Deciphering Spinoza’s Optical Letters - a line by line prospective commentary on Spinoza’s two optical letters to Jelles, letters 39 and 40, drawing on likely texts of influence to make clear Spinoza’s conception.

Descartes’ Dioptrics 7th Discourse and Spinoza’s Letters 39 and 40 - a posting of the likely text that Spinoza and Jelles had in mind in the discussion of the magnification of images in letters 39 and 40. The attempt is to ferrett out just what Spinoza’s objection to Descartes is.

Descartes’ 8th Rule: A Spinoza Touchstone - The entire text of Descartes 8th Rule from his Regulae is posted, with some observations on its possible influence on Spinoza, with a view toward determining Spinoza’s conception of instrumental knowledge.

A Diversity of Sight: Descartes vs. Spinoza - A summation of some of the metaphysical consequences of the investigation of Spinoza’s critique of Descartes in letters 39 and 40. Research had lead to the hypothesis that Spinoza had in mind Kepler’s Paralipomena, and a close examination showed that Kepler may have been the core influence of Descartes’ embrace of the hyperbolic form, an embrace that Spinoza critiques at its root assumptions, the analogy of vision.

The Hole at the “Center of Vision” - How Spinoza’s objection to Descartes’ hyperbolic lens relates to his General Defition of the Affects, and unseats a model of consciousness which is one of central clarity.

The Optica Promota and Spinoza’s concept of focus - an initial discussion of the correspondence between Gregory’s conclusion of the “infirmitas” of the hyperbolic lens, and Spinoza’s own idealization of spherical lenses.

An Origin of Spinoza’s “cones of rays” Explanation, Letter 40 - Kepler’s Paralipomena is proposed as the reference for Spinoza’s Letter 40 “cones of rays” explanation, suggesting a tighter bond between Kepler’s and Spinoza’s optics than otherwise assumed.

Spherical Aberration: Descartes’ Solution - a short illustration of the problem of spherical aberration, which is necessary to understand if the questions of letters 39 and 40 are to be solved.

Spinoza’s Blunder and the Spherical Lens - a close look at the potential for criticism of Spinoza’s optical knowledge as found in Letters 39 and 40. Alan Gabbey’s pessimistic view is considered, and an important mistranslation of the text - a missed subjunctive - is uncovered, changing just what it is that Spinoza may be asserting.

Spinoza’s “Spring Pole” Lathe: Experience to Metaphysics and Back - A hypothesis on the effects the dynamics of Spinoza’s lathe may have had on his conception of metaphysics. A discussion of Hegel’s treatment of the modes and the nature of Spinoza’s insistant notion of materiality.

Primary Sources

The Text of van Gutschoven’s Letter to Huygens No. 1148 - a 1663 letter from the mathematician van Gutschoven which shows lens-grinding techniques for small lenses typical of the period.

Huygens’ Comments On Spinoza’s Theory of the Microscope to His Brother - the original text of Christiaan Huygens’ May 11, 1668 letter to his brother Constantijn.

L’occhiale all’occhio (1660), Primary Source for 17th Century Lens Grinding Techniques - a link to the Italian text of Manzini’s L’occhiale is given.

The Optica Promota, by James Gregory (1663) - links to an on-line photocopy of the 1663 edition as would have been found in Spinoza’s library, and to Ian Bruce’s transcription of the Latin and English translation.

Spinoza: Letters 40 and 39 - the English translation of the relevant optical parts of Spinoza’s Letters 40, and 39, along with a link to the Latin text.

Spinoza’s Letter 39: Descartes’ Silence - the posting of an English translation and the Latin text of Letter 39 to Jelles.

The 1661 Technique of “Glass Drops”, a Possible Link to Bead Lens Microscopes - a transcription of the original published account of the Royal Society 1661 experiments with “glass drops”, found in the first English translation of Antonio Neri’s The Art of Glass.


The research here is nearing a hiatus, with a forthcoming article soon to be written. I want to thank a few people who have been most helpful and inspiring in this work. First, Graham Burnett, Associate Professor of History at Princeton University. His work and personal guidance has been the Ursprung of my study of Spinoza’s optics and techniques. Steven Nadler, Professor of Philosophy at the University of Wisconsin-Madison, has been invaluable with translations and in advisement on sources and ideas. Eric Schliesser, Professor of Philosophy at the University at Leiden, has been most helpful in support of my attempt to link Spinoza to scientific endeavour, and it has been his insistence that this is new ground for research that propelled me to much greater depths of investigation. I could not have achieved any of this without the dear tireless help and research of Linda Lucas at Orange County Community College, whose good cheer and diligence ever brought greater and greater opportunity. Stan Verdult is thanked, whose weblog, communications on Spinoza, and enthusiasm for the subject provided breakthrough research and resource for a variety of topics. I am sincerely appreciative of Michael Della Rocca, Professor of Philosophy at Yale, who most patiently and generously has considered my philosophical questions and responded with determined clarity and grace. And most certainly Spinoza scholar Wim Klever, whose quixotic and sparkling insights, love for the obscure yet highly relevant fact, and daring passion for the connection kept me reaching higher towards a notion that Spinoza indeed was not only a man of mind, but of science, technique and technology as well. There were many others who have been so helpful in answering my persistent emails, including I would have to say by name, the willing Edward Ruestow on the history of the microscope, Stuart Talbot on the telescope, Philip Steadman on Optics, Alvaro Amaro de Azevedo on simple microscopes, Eisso Atzema on Johannes Hudde but beyond this I will have to stop and thank all others more generally. This has been a community of efforts.

Any thoughts on the process or its conclusions:

Link to the larger portion of my Spinoza thoughts and considerations here

2 responses to “Spinoza’s Foci – Articles on Spinoza’s Optics and Lens-Grinding

  1. Pingback: Experiment Without Hypothesis « Mitochondrial Vertigo

  2. ibs January 23, 2011 at 6:21 pm

    i want to follow updates

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