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Category Archives: Christiaan Huygens

Spinoza’s Brilliant Neighbor, The Huygens Estate: Hofwijck

Christiaan Huygens drawing of Hofwijck, where Spinoza would have visited

To add to the picture of the quiet Huygens family estate at Voorburg we have a drawing of it by the hand of Christiaan Huygens himself (undated).

This brings a certain vividness to any imagined visit by Spinoza in the summer of 1665 [thought about here: What Spinoza and Huygens Would Have Seen that Summer Night ]. It would be likely that at one of these top floor windows Huygens would have placed his telescope, and through which he and Spinoza would have gazed at Saturn. An interesting sidenote: Spinoza is said by Colerus to have drawn portraits of some quality (and he lived in the house of a master painter), so in this the two men may have shared some small interest.

Huygens’s Lens

This struck me as such a remarkable image, one that I have found in my just nascent research into Spinoza’s lens-grinding techniques (Huygens was a companion and nearby neighbor of Spinoza’s in the years 1664 and ’65). This is the lens with which Huygens discovered the first moon of Saturn (in March of 1655), and then the rings, as unlike Descartes before him he embodied his studies on the nature of optics.

There are several things that are eye-catching. First is its thinness and size. Likely ground by hand, it is merely 5.7 centimeters across and yet has a focal length of over 3 meters. It is only 3.4 millimeters thick.

Then there is the inscription at the edges, found scratched into the wax-yellow material:

A line from Ovid:

Admovere oculis distantia sidera nostris : They carried distant stars to ours eyes.

In anagram:

Saturno luna sua circunducitur diebus sexdecim horis quatuor : With Saturn, his moon circles itself around in 16 days, 4 hours”

It is this artifact of discovery, the materiality of the lens, emphasized by inscription, the presence of the poetry and the observation, that we glimpse something of the physicality of sciences, and the conceptions that enlighten it.

Later, when other moons besides this one were discovered, Huygens simply called this moon, “my moon”. One gets a sense of the personal, material and historic conception of invention.


Spinoza’s Comments on Huygens’s Progress

The Particularities of Spinoza’s Questions of Technique 

In Spinoza’s letter (15/32) to Royal Society secretary, Henry Oldenburg, after a summary of the reasons why Spinoza believes that “each part of nature agrees with its whole,” in which our knowledge position is compared to that of a worm living in our blood, the letter finishes with a few seemingly mundane topics, one of which is on Oldenburg’s interest in scientist Christiaan Huygens’s work. It is a passing note, but telling, both in its tone and substance:

The said Huygens has been a totally occupied man, and so he is, with polishing glass dioptrics; to that end a workshop he has outfitted, and in it he is able to “turn” pans – as is said, it’s certainly polished – 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.

Dictus Hugenius totus occupatus fuit, et adhuc est, in expolientis vitris dioptricis; in quem finem fabricam adornavit, in qua et patinas tornare potest, fatis quidem nitidam; quid autem ea promoverit adhuc nescio, nec, ut verum fateor, valde scire desidero. Nam me experientia fatis docuit, in patinis sphaericis libera manu tutius et melius expoliri, quam quavis machina.


In terms of tone, we get a sense of what Spinoza thinks of the wealthy Huygens’s fabrica. The shop has been fully furnished [ adornavit ] and perhaps Spinoza’s humorous word-play is evident as he calls it nitidam, a shiny, glossy or polished thing. It is a workshop for polishing lens, and itself is quite polished: spiffy. We can feel a contrast to Spinoza’s much more humble abode and hand-polishing buisness. He is the still the merchant thinker, the “Jew of Voorburg” (a village outside The Hague) or at times the “Isrealite” whose small lenses have a “remarkable polish”, in the mind of Huygens. Huygens, at the cusp of a mechanical age when the machines still have the aura of the divine about them, is pursuing a mechanized way of producing lenses, one that Spinoza cannot embrace at quite a few levels.


Also interesting is that there seems some lexical ambiguity which obscures just what is being turned. Is it the patinae (templates), or is it the patinae (understood as “tools”)? There are various descriptions of the full lathing process. By Cherubin’s report (1671), which may be rather late, and more complex than usual, there are three stages to lens-making: turning, grinding, and polishing, all of which though can be called “turning”. Turning first involves the making of templates proably made of iron, but in Huygens’s case may even be made of the superior material brass. Two are made in a convex/concave pair, and these are ground against each other to insure sphericality. These turned metal templates are then used to grind and polish a pair of brass or iron “tools” which are then used to grind and polish the glass blank. It seems the case that what Huygens’s workshop is capable of is not only polishing lenses, but also of grinding tools, and even perhaps turning the templates themselves. There is some evidence that the turning of the template was in the case of spectacle making done by a guilded turner (17).¹ So it is not perfectly clear enough if the patinae are templates or tools. But what does seem clear is that Huygens’s is a kind of impressive all-in-one machine, or workshop, one that does more than the usual. This is also suggested from his notebook drawings from the period. Possibly, everything from the work of the turner on to the final glass product can be achieved. [Spinoza, by the evidence of his letter to Hudde shown below, at least at the time of the writing of that letter, may have not only had his patinae (templates or tools) made for him, but perhaps even both, as he there uses the term scutellae (dishes), which are to be fashioned by someone else. Whether this term is synonymous with patinae is undecided.

In the latter half of our considered passage the image becomes potentially more complex. It is commonly translated and understood that Spinoza is talking about his experience with polishing of the patinae (templates/tools) themselves. Perhaps. Yet, in patinis sphaericis really gives the perspective of the polishing being carried out in respect to the use of patinae – perhaps even “within pans”, as in: “being polished by a free hand in spherical pans, is safer and better”. A free interpretation of the Latin does not easily produce the idea that the polishing is solely being done to the pans themselves. This is further supported, I believe, by the passive form of the infinitive expoliri. The sense is that being polished by the means of a free hand (the technique for hand-holding a glass blank, or any polishing device onto the pan) is both safer and better, with the infinitive operatating as the subject of the clause.

These are of course tentative thoughts about this passage, but it seems that instead of reading Spinoza’s comments as pertaining only to his long-time experience of polishing metal pans – patinae – Spinoza seems to be talking instead about his preference for using a free hand for glass itself, in metal forms. This matches up with the known fact that Huygens’s machines were ones that held the glass blank fixed in some mechanically guided way, put against the form as part of the final process. It makes more sense for Spinoza to be responding to this semi-automated, glass-grinding aspect of Huygens’ machine, and not just a form-polishing technique. The entire mechanism is organized in a way that defies Spinoza’s experienced wisdom of grinding and polishing.

Lastly, by specifying the sphericality of the patinae, he is also setting himself against any of the much-pursued quests for a way to mechanically produce Hyperbolic Lenses, (initiated by Descartes own discovery of a law of refraction, his own belief that the Hyperbola was a revealing form). Not only is Spinoza commenting upon Huygens’s social affluence, in an off-hand way, but also upon any non-spherical lens aims, and the idea that an insensate hand could create the fineness of results needed.

Here is Elwes’ translation of the passage:

The above-mentioned Huyghens is entirely occupied in polishing lenses. He has fitted up for the purpose a handsome workshop, in which he can also construct moulds. What will be the result I know not, nor, to speak the truth, do I greatly care. Experience has sufficiently taught me, that the free hand is better and more sure than any machine for polishing spherical moulds. I can tell you nothing certain as yet about the success of the clocks or the date of Huyghens journey to France.

And Shirley:

The said Huygens has been, and still is, fully occupied with polishing dioptical glasses. For this purpose he has devised a machine in which he can turn plates and a very neat affair it is. I don’t yet know what success he has had with it, and, to tel the truth, I don’t particularly want to know. For experience has taught me that in polishing spherical plates a free hand yield safer and better results than any machine.

I hesitate of course to re-translate such esteemed translators, but it seems that there are good arguments for reading Spinoza’s meaning another way. At the very least, the possibility of a second meaning seems present.


For evidence that Spinoza himself did not fashion his own templates (and perhaps not even his own “tools”), from the letter to the mathematician Hudde (41/36):

“Hisce finirem; verum, quia, ut mihi novae ad polienda vitra scutellae fabricentur, animus est, tuum hac in re consilium audire exoptem. Non video, quid vitris convexo-concavis tornandis proficiamus”

“With these I may have ended, in truth, but because for me new dishes for glasses being polished may be fashioned, such is the spirit, your council in this matter I would be eager to hear. I do not see what we may profit in ‘turning’ convex-concave glasses.”

“I might have ended here, but since I am minded to get new plates made for me for polishing glasses, I should very much like to have your advice on this matter. I cannot see what we gain by polishing convex-concave glasses” (trans. Shirley: likely June 1666; page 142 Opera).

It does not seem likely that Spinoza had very much experienced, first hand, the safety of fashioning metal plates (it may of course be the case that though not fashioning them, he did polish them, but then the safety of the process – mentioned in the letter to Oldenburg – would seem to be less of an issue).  To sum up, it seems more the case that Spinoza is, first, noting the furnished and “spiffy” nature of Huygens’s fabrica, as it polishes lenses (and even patinae ), and then secondly, that Spinoza is referring to and judging a more particular aspect of Huygens’s machine – one well-known, since Huygens was working on a semi-mechanized process for polishing lenses for a decade – that the glass is not held in a free hand.



1. D. J. Bryden and D. L. Simms. “Spectacles Improved to Perfection and Approved by the Royal Society.” Annals of Science 50 (1993) 1-32.