An Odd Kind of Sympathy

A successful cabinet of wonders should mercilessly mock the taxonomies we impose upon the world; its contents should serve as constant reminders that “there are more things in heaven and earth” than are dreamt of in our philosophies.  Our second wonder, which may induce a brief sensation of doubt in the laws of mechanics, was chosen in just this spirit.  In this episode we demonstrate the curious phenomenon (first discovered by Christiaan Huygens in 1665) that several pendulum clocks placed in a room together will mysteriously synchronize with each other. How can mechanical objects transmit an influence when they aren’t touching? What is the cause of this “odd kind of sympathy”? Watch the video to find out!




Intro Sequence (0:00-0:18)

When I made the intro sequence for the first episode I just assumed it was a fixed and finished thing (or, more accurately, I didn’t think that far ahead).  But it has since occurred to me that I can swap-out the 3 images which appear during the “intra-cave-fly-by”, thus opening-up the possibility for infinite, Simpson’s-like variations on the intro.  Of course, it’s going to be tricky to find 3, full-color, visually-arresting images for each episode, but I think the new trio I compiled is every bit as cool as the previous set.  Hopefully in future postings this challenge won’t become all-consuming to the point of despair…
Opening music: “Prospero’s Magic” by Michael Nyman, from the soundtrack to Peter Greenaway’s film Prospero’s Books.
(0:01) KIRCHER, Athanasius.  Mundus subterraneus, Janssonius & Weyerstraten, Amsterdam, 1665, Tome 1, p. 233.  Digitized photographic reproduction provided by the Herzog August Bibliothek, Wolfenbüttel, Germany.
(0:03) The same image, embellished lovingly with colored pencil.
(0:07) DESCARTES, René.  De homine (figuris et latinitate donatus a Florentio Schuyl), Leffen & Moyard, Leyden, 1662, p. 6.  Digitization provided by Google Books.  The color was added by me using the GIMP.  A big reason of why I’m obsessed with the early-modern period is that the imagery is so incredibly powerful (this heart being an excellent example).  Not many book illustrations from this period are in color, but as I become more adept with various graphics programs I think there may be hope in producing more color images like this one.  We’ll see…
(0:09) PACIOLI, Luca.  De divina proportione, with illustrations by Leonardo da Vinci, 1509.  Image downloaded from the Mathematical Association of America‘s digital library, 25-sept-2011.
(0:11) DÜRER, Albrecht.  Hirschkäfer (stag beetle), 1505.  J. Paul Getty Museum, Los Angeles, CA.  Image downloaded from Wikimedia commons, 25-sept-2011.


Wunderkammer Checklist (0:19-0:36)

(0:19) To my left, a lovely print of Dürer’s 1508 illustration of an owl.  And to my right…By the baleful caterwaul of Bastet!  It’s Thom’s cat, Paquita!  The original sass-beast herself.  It was a miracle we were able to get this footage relatively unsassed.
(0:26) WORM, Ole.  “Fasti Danici”,  Museum Wormianum, Elzevir, Amsterdam, 1655, p. 367.  Digitized photographic reproduction provided by Google Books.
(0:29) KESTLER, Johannes Stephan.  “Memnon’s Birds”, Physiologia Kircheriana Experimentalis, Jansson-Waesberg, Amsterdam, 1680, p. 217.  Kestler was a student and assistant of Kircher and edited this compilation of “physical, mathematical, medical, chemical, musical, magnetical and mechanical experiments” extracted from Kircher’s oeuvre.  Here he describes how to make “Memnon’s birds”, metallic automata which chirp and flap their wings when exposed to the light of the rising sun.  Possibly an excellent project for a future episode…
(0:31) ALDROVANDI, Ulisse.  “Lamb with monsterific head”, Monstrorum historia, Nicola Tebaldino, Bologna, 1642, p. 471.  Digitized photographic reproduction provided by the University of Strasbourg.  Colorization by AB.


Huygens’ Hypochondriac Hypothesis at the Hague (0:37-1:25)

(0:37) “… just as surprising today as when it was first discovered in the 1660s.”  This statement, insofar as it refers to pendulum clocks, is indeed accurate (the very least, I hope, you’ve come to expect from this site).  But I was all the more surprised–no, I was shocked–to discover that mention of the sympathy of clocks actually predates Huygens.  I came across a reference to horologii sympatici (sympathetic clocks) in Niccolò Cabeo’s 1646 commentaries on Aristotle’s Meteorologica, written nearly 20 years before Huygens’ observations!!  The specific reference is:
CABEO, Niccolò.  In quattuor libros meteorologicorum Aristotelis commentaria et questiones quattuor tomis compræhensa, the Heirs of Francesco Corbelletti, Rome, 1646, Tome I, pp. 31-3.  I have not been able to find any version of this text to link-to online, but oddly enough I have a copy of it on my computer (it’s enormous) from a previous project.  The passage of interest addresses the question: Utrum ad actionem requiratur contactus (Whether contact is required for action).  Action-at-a-distance was an absurdity in Aristotelian physics, but Cabeo here takes the opportunity to discuss the phenomenon of sympathy, of which he gives four examples: (1.) the sympathetic cure of wounds, (2.) burning the excrement of an animal causes that animal to evacuate its bowels even unto its own death, (3.) that the poison from a tarantula bite (another topic of prime concern to the Baroque mind) looses its toxicity once the spider dies, and (4.) the sympathetic synchrony of clocks.  A lengthy discussion ensues, but Cabeo is firm in denying the possibility of action at a distance and he is especially insistent that there is no such thing as sympathetic clocks.  That a notion of the sympathy of clocks predates Huygens (and, therefore, the pendulum clock) is amazing and, I think, not widely recognized.
(0:56) PORCELLOTTI, Eustachio. Model of a pendulum clock according to a description by Galileo Galilei.  This model dates from 1879 and is housed at the Museo Galileo, (formerly the Institute and Museum of the History of Science), Florence, Italy.  Image downloaded 11-oct-2011 and colorized by AB.
(1:01) NETSCHER, Caspar.  Portrait of Christiaan Huygens, oil on paper, 1671.  Haags Historisch Museum, the Hague, the Netherlands.  Image downloaded from Wikimedia Commons,  28-oct-2011.
(1:05) HUYGENS, Christiaan.  Horologium Oscillatorium, F. Muguet, Paris, 1673, p. 4.  Digitization of the complete text provided by Google Books.  Image colorized by AB.
(1:07) “And he’s surrounded be pendulum clocks because, well, he invented them…” Like many technological advances, the precise chronology of the pendulum clock is somewhat mysterious.  Certainly the idea seems to have originated with Galileo and his earliest description, as far as I can tell, is in his 1637 letter to Laurens Raeal, the Dutch statesman and seafarer (would that those occupations aligned more in our times!)  The full reference is,
GALILEI, Galileo.  Letter #3496, Galileo to Laurens Raeal, 5 June 1637, in Le opere di Galileo Galilei, edited by Antonio Favaro, Tipografia Barbèra, Florence, 1890-1909, Vol. XVII, pp. 100-3.  A digitized version of the complete volume is provided by Gallica, the digital repository of the Bibliothèque nationale de France.
The Museo Galileo in Florence holds a copy of an early drawing of a pendulum clock supposedly made for Vincenzo Galilei (Galileo’s son) and Vincenzo Viviani (Galileo’s student and editor).  It’s not clear what year such a drawing would have been made.  Galileo introduced the pendulum clock as part of a system for finding the longitude at sea (which also involved his telescope for observing the eclipses of Jupiter’s moons), an application which connects all of the sundry protagonists of our story.
Hugyens’ status as the father of the pendulum clock derives from the fact that he was the first to design a successful working model (though he contracted out its manufacture) and the first to obtain a patent, in 1657.  Inasmuch as I feel no particular obligation to verify these assertions by hunting around for original documentation, the reader may regard this list (from as authoritative in proportion to its apparent exhaustiveness.  And, as all students of physics know, it was in the context of refining the pendulum clock that Huygens proved that the tautochrone is a cycloid (see, Horologium oscillatorium, pars II, prop. XXV, op. cit.).
(1:12) Reconstruction of a pendulum clock designed by Huygens and manufactured by Salomon Coster, 1657.  Science Museum, London, UK.  Image1 and Image2 downloaded from, 3-nov-2011.  To make things more interesting, I placed the first image on top of p. 32 of Huygens’ Horologium Oscillatorium (op. cit.)
(1:22) “… and so, in his letters, he writes of the clocks as having a sort of ‘sympathy’ between them.”  The account given here of Huygens’ discovery of the sympathy of clocks is reconstructed from his correspondence.  Impressively, the complete works of Huygens have been digitized, and the letters in question can be found in:
HUYGENS, Christiaan.  Œuvres complètes, edited by Martinus Nijhoff, Société Hollandaise des Sciences, La Haye, 1888-1950, Tome V.  Digitized photographic reproduction of the complete volume is provided by the Open Library (which has the extremely nice feature of letting you link directly to individual pages).
Huygens’ first letter on this topic is addressed to his famous father, Constantijn, but the remainder of the story is found in his letters to Robert Moray, his contact at the Royal Society in London.  Since these letters are between two Dutchmen (Huygens père et fils) and a Scot (Moray), I naively thought they would be written in a proper language like Latin.  Silly me; they’re all in French.  Now, I make no pretensions of being able to speak French, but inasmuch as the last time I checked French was still a romance language in good-standing, I can generally get by with a dictionary and some verb tables.  But I found these letters to be especially tricky in that the irregular 17th century spellings were incomprehensible to most online dictionaries.  Praise, then, should go to Wiktionary (whose comprehensiveness seems to have progressed remarkably from the last time I checked) for having entries for most of the archaic morphologies; praise must also go to Google Books for having digitized a French-English dictionary from 1673 which turned out to be absolutely vital for deciphering some of the key terms.
But most of all, praise must go to my great friend, the illustrious Dr. Guido Nicola Innocenzo Festuccia.  Guido, who is a theoretical physicist at the Institute for Advanced Study in Princeton, NJ, was already the official Idols of the Cave advisor for theoretical physics, all things Italian, and exotic fruits.  But so vast is his polymathy that, in my moment of need, Guido had no trouble serving as Idols of the Cave Gallic Advisor pro-tempore.  It is my strong hope that this ornament of our age will feature prominently in future episodes.  As to whether the world is truly ready for the splendor that is the Guidosfera, I will not hazard to speculate.  Guido was able to quickly sketch-out translations for several of the letters of interest and to assist me with the others.  The resulting translations, which I provide here for the benefit of my readers, are a combined effort, but the contributions are something like 80% GF and 20% AB.  Any errors are, of course, 100% the fault of AB.
The main affair of the sympathetic clocks is, as far as I can tell, recounted in 5 letters (No. 1335, No. 1338, No. 1345, No. 1348, and No. 1362) as well as two references in the minutes of the Royal Society from 1664/5 (pp. 19, 21).  I mention this here so as to provide all the links together in one place.  But I will discuss each in their turn according to their place in our story, providing translations of those passages which seem particularly noteworthy.  Here, then, are the first two letters, which recount Huygens’s initial discovery of the phenomenon:
26 February 1665, Christiaan Huygens to his father, Constantijn Huygens (No. 1335)
“… Having been forced to keep to my chambers for some days, which I occupied in making some observations of my clocks of a new design, I noticed an intriguing effect, and one which no one ever would have thought of.  That is, that these two clocks, being suspended the one next to the other at a distance of one or two feet, keep a precision between them that is so exact that the two pendulums always beat together without ever varying.  Having admired this greatly for some time, I finally found that it happened because of some sort of sympathy [une espece de sympathie], such that by making the pendulums strike with mixed beats I found that within a half an hour they would always put themselves back into consonance and keep to it constantly afterwards for as long as I let them go.  I then separated the one from the other, hanging one at one end of the room and the other fifteen feet from it; and then I saw that in a day there were 5 seconds of difference and that consequently their previous agreement had not come but from some sympathy which, in my opinion, cannot have any other cause than an imperceptible agitation of the air which is produced by the movement of the pendulums.  The clocks are however enclosed in their boxes, which with all the lead which is inside, can hardly weigh less than a hundred pounds each.  And the vibrations of the pendulums, when they are put in consonance, don’t go such that the one is parallel to the other, but on the contrary, they approach and separate with contrary movements.  Upon bringing the clocks close together again, I saw that afterwards the pendulums were put back into the same cadence.  I moreover took a table-mat (?) [quarrè de table] of three-feet per side, one-inch thick, which I put in between the two such that the bottom touched the floor, and it was so tall that it entirely covered the clocks and separated them in this manner one from another.  But nevertheless the concordance remained as before, lasting entire days and nights, and even if disturbed by me, it reestablished itself in little time.  I am now attempting to bring them together very precisely (being separated) and I will test to what distance the aforementioned sympathy extends, imagining, by what I have already seen, that it may well be up to five or six feet.  But to have a better certainty of these things it is necessary, if it please you, to wait until I have examined them further and investigated the causes more exactly.  But nevertheless, here two clocks are found which never deviate at all, which will seem incredible and yet it is entirely true.  Never have any other pendulums, except this new invention, been able to do the same thing; and one can see by this how exact they are since it takes so little to keep them in perpetual accord.”
27 February 1665, Christiaan Huygens to Robert Moray (No. 1338)
The portion of this letter dealing with the sympathy of clocks is nearly identical to letter translated above. Huygens additionally requests that Moray convey these findings to the Royal Society in London.


Sympathy, Its Power and Powder (1:26-2:28)

(1:34) BRUEGHEL, Pieter (the elder).  De Gaper (Yawning Man), miniature, 1563. Musées royaux des Beaux-Arts, Brussels, Belgium.  Image downloaded from, 2-nov-2011.
(1:38) “… and it’s the reason why a drum made out of lambskin will go quiet if there’s a drum made out of wolfskin nearby.”  The astute viewer will recognize that this is, in fact, an example of sympathy’s evil twin antipathy, but it was the example I liked the best so I decided to use it nonethelss.  Moreover, this curious chestnut seems to have acquired an especially wide currency at the time.  We can find mention of it in the following sources (though I’m sure one find others without too much trouble):
1. FRACASTORIUS, Hieronymus. Liber unus de sympathia et antipathia de rerum, Jean de Tournes & Guillaume Gazeu, Lyon, 1554, p. 20.  Digitized photographic reproduction of the full text provided by the Bayerische Staatsbibliothek.
2. DESCARTES, René. Compendium musicæ, Joannes Jansonnius Jr., Amsterdam, 1656, p. 1.  Digitized photographic reproduction of the full text provided by google books.  However, see also Descartes’ position on sympathy as given in the Principia philosophiæ, op. cit. infra
And see also, SHEA, William R.  Designing Experiments & Games of Chance: The Unconventional Science of Blaise Pascal, Watson Publishing, Canton, MA, 2003, Cap. 5.
(1:41) GULDENMUND, Hans.  Der Fendrich. Laytinger. Pfeyffer und Drummelschlager. Woodcut, mid 1500s, Herzog Anton Ulrich Museum, Braunschweig, Germany.  Image downloaded from Europeana, 2-nov-2011.
(1:46) Jan Ziska, or Zisca (or Žižka according to the ever punctilious editors of Wikipedia).  The fun fact about having his skin made into a drum comes from (where else?) Robert Burton’s Anatomy of Melancholy:
… And as that great captain Zisca would have a drum made of his skin when he was dead, because he thought the very noise of it would put his enemies to flight, I doubt not but that these following lines, when they shall be recited, or hereafter read, will drive away melancholy (though I be gone) as much as Zisca’s drum could terrify his foes.”
A prophetic prognostication indeed.  See BURTON, Robert.  The Anatomy of Melancholy, originally published 1621, this edition printed for Thomas McLean in Haymarket, et al., 1826, Vol. 1, p. 24.  Digitization of the complete text provided by Google Books.
Not knowing exactly how to illustrate this point, I made a little ‘tetratych’ of (one hopes) suitably didactic images:
1: A heroic statue of Jan Ziska located in Tábor, Czech Republic. Image downloaded from Wikimedia Commons, 8-nov-2011.
2:   VALVERDE de AMUSCO, Juan.  Anatomia del corpo humano. Salamanca & Lafrery, Rome, 1560, p. 64.  Image downloaded from  Historical Anatomies on the Web, 8-nov-2011, colorized by AB.
3. Detail of a drum from the Hans Guldenmund woodcut cited earlier.
4. MÜNSTER, Sebastian.  This image was downloaded (8-nov-2011) from a website ( which is devoted to UNIX and the owner’s private collection of antique maps.  Needless to say, I think that’s a pretty fantastic combination.  I can’t source the image as thoroughly as I’d like, but the website seems to imply it’s from Münster’s Cosmographia. Maybe I’ll just have to ask the man himself…
(2:00) GERSDORFF, Hans von.  Feldtbůch der Wundartzney, Hans Schotten, Strassburg, 1528, p. 21V.  Image downloaded from Historical Anatomies on the Web, 7-nov-2011, and colorized by AB.  This excellent site, which I was unaware of until now, is a venture of the National Library of Medicine and the National Institutes of Health.  I found it by doing a google image search for “wound man”, of which this image is an excellent example.  Wound-man images were a staple of medieval and renaissance surgery books because, hey, why have separate illustrations to show the all the various life-ending traumas one could receive in battle when you can save space and combine them into one single, horrifying woodcut?
(2:12)  VANDERBANK, John.  Francis Bacon, Viscount St. Alban, 1731.  Oil on canvas.  National Portrait Gallery, London, UK.  Image downloaded from Wikimedia Commons, 10-nov-2011.
(2:14) Van UTRECHT, Adriaen.  Vanitas–Still Life with Bouquet and Skull, mid-1600s.  Oil on canvas.  I can’t figure out where this painting is held (o internet! you’re supposed to know these things!) but various hints suggest that it’s actually part of a private collection.  Anyways, the image was downloaded from Wikimedia commons, 10-nov-2011.
(2:16) “… a mixture of skull-moss and the fat from a boar and a bear killed in the act of mating.”  You may think I’m making this stuff up, but really, I promise, I’m not.  The reference is:
BACON, Francis.  Sylva Sylvarum, in The Works of Francis Bacon, collected and edited by James Spedding, Robert Leslie Ellis, and Douglas Dennon Heath, originally published 1857-74, this edition published by Houghton Mifflin & Co., Boston, 1900, Vol. 5, p. 161, century X, §998.  Digitized photographic reproduction provided by the Open Library. The description is sufficiently astounding that I’ll transcribe it here:
“… the ointment wherewith this is done is made of divers ingredients; whereof the strangest and hardest to come by, are the moss upon the skull of a dead man unburied, and the fats of a boar and a bear killed in the act of generation.  These last two I could easily suspect to be prescribed as a starting-hole; that if the experiment proved not, it might be pretended that the beasts were not killed in the due time: for as the moss, it is certain there is great quantity of it in Ireland, upon slain bodies, laid on heaps unburied.”
Right, so you can all stop complaining to me that it’s just too hard to find skull-moss.  Apparently there’s plenty in Ireland, so go bother them for a change.  And as for you who are always insisting that the Lord Chancellor is nothing more than a pompous boob, I think you owe him an apology.  As you can see, he’s clearly astute enough to suspect the whole boar-bear love-fat thing might be a trap.  I only wish that the baron had applied his razor-like acuity to what I consider the most contentious issue here, namely, are the boar and bear supposed to be killed in the act of generation in general or expressly in an unlikely pairing with each other?  Hmm, perhaps this is a trap as well.  (Note to the fastidious reader: Yes, it’s true, Bacon is here referring to an ointment and not a powder, that is, the unguentum armarium ‘weapon-salve’ as opposed to the pulvis sympatheticus ‘powder of sympathy’.  So what right, you ask, do I have in conflating the two?  An excellent question. But my answer remains the same: skull-moss).
(2:17) 1: SNYDERS, Frans.  Wild Boar Hunt, mid-1600s.  Oil on Canvas, Museum Rockoxhuis, Antwerp, Belgium.  Image downloaded from Wikimedia Commons 10-nov-2011.
2: de VOS, Paul.  Bear Hunt, mid-1600s.  Oil on canvas, The Hermitage, St. Petersburg, Russia.  Image downloaded from Wikimedia Commons 10-nov-2011.


The Mechanical Philosophy (2:29-2:44)

(2:29) DESCARTES, René.  Title page from Principia philosophiæ, L. Elzevir, Amsterdam, 1644. Digitization of the complete text available from google books.
(2:33) DESCARTES, René.  “The universe as plenum”, from Principia philosophiæ, op. cit., p. 110. Image colorized by AB.
(2:37) “nothing more than matter in motion“.  And just to make explicit the incompatibility of sympathy with the mechanical philosophy, Descartes writes:
And indeed, if anyone will consider how wondrous are the properties of the magnet and of fire…and the rest whose causes–sufficiently evident in my judgment–I have deduced in this text from principles that are both known to all and admitted by all, namely, the shape, size, position, and motion of the particles of their material, he will easily persuade himself that there are no powers in stones or plants so occult, no miracles of sympathy or antipathy so stupendous, in the end, nothing in all of nature which ought not be reduced to causes corporeal only, that is, devoid of mind and thinking–nothing whose reasons cannot be deduced from these same principles such that it is unnecessary to adjoin to them any others.”
DESCARTES, René.  Principia philosophiæ, op. cit., book IV, §187, pp. 296-7.
(2:43) Orrery after a design by James Ferguson.  This model was built ca. 1775 and is housed at the Museo Galileo (formerly the Institute and Museum of the History of Science), Florence, Italy.


The Longitude (2:45-3:08)

(2:51) BRUEGHEL, Pieter (the elder). Storm at Sea, 1568.  Oil on wood, Kunsthistorisches Museum, Vienna, Austria.  Image downloaded from, 12-nov-2011.
(2:53) “… the most pressing technological and scientific challenge of the day.”  The story of the longitude problem is one of those truly ripping yarns in the history of science.  It was generally straightforward for a ship at sea to determine its latitude (just find the elevation of the North star); a ship’s longitude, however, was exceptionally difficult to calculate.  Fundamentally, though, what was required was something very simple: an accurate method for telling time.  That is, if a ship could know its own local time (say, by marking as noon when the sun is directly overhead) and simultaneously know the time at a known longitude (say, if at that exact moment it was 3pm in Greenwich), the ship would, in this instance, know that it was 45° west of Greenwich.  The trick was for the ship to know what time was back home. As the various European powers competed for dominance of the seas, the effort to develop an accurate method for finding the longitude became an issue of importance at the highest levels of state.  This history has been told many times and told well.  The most famous account is
SOBEL, Dava.  Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, Walker Publishing, New York, 1995.  The lone genius in the title is John Harrison (1693-1776) who developed a series of increasingly accurate marine clocks.
(2:56) “And Huygens saw the sympathy of his clocks as proof of just how amazingly well suited they were to this task.”  Following Galileo’s lead, Huygens believed the increased accuracy of pendulum clocks might be enough to allow them to function as useful marine chronometers and he was in consultation with the Royal Society in London for precisely this end.  And during the exact period when he observed the sympathy of his clocks, Huygens was corresponding with members of the Royal Society about the sea-trials of some other clocks of his on the ship Jersey, commanded by Major Robert Holmes.  These events are all the more interesting when one considers that all of this was happening during the tense run-up to the Second Anglo-Dutch War, with open hostilities commencing in March of 1665 (and where Major Holmes would play a prominent role).  An excellent account of this history, with special attention given to Huygens, can be found in
JARDINE, Lisa.  Going Dutch: How England Plundered Holland’s Glory, Harper Collins, New York, 2008.
It is here that we will reprise the narration of Huygens’ discovery as told in his correspondence.  When we last left our hero, he had sent notice of his discovery to his father (Letter No. 1335, on 26 Feb. 1665) and to Robert Moray, his contact at the Royal Society in London (Letter No. 1338, on 27 Feb. 1665).  Moray responds with a letter dated 24 February.  But wait!  How can Moray respond (on the 24th) to a letter Huygens hasn’t yet written (on the 27th)?  Well, it’s because England in its Protestant fervor insisted on keeping the old Julian calendar instead of adopting the superior (but suspiciously popish) Gregorian calendar with the result that during this time England would have been 10 days behind most of continental Europe.  So, from Huygens’ perspective, Moray would have responded on March 6th, which is the date given in the Œuvres complètes.  Moray astutely points out that, despite Huygens’ excitement, Huygens’ observations of sympathy seem rather to indicate the clocks’ unsuitability for service at sea. The passage in Moray’s letter addressing the sympathy of clocks is as follows:
6 March 1665, R. Moray to Christiaan Huygens (No. 1348)
“… It was indeed a very welcome surprise for our president [William Brouncker] and for me to learn about this new sort of sympathy which you have observed in your clocks.  It will doubtless be good to discuss and we intend to speak about it at our first assembly.  But it’s possible that we won’t deliberate on it until the assembly eight days later so that we may think before discussing it.  Be this as it may, I’ll do my part in communicating to you what is said about it if I find there is something worthwhile.  But I will tell you that if it were not the case (as each of us knows) that you are thoroughly capable of inventing on your own all the experiments necessary, both to penetrate further into this matter and to draw useful consequences from it, perhaps we could propose some for you to do on this subject.  But inasmuch as you are undertaking the pursuit of this, it is necessary to rely on you.  I would only mention that I’d be pleased if you could know precisely to what extent it is necessary for the two clocks to approach each other in precision before this sympathy will appear; that is to say, whether 2, 3, 4 or some other number of seconds in 24 hours.  Next, if 3 or 4 watches will be able to agree with each other in this way; and lastly, since when there is a difference of 2 or 3 seconds in 24 hours between the two clocks they do not fail but to come into accord, that you could learn which yields to the other, as apparently one rectifies the other.  These differences can be observed, it seems to me, as well as the solution to that last difficulty, by comparing them to your large clock which strikes the seconds.  For the rest, if any imperceptible movement of the air can cause this isochronicity, I fear that one would have reason to suspect that some irregular motions of the air could rather make them deviate from their true exactness which renders their vibrations equal.  And since, in the end, the clocks which feel these movements can more easily stray than those which do not feel them at all, it follows that it would be better if the two clocks which are used at sea might not be in so well an agreement as otherwise, insasmuch as their difference being always the same, it serves just as well as if the there weren’t any at all.  Instead, by keeping themselves always together, one cannot be so well assured that they do not lose any of their precision, since what is evident from you experiences is that whenever in reality they are 2 or 3 seconds away from being said to be both equally correct, that this does not hinder them from going equally fast when they are within one or two feet of each other.
“I have let myself go much further in this material than I thought when I set myself to write. But it is to justify what I said to you at the beginning, that I interact with you without any manner of constraint. You will tell me that perhaps what I was just saying settles nothing to the disadvantage of the clocks with regards to their usefulness, and I shall well vouch this to you. You will always find that I do not but discourse in my usual way on whatever comes up in conversing with you. But, for fear lest I be soon interrupted as almost always happens to me, I leave this material aside for the present, to be taken up again another time, and I go to see what I have to say to you about the other passages in your letter.”
True to his word, Moray does mention Huygens’ observations at the Royal Society, and this is recorded in the Society’s minutes.  The record is not terribly illuminating, but it is the source of the TITULAR LINE of this episode so, naturally, I feel compelled to transcribe it in full.  The reference is:
BIRCH, Thomas.  The History of the Royal Society of London for Improving of Natural Knowledge from its First Rise, printed for A. Millar in the Strand, London, 1756, Vol. 2, p. 19.  Digitization of the complete text provided by google books.  The entry is dated March 1, 1664/5 (which would correspond to March 11, 1665 in the Gregorian calendar.  Note also that in England the new year began on March 25th which is why the year is marked as 1664/5).
A letter of Monsieur Huygens to Sir Robert Moray, dated at the Hague Feb. 27, 1664/5, N.S. was read, giving notice 1. Of his instructions printed in Dutch for pilots, about the use of his pendulum watches at sea.  2. Of an odd kind of sympathy perceived by him in these watches suspended by the side of each other.  3. Of his agreement with Dr. Wren about the place of the comet.  4. Of his opinion concerning Monsieur de Son’s chariot, together with his thoughts of one of his own devising.
“It was thought proper hereupon, 1. That the said instructions should be compared with those of the president, to have them printed in English.  2. That the president and Sir Robert Moray should be desired to think upon and make some experiments, to find out upon what account this pretended sympathy should happen; whether from a magnetical cause, or from the agitation of the air; and, among other things, to observe whether pendulums, that go alike in any clock-work, go together, hanging near to one another; as also whether three or four watches do the same, that two do.  3. That Mr. Hooke should extract out of his lecture a discourse upon the late comet, and fit it for the press, together with the necessary schemes.  4. That Col. Blount having given several good hints for improving carriage, and particularly for trying experiments about chariots by weights, should be desired to bring in, after more trials upon this subject, a model of his conceptions about it.”
(3:04) DESCARTES, René.  “Formation of clouds by the winds”, from “Meteora” in the Specimina philosophiæ, p. 256, published in one volume together with the Principia philosophiæop. cit. Image colorized by AB.
(3:05) “And like a good Cartesian, he initially suspected subtle currents of air…”  Huygens’ account is found in letters No. 1335 and No. 1338, with the translation to letter No. 1335 provided above.  Philosophers of the Cartesian persuasion were often obliged to rely on hypothetical currents of air insofar as they denied action-at-a-distance and denied the existence of the vacuum.  This made the development of the air-pump (a device for evacuating the air from a glass chamber) a somewhat sore topic for them.  An excellent account of Thomas Hobbes’ rather pathetic obstinance  in this regard (as well as some brazen propaganda for the sociology of scientific knowledge) can be found in:
SHAPIN, Steven, and SCHAFFER, Simon.  Leviathan and the Air-Pump: Hobbes, Boyle and the Experimental Life, Princeton University Press, Princeton, NJ, 1989.


The Powder of Sympathy, Mechanized (3:09-3:35)

(3:18) van DYCK, Anthony.  Portrait of Kenelm Digby, oil-on-canvas, 17th century, part of a private collection.  Image downloaded from Wikimedia commons, 13-nov-2011.  There is, at least in my opinion, a much more interesting portrait of Sir Kenelm in the possession of the National Maritime Museum, Greenwich, UK which I did not use because of their somewhat mystifying insistence on copyright.  I’m generally sympathetic to the situation content-providers must find themselves in in this brave, new, internet-y world (that’s why I didn’t use the image).  Indeed, I like to think that with all the effort I put in to sourcing my material, that this site can be a model of sorts of how internet images can be used in an above-board kind of way.  And while I found the museum’s API to be a fairly forward-looking attempt to address the issue, fundamentally I think it’s shameful for a public museum to insinuate that there’s even a hint of copyright on a work that’s over 300 years old! There.  That’s my rant for the day (or at least the next 5 minutes).
(3:25) “… who in 1658 authored a treatise…” This treatise is purportedly a transcription of a talk given by Digby to a ‘famous assembly’ in Montepllier, France (not the Académie des sciences which wasn’t founded until 1666, but presumably one of its several forerunners).  Appropriately enough, the earliest edition is in French:
DIGBY, Kenelm. Discours fait en une celebre assemblee par le chevalier Digby, chancelier de la reine de la Grande Bretagne &c., touchant le guerison des playes par la poudre de sympathie, Augustin Courbe & Pierre Moet, Paris, 1658.  Digitized photographic reproduction of the full text provided by the Bayerische Staatsbibliothek.
An English translation appeared soon after and underwent multiple printings:
DIGBY, Kenelm. A Late Discourse Made in a Solemn Assembly of Nobles and Learned Men at Montpellier in France , by Sir Kenelm Digby, Kt. &c., Touching the Cure of Wounds by the Powder of Sympathy, translated by R. White, gentleman, 4th edition, printed by J.G. and to be sold by Octavian Pulleyn, London, 1664.  Digitization provided by Google Books.
One thing I like in all these powder of sympathy texts is the evident pride its proponents project in being able to showcase a discovery that was ‘unknown to the ancients’.  Unfortunately, though, if all you’ve got is polyphonic music and the powder of sympathy, it’s hard to make an argument that your civilization is superior to Greece and Rome (but, hey, at least polyphonic music is pretty).  Anyways, one finds claims that Paracelsus (1493-1541) was the first discoverer, but I didn’t follow the threads back to determine what the original source would have been.  Certainly, though, it does seems that it’s Digby, with his rambling though comparatively intelligible account, who was responsible for kicking powder-of-sympathy-mania into high gear.  Thus it’s only a few years after Digby’s talk that the Powder of Sympathy All-Star Collectors’ Latin edition hit the bookstores of Europe with the fabulous title Theatrum Sympatheticum (“The Theater of Sympathy”). The proper reference is:
Various authors.  Theatrum sympatheticum, Johann Andreas Endter & the Heirs of Wolfgang Endter Jr., Nuremberg, 1662.  Digitized photographic reproduction of the full text provided by the Herzog August Bibliothek.
This massive brick of a book contains not only a Latin translation of Digby’s speech, but also treatises and excerpts from various authors who together make up something like a Baroque Insanity Dream Team: there’s Kenelm Digby (naturally), Jan van Helmont, Athanasius Kircher and Robert Fludd all in one volume! (Order now! )  But more importantly for our purposes, the Theatrum sympatheticum contains quite possibly the only contemporary illustration of the powder of sympathy (certainly the only illustration I was able to find).  The illustration accompanies the Latin edition of Digby’s speech as translated by Lorens Strauss, a physician from Ulm, Germany.  At first the graphic was completely incomprehensible to me, but fortunately, in true Baroque style, the illustration is accompanied by an explanatory Latin poem.  I translated the poem in order to figure out what was going on in the picture; it’s a rough translation and certainly something I’d want to revise if it were ever to appear anywhere besides this website.  But considering that it’s extremely unlikely that anyone ever has or ever again will take the time to translate this madness, I decided to post it here for the benefit of, well, oh probably no one:
(3:20-3:35) STRAUSS, Lorens.  “Illustration of the powder of sympathy with explanatory poem”, affixed to his “Letter to Kenelm Digby” in the Theatrum sympatheticum, op. cit., pp. 125-6.
Behold, a wondrous cure of wounds!
Which Celsus himself, the artisan, did not know,
And whatever in the world that more ancient healer favored,
Perhaps (by Hercules!) even he had failed to note.
With Pamphilus lend your ears, you who do not know these things,
And look with lynx’s eyes at the front of this book.
A cloth is washed in water, which is red with blood,
From the gore of a recently wounded man.
But the powder was previously dissolved in the water,
The cloth is then dried.  What more?
The pain of the wound ceases and is removed.
Each of these things benefits from a temperate warmth,
For if they are done with heat and blazing fire,
The wound is scorched with a fiery burning.
To many the author seems here mystical,
And the spirit astral. Very many are they, besides,
Who ascribe the force and power to the occult quality of a lurking sorcerer,
And go on and on about the
Anima Mundi.
But Digby is another Oedipus before this sphinx,
And presumes something different than the rest,
And everywhere unties the knots of enigmas,
With which intricate Nature abounds.
For he would have that all the air is full of light,
And that light presides over everything,
And carries atoms with itself across long intervals of space,
And after a while, carries them back,
Just like a ball bounced forcefully from a wall,
Draws out quite a few corpuscles.
Nor is it dissimilar to a cloth on which liquid was poured,
Which, when it is warmed by a nearby fire,
Produces a mist, or something like it.
And thus we see that a lamp is reflected,
In the morning when the radiance of Phoebus,
Illuminates the earth, drunk with a dewy moisture.
A thick air rises, seeking the heavens,
And forms a little cloud which thereupon is carried,
From the orbit of the sun until it disappears from sight.
And nothing, the author continues, is therefore empty of air,
As he proves by the corpuscles already mentioned,
And by baby vipers which are closed-up,
In a glass prison but thrive,
And feed upon the atoms with great profit,
For day by day they grow larger.
But, Argus, you perceive a knot is lurking here:
Why does a wart, when the rays of the moon are seen,
No longer oppress the hand with its presence?
But proceed, Muse, and turn the pages!
It is still, asserts our author, that these corspuscles,
However much they be divided, will never find an end.
Wherefore he narrates very many things,
About these corpuscles and atoms,
By which a canny dog finds his prey, and about hammered gold,
In order that these examples may sparkle with light.
However (he later adds), these are not attracted,
In just one way, but oftentimes they emulate filtration,
Whereby a fluid moves upwards toward the pole,
Or often they obey the laws of fire which attracts what is wet.
But more strongly are they glued together,
Whose nature most agrees,
As a burden and scale add their own weight,
So that they may correspond in all things.
But of things whose nature is very discrepant,
It is the greatest effort to draw them together.
He points to that wet Chaos which, he briefly relates,
Some people keep in a glass vessel,
To indicate what is the order and place,
Of the four natural things, the
Grand Sophos,
The prime elements which thereupon he names:
Figure, Quantity, Imagination,
These are believed to be of the greatest weight.
Indeed!  Great is the force of Imagination;
Figure and quantity are exceptionally powerful!
Hence if somebody yawns, another will yawn as well,
Hence the harmony of lutes;
Hence will you dance if bitten on the foot by a tarantula.
Lastly the author adds to these what he maintains thus:
Namely, that a body which attracts these spirits,
Attracts also whatever is adjacent to them.
Thus when milk boils over and spills,
And experiences the force of fire on the coals,
The cow suffers from tremendous pain,
And is racked with a fiery heat in her udders.
And thus the ulcerated foot of an ox,
Feels relief or is afflicted with pain,
According to how much the breeze of a benificial spirit soothes,
Or a malignant one aggravates it.
Thus also at the lightening bolts of Mars,
Does fiery Vulcan sink down on the anvil,
And along with the falling, black soot,
The anger of the raging fire vanishes.
And many things, which narrow meter cannot hold,
Digby, worthy of all praise, inserts.
He concludes that in the treatment of the wound,
The sun and light attract spirits of the gore from the bandage,
Along with corpuscles of the powder.
But meanwhile, he says, the wound is exhaling spirits,
That are full of heat and fiery,
And which are always drawing new air to themselves,
And when thus the spirits of the gore and powder,
Finally arrive, those spirits, as they are returned to themselves,
And their origin, they dig in their heels.
And each enjoys his own proper seat.
Therefore, so long as the horde of powder corpuscles,
Is mixed tightly with the rest,
And every current from the wound,
Passes through each other, Lo! A cure arises!
Even the surgeon was summoned as a joke,
With Momus shouting: Go away, come back after the feast!


Longitude Redux (3:36-4:10)

(3:36) HOGARTH, William.  The Rake’s Progress, Plate 8: “Scene in a Madhouse”, 1735.  Image downloaded from Wikimedia Commons 15-nov-2011.  The Rake’s Progress was, to my surprise, originally a series of paintings, now kept in Sir John Soane’s Musuem, London, UK.  Apparently, though, the paintings functioned mainly as a vehicle to advertise subscriptions for the set of engravings which appeared in 1735.  This image is the final plate of the series and shows the protagonist, Tom Rakewell (center, front, shirtless and bald), fallen so low that he has now been locked-up in Bedlam, London’s notorious mental asylum.  That the poor lunatic in the background is indeed trying to solve the longitude problem is attested here:
NICHOLS, John.  Biographical Anecdotes of William Hogarth, 2nd edition, printed by and for John Nichols, London, 1782, p. 181.  Digitization of the complete text by Google Books.  Indeed, we learn the juicy tidbit that the sketch is a very specific send-up of William Whiston’s scheme for finding the longitude by using an explosion as a flare or beacon.  Whiston’s slender idea can be read in a slender treatise here:
WHISTON, William, and DITTON, Humphrey.  A New Method for Discovering the Longitude Both at Sea and Land, Humbly Proposed to the Consideration of the Publick, printed for Mr. Whiston and Mrs. Ditton; and sold by J. Roberts near the Oxford-Arms-Inn in Warwick-Lane, 1715.  Digitization of the full text by Google Books.
This rather impractical scheme has the distinction of having provoked mockery from both Hogarth and Jonathan Swift (which, as far as mockery goes, would pretty much have to be any 18th-century Londoner’s worst nightmare).  See,
SWIFT, Jonathan.  The Works of Dr. Jonathan Swift,  8 vols., printed for A. Donaldson at Pope’s Head, Edinburgh, 1759, vol. 6, p. 125.  Full text digitized by Google Books.  Since Swift’s contribution to our story is rather more ribald than long, I’ll transcribe it in full:

The longitude miss’d on
By wicked Will. Whiston;
And not better hit on
By good Master Ditton.

So Ditton and Whiston
May both be bep-st on;
And Whiston and Ditton
May both be besh-t on.
Sing Ditton
Besh-t on;
And Whiston
Bep-st on.
Sing Ditton and Whiston,
And Whiston and Ditton,
Besh-t and Bep-st on,
Bep-st and Besh-t on.


(3:47) Anonymous. Curious Enquiries, Being Six Brief Discourses, viz. I. Of the Longitude.  II. The Tricks of Astrological Quacks.  III. Of the Depth of the Sea.  IV. Of Tobacco.  V. Of Europe’s being too full People.  VI. The various Opinions concerning the Time of Keeping the Sabbath, Printed and are to be Sold by Randal Taylor, near Stationers Hall, London, 1688.
This highly amusing text (and short! only 24 pages) is digitized by Early English Books Online which, unfortunately, requires a subscription to access.  Many thanks, then, go to Catherine Wehrey and Kevin Miller at Paradise on Earth the Huntington Library for providing me with a copy.  In addition to its native curiousness, this text has the additional curious feature that no one can seem to decide whether it’s serious or satirical.  Upon reading it, I was also surprised to find that this wasn’t entirely obvious, although I’m going to have to come down on the side of satire for the following reasons: 1. yes, it has quite a bit of droll humor; 2. the quote from Juvenal on the title-page is fairly incriminating; and most of all 3. it’s exceptionally well-written.  It strikes me that, certainly at that time, it was an essential characteristic of half-witted quackery to be expressed in a pompous and constipated writing-style.  Consider, for just a few ready examples, DIGBY, op. cit., and WHISTON, op. cit. (and no mean jokes about this website, please!)  All the same, I’d have to think that it couldn’t be too difficult for someone with a passing knowledge of the Grub Street scene to identify the author once and for all.  Anyone care to take up the challenge?
(3:50) Powder of Sympathy Diorama, National Maritime Museum, Greenwich, UK.  Only slightly less notorious than the powder-of-sympathy-longitude-scheme itself is the animatronic diorama of it that someone built for the National Maritime Museum (which is a fantastic museum, by the way).  As one wanders through the museum examining all manner of maritime memorabilia, one’s ears are continuously assaulted with the horrible reminder that somewhere nearby there’s a poor, animatronic dog condemned to an eternal loop of yelping in sympathetic anguish.  I nabbed this photo (on 24-sep-2011) from somebody’s flickr account because, well, I just had to include something and it’s not like I can just hop on a plane to England to take my own photos any old time I want (sigh). So whoever’s photo this is, thanks!
Now, if some exceptionally fastidious viewer should object that my description of how this scheme is supposed to work does not entirely jibe with what’s shown in the diorama, it’s because in my opinion the author of the Curious Enquiries was himself not entirely faithful to his avowed source, Digby.  And since this same viewer is, by assumption, exceptionally fastidious, he or she will have no problem delving into those sources and discovering for themselves to which details I refer.


Subtle Vibrations (4:11-4:27)

As we saw earlier, Huygens’ had initially suspected that the sympathy he observed in his clocks was somehow the result of air-currents.  However, Huygens being Huygens, it took him less than two weeks to uncover the true reason for his clocks’ behavior.  Huygens detailed his revised assessment in a second letter to Robert Moray, letter No. 1345, dated 6 March 1665.  Thus this letter was written on the same day as Moray’s initial reply (letter No. 1348, translated, above).  We present Huygens’ second letter here since this is its logical place in the story.
6 March 1665, Christiaan Huygens to Robert Moray (No. 1345)
“… My [clocks] go with a very high precision, especially after I found by experience that it’s necessary to attach them to some beam or other unwavering thing, because unless this is so, the movement of the pendulum, notwithstanding the great weight of the box, gives a small movement to the entire clock which alters its precision and causes it to move more quickly in proportion as there is an excess.  Thus I found that the cause of the sympathy of which I wrote in my last letter does not come from the movement of the air but from this aforementioned wavering [branslement], which being entirely insensible I had not noticed at the time.  You must know, then, that our two clocks were each attached to a board 3-inches square and 4-feet long and placed on the same two chairs at a distance of 3-feet.  This being so, and the chairs being capable of a slight movement, I can show that the pendulums must necessarily reach consonance within a short time and not depart from it thereafter, and that the beats must go contrariwise and not parallel as experience has already shown.  Having arrived at the said consonance the chairs no longer move except only to hinder the clocks from deviating since as soon as they attempt to do this, that small movement puts them back as before.”
Huygens did not believe this newly-discovered coupling would render his clocks unseaworthy.  He does, however, offer some advice for their usage and calibration in a subsequent letter to Moray:
27 March 1665, Christiaan Huygens to Robert Moray (No. 1362)
“I received your letters from 24 February and 3 March, the first of which I found upon returning from a voyage to Amsterdam.  I was well pleased to see confirmation of what Major Holmes reported.  As for the scruple you conceived regarding the incorrect reason I gave for the wondrous agreement of my clocks, I will not say anything since you have not said more after I made known to you the true cause of the alleged sympathy.  It is better, in fact, that what I have found is such since the other would have caused some inconveniences and would have at least necessitated separating the clocks so that the one one would not entrain the other.  At Paris there has been a rush to put my observation in the weekly journal without my knowledge, concerning which I was not very pleased.
“Although you might not plan to add anything to the Instruction I have sent you, it would nevertheless be necessary to adjoin an article touching on the suspension of the clocks, namely, that one must take care to attach them firmly with their screws to some beam of the vessel, and that on land, when getting them to agree, it is necessary likewise to seek such a suspension, one entirely fixed and unwavering, since without it one would not only have more trouble getting them to agree with each other, but having been in agreement on land, they would not be so at sea.  For this is what I found by my observations (and, I can say, at my expense), that the movement of the pendulum, though of so little weight in comparison to the whole clock, also gives some movement to the body from which it is suspended if the latter is capable of the slightest wavering.”
Even so, breaking the chronological sequence once more, we give the last word on the matter to the Royal Society (in BIRCH, op. cit., p. 21):
“There was read a letter of Monsieur Huygens to Sir Robert Moray, from the Hague, dated the 6th of March, 1664/5, N.S.; containing, first, his desire of being more particularly informed about the pendulum watches committed to Major Holmes; and a rectification of a mistake concerning a certain sympathetical agreement, produced in such watches by the motion of two chairs.
“Occasion was taken here by some of the members, to doubt the exactness of the motion of the watches at sea, since so slight and almost insensible motion was able to cause an alteration in their going.”


Metronomes! (4:28-7:35)

(5:00) The metronomes are both set to 176 Hz and initially oscillate 180° out of phase (i.e., their motions are opposite).  It would be exceptionally difficult to get two metronomes to oscillate at exactly the same frequency and so, in practice, there is always a slight frequency difference between the two.  This manifests itself in that the faster metronome will “lead” the slower one (or, conversely, the slower will “lag” the faster).  In the absence of any coupling, then, the two metronomes would cycle into and out of phase continuously at a frequency equal to the difference in their oscillation-frequencies (their beat frequency).  But our system includes a coupling designed to halt this process once the metronomes beat in-phase (i.e., with identical motions), thereby “locking” them together.
(5:00-5:45) The metronome on the right “leads” the metronome on the left (or, if you prefer, the metronome on the left “lags” the metronome on the right).
(5:45)  At approximately this instant, the two metronomes are now in-phase, that is, the motions of their pendulums are now in-sync.
(5:45-6:15) Continuing through their cycle, the metronome on the right now “lags” the metronome on the left.
(6:15-7:33) But instead of being allowed to beat through an entire cycle, the metronomes never go back to being out-of-phase.  Instead, the coupling effect of the rolling shelf brings them back into phase where they will remain indefinitely (until they run out of juice, that is).
Oddly enough, there are quite a few technical publications about this phenomenon that have appeared in the literature in recent years.  Here is a sampling of some that caught my eye:
BENNETT, M., SCHATZ, M., ROCKWOOD, H., & WIESENFELD, K.  “Huygens’s Clocks”, Proceedings of the Royal Society of London A, Vol. 458, No. 2019, 8 March 2002, pp. 563-579, doi: 10.1098/rspa.2001.0888.
PANTALEONE, James. “Synchronization of Metronomes”, American Journal of Physics, Volume 70, Issue 10, pp. 992-1000 (2002).  doi: 10.1119/1.1501118.  The AJP article is subscription only, so the version linked-to above is a proof copy from the University of Alaska at Anchorage Department of Physics website.
ANDRIEVSKY, B.R. “Phase Relations in the Synchronized Motion of Two-Pendulum System”, Physics and Control International Conference Proceedings, A.L. Fradkov, A.N. Churilov, eds., St. Petersburg, Russia, 2003, pp. 569-76.  The paper is downloaded from the publications page of the Control of Complex Systems Laboratory, Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia.
CZOLCZYNSKI, K., PERLIKOWSKI, P., STEFANKSI, A. & KAPITANIAK, T. “Huygens’ odd sympathy experiment revisited”, International Journal of Bifurcation and Chaos, 21(7), 2011. doi: 10.1142/S0218127411029628 (copyright World Scientific Publishing Company).  The version of the paper linked to above comes from the publications page of Przemyslaw Perlikowski at the Technical University of Lodz, Poland.
These articles attempt to elucidate what non-linear conditions are necessary to cause a coupling between two pendulums and which of the possible couplings will be stable over time.  In a simple, linear treatment of two coupled pendulums (a standard homework problem in any undergraduate physics curriculum) there are two fundamental solutions: the pendulums oscillate in-phase (their motions are perfectly in-sync) or the pendulums oscillate out-of-phase (their motions are exactly opposite).  To these we may add a third, trivial solution where no oscillation occurs.  But this simple treatment doesn’t tell us which solution (in-phase or anti-phase) is more likely to occur in a realistic set-up that includes all sorts of real-world non-linear factors.
It’s somewhat funny, but the articles don’t agree with each other at all.  As we read earlier, Huygens’ pendulums exhibited anti-phase coupling.  BENNET et al. argue that this was the only possible coupling given Huygens’ set-up.  The other papers offer competing assessments, both of Hugyens’ observations and of the general case.  In the absence of theoretical clarity, we let our video serve as just one humble example of a set-up where the stable coupling is in-phase.
By the way, I would be remiss if I did not mention that our final set-up was, if not inspired by, then certainly influenced by this video posted by an outfit called Vibrationdata.  But whereas their use of soda-cans for rollers emphasizes the coupling, I felt my task was to come-up with a set-up that kept the coupling fairly inconspicuous.
(6:09) “And Newtonian gravitation, which Huygens found deeply troubling…” Huygens expressed this sentiment repeatedly, but its most direct version can be found in a letter to Leibniz.  Like his other correspondence, this letter is reproduced in the Œuvres complètesop. cit., but in Tome IX.  The relevant passage is:
18 November 1690, Christiaan Huygens to G.W. Leibniz (No. 2633)
“As for what regards the cause of the tides which Mr. Newton gives, I am not at all satisfied, nor by all his other theories which he builds upon his principle of attraction which seems absurd to me, as I have already attested in the addition to the Discourse on Gravity…”
Huygens’ discomfort with Newtonian action-at-a-distance was widely shared (not least by Newton himself).  However, the sheer number and importance of the problems which could be solved by Newtonian gravitation was such that natural philosophers learned to ignore their metaphysical qualms.  It was for precisely these scenarios, though, that the Greeks, in their wisdom, prescribed that metaphysics must always come after physics and never before.  Ultimately gravity grew out of its awkward action-at-a-distance phase when Einstein reworked it as a field theory (viz., the general theory of relativity).  But gravity was not the first, and nor would it be the last, instance where the conventional metaphysics of the day had to yield before the superior predictive capabilities of a strange new physics.  See, for example, mechanics, quantum.
(6:32) “The so-called McClintock Effect.”  See, McCLINTOCK, M.  “Menstrual synchrony and suppression”, Nature, Vol. 229, 22 January 1971, pp. 244-5, doi:10.1038/229244a0.  Since a subscription is required, a more accessible, albeit brief, description can be found in
O’CONNOR, Anahad.  “The Claim: Menstrual Cycles Can Synchronize Over Time”, The New York Times, 5 February 2008.
Inasmuch as my native skepticism is here put in direct conflict with my delight that such a theory could emerge in (relatively) modern times, and in the full glare of modern science, I will summon what little restraint I have and say nothing on this topic.  I apologize, of course, to whoever was unhinged enough to read all of these notes up to this point only to find, at their conclusion, an unseemly void.
(7:05-7:35) In accordance with tradition, I’ve selected another Michael Nyman gem for the closing music.  It’s a snippet from “Wedding Tango”, which is track #10 from his soundtrack to Peter Greenaway’s film Drowning by Numbers.  I bought the soundtrack and so should you!


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