- Infantry Tactics
The Decimal System of notation, also called ’Arabic Numbers’, opens up entirely new lines of Advances in pure and applied Science. By making geometric calculations easier, it also helps to produce the Castle, a defensive work with concentric defenses and interlocking angles of fire from towers, keeps, and curtain walls.
The ancient Babylonians had a base 12 system of numbers, but most of the world used a base 10 system derived from primitive counting on the ten fingers of a human hand: the most basic "digital numbers". The first written numerical notation that has survived was a series of lines, vertical or horizontal, with symbols for 10s and 100s, used by accountants in the Bronze Age Egyptian and Mycenean Greek civilizations. These evolved into the Roman Numerals which, although comprehensive for numbers up to the millions, was incredibly cumbersome for any kind of calculation. Even simple multiplication and division with these numbers is, basically, a system of trial and error. In 975 AD "Arabic Numbers" arrived in Europe. Actually originating in India, this system used the placement of the numbers to indicate quantity: instead of a separate symbol for 10 or 100, the position of the number indicated that it was automatically multiplied by 10 or 100, and the zero symbol acted as a ’place holder’ to help indicate the proper position of other numbers. When the decimal point was added to indicate numbers that were in the 1/10, or 1/100 position, precise notation and calculation of fractions, percentages, interest, and value became immeasurably easier. Within 20 years one of the indicators of an educated man in Europe was his knowledge of ’algorism’ - the art of using "Arabic" numbers.
Among the myriad applications of the mew mathematics was in calculating angles and geometry, which was immediately applied to fortifications. The Motte and Bailey castle, basically a wooden palisade surrounding a solid tower on an earthen mound, had evolved between 1100 and 1200 AD into a stone structure with projecting towers and ramparts all designed to cover all parts of the approaches to the castle with archery or crossbow fire. Algorism contributed to the practical calculation of the angles necessary to build round towers, concentric walls, and precisely angled arrow slits, crenellations and ’murder holes’.