A sand table uses constrained sand for modelling or educational purposes. The original version of a sand table may be the abax used by early Greek students. In the modern era, one common use for a sand table is to make terrain models for military planning and wargaming.
An abax was a table covered with sand commonly used by students, particularly in Greece, to perform studies such as writing, geometry, and calculations. [2]
The abax was the predecessor to the abacus. Objects, such as stones, were added for counting and then columns for place-valued arithmetic. The demarcation between an abax and an abacus seems to be poorly defined in history; [3] moreover, modern definitions of the word abacus universally describe it as a frame with rods and beads [4] and, in general, do not include the definition of "sand table".
The sand table may well have been the predecessor to some board games. ("The word abax, or abacus, is used both for the reckoning-board with its counters and the play-board with its pieces, ..."). [5] Abax is from the old Greek for "sand table". [6]
An Arabic word for sand (or dust) is ghubar (or gubar), and Western numerals (the decimal digits 0–9) are derived from the style of digits written on ghubar tables in North-West Africa and Iberia, also described as the 'West Arabic' or 'gubar' style. [7]
Sand tables have been used for military planning and wargaming for many years as a field expedient, small-scale map, and in training for military actions. In 1890 a Sand table room was built at the Royal Military College of Canada for use in teaching cadets military tactics; this replaced the old sand table room in a pre-college building, in which the weight of the sand had damaged the floor. [8] The use of sand tables increasingly fell out of favour with improved maps, aerial and satellite photography, and later, with digital terrain simulations. More modern sand tables have incorporated Augmented Reality, such as the Augmented Reality Sandtable (ARES) developed by the Army Research Laboratory. [9] Today, virtual and conventional sand tables are used in operations training.
In 1991, "Special Forces teams discovered an elaborate sand-table model of the Iraqi military plan for the defense of Kuwait City. Four huge red arrows from the sea pointed at the coastline of Kuwait City and the huge defensive effort positioned there. Small fences of concertina wire marked the shoreline and models of artillery pieces lined the shore area. Throughout the city were plastic models of other artillery and air defense positions, while thin, red-painted strips of board designated supply routes and main highways." [10]
In 2006, Google Earth users looking at satellite photography of China found a several kilometre large "sand table" scale model, strikingly reminiscent of a mountainous region (Aksai Chin) which China occupies militarily in a disputed zone with India, 2400 km from the model's location. Speculation has been rife that the terrain is used for military exercises of familiarisation. [11] [12]
A sand table is a device useful for teaching in the early grades and for special needs children. [13] [14]
An abacus, also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu-Arabic numeral system. An abacus consists of a two-dimensional array of slidable beads. In their earliest designs, the beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation.
The ten Arabic numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are the most commonly used symbols for writing numbers. The term often also implies a positional notation using the numerals, as well as the use of a decimal base, in particular when contrasted with other systems such as Roman numerals. However, the symbols are also used to write numbers in other bases such as octal, as well as for writing non-numerical information such as trademarks or license plate identifiers.
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value. Modern style uses only these seven:
A wargame is a strategy game in which two or more players command opposing armed forces in a simulation of some military operation. Wargaming may be played for recreation, to train military officers in the art of strategic thinking, or to study the nature of potential conflicts. Many wargames re-create specific historic battles, and can cover either whole wars, or any campaigns, battles, or lower-level engagements within them. Many simulate land combat, but there are wargames for naval and air combat, as well.
0 (zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and consequently, division by zero has no meaning in arithmetic.
A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or results. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to the vague heuristics of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people.
A numerical digit is a single symbol used alone or in combinations, to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal digits.
Positional notation usually denotes the extension to any base of the Hindu–Arabic numeral system. More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred. In modern positional systems, such as the decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string.
The Ancient Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of earlier abacuses like those that were used by the Greeks and Babylonians.
A military exercise, training exercise, maneuver (manoeuvre), or war game is the employment of military resources in training for military operations. Military exercises are conducted to explore the effects of warfare or test tactics and strategies without actual combat. They also ensure the combat readiness of garrisoned or deployable forces prior to deployment from a home base.
The Hindu–Arabic numeral system is a decimal place-value numeral system that uses a zero glyph as in "205".
The Hindu–Arabic numeral system is a positional base ten numeral system for representing integers; its extension to non-integers is the decimal numeral system, which is presently the most common numeral system.
Kriegsspiel is a genre of wargaming developed by the Prussian Army in the 19th century to teach battlefield tactics to officers. The word Kriegsspiel literally means "wargame" in German, but in the context of the English language it refers specifically to the wargames developed by the Prussian army in the 19th century. Kriegsspiel was the first wargaming system to have been adopted by a military organization as a serious tool for training and research. It is characterized by high realism, an emphasis on the experience of decision-making rather than on competition, and the use of an umpire to keep the rules flexible and manage hidden information. After Prussia's impressive victory over France in the Franco-Prussian War, other countries began designing similar wargames for their own armies.
Tobruk, subtitled "Tank Battles in North Africa 1942", is a board wargame published by Avalon Hill in 1975 that simulates tank combat in North Africa during World War II.
A timeline of numerals and arithmetic.
The Kaktovik numerals or Kaktovik Iñupiaq numerals are a base-20 system of numerical digits created by Alaskan Iñupiat. They are visually iconic, with shapes that indicate the number being represented.
Principles of Hindu Reckoning is a mathematics book written by the 10th- and 11th-century Persian mathematician Kushyar ibn Labban. It is the second-oldest book extant in Arabic about Hindu arithmetic using Hindu-Arabic numerals, preceded by Kibab al-Fusul fi al-Hisub al-Hindi by Abul al-Hassan Ahmad ibn Ibrahim al-Uglidis, written in 952.
The Augmented Reality Sandtable (ARES) is an interactive, digital sand table that uses augmented reality (AR) technology to create a 3D battlespace map. It was developed by the Human Research and Engineering Directorate (HRED) at the Army Research Laboratory (ARL) to combine the positive aspects of traditional military sand tables with the latest digital technologies to better support soldier training and offer new possibilities of learning. It uses a projector to display a topographical map on top of the sand in a regular sandbox as well as a motion sensor that keeps track of changes in the layout of the sand to appropriately adjust the computer-generated terrain display.
A wargame, generally, is a type of strategy game which realistically simulates warfare. A professional wargame, specifically, is a wargame that is used by military organizations to train officers in tactical and strategic decision-making, to test new tactics and strategies, or to predict trends in future conflicts. This is in contrast to recreational wargames, which are designed for fun and competition.
A wargame is a strategy game that realistically simulates warfare. Wargames were invented for the purpose of training military officers, but they eventually caught on in civilian circles, played recreationally.