Had the computer been invented in 1990 it might well have been called an Information Processor or a Symbol Manipulation Machine. It wasn’t invented in 1990 and it has a much longer history. The very name computer describes the role it originally performed—a machine that carries out tedious arithmetic operations, computations. 

Mathematics was invented for two reasons. The most obvious reason was to blight the lives of generations of high-school students by forcing them to study geometry, trigonometry, and algebra. A lesser reason is that mathematics is a powerful tool enabling us to describe the world, and, more importantly, to make predictions about it. Long before the ancient Greek civilization flowered, humans had devised numbers, the abacus (a primitive calculating device), and algebra. The very word digital is derived from the Latin digitus (finger) and calculate is derived from the Latin calculus (pebble). 

Activities from farming to building require calculations. The mathematics of measurement and geometry were developed to enable the construction of larger and more complex buildings. Extending the same mathematics allowed people to travel reliably from place to place. Mathematics allowed people to predict eclipses and to measure time.

 As society progressed, trading routes grew. Longer journeys required more reliable navigation techniques and provided an incentive to improve measurement technology. The great advantage of a round Earth is that you don’t fall off the edge after a long sea voyage. On the other hand, a round Earth forces you to develop spherical trigonometry to deal with navigation over distances greater than a few miles. You also have to develop the sciences of astronomy and optics to determine your location by observing the position of the sun, moon, stars, and planets. Incidentally, the Ancient Greeks measured the diameter of the Earth and, by 150 AD, the Greek cartographer Ptolemy had produced a world atlas that placed the prime meridian through the Fortunate Islands (now called the Canaries, located off the west coast of Africa).

 As early as the 1580s an instrument maker in Augsburg, Germany, devised a machine that recorded the details of a journey on paper tape [Price84]. The movement of a carriage's wheels advanced a paper tape and, once every few turns, a compass needle was pressed onto the paper’s surface to record the direction of the carriage. By examining the paper tape, you could reconstruct the journey for the purpose of map making. 

By the middle of the 17^th Century several mechanical aids to calculation had been devised. These were largely analog devices in contrast to the digital calculators we discuss in the next section. Analog calculators use moving rods, bars, or disks to perform calculations. You move one engraved scale against another and then read the result of the calculation. The precision of these calculators depends on how fine you can make the engraving on the scale and how well you can read the scale. Up to the 1960s, engineers used a modern version of these analog devices called a slide rule. Even today, some aircraft pilots use a mechanical contraption with a rotating disk and a sliding scale to calculate their true airspeed and heading from their indicated airspeed, track, wind speed and direction