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Quipus (or khipus), sometimes called talking knots, were recording devices historically used in the region of Andean South America. A quipu usually consisted of colored, spun, and plied thread or strings from llama or alpaca hair. It could also be made of cotton cords. The cords contained numeric and other values encoded by knots in a base ten positional system. Quipus might have just a few or up to 2,000 cords.
Archaeological evidence has shown that systems similar to the quipu were in use in the Andean region from c. 3000 BC. They subsequently played a key part in the administration of Tahuantinsuyu, the empire controlled by the Incan ethnic group, which flourished across the Andes from c. 1450 to 1532 AD. As the region was subsumed under the invading Spanish Empire, the use of the quipu faded from use, to be replaced by European writing systems. However, in several villages, quipu continued to be important items for the local community, albeit for ritual rather than recording use.
Quipu is the Spanish spelling and the most common spelling in English. Khipu (pronounced [ˈkʰipu]) is the word for “knot” in Cusco Quechua (the native Inca language); the kh is an aspirated k. In most Quechua varieties, the term is kipu.
The word “khipu”, meaning “knot” or “to knot”, comes from the Quechua language, the “lingua franca and language of administration” of Tahuantinsuyu.
“The khipu were knotted-string devices that were used for recording both statistical and narrative information, most notably by the Inka but also by other peoples of the central Andes from pre-Inkaic times, through the colonial and republican eras, and even – in a considerably transformed and attenuated form – down to the present day.”
Most information recorded on the quipus consists of numbers in a decimal system.
In the early years of the Spanish conquest of Peru, Spanish officials often relied on the quipus to settle disputes over local tribute payments or goods production. Spanish chroniclers also concluded that quipus were used primarily as mnemonic devices to communicate and record numerical information. Quipucamayocs could be summoned to court, where their bookkeeping was recognised as valid documentation of past payments.
Some of the knots, as well as other features, such as color, are thought to represent non-numeric information, which has not been deciphered. It is generally thought that the system did not include phonetic symbols analogous to letters of the alphabet. However Gary Urton has suggested that the quipus used a binary system which could record phonological or logographic data.
To date, no link has yet been found between a quipu and Quechua, the native language of the Peruvian Andes. This suggests that quipus are not a glottographic writing system and have no phonetic referent. Frank Salomon at the University of Wisconsin has argued that quipus are actually a semasiographic language, a system of representative symbols—such as music notation or numerals—that relay information but are not directly related to the speech sounds of a particular language. The Khipu Database Project (KDP), begun by Gary Urton, may have already decoded the first word from a quipu—the name of a village, Puruchuco, which Urton believes was represented by a three-number sequence, similar to a ZIP code. If this conjecture is correct, quipus are the only known example of a complex language recorded in a 3-D system.
|Numeral systems by culture
|Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil
||Burmese Khmer Lao Mongolian Thai
|East Asian numerals
|Chinese Japanese Suzhou
||Korean Vietnamese Counting rods
|Abjad Armenian Āryabhaṭa Cyrillic
||Ge’ez Greek Georgian Hebrew
|other historical systems
|Aegean Attic Babylonian Brahmi Egyptian Etruscan Inuit
||Kharosthi Mayan Quipu Roman
|Positional systems by base
|2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 20, 24, 27, 30, 36, 60, 64
|Unary numeral system (Base 1)
|List of numeral systems
Marcia and Robert Ascher, after having analyzed several hundred quipus, have shown that most information on quipus is numeric, and these numbers can be read. Each cluster of knots is a digit, and there are three main types of knots: simple overhand knots; “long knots”, consisting of an overhand knot with one or more additional turns; and figure-of-eight knots. In the Aschers’ system, a fourth type of knot—figure-of-eight knot with an extra twist—is referred to as “EE”. A number is represented as a sequence of knot clusters in base 10.
- Powers of ten are shown by position along the string, and this position is aligned between successive strands.
- Digits in positions for 10 and higher powers are represented by clusters of simple knots (e.g., 40 is four simple knots in a row in the “tens” position).
- Digits in the “ones” position are represented by long knots (e.g., 4 is a knot with four turns). Because of the way the knots are tied, the digit 1 cannot be shown this way and is represented in this position by a figure-of-eight knot.
- Zero is represented by the absence of a knot in the appropriate position.
- Because the ones digit is shown in a distinctive way, it is clear where a number ends. One strand on a quipu can therefore contain several numbers.
For example, if 4s represents four simple knots, 3L represents a long knot with three turns, E represents a figure-of-eight knot and X represents a space:
- The number 731 would be represented by 7s, 3s, E.
- The number 804 would be represented by 8s, X, 4L.
- The number 107 followed by the number 51 would be represented by 1s, X, 7L, 5s, E.
This reading can be confirmed by a fortunate fact: quipus regularly contain sums in a systematic way. For instance, a cord may contain the sum of the next n cords, and this relationship is repeated throughout the quipu. Sometimes there are sums of sums as well. Such a relationship would be very improbable if the knots were incorrectly read.
Some data items are not numbers but what Ascher and Ascher call number labels. They are still composed of digits, but the resulting number seems to be used as a code, much as we use numbers to identify individuals, places, or things. Lacking the context for individual quipus, it is difficult to guess what any given code might mean. Other aspects of a quipu could have communicated information as well: color coding, relative placement of cords, spacing, and the structure of cords and sub-cords.
Some have argued that far more than numeric information is present and that quipua are a writing system. This would be an especially important discovery as there is no surviving record of written Quechua predating the Spanish invasion. Possible reasons for this apparent absence of a written language include an actual absence of a written language, destruction by the Spanish of all written records, or the successful concealment by the Incan peoples of those records. Historians Edward Hyams and George Ordish believe quipus were recording devices, similar to musical notation, in that the notes on the page present basic information, and the performer would then bring those details to life.
In 2003, while checking the geometric signs that appear on drawings of Inca dresses from the First New Chronicle and Good Government, written by Felipe Guaman Poma de Ayala in 1615, William Burns Glynn found a pattern that seems to decipher some words from quipus by matching knots to colors of strings.
The August 12, 2005, edition of the journal Science includes a report titled “Khipu Accounting in Ancient Peru” by anthropologist Gary Urton and mathematician Carrie J. Brezine. Their work may represent the first identification of a quipu element for a non-numeric concept, a sequence of three figure-of-eight knots at the start of a quipu that seems to be a unique signifier. It could be a toponym for the city of Puruchuco (near Lima), or the name of the quipu keeper who made it, or its subject matter, or even a time designator.
Beynon-Davies considers quipus as a sign system and develops an interpretation of their physical structure in terms of the concept of a data system.
Representation of a quipu
Quipucamayocs (Quechua khipu kamayuq, “khipu-authority”), the accountants of Tawantinsuyu, created and deciphered the quipu knots. Quipucamayocs could carry out basic arithmetic operations, such as addition, subtraction, multiplication, and division. They kept track of mita, a form of taxation. The quipucamayocs also tracked the type of labor being performed, maintained a record of economic output, and ran a census that counted everyone from infants to “old blind men over 80”. The system was also used to keep track of the calendar. According to Guaman Poma, quipucamayocs could “read” the quipus with their eyes closed.
Quipucamayocs were from a class of people, “males, fifty to sixty”, and were not the only members of Inca society to use quipus. Inca historians used quipus when telling the Spanish about Tahuantinsuyu history (whether they only recorded important numbers or actually contained the story itself is unknown). Members of the ruling class were usually taught to read quipus in the Inca equivalent of a university, the yacha-huasi (literally, “house of teaching”), in the third year of schooling, for the higher classes who would eventually become the bureaucracy.
In 1532, the Spanish Empire‘s conquest of the Andean region began, with several Spanish conquerors making note of the existence of quipus in their written records about the invasion. The earliest known example comes from Hernando Pizarro, the brother of the Spanish military leader Francisco Pizarro, who recorded an encounter that he and his men had in 1533 as they traveled along the royal road from the highlands to the central coast. It was during this journey that they encountered several quipu keepers, later relating that these keepers “untied some of the knots which they had in the deposits section [of the khipu], and they [re-]tied them in another section [of the khipu].
The Spanish authorities quickly suppressed the use of quipus.The conquistadors realized that the quipucamayocs often remained loyal to their original rulers rather than to the king of Spain, and quipucamayocs could lie about the contents of a message. The conquistadors were also attempting to convert the indigenous people to Roman Catholicism. Anything representing the Inca religion was considered idolatry and an attempt to disregard Catholic conversion. Many conquistadors considered quipus to be idolatrous and therefore destroyed many of them.
Continuing ritual use
Anthropologists and archaeologists working in Peru have highlighted two known cases where quipus have continued to be used by contemporary communities, albeit as ritual items seen as “communal patrimony” rather than as devices for recording information.
In 1994, the American cultural anthropologist Frank Salomon conducted a study in the Peruvian village of Tupicocha, where quipus are still an important part of the social life of the village. As of 1994, this was the only village where quipus with a structure similar to pre-Columbian quipus were still used for official local government record-keeping and functions, although the villagers did not associate their quipus with Inca artifacts
San Cristóbal de Rapaz, Peru
One of these is in the village of San Cristóbal de Rapaz, located in the Province of Oyón, where the local villagers, known as the Rapacinos, keep a quipu in an old ceremonial building, the Kaha Wayi, that is itself surrounded by a walled architectural complex. Also within the complex is a disused communal storehouse, known as the Pasa Qullqa, which was formerly used to protect and redistribute the local crops, and some Rapacinos believe that the quipe was once a record of this process of collecting and redistributing food. The entire complex was important to the villagers, being “the seat of traditional control over land use, and the centre of communication with the deified mountains who control weather”.
In 2004, the archaeologist Renata Peeters (of the UCL Institute of Archaeology in London) and the cultural anthropologist Frank Salomon (of the University of Wisconsin) undertook a project to conserve both the quipus in Rapaz and the building that it was in, due to their increasingly poor condition.
The archaeologist Gary Urton noted in his 2003 book Signs of the Inka Khipu that he estimated “from my own studies and from the published works of other scholars that there are about 600 extant khipu in public and private collections around the world.
According to the Khipu Database Project undertaken by Harvard professor Gary Urton and his colleague Carrie Brezine, 751 quipus have been reported to exist across the globe. Their whereabouts range from Europe to North and South America. Most are housed in museums outside of their native countries, however some reside in their native locations under the care of the descendants of those who made the mystery knot records. The largest collection of all is found in western Europe at the Berlin Ethnologisches Museum in Berlin, Germany, with a reported 298 quipus. The next largest collection in Europe can be seen at the Museum für Völkerkunde in Munich. Pachacamacin Peru and the Museo Nacional de Arqueologia, Antropologia e Historia in Lima, Peru, each house 35 quipus and the Centro Mallqui in Leymebamba, Peru, holds a collection of 32. The Museo Temple Radicati, Lima, Peru, houses 26, the Museo de Ica, Ica, Peru, has 25 and the Museo Puruchuco, Ate, Peru, has 23. While patrimonial quipu collections have not been accounted for in this database, their numbers are likely to be unknown. One prominent patrimonial collection held by the Rapazians of Rapaz, Peru, was recently researched by University of Wisconsin–Madison professor, Frank Salomon. The Anthropology/Archaeology department at the University of California at Santa Barbara also holds one quipu.
Quipus are now preserved using techniques that will minimise their future degradation. Museums, archives and special collections have adopted preservation guidelines from textile practices. Quipus are made of fibers, either spun and plied threa such as wool or hair from camelids, such as alpacas, llamas and camels, or cellulose like cotton. The knotted strings of quipus were often made with an “elaborate system of knotted cords, dyed in various colors, the significance of which was known to the magistrates“. Fading of color, natural or dyed, cannot be reversed, and may indicate further damage to the fibers. Colors can darken if attacked by dust or by certain dyes and mordants. Quipus have been found with adornments, such as animal shells, attached to the cords, and these non-textile materials may require additional preservation measures.
All textiles are damaged by ultraviolet (UV) light. This damage can include fading and weakening of the fibrous material. Environmental controls are used to monitor and control temperature, humidity and light exposure of storage areas. The heating, ventilating and air conditioning, or HVAC systems, of buildings that house quipu knot records are usually automatically regulated. Relative humidity should be 60% or lower, with low temperatures. High temperatures can damage the fibres and make them brittle. Damp conditions and high humidity can damage protein-rich material. As with all textiles, cool, clean, dry and dark environments are most suitable. When quipus are on display, their exposure to ambient conditions is usually minimized and closely monitored.
Quipus are also closely monitored for mold, as well as insects and their larvae. As with all textiles, these are major problems. Fumigation may not be recommended for fiber textiles displaying mold or insect infestations, although it is common practice for ridding paper of mold and insects.
Damage can occur during storage. The more accessible the items are during storage, the greater the chance of early detection. Storing quipus horizontally on boards covered with a neutral pH paper (paper that is neither acid or alkaline) to prevent potential acid transfer is a preservation technique that extends the life of a collection. Extensive handling of quipus can also increase the risk of further damage. The fibers can be abraded by rubbing against each other or for those attached to sticks or rods by their own weight if held in an upright position.
When Gary Urton, professor of Anthropology at Harvard, was asked “Are they [quipus] fragile?”, he answered, “some of them are, and you can’t touch them – they would break or turn into dust. Many are quite well preserved, and you can actually study them without doing them any harm. Of course, any time you touch an ancient fabric like that, you’re doing some damage, but these strings are generally quite durable.
Ruth Shady, a Peruvian archeologist, has discovered a quipu or perhaps proto-quipu believed to be around 5,000 years old in the coastal city of Caral. It was in quite good condition, with “brown cotton strings wound around thin sticks”, along with “a series of offerings, including mysterious fiber balls of different sizes wrapped in ‘nets’ and pristine reed baskets. Piles of raw cotton – uncombed and containing seeds, though turned a dirty brown by the ages – and a ball of cotton thread” were also found preserved. The good condition of these articles can be attributed to the arid condition of the 11,500 feet (3,500 metres) elevated location of Caral.
Even when people have tried to preserve quipus, corrective care may still be required. Conservators in the field of library science have the skills to handle a variety of situations. If quipus are to be conserved close to their place of origin, local camelid or wool fibres in natural colors can be obtained and used to mend breaks and splits in the cords. Even though some quipus have hundreds of cords, each cord should be assessed and treated individually. Quipu cords can be “mechanically cleaned with brushes, small tools and light vacuuming”. Just as the application of fungicides is not recommended to rid quipus of mold, neither is the use of solvents to clean them. Rosa Choque Gonzales and Rosalia Choque Gonzales, conservators from southern Peru, worked to conserve the Rapaz patrimonial quipus in the Andean village of Rapaz, Peru. These quipus had undergone repair in the past, so this conservator team used new local camelid and wool fibers to spin around the area under repair in a similar fashion to the earlier repairs found on the quipu.
Americas > South America
2600 BCE to 1550 CE
Civilization in the New World has very deep and ancient roots. The first cities first sprang up in the bone-dry valleys of northern Peru’s coast in the 3rd millennium BCE, and then spread along the coast and up into the high Andes, leading to an incredible flowering of different cultures and empires through time. When the Spanish conquistadores encountered the Tahuantinsuyu, known to the modern world as the Inca Empire, they had stumbled upon the most politically sophisticated and technologically advanced urban culture of the New World.
There is still much to be learned about the Incas and their forebearers but one of the most intriguing mysteries is their writing systems, or the apparently lack thereof. Nothing like the written characters of the Old World or even of their distant northern neighbors in Mesoamerica have been recorded by the Spaniards nor discovered in the archaeological record. In other words, according to our definition, Andean cultures never developed writing.
Or did they? One thing appearing in both Spanish chronicles as well as archaeological records is the quipu (also variously written as khipu and kipu), an accounting device based on ropes and knots. A single quipu is often several ropes tied together. At the simplest form, a “main” cord ties a number of “pendant” cords into a unit. This setup can repeat itself up to four levels deep.
The main content of quipus are numbers, which are expressed by knots on a section of rope. Unlike our “Arabic” numbers which uses ten different symbols for each digit (0 to 9), quipu makers tied multiple knots in a tight sequence represent a “digit”. Digits can range from no knots (empty space) representing zero, to nine knots representing nine. For example, seven knots in a sequence equals the digit 7.
Multiple sequences of knots represent “digits” that make up a number larger than ten. In other words, quipu was a positional ten-based numeric system that, instead of encoded in written symbols, is encoded in knots. In a positional number system, the position of where a “digit” occurs determines its actual value. For example, in the “Arabic” system, the digit 3 in the number 123 stands for the amount “three” because it is at the very end of the number. Mathematically, 3 x 100 = 3 x 1 = 3. On the other hand, in the number 321 the digit 3 stands for 300 because it is the third to the last digit (3 x 102 = 3 x 100 = 300). The position of the 3 determines its multiplier’s exponent.
Similarly, the number 321 would be represented as three sequences of knots, the first one with three knots, the second with two knots, and the last one with one knot. However, there is a twist (pardon the pun). Three different kinds of knots are used in quipu. Commonly, the single knot (S) is used to represent the value of one except in the very last position (or digit). In the last position, two different knot types are used. The figure eight knot (E) represents the value one in the last digit, where as multiple four-turn long knots (L) represent values higher than one in the last position. In other words, the figure eight knot and the four-turn long knot are both used to signal the end of a number.
From Spanish colonial sources, quipu was used as an accounting device employed by the Incan bureaucracy to record amount of goods, animals, and human resources moving through the empire. As such it was never considered a true writing system. However, some recent developments are challenging this notion.
In 1996 a manuscript called Historia et Rudimenta Linguae Piruanorum came to light in Italy among the family possessions of a Naples historian. This document was supposedly written in the early 17th century by Jesuits and contains a fragment of quipu as well as an explanation of how quipu was used to encode spoken language. According to the manuscript, “ideograms” or symbols with well-known meaning from Incan art were used as either phonograms (to represent sounds) or logograms (to denote words).
To represent a sound in this system, a symbol is woven at the beginning of a cord, followed by a number. The symbol is drawn from Andean iconography and would represent a well-known deity or a concept, and the number would point to which syllable of the word represented by the symbol to pronounce. One example given in the manuscript is a symbol for the god Pachamacac, which consists of the syllables pa, cha, ca, and mac. To represent the sound of pa, the quipu maker would weave the Pachacamac symbol followed by a knot for “one”, telling the reader to only read the first syllable of the word Pachacamac. It is also possible to represent paby weaving the symbol of Allpachamasca followed by two knots, meaning the second syllable should be read.
It is also possible to represent a logogram in this system. If the woven symbol does not have any accompanying knots, then the symbol serves as a logogram that represent the entire word of the symbol’s meaning. Hence, for example, the Pachacamac symbol by itself on a quipu cord would read as pachacamac.
This system of mixing symbols with numbers does not exactly mean that quipu is a full writing system, since it relies on non-quipu symbols. However, the same manuscript also describes a translation of these symbols to distinct numeric values, meaning that it is possible to completely represent a phonogram or logogram with a group of two quipu numbers.
There is considerable controversy surrounding this manuscript both from its radical claims about well-known historical figures as well as unwillingness of the owner to allow more than one research team to examine and study it. Many well-respected scholars have cast doubt the authenticity of its content. Until substantial and independent studies have been done on this document, its revelations about literary quipu will be dubious.
Puruchuco was a major regional and administrative site in the central highlands of the Inca Empire. During excavations in the 1950’s a cache of quipu was discovered in an urn near the ruins of the palace. Its location suggested the house or office of a quipu keeper or quipucamayoq. Recent research into this collection of quipu showed that it contains some form of hierarchical accounting information. Each quipu contains many pendant numeric cords that represent numbers ranging from zero to the thousands. Based on the number of numeric cords, the quipus can be divided into three groups that the scholars labeled levels I, II, and III.
A Puruchuco quipu can be divided into multiple sections based on bigger space between groups of pendant cords. Level I quipus have six sections, level II’s have three, and level III’s have only one. On all levels, these sections almost always have the same number of pendant numeric cords arranged in the same color pattern, implying that they all record the same set of goods (they may be number of llamas or bushels of corn, but there is no way for us to know). If one adds up numeric cords in the same position across different sections of a level I quipu, the sum is equal or very close to a single numeric cord in the same position in one section of a level II quipu. Similarly, level II numeric cords sum up to a single level III numeric cord. This tells us that the accounting information is being summarized at an increasingly higher level, with the level III quipus most likely representing the grand total of goods from the area administered by Puruchuco. It is very likely that level III quipus were meant to be sent to Cuzco for imperial bookkeeping.
The following example are three segments from a level II cord (UR068) and a segment from a level III cord (UR067), laid out such that the summation of level II numbers match the values in the same relative positions on the level III cord.
In addition, level II and III quipus also have what is called “introductory segments”, a number of pendant cords that appear before the numeric cords. In every introductory segment there is always a pendant cord that contains three figure eight (E) knots. If you recall from earlier, figure eight knots can only serve as the number one in the last digit of a quipu number, so a sequence of three figure eight knots is clearly not a number. Instead, it is argued that their appearance on level II and III quipus (which are possibly bound for the central government) imply that the sequence is a “toponym”, an place identifier for Puruchuco.
The three figure eight knots representing Puruchuco is the first non-numeric information identified from quipu cords. While it is tempting to claim that this sequence of three figure eight knots is a logogram, we cannot tell if this toponym carries any linguistic value. In other words, the three knots represent the town of Puruchuco, but we do not know if it can also represent the word “Puruchuco”. However, regardless of whether the three figure eight knot sequence has linguistic value or not, it tells us that it is quite possible to expect non-numeric and perhaps even non-accounting information encoded in quipu.
It can be established without doubt that quipu was a living and breathing communication system employed by the Inca Empire successfully to keep track of its financial, tributary, and commercial records. However, much remains to unknown and obscure. It might be more than an accounting tool and might in fact be a bona fide writing system, but we are uncertain of what contents are kept within the knots. Quipu research is ongoing and many discoveries are yet to be made, but the pace will be tempered by a lack of a viable “Rosetta Stone”. Only time will tell what secrets quipus are holding.