Computer Science Illuminated, Third Edition


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The development of the abacus was an enormously significant event; for in many ways, the abacus is the foundation for modern day computers. It is a device invented long before electricity that allows for addition, subtraction, multiplication, and division, without requiring a pencil or paper. This early mathematical tool enabled our ancestors to perform difficult calculations more accurately and efficiently. Merchants and traders for example, could use early abaci (plural for abacus) to keep track of goods, or to sum the cost of their goods for a customer. Let's take a brief look at the history of the abacus.

Evidence suggests that the first abaci were developed in Babylonia in the fourth century BCE. Notably, there are two types of abaci: the model which we are familiar with is the bead frame abacus, but there is an earlier version called a counting table which is a marked flat surface. Interestingly, our word "counter" or "countertop" which indicates a flat surface is likely to have its origin from these mathematical counters. In 1899, the earliest example of a counting table abacus was discovered in Salamis Greece. On this stone slab, place value was indicated by carved indentations or slits into the stone. The abacus that we think of today with the vertical wires and one horizontal divider, however, was likely developed by in China in approximately 1200 ADE. Above the divider each wire has two beads, and below the divider each wire has five beads. Approximately 1600 ADE, the Japanese developed the abacus even further, adding it in its evolution.

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There are many great sites that describe the history of the abacus. Start exploring this topic more by visiting The Abacus: History website.

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Napier's Bones

The John Napier, inventor and scholar, was born in 1550 to Archibald Napier and his wife Janet Bothwell. Archibald Napier was a prestigious man in Scottish society, and provided for his son by sending him to St. Salvador’s College of St. Andrew’s University when Napier was only 13 years old. While he did not graduate from St. Andrews, it was there that Napier acquired a genuine passion for theology, and developed an interest in academia that led him to continue his studies in other parts of Europe. In 1571, Napier returned to Scotland and soon took up residence with his wife at a castle at Gartness, where he actively engaged himself in agricultural research. He learned much and applied his knowledge; he devised techniques to improve the quantity and quality of his agricultural harvest. Meanwhile, he was very interested in the theological discussions of the day and, being a fervent Protestant, made his viewpoint known through publishing one of his most important works, Plaine Discovery of the Whole Revelation of St. John.

It seems that Napier influenced mathematics more profoundly then mathematics influenced him. Math was a hobby for Napier; he studied and worked on various mathematical topics only when he had time and was not engaged in his theological and agricultural interests. His mathematical discoveries, however, were the foundation for many important and influential events in scientific history. Napier wrote a work on logarithms that inspired Henry Biggs, who later would visit Napier and together they would develop a more sophisticated concept of logarithms. Motivated by an idea to help mathematicians avoid “slippery errors” in calculations, Napier also hoped that logarithms would save time. His inventive spirit clearly extended beyond his agricultural ambitions.

Napier’s bones, or rods, were also a significant contribution to mathematics. Each of the nine ivory rods served as a multiplication table for one digit, and aligned together, these rods made calculations easy. This early calculator has its origin in many of the same factors that motivate current advances in computer technology today; Napier strove for a faster way of solving difficult calculations.

Napier died in April of 1617, having made a profound impact on mathematics that would stretch forth for centuries to come.

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Napier's Bones
Looking for more on Napier's Bones? Check out this page, which is a page completely dedicated to this invention.

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