## The Sliderule

A slide rule is a simple, mechanical, analog computer. It has a single moving part – the central slider (and usually a movable cursor to read results). It has etched or printed scales on one or both sides for logarithms, exponents, roots, trigonometry, and sometimes more. A slide rule uses these scales to readily perform calculations. The basic principle is using logarithms to replace multiplication with addition. They advance calculation from simply counting to exploiting the relationships between numbers.

Most slide rules are linear ‘sticks’ that resemble everyday rulers. There are also circular and even cylindrical slide rules that extend the linear scales, fitting equivalent calculating power into a more compact device. There are also scales on the movable bar in the middle (slider). Scales are slid into position to set up a particular calculation, and the result is obtained using a precise cursor. The resolution of the scales (and the user’s eyesight) determine the precision of calculations. It is reasonable to get several significant digits at least.

Today, electronic calculators have almost completely replaced slide rules. In fact, early such pocket calculators were often called ‘electronic slide rules’.

## The Abacus

Counting is one of the most powerful human capabilities. In ancient times, common objects such as pebbles were used as abstract symbols to represent possessions to be tallied and traded. Simple arithmetic soon followed, greatly augmenting the ability of merchants and planners to manipulate large inventories and operations. Manipulating pebbles on lined or grooved ‘counting tables’ was improved upon by a more robust and easy to use device – the abacus. The name ‘abacus’ comes from Latin which in turn used the Greek word for ‘table’ or ‘tablet’. The abacus also had the advantage of being portable and usable cradled in one arm, a harbinger of the pocket calculator.

Variants included Roman, Chinese, Japanese, Russian, etc. Most commonly, they worked in base 10 with upper beads representing fives and lower beads representing ones. Vertical rods represented powers of 10, increasing right to left. Manual operation proceeded from left to right, with knowing the complement of a number being the only tricky part (eg. the complement of 7 is 10-7=3). The basic four operations + – x ÷ were fairly easy to learn, mechanical procedures. One did not have to be formally educated to learn to use an abacus, as opposed to pencil and paper systems. This was computation for the masses.

The abacus is comprised of beads and rods, grouped together into several ‘stacks’. The stack is the central object in concatenative programming languages, such as Forth. These are very well-suited for teaching and learning computational thinking.

The abacus was one of the most successful inventions in history. In fact, it’s still in use today, mostly in small Asian shops. It is a universal and aesthetic symbol of our ancient love of counting.