Calendars, Clocks, and SHOs
Galileo's Pendulum: From the Rhythm of Time to the Making of Matter
by Roger G. Newton
Harvard University press; 160 pp. $22.95
Draw a large circle on the ground. Now walk clockwise round the circle at a steady four miles per hour. What does your motion look like to a person watching from some distance away on ground level at (say) the west? Well, you will appear to him to be moving at four miles per hour only when you are at the eastern or western extremity of the circle, heading due south or north, respectively. At other times your speed will appear to be less, because the observer can see only the north-south "component" of your motion. At the northern and southern extremities of the circle, you will appear to slow down, stop, and reverse direction, thereafter picking up speed. As you continue your circumnavigations, the observer will see you oscillate north-south, south-north, your speed increasing as you move from the extremes towards the center, then decreasing symmetrically as you head back out towards the extremes.
This is an instance of what physicists call a "simple harmonic oscillator" (hereinafter "SHO"). Motion of this kind has the engaging property of being simple enough to yield to complete mathematical analysis, while at the same time being complex enough to be interesting. SHOs are omnipresent in nature, and underlie phenomena ranging from the swinging of a pendulum to the sub-sub-microscopic vibrations of Superstring Theory (a currently popular model for explaining matter and energy at the subatomic level). They are the subject of Roger Newton's new book, Galileo's Pendulum. Or perhaps they are not so much the subject as the underlying theme. Newton's book discusses numerous phenomena exhibiting, or causing, or just reminiscent of, SHOs.
The most obvious practical application of the SHO is in the measurement of time. A person at any point on the Earth's surface (other than the poles) describes a 24-hour circle relative to the Sun. The Sun's apparent movement in the sky therefore depends on an SHO, and this is the beginning of all time measurement. Newton gives us four chapters on calendars and clocks. On the former, he provides decent coverage of the long millennia of efforts to fit day, month and year into primitive systems of enumeration and computation. I thought he was rather shaky on some of the details here, though. He did not leave me convinced that he really understands the "Earthly Branches / Heavenly Stems" system used by the Chinese for calendrical purposes; and surely no-one with an eye for linguistic curiosities should present a discussion of the Mayan calendar without mentioning at least the first few month names: Pop, Uo, Zip, Zotz, …
With clocks, Newton is on firmer ground. He takes us on an excellent brief tour through the history of clock-making, from the clypsedras (water clocks) of early antiquity, via various gravity-driven devices, to the invention of the main spring (late 15th century), through the masterpieces of 18th-century nautical chronometery, to the timekeepers used by physicists today, which are based on the vibration of cesium atoms.
The long reign of the clypsedra — nearly three thousand years — was brought to an end with the invention of the mechanical escapement, either in 8th-century China or in 10th-century Europe, or perhaps independently in both. (Though I note that the beautiful and ingenious clock that the first Ming Emperor ordered smashed in 1368 was apparently a clypsedra. Said the odious Emperor after inspecting it: "To disregard matters of supreme importance and devote one's mind to the likes of this is what is called 'to do what is useless and thereby to harm what is useful' …") Newton includes helpful diagrams showing the operation of escapements both early and modern.
There is some social history of clock-making: an explanation of why the Swiss became watchmakers — John Calvin's prohibitions on jewelry drove them to it — and a recapitulation of the story told in Dava Sobel's 1995 bestseller Longitude, about the British parliament's Longitude Prize of £20,000 for the first method of determining a ship's longitude position to within half a degree. Newton misses, or perhaps just felt he had not space for, the rise of the wristwatch, originally a WW1 trench fad. He also covers the intersection of horology with geography, explaining such anomalies as daylight savings time — still shunned by three states of the Union — and the International Date Line.
The pendulum of the title did not become a regular feature of clock-making until the late 17th century, just in time to catch the attention of the greatest scientific genius of all time, Sir Isaac Newton. This gives our own Newton a neat segue into the modern physics of sound and light, in which the SHO is everywhere. In the space he has given himself — fourteen pages of text to get from Faraday to Einstein, then another fourteen to cover 20th-century physics — Newton can give us only a cursory overview, but he manages to keep the SHO in sight throughout, and I think a nonspecialist reader will get at least a rough idea of how spectral theory and quantum electrodynamics are both grounded in simple wave forms. The key here is Fourier analysis — the mathematical theory of how a function, any function whatsoever, can be represented as the sum of infinitely many SHOs of different frequencies.
The book's first chapter, which stands somewhat apart from the rest in content, deals with biological rhythms — the cellular "clocks" found in almost all living creatures at every level of complexity, from the daily opening and closing of flowers to the human menstrual cycle. This chapter must have presented the author with a problem of organization. It can't be left out, yet neither can it be fitted into the main historical narrative. I think he did the right thing putting it at the front of the book; but a reader could just as easily begin with Chapter 2 and leave this first one for later.
The trick with a book like this is to keep the connecting idea in sight while taking enough historical and biographical detours to supply human interest. Roger Newton has pulled it off very nicely, and given us an excellent brief survey of his subject.