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Abacus
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For other uses, see Abacus (disambiguation).
"Abaci" and "Abacuses" redirect here. For the Turkish surname, see Abacı. For the medieval book, see Liber Abaci.
A Chinese abacus, Suanpan
Calculating-Table by Gregor Reisch: Margarita Philosophica, 1503. The woodcut shows Arithmetica instructing an algorist and an abacist (inaccurately represented as Boethius and Pythagoras). There was keen competition between the two from the introduction of the Algebra into Europe in the 12th century until its triumph in the 16th.[1]
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system.[1] The exact origin of the abacus is still unknown. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone, or metal.
Abaci come in different designs. Some designs, like the bead frame consisting of beads divided into tens, are used mainly to teach arithmetic, although they remain popular in the post-Soviet states as a tool. Other designs, such as the Japanese soroban, have been used for practical calculations even involving several digits. For any particular abacus design, there usually are numerous different methods to perform a certain type of calculation, which may include basic operations like addition and multiplication, or even more complex ones, such as calculating square roots. Some of these methods may work with non-natural numbers (numbers such as 1.5 and 3⁄4).
Although today many use calculators and computers instead of abaci to calculate, abaci still remain in common use in some countries. Merchants, traders and clerks in some parts of Eastern Europe, Russia, China and Africa use abaci, and they are still used to teach arithmetic to children.[1] Some people who are unable to use a calculator because of visual impairment may use an abacus.
Contents
[hide]
1 Etymology
2 History
2.1 Mesopotamian
2.2 Egyptian
2.3 Persian
2.4 Greek
2.5 Chinese
2.6 Roman
2.7 Indian
2.8 Japanese
2.9 Korean
2.10 Native American
2.11 Russian
3 School abacus
4 Renaissance abaci gallery
5 Uses by the blind
6 Binary abacus
7 See also
8 Notes
9 Footnotes
10 References
11 Further reading
12 External links
12.1 Tutorials
12.2 Abacus curiosities
Etymology[edit]
The use of the word abacus dates before 1387 AD, when a Middle English work borrowed the word from Latin to describe a sandboard abacus. The Latin word came from Greek ἄβαξ abax which means something without base, and improperly, any piece of rectangular board or plank.[2][3][4] Alternatively, without reference to ancient texts on etymology, it has been suggested that it means "a square tablet strewn with dust",[5] or "drawing-board covered with dust (for the use of mathematics)"[6] (the exact shape of the Latin perhaps reflects the genitive form of the Greek word, ἄβακoς abakos). Whereas the table strewn with dust definition is popular, there are those that do not place credence in this at all and in fact state that it is not proven.[7][nb 1] Greek ἄβαξ itself is probably a borrowing of a Northwest Semitic, perhaps Phoenician, word akin to Hebrew ʾābāq (אבק), "dust" (or in post-Biblical sense meaning "sand used as a writing surface").[8]
The preferred plural of abacus is a subject of disagreement, with both abacuses[9] and abaci[9] in use. The user of an abacus is called an abacist.[10]
History[edit]
Mesopotamian[edit]
The period 2700–2300 BC saw the first appearance of the Sumerian abacus, a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.[11]
Some scholars point to a character from the Babylonian cuneiform which may have been derived from a representation of the abacus.[12] It is the belief of Old Babylonian[13] scholars such as Carruccio that Old Babylonians "may have used the abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations".[14]
Egyptian[edit]
The use of the abacus in Ancient Egypt is mentioned by the Greek historian Herodotus, who writes that the Egyptians manipulated the pebbles from right to left, opposite in direction to the Greek left-to-right method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument have not been discovered.[15]
Persian[edit]
During the Achaemenid Empire, around 600 BC the Persians first began to use the abacus.[16] Under the Parthian, Sassanian and Iranian empires, scholars concentrated on exchanging knowledge and inventions with the countries around them – India, China, and the Roman Empire, when it is thought to have been exported to other countries.
Greek[edit]
An early photograph of the Salamis Tablet, 1899. The original is marble and is held by the National Museum of Epigraphy, in Athens.
The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC.[17] Also Demosthenes (384 BC–322 BC) talked of the need to use pebbles for calculations too difficult for your head.[18][19] A play by Alexis from the 4th century BC mentions an abacus and pebbles for accounting, and both Diogenes and Polybius mention men that sometimes stood for more and sometimes for less, like the pebbles on an abacus.[19] The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus saw use in Achaemenid Persia, the Etruscan civilization, Ancient Rome and, until the French Revolution, the Western Christian world.
A tablet found on the Greek island Salamis in 1846 AD (the Salamis Tablet), dates back to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble 149 cm (59 in) long, 75 cm (30 in) wide, and 4.5 cm (2 in) thick, on which are 5 groups of markings. In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semicircle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.[20] Also from this time frame the Darius Vase was unearthed in 1851. It was covered with pictures including a "treasurer" holding a wax tablet in one hand while manipulating counters on a table with the other.[18]
Chinese[edit]
Main article: Suanpan
A Chinese abacus (suanpan) (the number represented in the picture is 6,302,715,408)
Abacus
Chinese
算盤
Literal meaning
"calculating tray"
[show]Transcriptions
Standard Mandarin
Hanyu Pinyin
suànpán
IPA
[swân.pʰǎn]
Yue: Cantonese
Yale Romanization
syun-pùhn
IPA
[sȳːnpʰǔːn]
Jyutping
syun3-pun4
Southern Min
Hokkien POJ
sǹg-pôaⁿ
Tâi-lô
sǹg-puânn
The earliest known written documentation of the Chinese abacus dates to the 2nd century BC.[21]
The Chinese abacus, known as the suanpan (算盤, lit. "counting tray"), is typically 20 cm (8 in) tall and comes in various widths depending on the operator. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam; beads moved toward the beam are counted, while those moved away from it are not.[22] The suanpan can be reset to the starting position instantly by a quick movement along the horizontal axis to spin all the beads away from the horizontal beam at the center.
Suanpan can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed. There are currently schools teaching students how to use it.
In the long scroll Along the River During the Qingming Festival painted by Zhang Zeduan during the Song dynasty (960–1297), a suanpan is clearly visible beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao).
The similarity of the Roman abacus to the Chinese one suggests that one could have inspired the other, as there is some evidence of a trade relationship between the Roman Empire and China. However, no direct connection can be demonstrated, and the similarity of the abaci may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern Korean and Japanese) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2. (Incidentally, this allows use with a hexadecimal numeral system, which was used for traditional Chinese measures of weight.) Instead of running on wires as in the Chinese, Korean, and Japanese models, the beads of Roman model run in grooves, presumably making arithmetic calculations much slower.
Another possible source of the suanpan is Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a place holder. The zero was probably introduced to the Chinese in the Tang dynasty (618–907) when travel in the Indian Ocean and the Middle East would have provided direct contact with India, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians.
Roman[edit]
Main article: Roman abacus
Copy of a Roman abacus
The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles (calculi) were used. Later, and in medieval Europe, jetons were manufactured. Marked lines indicated units, fives, tens etc. as in the Roman numeral system. This system of 'counter casting' continued into the late Roman empire and in medieval Europe, and persisted in limited use into the nineteenth century.[23] Due to Pope Sylvester II's reintroduction of the abacus with very useful modifications, it became widely used in Europe once again during the 11th century[24][25] This abacus used beads on wires, unlike the traditional Roman counting boards, which meant the abacus could be used much faster.[26]
Writing in the 1st century BC, Horace refers to the wax abacus, a board covered with a thin layer of black wax on which columns and figures were inscribed using a stylus.[27]
One example of archaeological evidence of the Roman abacus, shown here in reconstruction, dates to the 1st century AD. It has eight long grooves containing up to five beads in each and eight shorter grooves having either one or no beads in each. The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives –five units, five tens etc., essentially in a bi-quinary coded decimal system, obviously related to the Roman numerals. The short grooves on the right may have been used for marking Roman "ounces" (i.e. fractions).
Indian[edit]
There is no clear evidence for use of the abacus in India. The decimal number system invented in India replaced the abacus in Western Europe.[28]
The Abhidharmakośabhāṣya of Vasubandhu (316-396), a Sanskrit work on Buddhist philosophy, says that the second-century CE philosopher Vasumitra said that "placing a wick (Sanskrit vartikā) on the number one (ekāṅka) means it is a one, while placing the wick on the number hundred means it is called a hundred, and on the number one thousand means it is a thousand". It is unclear exactly what this arrangement may have been. Around the 5th century, Indian clerks were already finding new ways of recording the contents of the Abacus.[29] Hindu texts used the term śūnya (zero) to indicate the empty column on the abacus.[30]
Japanese[edit]
Main article: Soroban
Japanese soroban
In Japanese, the abacus is called soroban (算盤, そろばん, lit. "Counting tray"), imported from China in the 14th century.[31] It was probably in use by the working class a century or more before the ruling class started, as the class structure did not allow for devices used by the lower class to be adopted or used by the ruling class.[32] The 1/4 abacus, which is suited to decimal calculation, appeared circa 1930, and became widespread as the Japanese abandoned hexadecimal weight calculation which was still common in China. The abacus is still manufactured in Japan today even with the proliferation, practicality, and affordability of pocket electronic calculators. The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation. Using visual imagery of a soroban, one can arrive at the answer in the same time as, or even faster than, is possible with a physical instrument.[33]
Korean[edit]
The Chinese abacus migrated from China to Korea around 1400 AD.[18][34][35] Koreans call it jupan (주판), supan (수판) or jusan (주산).[36]
Native American[edit]
Representation of an Inca quipu
A yupana as used by the Incas.
Some sources mention the use of an abacus called a nepohualtzintzin in ancient Aztec culture.[37] This Mesoamerican abacus used a 5-digit base-20 system.[38] The word Nepōhualtzintzin [nepoːwaɬˈt͡sint͡sin] comes from Nahuatl and it is formed by the roots; Ne – personal -; pōhual or pōhualli [ˈpoːwalːi] – the account -; and tzintzin [ˈt͡sint͡sin] – small similar elements. Its complete meaning was taken as: counting with small similar elements by somebody. Its use was taught in the Calmecac to the temalpouhqueh [temaɬˈpoʍkeʔ], who were students dedicated to take the accounts of skies, from childhood.
The Nepōhualtzintzin was divided in two main parts separated by a bar or intermediate cord. In the left part there were four beads, which in the first row have unitary values (1, 2, 3, and 4), and in the right side there are three beads with values of 5, 10, and 15 respectively. In order to know the value of the respective beads of the upper rows, it is enough to multiply by 20 (by each row), the value of the corresponding account in the first row.
Altogether, there were 13 rows with 7 beads in each one, which made up 91 beads in each Nepōhualtzintzin. This was a basic number to understand, 7 times 13, a close relation conceived between natural phenomena, the underworld and the cycles of the heavens. One Nepōhualtzintzin (91) represented the number of days that a season of the year lasts, two Nepōhualtzitzin (182) is the number of days of the corn's cycle, from its sowing to its harvest, three Nepōhualtzintzin (273) is the number of days of a baby's gestation, and four Nepōhualtzintzin (364) completed a cycle and approximate a year (11/4 days short). When translated into modern computer arithmetic, the Nepōhualtzintzin amounted to the rank from 10 to the 18 in floating point, which calculated stellar as well as infinitesimal amounts with absolute precision, meant that no round off was allowed.
The rediscovery of the Nepōhualtzintzin was due to the Mexican engineer David Esparza Hidalgo,[39] who in his wanderings throughout Mexico found diverse engravings and paintings of this instrument and reconstructed several of them made in gold, jade, encrustations of shell, etc.[40] There have also been found very old Nepōhualtzintzin attributed to the Olmec culture, and even some bracelets of Mayan origin, as well as a diversity of forms and materials in other cultures.
George I. Sanchez, "Arithmetic in Maya", Austin-Texas, 1961 found another base 5, base 4 abacus in the Yucatán Peninsula that also computed calendar data. This was a finger abacus, on one hand 0, 1, 2, 3, and 4 were used; and on the other hand 0, 1, 2 and 3 were used. Note the use of zero at the beginning and end of the two cycles. Sanchez worked with Sylvanus Morley, a noted Mayanist.
The quipu of the Incas was a system of colored knotted cords used to record numerical data,[41] like advanced tally sticks – but not used to perform calculations. Calculations were carried out using a yupana (Quechua for "counting tool"; see figure) which was still in use after the conquest of Peru. The working principle of a yupana is unknown, but in 2001 an explanation of the mathematical basis of these instruments was proposed by Italian mathematician Nicolino De Pasquale. By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for the different fields in the instrument. Using the Fibonacci sequence would keep the number of grains within any one field at a minimum.[42]
Russian[edit]
Russian abacus
The Russian abacus, the schoty (счёты), usually has a single slanted deck, with ten beads on each wire (except one wire, usually positioned near the user, with four beads for quarter-ruble fractions). Older models have another 4-bead wire for quarter-kopeks, which were minted until 1916. The Russian abacus is often used vertically, with wires from left to right in the manner of a book. The wires are usually bowed to bulge upward in the center, to keep the beads pinned to either of the two sides. It is cleared when all the beads are moved to the right. During manipulation, beads are moved to the left. For easy viewing, the middle 2 beads on each wire (the 5th and 6th bead) usually are of a different color from the other eight beads. Likewise, the left bead of the thousands wire (and the million wire, if present) may have a different color.
As a simple, cheap and reliable device, the Russian abacus was in use in all shops and markets throughout the former Soviet Union, and the usage of it was taught in most schools until the 1990s.[43][44] Even the 1874 invention of mechanical calculator, Odhner arithmometer, had not replaced them in Russia and likewise the mass production of Felix arithmometers since 1924 did not significantly reduce their use in the Soviet Union.[45] The Russian abacus began to lose popularity only after the mass production of microcalculators had started in the Soviet Union in 1974. Today it is regarded as an archaism and replaced by the handheld calculator.
The Russian abacus was brought to France around 1820 by the mathematician Jean-Victor Poncelet, who served in Napoleon's army and had been a prisoner of war in Russia.[46] The abacus had fallen out of use in western Europe in the 16th century with the rise of decimal notation and algorismic methods. To Poncelet's French contemporaries, it was something new. Poncelet used it, not for any applied purpose, but as a teaching and demonstration aid.[47] The Turks and the Armenian people also used abaci similar to the Russian schoty. It was named a coulba by the Turks and a choreb by the Armenians.[48]
School abacus[edit]
Early 20th century abacus used in Danish elementary school.
A twenty bead rekenrek
Around the world, abaci have been used in pre-schools and elementary schools as an aid in teaching the numeral system and arithmetic.
In Western countries, a bead frame similar to the Russian abacus but with straight wires and a vertical frame has been common (see image). It is still often seen as a plastic or wooden toy.
The wire frame may be used either with positional notation like other abaci (thus the 10-wire version may represent numbers up to 9,999,999,999), or each bead may represent one unit (so that e.g. 74 can be represented by shifting all beads on 7 wires and 4 beads on the 8th wire, so numbers up to 100 may be represented). In the bead frame shown, the gap between the 5th and 6th wire, corresponding to the color change between the 5th and the 6th bead on each wire, suggests the latter use.
The red-and-white abacus is used in contemporary primary schools for a wide range of number-related lessons. The twenty bead version, referred to by its Dutch name rekenrek ("calculating frame"), is often used, sometimes on a string of beads, sometimes on a rigid framework.[49]
Renaissance abaci gallery[edit]
Uses by the blind[edit]
An adapted abacus, invented by Tim Cranmer, called a Cranmer abacus is still commonly used by individuals who are blind. A piece of soft fabric or rubber is placed behind the beads so that they do not move inadvertently. This keeps the beads in place while the users feel or manipulate them. They use an abacus to perform the mathematical functions multiplication, division, addition, subtraction, square root and cube root.[50]
Although blind students have benefited from talking calculators, the abacus is still very often taught to these students in early grades, both in public schools and state schools for the blind. The abacus teaches mathematical skills that can never be replaced with talking calculators and is an important learning tool for blind students.[51] Blind students also complete mathematical assignments using a braille-writer and Nemeth code (a type of braille code for mathematics) but large multiplication and long division problems can be long and difficult. The abacus gives blind and visually impaired students a tool to compute mathematical problems that equals the speed and mathematical knowledge required by their sighted peers using pencil and paper. Many blind people find this number machine a very useful tool throughout life.[50]
Binary abacus[edit]
Two binary abaci constructed by Dr. Robert C. Good, Jr., made from two Chinese abaci
The binary abacus is used to explain how computers manipulate numbers.[52] The abacus shows how numbers, letters, and signs can be stored in a binary system on a computer, or via ASCII. The device consists of a series of beads on parallel wires arranged in three separate rows. The beads represent a switch on the computer in either an "on" or "off" position.
See also[edit]
Chinese Zhusuan
Chisanbop
Logical abacus
Mental abacus
Napier's bones
Sand table
Slide rule
Soroban
Suanpan
Notes[edit]
Jump up ^ Both C. J. Gadd, a keeper of the Egyptian and Assyrian Antiquities at the British Museum, and Jacob Levy, a Jewish Historian who wrote Neuhebräisches und chaldäisches wörterbuch über die Talmudim und Midraschim [Neuhebräisches and Chaldean dictionary on the Talmuds and Midrashi] disagree with the "dust table" theory.[7]
Footnotes[edit]
^ Jump up to: a b c Boyer & Merzbach 1991, pp. 252–253
Jump up ^ de Stefani 1909, p. 2
Jump up ^ Gaisford 1962, p. 2
Jump up ^ Lasserre & Livadaras 1976, p. 4
Jump up ^ Klein 1966, p. 1
Jump up ^ Onions, Friedrichsen & Burchfield 1967, p. 2
^ Jump up to: a b Pullan 1968, p. 17
Jump up ^ Huehnergard 2011, p. 2
^ Jump up to: a b Brown 1993, p. 2
Jump up ^ Gove 1976, p. 1
Jump up ^ Ifrah 2001, p. 11
Jump up ^ Crump 1992, p. 188
Jump up ^ Melville 2001
Jump up ^ Carruccio 2006, p. 14
Jump up ^ Smith 1958, pp. 157–160
Jump up ^ Carr 2014
Jump up ^ Ifrah 2001, p. 15
^ Jump up to: a b c Williams 1997, p. 55
^ Jump up to: a b Pullan 1968, p. 16
Jump up ^ Williams 1997, pp. 55–56
Jump up ^ Ifrah 2001, p. 17
Jump up ^ Fernandes 2003
Jump up ^ Pullan 1968, p. 18
Jump up ^ Brown 2010, pp. 81–82
Jump up ^ Brown 2011
Jump up ^ Huff 1993, p. 50
Jump up ^ Ifrah 2001, p. 18
Jump up ^ Rowlett, Russ (2004-07-04), Roman and "Arabic" Numerals, University of North Carolina at Chapel Hill, retrieved 2009-06-22
Jump up ^ Körner 1996, p. 232
Jump up ^ Mollin 1998, p. 3
Jump up ^ Gullberg 1997, p. 169
Jump up ^ Williams 1997, p. 65
Jump up ^ Murray 1982
Jump up ^ Anon 2002
Jump up ^ Jami 1998, p. 4
Jump up ^ Anon 2013
Jump up ^ Sanyal 2008
Jump up ^ Anon 2004
Jump up ^ Hidalgo 1977, p. 94
Jump up ^ Hidalgo 1977, pp. 94–101
Jump up ^ Albree 2000, p. 42
Jump up ^ Aimi & De Pasquale 2005
Jump up ^ Burnett & Ryan 1998, p. 7
Jump up ^ Hudgins 2004, p. 219
Jump up ^ Leushina 1991, p. 427
Jump up ^ Trogeman & Ernst 2001, p. 24
Jump up ^ Flegg 1983, p. 72
Jump up ^ Williams 1997, p. 64
Jump up ^ West 2011, p. 49
^ Jump up to: a b Terlau & Gissoni 2006
Jump up ^ Presley & D'Andrea 2009
Jump up ^ Good Jr. 1985, p. 34
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Leushina, A. M. (1991). The development of elementary mathematical concepts in preschool children. National Council of Teachers of Mathematics. ISBN 978-0-87353-299-0.
Melville, Duncan J. (May 30, 2001). "Chronology of Mesopotamian Mathematics". St. Lawrence University. It.stlawu.edu. Archived from the original on June 19, 2014. Retrieved Jun 19, 2014.
Mish, Frederick C., ed. (2003). "abacus". Merriam-Webster's Collegiate Dictionary (11th ed.). Merriam-Webster, Inc. ISBN 0-87779-809-5.
Mollin, Richard Anthony (September 1998). Fundamental Number Theory with Applications. Discrete Mathematics and its Applications. Boca Raton, FL: CRC Press. ISBN 978-0-8493-3987-5.
Murray, Geoffrey (July 20, 1982). "Ancient calculator is a hit with Japan's newest generation". The Christian Science Monitor. CSMonitor.com. Archived from the original on July 31, 2014. Retrieved July 31, 2014.
Onions, C. T.; Friedrichsen, G. W. S.; Burchfield, R. W., eds. (1967). "abacus". The Oxford Dictionary of English Etymology. Oxford, UK: Oxford at the Clarendon Press.
Presley, Ike; D'Andrea, Frances Mary (2009). Assistive Technology for Students who are Blind Or Visually Impaired: A Guide to Assessment. American Foundation for the Blind. p. 61. ISBN 978-0-89128-890-9.
Pullan, J. M. (1968). The History of the Abacus. New York, NY: Frederick A. Praeger, Inc., Publishers. ISBN 978-0-09-089410-9. LCCN 72075113.
Reilly, Edwin D., ed. (2004). Concise Encyclopedia of Computer Science. New York, NY: John Wiley and Sons, Inc. ISBN 978-0-470-09095-4.
Sanyal, Amitava (July 6, 2008). "Learning by Beads". Hindustan Times.
Smith, David Eugene (1958). History of Mathematics. Dover Books on Mathematics. 2: Special Topics of Elementary Mathematics. Courier Dover Publications. ISBN 978-0-486-20430-7.
Stearns, Peter N.; Langer, William Leonard, eds. (2001). The Encyclopedia of World History (6th ed.). New York, NY: Houghton Mifflin Harcourt. ISBN 978-0-395-65237-4.
Terlau, Terrie; Gissoni, Fred (July 20, 2006). "Abacus: Position Paper". APH.org. Archived from the original on August 1, 2014. Retrieved July 31, 2014.
Trogeman, Georg; Ernst, Wolfgang (2001). Trogeman, Georg; Nitussov, Alexander Y.; Ernst, Wolfgang, eds. Computing in Russia: The History of Computer Devices and Information Technology Revealed. Braunschweig/Wiesbaden: Vieweg+Teubner Verlag. ISBN 978-3-528-05757-2.
West, Jessica F. (2011). Number sense routines : building numerical literacy every day in grades K-3. Portland, Me.: Stenhouse Publishers. ISBN 978-1-57110-790-9.
Williams, Michael R. (1997). Baltes, Cheryl, ed. A History of Computing technology (2nd ed.). Los Alamitos, CA: IEEE Computer Society Press. ISBN 0-8186-7739-2. LCCN 96045232.
Yoke, Ho Peng (2000). Li, Qi and Shu: An Introduction to Science and Civilization in China. Dover Science Books. Courier Dover Publications. ISBN 978-0-486-41445-4.
Further reading[edit]
Fernandes, Luis (2013). "The Abacus: A Brief History". ee.ryerson.ca. Archived from the original on July 31, 2014. Retrieved July 31, 2014.
Menninger, Karl W. (1969), Number Words and Number Symbols: A Cultural History of Numbers, MIT Press, ISBN 0-262-13040-8
Kojima, Takashi (1954), The Japanese Abacus: its Use and Theory, Tokyo: Charles E. Tuttle Co., Inc., ISBN 0-8048-0278-5
Kojima, Takashi (1963), Advanced Abacus: Japanese Theory and Practice, Tokyo: Charles E. Tuttle Co., Inc., ISBN 0-8048-0003-0
Stephenson, Stephen Kent (July 7, 2010), Ancient Computers, IEEE Global History Network, arXiv:1206.4349  , retrieved 2011-07-02
Stephenson, Stephen Kent (2013), Ancient Computers, Part I - Rediscovery, Edition 2, ISBN 1-4909-6437-1
External links[edit]
Look up abacus in Wiktionary, the free dictionary.
Wikimedia Commons has media related to Abacus.
Texts on Wikisource:
"Abacus". Encyclopædia Britannica (11th ed.). 1911.
"Abacus", from A Dictionary of Greek and Roman Antiquities, 3rd ed., 1890.
Tutorials[edit]
Heffelfinger, Totton & Gary Flom, Abacus: Mystery of the Bead - an Abacus Manual
Min Multimedia
Stephenson, Stephen Kent (2009), How to use a Counting Board Abacus
Abacus curiosities[edit]
Schreiber, Michael (2007), Abacus, The Wolfram Demonstrations Project
Abacus in Various Number Systems at cut-the-knot
Java applet of Chinese, Japanese and Russian abaci
An atomic-scale abacus
Examples of Abaci
Aztex Abacus
Authority control
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Judicial independence
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Judicial independence is the concept that the judiciary needs to be kept away from the other branches of government. That is, courts should not be subject to improper influence from the other branches of government, or from private or partisan interests. Judicial Independence is vital and important to the idea of separation of powers.
Different countries deal with the idea of judicial independence through different means of judicial selection, or choosing judges. One way to promote judicial independence is by granting life tenure or long tenure for judges, which ideally frees them to decide cases and make rulings according to the rule of law and judicial discretion, even if those decisions are politically unpopular or opposed by powerful interests. This concept can be traced back to 18th century England.
In some countries, the ability of the judiciary to check the legislature is enhanced by the power of judicial review. This power can be used, for example, by mandating certain action when the judiciary perceives that a branch of government is refusing to perform a constitutional duty, or by declaring laws passed by the legislature unconstitutional.
Contents
[hide]
1 Economic basis
2 Development of the concept
2.1 National and international developments
2.2 International standards
2.3 The justice system
3 Canada
4 Hong Kong
5 United Kingdom
5.1 England and Wales
5.1.1 History
5.1.2 Contemporary usage
6 United States of America
6.1 Federal courts
6.2 State courts
7 See also
8 References
9 External links
Economic basis[edit]
Constitutional economics studies issues such as the proper distribution of national wealth including government spending on the judiciary. In transitional and developing countries, spending on the judiciary may be controlled by the executive. This undermines the principle of judicial independence because it creates a financial dependence of the judiciary on the executive. It is important to distinguish between two methods of corruption of the judiciary: the state (through budget planning and privileges) being the most dangerous, and private. State corruption of the judiciary can impede the ability of businesses to optimally facilitate the growth and development of a market economy.[1]
In some countries, the constitution also prohibits the legislative branch from reducing salaries of sitting judges.
Development of the concept[edit]
National and international developments[edit]
The development of judicial independence has been argued to involve a cycle of national law having an impact on international law, and international law subsequently impacting national law.[2] This is said to occur in three phases: the first phase is characterized by the domestic development of the concept of judicial independence, the second by the spread of these concepts internationally and their implementation in international law, and the third by the implementation in national law of these newly formulated international principles of judicial independence.[2]
A notable example illustrating this cycle is the United Kingdom. The first phase occurred in England with the original conception of judicial independence in the Act of Settlement 1701.[3] The second phase was evident when England’s concepts regarding judicial independence spread internationally, and were adopted into the domestic law of other countries; for instance, England served as the model for Montesquieu’s separation of powers doctrine,[4] and the Founding Fathers of the US Constitution used England as their dominant model in formulating the Constitution’s Article III, which is the foundation of American judicial independence.[5] Other common law countries, including Canada, Australia, and India, also adopted the British model of judicial independence.[6]
In recent decades the third phase of judicial independence has been evident in the UK,[7] as it has been significantly influenced by judicial independence principles developed by international human rights constitutional documents. The European Court of Human Rights (ECtHR) has had a significant impact on the conceptual analysis of judicial independence in England and Scotland. This process began in the 1990s with the ECtHR hearing UK cases and, more significantly, in the application of the European Convention on Human Rights in British law through the Human Rights Act 1998, which came into force in the UK in 2000.[8]
Where British national law had previously impacted the international development of judicial independence, the British Constitutional Reform Act 2005[9] marked a shift, with international law now impacting British domestic law. The Constitutional Reform Act dramatically reformed government control over the administration of justice in England and Wales; importantly, it discontinued the position of the Lord Chancellor, one of the country’s oldest constitutional offices, who was entrusted with a combination of legislative, executive, and judicial capacities.[10] The Lord Chancellor served as speaker of the Upper House of Parliament, the House of Lords; as a member of the executive branch and member of the senior cabinet; and as the head of the judiciary. Historically, the appellate function had a connection with the executive branch due to the types of cases typically heard – impeachment and the hearing of felony charges against peers.[11] The Constitutional Reform Act established new lines of demarcation between the Lord Chancellor and the judiciary, transferring all the judicial functions to the judiciary and entrusting the Lord Chancellor only with what are considered administrative and executive matters. In addition, the Constitutional Reform Act replaced the Lord Chancellor by the Lord Chief Justice as head of the judiciary, separated the judicial Appellate Committee of the House of Lords from the legislative parliament, reforming it as the Supreme Court, and creating a Judicial Appointments Commission.[12] The creation of the Supreme Court was important, for it finally separated the highest court of appeal from the House of Lords.[13]
Thus, the United Kingdom, where judicial independence began over three hundred years ago, illustrates the interaction over time of national and international law and jurisprudence in the area of judicial independence. In this process, concepts and ideas have become enriched as they have been implemented in successive judicial and political systems, as each system has enhanced and deepened the concepts and ideas it actualized. In addition to the UK, similar developments of conceptual cross-fertilization can be seen internationally, for example in European Union law,[14] in civil law countries such as Austria, and in other common law jurisdictions including Canada.[15]
International standards[edit]
The International Association of Judicial Independence and World Peace produced the Mt. Scopus International Standards of Judicial Independence between 2007 and 2012. These built on the same association's New Delhi Minimum Standards on Judicial independence adopted in 1982 and their Montréal Universal Declaration on the Independence of Justice in 1983. Other influences they cite for the standards include the UN Basic Principles of Judicial Independence from 1985, the Burgh House Principles of Judicial Independence in International Law (for the international judiciary), Tokyo Law Asia Principles, Council of Europe Statements on judicial independence (particularly the Recommendation of the Committee of Ministers to Member States on the independence, efficiency and role of judges), the Bangalore Principles of Judicial Conduct 2002, and the American Bar Association's revision of its ethical standards for judges.[16]
The justice system[edit]
In recent years, the principle of judicial independence has been described as one of the core values of the justice system.[17]
Canada[edit]
Canada has a level of judicial independence entrenched in its Constitution, awarding superior court justices various guarantees to independence under sections 96 to 100 of the Constitution Act, 1867. These include rights to tenure (although the Constitution has since been amended to introduce mandatory retirement at age 75) and the right to a salary determined by the Parliament of Canada (as opposed to the executive). In 1982 a measure of judicial independence was extended to inferior courts specializing in criminal law (but not civil law) by section 11 of the Canadian Charter of Rights and Freedoms, although in the 1986 case Valente v. The Queen it was found these rights are limited. They do, however, involve tenure, financial security and some administrative control.
The year 1997 saw a major shift towards judicial independence, as the Supreme Court of Canada in the Provincial Judges Reference found an unwritten constitutional norm guaranteeing judicial independence to all judges, including civil law inferior court judges. The unwritten norm is said to be implied by the preamble to the Constitution Act, 1867. Consequently, judicial compensation committees such as the Judicial Compensation and Benefits Commission now recommend judicial salaries in Canada. There are two types of judicial independence: institutional independence and decisional independence. Institutional independence means the judicial branch is independent from the executive and legislative branches. Decisional independence is the idea that judges should be able to decide cases solely based on the law and facts, without letting the media, politics or other concerns sway their decisions, and without fearing penalty in their careers for their decisions.
Hong Kong[edit]
In Hong Kong, independence of the judiciary has been the tradition since the territory became a British crown colony in 1842. After the 1997 transfer of sovereignty of Hong Kong to the People's Republic of China pursuant to the Sino-British Joint Declaration, an international treaty registered with the United Nations, independence of the judiciary, along with continuation of English common law, has been enshrined in the territory's constitutional document, the Basic Law.[18][19] In recent years, this independence has been put into question after a number of interventions from China on several cases which swayed rulings in the Executive's favour, most notably the Hong Kong Legislative Council oath-taking controversy of 2016.[20]
United Kingdom[edit]
England and Wales[edit]
Main article: Judiciary of England and Wales
History[edit]
During the middle ages, under the Norman monarchy of the Kingdom of England, the king and his Curia Regis held judicial power. Judicial independence began to emerge during the early modern period; more courts were created and a judicial profession grew. By the fifteenth century, the king's role in this feature of government became small.[21] Nevertheless, kings could still influence courts and dismiss judges. The Stuart dynasty used this power frequently in order to overpower the Parliament of England. After the Stuarts were removed in the Glorious Revolution of 1688, some advocated guarding against royal manipulation of the judiciary. King William III approved the Act of Settlement 1701, which established tenure for judges unless Parliament removed them.[22][23]
Contemporary usage[edit]
Under the uncodified British Constitution, there are two important conventions which help to preserve judicial independence. The first is that the Parliament of the United Kingdom does not comment on the cases which are before the court. The second is the principle of parliamentary privilege: that Members of Parliament are protected from prosecution in certain circumstances by the courts.[citation needed]
Furthermore, the independence of the judiciary is guaranteed by the Constitutional Reform Act 2005.[24] In order to try to promote the independence of the judiciary, the selection process is designed to minimize political interference. The process focuses on senior members of the judiciary rather than on politicians. Part 2 of the Tribunals, Courts and Enforcement Act 2007 aims to increase diversity among the judiciary.[citation needed]
The pay of judges is determined by an independent pay review body. It makes recommendations to the government after taking evidence from a variety of sources. The government accepts these recommendations and will traditionally implement them fully. As long as judges hold their positions in "good order," they remain in post until they wish to retire or until they reach the mandatory retirement age of 70.[citation needed]
Until 1 January 2010, the legal profession was self-regulating; with responsibility for implementing and enforcing its own professional standards and disciplining its own members. The bodies which performed this function were the Bar Council and the Law Society. However, this self-regulation came to an end when approved regulators came under the regulation of the Legal Services Board, composed of non-lawyers, following the passage of the Legal Services Act 2007. This saw the establishment of the Solicitors Regulation Authority to regular solicitors and the Bar Standards Board to regulate barristers.[25]
United States of America[edit]
Federal courts[edit]
Article III of the United States Constitution establishes the federal courts as part of the federal government.
The Constitution provides that federal judges, including judges of the Supreme Court of the United States, are appointed by the President "by and with the advice and consent of the Senate." Once appointed, federal judges:
...both of the supreme and inferior Courts, shall hold their Offices during good Behavior, and shall, at stated Times, receive for their Services a Compensation which shall not be diminished during their Continuance in Office.
Federal judges vacate office only upon death, resignation, or impeachment and removal from office by Congress; only 13 federal judges have ever been impeached. The phrase "during good behavior" predates the Declaration of Independence. John Adams equated it with quamdiu se bene gesserint in a letter to the Boston Gazette published on 11 January 1773,[26] a phrase that first appeared in section 3 of the Act of Settlement 1701 in England.
The President is free to appoint any person to the federal bench, yet typically he consults with the American Bar Association, whose Standing Committee on the Federal Judiciary rates each nominee "Well Qualified," "Qualified" or "Not Qualified."
State courts[edit]
State courts deal with independence of the judiciary in many ways, and several forms of judicial selection are used for both trial courts and appellate courts (including state supreme courts), varying between states and sometimes within states. In some states, judges are elected (sometime on a partisan ballot, other times on a nonpartisan one), while in others they are appointed by the governor or state legislature.
The 2000 case of Bush v. Gore, in which a majority of the Supreme Court, including some appointees of President George H. W. Bush, overruled challenges to the election of the George W. Bush then pending in the Florida Supreme Court, whose members had all been appointed by Democratic governors, is seen by many as reinforcing the need for judicial independence, both with regard to the Florida Supreme Court and the US Supreme Court. This case has increased focus and attention on judicial outcomes as opposed to the traditional focus on judicial qualifications.
See also[edit]
Judicial reform
Judiciary in Russia
Political corruption § Judiciary corruption
Rule According to Higher Law
Rule of law
Separation of powers
References[edit]
Jump up ^ Peter Barenboim, Defining the rules, The European Lawyer, Issue 90, October 2009
^ Jump up to: a b S Shetreet, ‘The Normative Cycle of Shaping Judicial Independence in Domestic and International Law: The Mutual Impact of National and International Jurisprudence and Contemporary Practical and Conceptual Challenges’ (2009) 10 Chicago Journal of International Law 275-332
Jump up ^ See generally Shimon Shetreet book, Judges on Trial.
Jump up ^ See Baron de Montesquieu, The Spirit of the Laws (Hafner 1949) (Thomas Nugent, trans).
Jump up ^ Article III of the US Constitution provides that “the judges, both of the supreme and inferior courts, shall hold their offices during good behavior, and shall, at stated times, receive for their services, a compensation which shall not be diminished during their continuance in office.”
Jump up ^ Shetreet, Judicial Independence. See also Peter H. Russell, The Judiciary in Canada: The Third Branch of Government (McGraw-Hill Ryerson 1987); John Bell, Judicial Cultures and Judicial Independence, 4 Cambridge YB Eur Legal Studies 47 (2001).
Jump up ^ UK Human Rights Act - 1998
Jump up ^ Human Rights Act (1998), ch 42 (UK), available online at < "Archived copy". Archived from the original on 2010-09-01. Retrieved 2013-01-02. > (visited Mar 27, 2009).
Jump up ^ Constitutional Reform Act (2005), ch 4 (UK). For a detailed analysis of the history of this act, see Lord Windlesham, The Constitutional Reform Act 2005: The Politics of Constitutional Reform, 2006 Pub L 35; Lord Windlesham, The Constitutional Reform Act 2005: Ministers, Judges and Constitutional Change, 2005 Pub L 806. For accounts of the main players, see Lord Woolf, The Pursuit of Justice 161–74 (Oxford 2008); Lord Phillips, Constitutional Reform: One Year On, The Judicial Studies Board Annual Lecture (Mar 22, 2007); Lord Woolf, The Rule of Law and a Change in the Constitution, 2004 Camb L J 317; Tom Bingham, The Business of Judging: Selected Essays and Speeches 55–68 (Oxford 2000). All three authors served as lord chief justice in these formative years. Lord Woolf was active in the shaping of the legislation and Lord Phillips succeeded him
Jump up ^ Anthony Seldon, Ed., Blair's Britain, 1997-2007 (Cambridge University Press: 2007), at 294
Jump up ^ Robert Stevens, Law and Politics: The House of Lords as a Judicial Body, 1800-1976 (University of North Carolina Press, 1978), at 6
Jump up ^ Anthony Seldon, Ed., Blair's Britain, 1997-2007 (Cambridge University Press: 2007), at 294
Jump up ^ Anthony Seldon, Ed., Blair's Britain, 1997-2007 (Cambridge University Press: 2007), at 113
Jump up ^ See Treaty on European Union, art F, 1992 OJ (C 191) 1 (Jul 29, 1992). Paragraph 2 of Article F states, “The Union shall respect fundamental rights, as guaranteed by the European Convention for the Protection of Human Rights and Fundamental Freedoms . . . and as they result from the constitutional traditions common to the Member States, as general principles of Community law.”
Jump up ^ See, for example, Valente v The Queen, [1985] 2 SCR 673 (Canada)
Jump up ^ "Mt. Scopus Approved Revised International Standards of Judicial Independence Approved March 19, 2008". International Association of Judicial Independence and World Peace - International Project of judicial independence. Retrieved 11 October 2014.
Jump up ^ Shimon Shetreet, Fundamental Values of the Justice System, 23 THE EUROPEAN BUSINESS LAW REVIEW 61-76, (2012).
Jump up ^ "The Basic Law of the Hong Kong Special Administrative Region of the People's Republic of China"- Chapter 1, basiclaw.gov.HK, 17 March 2008. Retrieved 2016-07-14.
Jump up ^ "The Basic Law of the Hong Kong Special Administrative Region of the People's Republic of China"- Chapter 4, Section 4, basiclaw.gov.HK, 17 March 2008. Retrieved 2016-07-14.
Jump up ^ "Hundreds of Hong Kong lawyers in silent march against Beijing oath ruling". South China Morning Post. 8 November 2016.
Jump up ^ Justice Gerard La Forest, Provincial Judges Reference, Supreme Court of Canada, para. 305.
Jump up ^ "Independence". Courts and Tribunals Judiciary. Retrieved 9 November 2014.
Jump up ^ Justice Gerard La Forest, Provincial Judges Reference, para. 306.
Jump up ^ "Constitutional reform". Courts and Tribunals Judiciary. Retrieved 9 November 2014.
Jump up ^ UK Parliament. Legal Services Act 2007 as amended (see also enacted form), from legislation.gov.uk.
Jump up ^ Adams, John (1851). The Works of John Adams, Vol 3. Boston: Little and Brown. p. 522.
External links[edit]
Independence of the judicial system Part I. The Independence of Judges Part II - the Prosecution Service Venice Commission, 2010
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Tree-topper
From Wikipedia, the free encyclopedia
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Not to be confused with Tree Topper.
A Christmas tree crowned with a star tree-topper in Little Stanney, Cheshire, in England
A tree-topper or treetopper is a decorative ornament placed on the top (or "crown") of a Christmas tree or Hanukkah bush. Tree-toppers can take any form, but the most common shapes are a star (representing either the Star of Bethlehem or the Star of David), finials, angels ("Christmas angel"), or fairies. Other tree-toppers include paper rosettes, ribbon bows, Father Christmases or Santa Clauses, Christian crosses, owls, and sunbursts.
Tree-toppers may be made of blown glass, metal, or plastic, among other materials. Plastic tree-toppers are often electric and once connected with the tree's lights glow from within. Following World War II, various symbols of Christmastide, such as Santa Claus, were introduced as electrified tree-toppers.
Hans Christian Andersen's short story of "The Fir-Tree" describes the decoration of a Danish Christmas tree, including its topper, thus:
"On one branch there hung little nets cut out of colored paper, and each net was filled with sugarplums; and among the other boughs gilded apples and walnuts were suspended, looking as though they had grown there, and little blue and white tapers were placed among the leaves. Dolls that looked for all the world like men—the Tree had never beheld such before—were seen among the foliage, and at the very top a large star of gold tinsel was fixed."[1]
Contents
[hide]
1 Origin and use
2 Alternatives
3 Gallery
4 See also
5 References
6 External links
Origin and use[edit]
"That pretty German toy, a Christmas tree" (1848), The Illustrated London News
Use of a Christmas angel as a tree-topper represents to some the angel Gabriel from the Nativity of Jesus:
"And in the sixth month the angel Gabriel was sent from God unto a city of Galilee, named Nazareth, to a virgin espoused to a man whose name was Joseph, of the house of David; and the virgin's name was Mary."
—  Luke 1:26–27 (KJV)
Use of a star represents the Star of Bethlehem:
"Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem, saying, 'Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him.'"
—  Matthew 2:1–2 (KJV)
The use of the angel tree-topper goes back to the Victorian era, corresponding to the rise in popularity of Christmas trees in England. The Illustrated London News published a picture of Queen Victoria, Prince Albert, and their family around a Christmas tree topped with an angel, and by its influence the Christmas angel became the most common tree-topper.[2]
During the 1870s, in conjunction with the growing power of the British Empire, the Union Jack had become the most popular tree-topper.[3]
Alternatives[edit]
In Jewish homes that use a Hanukkah bush, the Star of David is used as a tree-topper.
Some Neo-pagan homes celebrate the winter solstice, which falls close to Christmas, by decorating an evergreen tree as a symbol of continuing life,[4] but make an effort to decorate it with non-Christian symbols and often choose tree-toppers representing the sun.
Gallery[edit]
Post-War NOMA plastic, electrified angel tree-topper
Croatian Christmas star
Homemade Christmas angel
A Christmas tree crowned with a star tree-topper Köln Germany
See also[edit]
Christmas tree
Christmas ornament
References[edit]
Jump up ^ Andersen's Fairy Tales, Project Gutenberg text
Jump up ^ History of Christmas Trees at Christmas Archives
Jump up ^ History of Tree-toppers
Jump up ^ Christmas Tree-topper at Mahalo
External links[edit]
Wikimedia Commons has media related to Christmas tree.
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