Did Johannes Kepler use the world's first computer?

While writing my article on the amazing 2000-year-old Antikythera Mechanism -- touted by many as "the world's first analog computer"-- I wondered: "What if Kepler had had the use of such a machine? Could he have cut off months, maybe years, from his laborious calculations of the positions and orbits of the planets?"

Of the 5 planets known to the Greeks, the one that bedeviled Kepler was Mars. It was the refusal of Mars to fit into a circular orbit that forced Kepler to abandon that system and discover, first, the elliptical orbit of Mars, and then his famous law of the elliptical orbits of all the planets.

Though Kepler had been converted to the sun-centered Copernican revolution and no longer had to mess with the numerous epicycles of an earth-centered Ptolemaic system, he still had to work through an enormous number of calculations on the planetary positions recorded by his friend Tycho Brahe and others.

Kepler himself complained about how tedious and time-consuming his calculations had become, and his complaint led directly to the invention of the first modern computer.

Until recently, it was believed that the first "modern" computer was invented in 1641 by Blaise Pascal, the French mathematician and philosopher who, while still in his teens, built a mechanical adding machine: the Pascaline. Similar work was done by the philosopher Leibniz in 1671, when he proposed a binary system for doing calculations on a machine he called a Stepped Reckoner. It used a "Leibniz wheel," a long cylinder that ran across it and let one multiply as well as add. When it worked. It was so complicated, it rarely did.


Wilhelm Schickard of Tübingen

But even earlier, in 1623, in response to Kepler's complaints about the tedium of his hand-calculations, his friend Wilhelm Schickard of Tübingen built the first mechanical calculator and thus became the father of the computing era. Since Schickard's machine used techniques such as cogs and gears and rotating wheels first developed for clocks, he called it the "Calculating Clock."

In a letter to Kepler, written on September 20, 1623, Schickard described his machine as follows: "What you have done by calculation I have just tried to do by way of mechanics. I have conceived a machine consisting of eleven complete and six incomplete sprocket wheels; it calculates instantaneously and automatically from given numbers, as it adds, subtracts, multiplies and divides. You will smile when you see how the machine carries over spontaneously a ten or a hundred to the left and, vice-versa, how it does the opposite if it is subtracting ..."

Schickard had by this time finished building a prototype of his Calculating Clock. Eager to try it, Kepler must have ordered one for himself. Months later, on February 25, 1624, he received another letter from Schickard, giving him a detailed description and drawings to show how the calculator was constructed and how it worked. But no machine.

And without Schickard's drawings of the machine, lost for three centuries, it was nearly impossible, until recently, to figure out from his descriptions how it worked.

Then, by chance, a few years ago scholars poring over a volume of Kepler's Rudolphine Tables in a Leningrad observatory spotted a slip of paper that someone, maybe Kepler, might have used as a book mark. On it were Schickard's drawings of his machine! Crude as they are, with these sketches, one can make some sense of Schickard's account of it in his letter to Kepler. Here they are, followed by Schickard's descriptions:


It is unclear when Schickard sent this crude sketch of his machine to Kepler or when it was found. Was it sent in his letter of September 20, 1623? In his Feb 25,1624 letter? Or at some other time? Notice that it shows only five wheels or dials, not six.


This is the drawing Schickard sent to Kepler in his letter of February 25, 1624. It, and maybe the previous one, is from the estate of Johannes Kepler, Leningrad Akademija Nauk. Source: Wilhelm Schickard. 1592 - 1635. Astronom. Geograph, Orientalist, Erfinder der Rechenmaschine, F. Seck (ed.), Tübingen 1978, pp. 296-7 © Univ of Tübingen

Here is Schickard's explanation of this drawing, from his letter to Kepler of February 25, 1624: (He starts from the top of the machine, and works down. The letters "aaa" etc. should be read as "aaaaaa" etc. to complete a row of six.)

"...When I get a chance I will send you a more detailed description of the design of this arithmetic machine. In summary, it works like this: aaa [the 6 knobs along the top] are the buttons of the vertical cylinders with the digits of the multiplication table, which can be displayed at will in the windows provided for the slides bbb [the 9 sliding rods along the sides, i.e. Napier rods, often made of bone and called "Napier's bones," a logarithmic calculating/multiplying device that was also placed on the cylinders that could be selected by turning dials]. The dials ddd are attached to internal toothed wheels, each one having ten teeth geared in such a way that, if the wheel on the right makes ten turns, the wheel on its left makes only one turn,; and if the first wheel on the right side makes one hundred turns, the third wheel on the left makes one turn, and so on."

As you can see, Schickard's machine had six wheels or dials, and when the units wheel (which is on the right end, just as we write our numbers) came full circle it moved the tens wheel on its left one place, and so on, just as your electric company's meter tracks your kilowatt-hours. With six wheels it could add and subtract (by reversing the wheels), and multiply and divide nunbers up to 6 digits. If a number got bigger than 999,999 it warned you of the overload by ringing a bell. Schickard continues:

"All the wheels rotate in the same direction, making it necessary to use another wheel of the same size geared permanently to [fit into? and turn? but then why the same size? same size teeth?] the wheel at its left, but not with [into?] the one at its right [so as not to turn that one?], which requires special attention during its construction. The digits marked in [on the rims of?] each wheel are displayed in the openings ccc of the central plate.

"Finally, over the base are located the buttons eee used to note [simply as a mnemonic device? or do they actually help operate the wheels & gears above them?] in the openings fff the numbers that need to be used during the operations. This brief description would be better understood by using the real instrument."

But now the bad news: "I had placed an order with a local man, Johann Pfister, for the construction of a machine for you; but when half finished, the machine, together with some other things of mine, especially several metal plates, fell victim to a fire which broke out unseen at night.... I take the loss very hard, now especially since the mechanic does not have time to produce a replacement soon."

We do not have Kepler's reply, but apparently neither Kepler nor his friend had the second machine produced. And though Kepler may originally have given suggestions to Schickard on what he would like in such a machine, after seeing the plans for it he may have decided it would not do the tasks he wanted it to do. With its tricky gear system, and its 6-cylinder/6-wheel limit of 999,999, it was probably too unreliable and too small to accomodate Kepler's large calculations. In a paper given in 2004, Steinar Thorvaldsen concluded that though Schickard's machine used logarithms like those used by Kepler, it would not have been accurate enough for Kepler's actual calculations.

Today, no one knows the location of Schickard’s original prototype, or even whether it still exists. Both the machine and his plans for it disappeared during the Thirty Years War, probably in 1635 when Schickard died of bubonic plague. Its existence was then forgotten until his papers were found in the 1930s by Franz Hammer.. They were lost again during World War II, until Hammer found them again in 1956. The machine itself was reconstructed in 1960 by Baron Bruno von Freytag-Löringhoff. . And it worked!


Von Freytag's 1963 reconstruction of Schickard's "Calculating Clock"

To run a simulation of the reconstructed calculator using a Java 3-D applet, or to look at some screen shots in a picture gallery, go to:
http://www.gris.uni-tuebingen.de/edu/projects/schickard/index.html