Deus Ex Machina

Mechanical devices have always formed part of the astronomer's armory; since mathematics is essential to understanding and predicting celestial events, the abacus was among the first such mechanical devices because it made arithmetic a great deal easier. Abaci were used in ancient Sumeria more than 4,000 years ago, and the earliest Greek abacus in existence has been dated to 300 BCE.

In pre-Columbian Central America, from around 1,000 BCE, the complicated calculations involving the 260-day festival calendar was made easier by the use of calendar wheels. The festival calendar, known as a tzolkin, was based on physical objects, animals, and deities, and it revolved around the numbers 20 (the digits of the 'whole person') and 13 (in their philosophy there were 13 directions in space). Rotations of meshed wheels of 20 and 13 spaces enabled each day to be associated with a different object, and the whole cycle with respect to the 365-day solar calendar repeated itself every 52 years. Calendar wheels were therefore useful for planning events and for telling the future.

Simple naked-eye cross-staffs enabling the measurement of celestial angles have been used since antiquity. More complicated astronomical instruments that permitted calculations to be made in advance included the planisphere and the astrolabe, both of which first appeared in ancient Greece. Consisting of a map of the stars and an overlay that could be rotated to approximate the position of the horizon at any given date and time, the planisphere is an elegant, though rudimentary, device that allows the operator to calculate the rising and setting times of the Sun and stars and their elevation above (or below) the horizon at any given time. Planispheres are still beloved by amateur astronomers; indeed, most modern astronomical computer programs contain a facility to create a planisphere display. Astrolabes are a potent combination of the planisphere and a sighting device called a dioptra; thought to have been invented by Hipparchus, astrolabes permitted calculations to be made on the basis of observations, enabling numerous problems in spherical astronomy to be solved. Perhaps the most prolific and proficient exponents of the astrolabe were astronomers of the medieval Islamic world, where they were employed for astronomy, navigation, and surveying, in addition to being put to use as timekeepers for religious purposes.

Planispheres and astrolabes were used extensively by astrologers in medieval Europe to construct horoscopes (Figure 1.3). Although we now know that astrology is pseudoscience, without any scientific merit, there was no shortage of eminent

Figure 1.3. A superb brass astrolabe manufactured by Georg Hartmann in Nuremberg in 1537, now in the Scientific Instruments Collection of Yale University (Ragesoss, Wikimedia Commons).

practitioners in the West who combined astrology with their more serious astronomical pursuits. For example, Johannes Kepler (1571-1630), brilliant mathematician and originator of the laws of planetary motion, was convinced of the merits of astrology and devised his own system based upon harmonic theory. Some 800 horoscopes formulated by Kepler are still in existence, and certain lucky predictions for the year 1595 - including foretelling a peasants' revolt, forebodings of incursions by the Ottoman Empire in the east, and predictions of a spell of bitter cold - brought his astrological talents into great renown.

Figure 1.4. A celestial globe and a copy of Adriaan Metius' book Institutiones Astronomiae Geographicae feature in Johannes Vermeer's painting The Astronomer (1668). The book is open at Chapter Three, where it is stated that along with knowledge of geometry and the aid of mechanical instruments, there is a recommendation for 'inspiration from God' for astronomical research. Nowadays many amateurs echo this sentiment by praying that the battery on their laptop or PDA holds out during a night's observing session.

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