Experiment!: Planning, Implementing and Interpreting

4.4 Getting the Swing of Things

Measuring time makes us think of accurate clocks and precisely defined units like seconds. Galileo was thinking in terms of ratios and, for him, it was sufficient to be able to divide time into equal intervals. Stillman Drake, Galileo's biographer, thought that he was able to do that using music.

As we have mentioned, Galileo composed music and is said to have played the lute quite well. Musicians are actually able to keep the time quite accurately for long periods while playing. They do this without external aids and without thinking of standard units like seconds. An internal rhythm allows them to keep an even beat, and to divide that beat in half again and again with a precision rivaling that of any mechanical instrument. Drake notes that, if the cymbalist in an orchestra were to miss his entry even by a 64th note, everyone in the audience would immediately notice it. For a musical person it should be perfectly feasible to accurately divide a period into equal intervals without any external timekeeper [5].

In the 1970s, Drake studied a previously unpublished page of Galileo's working notes. It contained lists of figures scribbled on a page. He says that it looked singularly unpromising at first glance but he slowly realized that it recorded an actual experiment. There were three columns on the page, which are reproduced in Table 4.1. The second column seemed to be an index, containing the integers from one to eight. The first column contained ...