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Category Archives: Huygens

Spinoza: Not As Abused As Is Said

Two Kinds of Disparagment Found In the Huygens Letters

I am looking at the references to Spinoza made by Christiaan Huygens, coming to them with the expectation that they would reveal a general disparagement of the man, either in terms of his optical knowledge, or in terms of his person, for these letters have been characterized as proof of a certain diminishment Spinoza had suffered in the minds of those who came to know him.

I quote below two sources that typify this kind of conclusion.

It is however the letters which Christiaan Huygens wrote to his brother Constantijn between 9 September and 11 May 1668, which provide us with the clearest evidence that by then, those engaged on actual research into dioptrics had begun to take a somewhat patronizing attitude to Spinoza’s theorizing on the subject. They make it perfectly clear that although Huygens valued “our Israelite’s” practical skill in producing first-rate lenses, he thought it very unlikely that he was capable of adding anything of value to the understanding of optical phenomena (97)

Spinoza’s Algebraic Calculation of the Rainbow & Calculation of Chances, by Michael John Petry  

Over time, he earned praise from some notable experts for his expertise in lens and instrument construction. Huygens, writing to his brother from Paris in 1667 (when Spinoza was living in Voorburg) noted that “the [lenses] that the Jew of Voorburghas in his microscopes have an admirable polish.” A month later, still using the somewhat contemptuous epithetet – occasionally replaced in his letters by “our Israelite” – he wrote that “the Jew of Voorburg finishes [achevoit] his little lenses by means of the instrument and this renders them very excellent (183) 

Spinoza: A Life, by Steven Nadler

The Optical Israelite

While Petry finds in these letters clear evidence for an accumulation of doubt as to Spinoza’s capacities as an optical thinker, the relegation of him to simply that of an excellent craftsman, Nadler acknowledging that although Spinoza’s instrument achievements were much respected, strongly suggests that he was seen merely as a “Jew”, or perjoratively as “our Israelite”. The picture that is left by these writers and others is that somehow Spinoza was seen in a poor intellectual and ethnic light by the Huygnses.

In looking at these letters, this simply does not seem to be the case. Firstly, Nadler’s implied characterization that in these letters Spinoza is ONLY the Jew or Israelite does not hold. He is also “Le Sieur Spinoza” , “Sir Spinoza” (September 9, 1667, May 11 1668), and just “Spinoza” several times. He is also addressed in combination of “Spinoza et Monsieur Hudde” (Semptember 23, 1667); whether this is a sign of his diminishment in contrast to Mr. Hudde, or one of familiarity is hard to weigh. In fact it is hard to measure the full texture of the Jewish nomenclatures, some of which Nadler finds distinctly “contemptuous”. There very well may be social contempt in these, but the title “the Jew of Voorborg” may be a title Spinoza had somehow informally gained in circles, and not simply one of Christiaan’s invention, and though “our Israelite” may strike our eyes in a jarring fashion, it is difficult to parse out the affection from the diminishment, if indeed there is such. (To understand what Huygens means by “our Israelite” one for instance may have to anachronistically ask, Is Spinoza diminishing others when he refers to the “Brazilian” in his waking dream, as an “Ethiopian” [Ep. 17].)  Because of these telescopic difficulties across centuries, at the very least I want to present the picture of the Huygenes social relationship to Spinoza as more complex and varied than what I assumed by reading the tale of these references without looking at them. And I wish to open the possibility that there was more social respect there, against the tremendous currents of the prejudice of the times, than otherwise would be assumed possible in a less nuanced reading, a respect that Spinoza had personally earned across social barriers.

Petry’s point I am unclear on, for in the letters Spinoza’s optical (vs. craft) acumen does not seem to be in question. There seems to me to be clear evidence rather that Spinoza rather had collaborated with the well-respected mathematician Johannes Hudde on calculations for a 40 ft. lens (Sept 23, 1667), and that these calculations had perhaps influenced Huygens’ own calculations for even longer lenses. Perhaps Petry has in mind Huygens’ thoughts in his May 11, 1668 letter, where Huygens discusses his new eyepiece with Constantijn. Spinoza certainly had no knowledge of the optics of this eyepiece, or its principles, but if I am reading Huygens correctly, this is his proposed solution to spherical aberration using only spherical lenses (against a hyperbolic solution). Not only would Spinoza have no knowledge of these principles, neither would any other man in Europe, Johannes Hudde included. I am unsure if we could say that this was a “patronizing attitude”. I am certainly open to evidence to the contrary.

Others have suggested Christiaan’s warnings to Constantijn should keep quiet about his invented lenses, and not reveal them to Spinoza, proves that he regarded Spinoza to be a “competitor” in lens-making. I find this an odd, or perhaps incomplete conclusion. Christiaan’s invention simply was not ready to be made public, and he knew Spinoza to be at times in close contact with Oldenburg, the secretary of the Royal Society of London. Spinoza had kept Oldenburg abreast of the details of Huygens’s progress. There is a sense though in which Spinoza may have been a competitor to Christiaan. The Huygens brothers may have had an intimate relationship to lens-grinding, and there are signs that Constantijn grew cold to Christiaan’s instructions when Christiaan had gone to Paris. The lenses ground during the time of their separation are thought by Anne van Helden to have been entirely farmed out to craftsmen. If though Constantijn continued his conversations about optics and lenses with his neighbor Spinoza, having lost his brother partner to fame in Paris, indeed Spinoza may have represented, however slightly, an emotional threat to Christiaan. It seems, by several accounts, that Spinoza was an engaging man to talk with. Any disparagement we may find in these letters from Christiaan, insofar as we find it, I think should be understood within this context as well, that the brothers were extremely close on the subject and practice of lens-grinding.

The Text of van Gutschoven’s Letter to Huygens No. 1148

[Posted here is the full original text of Huygens letter 1147, for which there are some comments here A Method of Grinding Small, Spherical Lenses: Spinoza ]

No. 1147.

[G. van Gutschoven] à [Christiaan Huygens].


Apendice au No. 1146.

Instrumentum ad vitra minoris sphaerae terenda.

Laminam eream AB schamno tornatorio affixam excavabis secundum circulum CD cuneo parato in formam circuli aequalis circulo vitri formandi. dice aequalis circulo maximae sphaerulae cuius lens particulam referat. in hoc excabato canali CD, atteres vitra capulae affixa et canali appressa : modo capulam in manu continuo dum vitrum attertur vertas, ut ex omni parte vitrum aequaliter atteratur : consultissimum autem erit laminam horizontalier circumagatur, nam hoc modo non tam facile arena decidet, vltimam autem polituran vitro addes simili lamina sed stannea terra tripolitana inserta : vel lamina simili lignea ex lingo aliquot molliori, quale est salicis, vel populi.

Lentes cavas formabis sphaerula stannea vel plombea EF schamno tornatorio affixa ut vides, polies vero eadem sphaerula vel lignea ut superius dictum terra tripolitana inserta.

Hoc concavo cono schamno tornatorio affixo, scabies vitrorum limbos polies, ne dum ultimam in charta inducimus vitro polituram, particulae tenuiores vitri exfilientes et in poros chartae sese infinuantes vitrum deturpent.

Huygens’s Comments On Spinoza’s Theory of the Microscope to His Brother

[Opening Comment: I post below an extensive excerpt from a significant letter by the hand of Christiaan Huygens. It is has been cited by biographers for two main reasons. For one, the initial sentence is stated as evidence for Huygens’ regard for apparently an argument or demonstration that Spinoza had put to him in Voorburg, one possibly with some conjunction with Johannes Hudde:

“It is true that experience confirms what is said by Spinoza, namely that small objectives in the microscope represent the objects much finer than the large ones.”

What is not mentioned is that this is the first sentence of a letter devoted to its theme of a compromise with Spinoza (and Hudde) over the issue of small lenses and greater magnfication). Far from being a sidenoteof the letter, Huygens has Spinoza’s argument in the forefront of his mind.

What is also considered significant about this letter (and others like it) is the way that Spinoza is addressed. Here, at the end, not by his name, but as being called “the Israelite”, (and elsewhere as “the Jew”). This is meant in the eyes of many interpreters to signify the distance that Huygens kept between himself and Spinoza, implying that he is merely “the Jew” or “the Israelite” in letters. Indeed there were likely uncrossable social status barriers between the two, but the impression left by some that Spinoza was merely “the Israelite” is not deserved, for the very letter opens with his name and his overarching position.

Other than these two much-traveled points, grafted from the letter, and others related to it, what I find most suggestive is that Spinoza’s position seems to be one shared with Johannes Hudde (they are paired at the end of the selection), and Huygens has responded to Spinoza’s point by with a compound microscope construction of a unique design, whose compromise magnification is measured at 30x. This leaves open the question as to whether Spinoza’s argument was for simple or complex microscopes (or both), but gives us a baseline from which to assesss the magnification achieved by Spinoza’s instruments, for they must be significantly greater than 30x. 

For those unfamiliar, Christiaan Huygens, was one of the most incandescent scientific minds of the 17th century (he invented the pendulum clock and discovered the rings of Saturn in the same year!). It is thought that Spinoza and he spent some significant time together in discussion between at least 1664 and the summer of ‘1665, as they were neighbors in the town of Voorburg until Christiaan left for Paris in the summer of ’66. At the time of the writing of this letter Huygens had already become the Secretary to the newly formed Royal Academy of the Sciences of France, and he write to his brother Constantijn Jr., who remained a neighbor to Spinoza. Constantijn was Christiaan’s partner in lens-grinding and instrument making, something that seemed to be a bond between them.

Christiaan Huygens
Huygens’ Letter to Constantijn  
Letter No. 1638

Christiaan Huygens à Constantyn Huygens, frère.
A Paris ce 11 Maj 1668

Il est vray que l’experience confirme ce que dit Spinosa que les petits objectifs au microscope representent plus distinctement les objects que les grands, avec des ouventures proportionelles, et sans doute la raison s’en peut donner, quoyque le Sieur Spinosa ni moy ne la scachions pas encore, mais aussi de l’autre costè il est certain qu’on distingue plus de profondeur aux objects quand l’objectif est moins convexe. de forte qu’il faut tenir le milieu entre l’un et l’autre pour avoir des microscopes qui sassent uneffect agreeable, mais si on ne cherche qu’a grosser beaucoup il faut des petites lentilles. I’ay essayè vostre derniere proportion avec vos objectifs et deux oculaires joints l’un contre l’autre qui font un bon effect sinon que les points paroissent trop, et bien plus que lors qu’on n’emploie qu’un oculaire seul de 2 pouces, et la raison y est toute evidente, puis que l’un est de 3 pouces et l’autre de 2 ½. Il vaudroit donc mieux que l’un fut de 4 ou 5 pouces du premier, parse qu’ainsi les points de l’un ni de l’autre ne paroistront pas.

Nostre anciene maniere avoit les deux oculaires si pres de l’oeil que cela empeschoit les points d’estre veus, a quoy contribuoit encore beaucoup l’ouuerture de l’objectif un peu grande. car estant petite et la multiplication forte, il est malaise que les points de l’oculaire pres de l’oeil ne paroissent, et le meilleur remede est de faire d’une matiere qui n’aye que fort peu de points. I’ay dans mon microscope un petit oculaire de 6 lignes, qui est de telle matiere, et aussi blanche que du crystal de roche; avec cela elle est fort bonne et souffe pour le moins aussi grande ouuerture que vostre petite que je vous renvoie. Je retiens l’autre pour faire des essays et vous en remercie. le poly est fort bon.

Voicy les mesure de la vraye Campanine, avec la quelle j’ay estè comparer la miene, qui a cause de la grande ouverture que j’avois donnè a l’objecif estoit beaucoup plus Claire, mais en recompense un peu moins distincte que l’autre, qui en effect est un peu somber, mais, pourtant tres excellente. J’ay du depuis ester cy mon ouverture, mais cela fait paroistre les points des oculaires qui en sont assez chargez.

L’ouverture chez l’Abbè Charles est cellecy. [insert the figure of a circle, approx. 1.25 cm in diameter]

Le diaphragme tel [insert the figure of a circle, perhaps a touch less in diameter]

Du trou de l’oeil au premier oculaire [insert the figure of a line segment, approx. 2.5 cm]
Du premier au second oculaire.
[insert the figure of a line segment, approx. 6.5 cm]
Du second oculaire au troisieme.
[insert the figure of a line segment, approx. 6.75 cm]

Je prens tousjours du milieu de l’epaisseur des verres.
Les 3 oculaires ont chacun leur distance de foier d’ 1 pouce 10 lignes.
L’objectif est de 2 pieds 5 pouces.
Toute la longueur de la lunette 3 pieds 3 pouces, qui est moindre de 4 pouces que la meine. tout est mesure de Rhynlande.
Pour ce qui est de ma nouuelle methode de composer un petit cave avec un objectif, le ne trouve pas qu’il y ait de vos petites formes qui vous puissent servir. mais pour un verre planoconvexe de 2 pieds 8 pouces comme vous en saites, il saut un oculaire don’t l’une des superficies soit travillee dans un creux comme cettuicy [insert figure of a small concave-plano lens] dont le demidiametre soit 289/1000 d’un pouce, et l’autre sur une boule don’t le demidiametre soit 187/1000 d’un pouce, [insert figure of a circle approx. .6 cm in diameter] qui est telle, de forte que vostre lentille creuse sera de cette forme [insert a concave-convex figure, with two small protruding notches near the axis], et il faut tourner le costè convexe vers l’oeil. Cette lunette grossira 30 fois, er pour cela il faut travailler l’objectif un peu grand, a fin de luy donner grande ouverture. Le costè convexe doit estre en dehors. Ce composè, suivant la demonstration, doibt faire autant que les verre hyperboliques, parce que le concave corrige les defauts de l’objectif qui vienent de la figure spherique, c’est pourquoy je ne puis pas determiner l’ouverture de l’objectif qui peut ester pourra ester 3 ou 4 sois plus grande qu’a l’ordinaire, mais si nous la pouvons seulement faire double ce fera beaucoup gaignè et la clartè sera assez grande pour la multiplication de 30. L’oculaire ne doibt avoir qu’une petite ouverture et qui soit prise justement au milieu. Il n’est pas necessaire de vous recommander le secret. et quand mesme l’invention ne reussiroit pas je ne voudrois pas que vous en dissiez rien l’Israelite, a fin que par luy, Hudden ou d’autres ne penetrassent dans cette speculation qui a encore d’autres utilitez.

Pour autheur de dioptrique je n’en vois pas encore de meileur que Kepler, dont il y a un exemplaire dans la bibliotheque de mon Pere, outre celuy que j’ay emportè, qui est reliè avec d’autres traitez. demandez moy ce que vous n’y comprendrez pas, et ce que vous voulez scavoir d’avantage, et je vous esclairci…


[I post this letter for two reasons. Firstly, its body should be made easily available to others researching, or even thinking about Spinoza and his place amid 17th century sciences. It is an informed, first-hand response to a theoretical position that Spinoza held. Secondly, and unfortunately, because my French is nearly non-existent, aided by software and careful thought.

It is my hope that someone would be moved so as to accurately translate the text into English (or another language for that matter), which we may be able to post as an effective and accurate on-line source. Perhaps even the donation of a paragraph or so by individuals, so that this would be translated by community would be interesting. My email is 

It should be noted, the measurements of the figures to be inserted are only thumbed approximations meant only for visualization, and not for fact. ]