Christiaan Huygens

Christiaan Huygens (14 April 1629 – 8 July 1695) was a Dutch mathematician, astronomer, physicist, probabilist and horologist. His 1673 scientific masterpiece was Horologium Oscillatorium, a treatise on the mathematical theory and applications of the isochronous pendulum clock, which led to improved accuracy in the measurement of time. He is also noted for his opposition to the Newtonian corpuscular theory of light, providing a longitudinal wave theory which hypothesized propagation by spherical waves emitted along a wave front.

What a wonderful and amazing Scheme have we here of the magnificent Vastness of the Universe!

How must our wonder and admiration be encreased when we consider the prodigious distance and multitude of the Stars?

Quotes

ordered chronologically

• ...the power of this line [the cycloid] to measure time.
  • Horologium Oscillatorium (1673) as quoted by Joella G. Yoder, "Christiaan Huygens, Book on the Pendulum Clock" in Landmark Writings in Western Mathematics 1640-1940 ed., Ivor Grattan-Guinness (2005)

• I believe that we do not know anything for certain, but everything probably.
  • Letter to Pierre Perrault, 'Sur la préface de M. Perrault de son traité de l'Origine des fontaines' (1673), Oeuvres Complètes de Christiaan Huygens (1897), Vol. 7, 298. Quoted in Jacques Roger, The Life Sciences in Eighteenth-Century French Thought, ed. Keith R. Benson and trans. Robert Ellrich (1997), 163

• I do not mind at all that [Newton] is not a Cartesian provided he does not offer us suppositions like that of attraction.
  • Letter to Fatio de Duillier (11 July 1687), quoted in René Dugas, Mechanics in the seventeenth century (1958), p. 440

• One finds in this subject a kind of demonstration which does not carry with it so high a degree of certainty as that employed in geometry; and which differs distinctly from the method employed by geometers in that they prove their propositions by well-established and incontrovertible principles, while here principles are tested by inferences which are derivable from them. The nature of the subject permits of no other treatment. It is possible, however, in this way to establish a probability which is little short of certainty. This is the case when the consequences of the assumed principles are in perfect accord with the observed phenomena, and especially when these verifications are numerous; but above all when one employs the hypothesis to predict new phenomena and finds his expectations realized.
  • Treatise on Light (1690) - preface, Translated by Michael R. Matthews, Scientific Background to Modern Philosophy. 1989. p. 126

• I had not thought of this regular decrease of gravity, namely that it is as the inverse square of the distance; this is a new and highly remarkable property of gravity.
  • (1691) quoted in Popular Astronomy, Vol. 56 (1948), pp. 189–190.

• I esteem his [Newton's] understanding and subtlety highly, but I consider that they have been put to ill use in the greater part of this work, where the author studies things of little use or when he builds on the improbable principle of attraction.
  • (1692) writing five years after the appearance of Newton's Principia, as quoted in A. R. Manwell, Mathematics Before Newton (Oxford University Press, 1959), p. 56 – «He [Huygens] said, indeed, that the idea of universal attraction [gravitation] 'appears to me absurd'.»

Cosmotheoros (1695; publ. 1698)

As quoted in the English translation The Celestial Worlds Discover'd (1722) unless otherwise noted.

• A Man that is of Copernicus’s Opinion, that this Earth of ours is a Planet, carry’d round and enlighten’d by the Sun, like the rest of the Planets, cannot but sometimes think, that it’s not improbable that the rest of the Planets have their Dress and Furniture, and perhaps their Inhabitants too as well as this Earth of ours...
  • Book 1, p. 1

• It's evident God had no design to make a particular Enumeration in the Holy Scriptures, of all the Works of his Creation.
  • Book 1, p. 7

• These Gentlemen must be told, that they take too much upon themselves when they pretend to appoint how far and no farther Men shall go in their Searches, and to set bounds to other Mens Industry; as if they knew the Marks that God has placed to Knowledge...
  • Book 1, p. 8

• There are many degrees of Probable, some nearer Truth than others, in the determining of which lies the chief exercise of our Judgment.
  • Book 1, p. 10

• Here we may mount from this dull Earth, and viewing it from on high, consider whether Nature has laid out all her Cost and Finery upon this small Speck of Dirt.
  • Book 1, p. 10

• We shall be less apt to admire what this World calls Great, shall nobly despise those Trifles the generality of Men set their Affections on, when we know that there are a multitude of such Earths inhabited and adorned as Well as our own.
  • Book 1, p. 11

• Now since in so many Things they... agree, what can be more probable than that in others they agree too; and that the other Planets are as beautiful and as well stock'd with Inhabitants as the Earth? Or what shadow of Reason can there be why they should not?
  • Book 1, p. 18

• Since 'tis certain that Earth and Jupiter have their Water and Clouds, there is no reason why the other Planets should be without them. I can't say that they are exactly of the same nature with our Water; but that they should be liquid their use requires, as their beauty does that they be clear. This Water of ours, in Jupiter or Saturn, would be frozen up instantly by reason of the vast distance of the Sun. Every Planet therefore must have its own Waters of such a temper not liable to Frost.
  • Book I, p. 27

• What a wonderful and amazing Scheme have we here of the magnificent Vastness of the Universe! So many Suns, so many Earths, and every one of them stock’d with so many Herbs, Trees and Animals, and adorn’d with so many Seas and Mountains! And how must our wonder and admiration be encreased when we consider the prodigious distance and multitude of the Stars?
  • Quam mirabilis igitur, quamque stupenda mundi amplitudo, & magnificentia jam mente concipienda est. Tot Soles, tot Terrae atque harum unaquaeque tot herbis, arboribus, animalibus, tot maribus, montibusque exornata. Et erit etiam unde augeatur admiratio, si quis ea quae de fixarum Stellarum distantia, & multitudine hisce addimus, pependerit.
  • Book 2, pp. 150-151

Disputed

• The world is my country, to promote science is my religion.
  • The earliest found citation is in K.O. Meinsma, Spinoza en zijn kring. Historisch-kritische studiën over Hollandsche vrijgeesten (Martinus Nijhoff, 's-Gravenhage, 1896). This influential study was translated in French and German, but not in English. In the original Dutch context it seems as though this is not a quote from Huygens, but a characterisation by the author (Meinsma) of what 'could haven been' Huygens' devise.
  • In Cosmos: A Personal Voyage (Episode 6) from 1980 it is phrased The world is my country, science my religion.
  • Also in The Making of Modern Europe, 1648-1780 (1985) by Geoffrey Treasure, p. 474, it is declared that this was Huygens' "motto" — but this seems very similar to the much more famous and long attested declaration of Thomas Paine in Rights of Man (1791): "My country is the world, and my religion is to do good" which has long been paraphrased "The world is my country, and to do good is my religion."

Quotes about Huygens

• Like Hooke, Huygens made fundamental improvements to the clock as a time-keeping mechanism; and Hooke invented the first passable escapement for the same purpose. ...Huygens discovered the rings of Saturn, and the formula for centrifugal force. He did important work in mechanics and optics, and one of his merits was that he made young Leibnitz enthusiastic for these subjects.
  • Jacob Bronowski The Common Sense of Science (1951) "The Scientific Revolution and the Machine."

• Having converted Galileo's discovery of the isochronism of the pendulum into an accurate timepiece in 1656, Huygens had, in 1662, developed a marine variation employing a short pendulum which had subsequently been subjected to tests at sea with the aid of the English. News of the device having come to Colbert... the new director of France's economic life was determined to secure its advantages for his nation. Accordingly, Huygens was lured to Paris in 1665.
  • Seymour Chapin, "The Men from Across La Manche: French Voyages, 1670-1790" in Background to Discovery: Pacific Exploration from Dampier to Cook (1990) ed., Derek Howse

• The academicians—especially in the person of Picard—were carrying through a revolution in observational astronomy made possible by Huygens' astronomical pendulum clock, the filar micrometer perfected (if not invented) by Auzout, and the application of telescopes to large-scale graduated instruments appropriate for the measure of small angles. It was with this equipment that Picard undertook to measure the distance between two localities approximately on the meridian of Paris, to determine the differences in their latitudes, and to deduce from those results the length of degree of meridian. The eminently successful arc measure, marked by a precision thirty to forty times greater than any previously achieved...
  • Seymour Chapin, "The Men from Across La Manche: French Voyages, 1670-1790" in Background to Discovery: Pacific Exploration from Dampier to Cook (1990) ed., Derek Howse

• Mons. Huygens found out a Method whereby the Ball of a Pendulum may be always carried along the Arch of a Cycloid.
  • John Keill, "An introduction to natural philosophy" (1745)

• Huygens stated everything verbally when he was in his "geometric mode" and used [mathematical] symbols... only when he switched to his "algebraic mode." Facile mathematician that he was, he switched back and forth between the two modes as his needs changed within the same problem...
  • Joella G. Yoder, Unrolling Time: Christiaan Huygens and the Mathematization of Nature (2004)

• One of the masterpieces of seventeenth-century scientific literature was... published in 1673 under the title Horologium Oscillatorium (The Pendulum Clock). Much more than a mere description of a clock... it was in fact a treatise on the accelerated motion of a falling body, as exemplified by the bob of a pendulum clock. ...The culminating proposition is Huygen's proof that a body falling along an inverted cycloid reaches the bottom in a fixed amount of time. In other words, the cycloid is isochronous. The third section... introduces his theory of evolutes... that, among other applications, allows one to find the length of a curve. Using evolutes... he proves mathematically that the cycloidal-shaped plates will force the bob of the pendulum to move along the isochronous cycloidal path. The fourth... section... presents his theory of the compound pendulum, in which the motion of a pendulum with mass distributed along its length is compared with that of an ideal simple pendulum... The last part of the book introduces... a variant of a conical clock in which the pendulum, instead of swinging, rotates about a vertical axis... kept on an isochronous path... by the theory of evolutes.
  • Joella G. Yoder, Unrolling Time: Christiaan Huygens and the Mathematization of Nature (2004)

• This [Horologium Oscillatorium] is the first modern treatise in which a physical problem is idealized by a set of parameters then analyzed mathematically. It is one of the seminal works of applied mathematics.
  • Joella G. Yoder, "Christiaan Huygens, Book on the Pendulum Clock" in Landmark Writings in Western Mathematics 1640-1940 ed., Ivor Grattan-Guinness (2005)

• Foremost, Huygens gave us precise time. His clocks were the first timekeepers to be accurate enough to be reliable in scientific experiments.
  • Joella G. Yoder, "Christiaan Huygens, Book on the Pendulum Clock" in Landmark Writings in Western Mathematics 1640-1940 ed., Ivor Grattan-Guinness (2005)

• The lasting importance of Horologium Oscillatorium stemmed more from its applied mathematics than from its pure mathematics. The next generation of mathematicians spent a great deal of time trying to find curves that satisfied specific physical properties. What other curve, if any, is a tautochrone? What curve does a hanging chain delineate? What shape does a sail take? What is the curve of fastest descent? These were the test cases for the new mathematical technique Leibniz called 'calculus.'
  • Joella G. Yoder, "Christiaan Huygens, Book on the Pendulum Clock" in Landmark Writings in Western Mathematics 1640-1940 ed., Ivor Grattan-Guinness (2005)