Mathematics in Ethiopia

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Since ancient times, traditional mathematics in Ethiopia have related to various aspects of astrology, the calendar, and measurements of physical properties such as length, weight, and distance. Ethiopians used alternate units of measurement which differ from fundamental law; traditionally, scaling and counting values have been described using draft animals such as goats, mules, sheep, or camels, and in modern times, steelyards.

Contents

Measurements

Weight

Since measurements of weight often require accurate units or standardized scales, they were used less frequently than measurements of capacity (volume) in the past in Ethiopia. Still, there are three basic ways in which weight has been traditionally determined. [1]

First, an object's lightness or heaviness could be simply assessed by feel (holding in one's hand) or sight (visual approximation). [1] [2] Second, a basic estimation of weight (such as of a load carried by a porter or draft animal) might be compared to a fundamentally different but familiar unit of another measure, such as the length of a human arm or the volume held in a hand. Third, more accurate comparisons of relative weights were done using scales or other apparatus. [1]

Hand measurements were used in many parts of the country to purchase market goods, such as butter. The concepts of load and capacity were often used in lieu of weight when measuring cheap, bulk commodities, such as grain. More sophisticated and accurate techniques were only used for valuable goods such as medicine, gold, and silver. In fact, in the case of gold and silver, weight was essentially considered a concept of value. [1]

Load

The concept of load—a rough measurement based on the average weight carried by a human porter, donkey, mule, or camel—has long been a widely used unit of weight in traditional Ethiopia, due to its natural emergence from traditional transport. Portuguese Jesuit missionary Manuel de Almeida noted in the 17th century that "the Emperor 'raises ten or twelve thousand loads of provisions' from State lands", while the chronicle of Emperor Iyasu I (r. 1682–1706) "reveals that taxes on trade were likewise largely based on mule and donkey loads". [1]

Scales and steelyards

The balance has been the most renowned instrument within Ethiopian society. [3] It has various terms in native languages: the Ge'ez word madalew (Ge'ez : መድሎት, romanized: madelot; plural: መዳልው, madalew) is first mentioned by the chronicle Emperor Gelawdewos (1540–1559), in which the ruler spent 10,000 madalew of gold for purchase of books. However, the text may be a mistake by a French editor, and actually refer to 10,000 waqet (Amharic : ወቄት). [1]

Two types of weighting instruments were used. The first was a conventional balance consisting of two equal-length lever arms with two trays: one to hold the object to be weighted and the other to hold a comparison weight. The second was a steelyard balance based on a single tray subtended from a level with unequal arms, the longer arm counteracting the tray. [1] As the more sensitive of the two instruments, steelyards were used to measure the weight of precious metals and other valuable goods. The use of the steelyard was first mentioned in Johnston's[ who? ] early-19th century account of Shewan market in Aliyu Amba, where he recorded "a rude kind of balance".

Traditional scales are known by various names, such as amole masa (Amharic: አሞሌ ማሳ), which are used to measure bars of salt or cotton. This type of scale had three notches for weighing different objects. The first, near the end of piece of wood, was used to weigh heavy objects (also known as amole mass); the second, known as senbet (lit. 'notch'), was used to measure smaller articles including salt, pepper, flour, coffee, and butter; the third, known as bäkus (በኩሽ) or just (ኩሽ), was equal to half of a senbet and a quarter of an amole masa. The modern type of steelyard balance was introduced by Italians during their second occupation of Ethiopia, and are still used by Gurage merchants for fruit and vegetables. [1]

Length and volume measurements

The following lists are traditional Ethiopian measurements of length and volume. [4]

Traditional Ethiopian length measurements
UnitsNotes
AzqDistance from the tip of the index finger to the first joint (Angua). About one inch.
SinzirDistance from the tip of the middle finger to the tip of the thumb while hand is fully extended. Depending on the size of the hand, it could be anywhere from six to twelve inches.
KendDistance from the tip of the elbow to the tip of the middle finger. Depending on the size of the arm, it could be between one and two feet.
AarbDistance of about a yard. Used to measure woven fabrics.
ChammaDistance from the back of the heel to the tip of the big toe. Depending on the size of foot, it could be either a few inches or a dozen or more.
Traditional Ethiopian volume measurements
UnitsNotes
DawullaVolume for grain of approximately 50 kg. Depends on the size of the animal (goat or sheep) from which the dawulla was made.
Tassa, Ensira, Gerwoina, and GanContainers of liquids used to measure volume. A tassa is about a litre; an ensira is anywhere from two to several gallons (depending on size); a gerwoina is about 20–30 litres; a gan is several gallons.
FeresullaUnit of volume that changes based on item being measure.

Astrology

Mathematics is often associated with astrology in traditional Ethiopia. [5] Ethiopian astrology, known as hasabe kewakibit, is part of bahire hasab, which is known as Ethiopian astrology and computus (church calendar). According to expert Yared Fenta, there are 28 stars for the 28 days, and 91 stars in one season that are dominant groups than billion stars that can be seen in naked eye, and 13 stars dominate the scene.[ incomprehensible ] Stars were also used in ancient times to determine the timing of the harvest season or human behavior. [6]

Aside from this, Ethiopia used zodiac system as fortune telling. [7] [ relevant? ]

Calendar

The Ethiopian calendar, also known as Ge'ez calendar, was adapted from the Alexandrian or Coptic calendar which in turn derived from the Egyptian calendar. Like the Julian calendar, the Ethiopian calendar employs leap years, beginning on 29 August or 30 August. The calendar is distinguished from the Gregorian calendar by a gap of 7–8 years which results from alternative calculations in determining the date of the Annunciation of Jesus. [8]

The Ethiopian calendar is also used as a liturgical calendar for Eritrean Christians belonging to the Eritrean Orthodox Tewahedo Church, Eastern Catholic Church, and Lutheran Evangelical Church of Eritrea. Like the Coptic calendar, the Ethiopian calendar has a thirteenth month composed of five or six epagomenal days. Months begin on the same days as in the Coptic calendar but are named in the Ge'ez language. The six epagomenal days are added every four years on 29 August of Julian calendar, six months before the Julian leap day. Therefore, 1 Mäskäräm is the first day of the years between 1901 and 2099 inclusively, and falls on 11 September of Gregorian calendar (or 12 September before Gregorian leap year). For example, the year 2012 is 2005 in the Ethiopian calendar, which began on 11 September 2012. [8]

The Oromo calendar was developed in 300 BC. Based on lunar-stellar composition, the calendar relies on astronomical observation of the moon in conjunction with seven particular stars of constellations. The Oromo months (based on stars and lunar phases) are Bittottessa (Triangulum), Camsa (Pleiades), and Bufa (Aldebaran). [8]

New Year's Day

Enkutatash is the New Year holiday of Ethiopia and Eritrea. It occurs from 11 September – 12 September except for Gregorian leap years. The date correspondence applies from the Gregorian years 1900 to 2099. The Ethiopian calendar has a leap year every four years, without exception, while the Gregorian calendar has a leap year every four years except centennial years not divisible by 400. Thus, the date difference between the two calendars increases by about one day per century (or more precisely, one day per non-quadcentennial century). [8]

Eras

Ethiopians and Eritreans follow Incarnation Era starting from Annulation or Incarnation of Jesus on 25 March 9 AD, calculated by Annianus of Alexandria c. 400 AD. Thus, the first civil year began seven months earlier, on 29 August 8 AD. This calendar differs from European calendars due to the adoption of subsequent calculation by Dionysus Exiguus in 525 AD, which placed the Annunciation eight years earlier than had Annianus. This places the Ethiopian calendar about 7–8 years behind the Gregorian calendar, depending on which part of the year is being compared. [8]

In the past, numbering era[ clarification needed ] was widely used in the Aksumite Kingdom.

Era of the Martyrs

"Era of the Martyrs", also known as Diocletian Era, is mostly used by Eastern Churches and the Coptic Church, and began on 29 August 284. Three months later then the Gregorian and Julian calendars, the difference between the Era of Martyrs and Anno Domini is 285 (15×19) years, caused in 525 AD. Dionysus Exiguus decided to add 15 Metonic cycles to the existing Diocletian Era (15×19 + 13×19 = 532) to obtain the 532-year medieval Easter cycle, whose first cycle ended with the Era of Martyrs year 247 (13×19), equal to year DXXXI. 532 years is a product of Metonic cycle of 19 years and Solar cycle of 28 days[ further explanation needed ]. [8]

Anno Mundi according to Panodoros

Around 400 AD, an Alexandrian monk named Panodorus fixed the Alexandria Era, which determines Anno Mundi (the year of world) starting from 29 August 5493 BC. After 6th century, the era was used by Egyptian and Ethiopian chronologists. The twelfth 532-year-cycle of this era began on 29 August 360 AD, which is 76 (4×19) years after the Era of Martyrs. [8]

Related Research Articles

<i>Anno Domini</i> Western calendar era

The terms anno Domini (AD) and before Christ (BC) are used when designating years in the Julian and Gregorian calendars. The term anno Domini is Medieval Latin and means "in the year of the Lord" but is often presented using "our Lord" instead of "the Lord", taken from the full original phrase "anno Domini nostri Jesu Christi", which translates to "in the year of our Lord Jesus Christ". The form "BC" is specific to English, and equivalent abbreviations are used in other languages: the Latin form, rarely used in English, is Ante Christum natum (ACN) or Ante Christum (AC).

Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.

The Julian calendar is a solar calendar of 365 days in every year with an additional leap day every fourth year. The Julian calendar is still used as a religious calendar in parts of the Eastern Orthodox Church and in parts of Oriental Orthodoxy as well as by the Amazigh people.

A leap year is a calendar year that contains an additional day compared to a common year. The 366th day is added to keep the calendar year synchronized with the astronomical year or seasonal year. Because astronomical events and seasons do not repeat in a whole number of days, calendars that have a constant number of days in each year will unavoidably drift over time with respect to the event that the year is supposed to track, such as seasons. By inserting ("intercalating") an additional day, a leap day, or month, a leap month, into some years, the drift between a civilization's dating system and the physical properties of the Solar System can be corrected.

<span class="mw-page-title-main">Year</span> Time of one planets orbit around a star

A year is the time taken for astronomical objects to complete one orbit. For example, a year on Earth is the time taken for Earth to revolve around the Sun. Generally, a year is taken to mean a calendar year, but the word is also used for periods loosely associated with the calendar or astronomical year, such as the seasonal year, the fiscal year, the academic year, etc. The term can also be used in reference to any long period or cycle, such as the Great Year.

The Julian day is the continuous count of days since the beginning of the Julian period, and is used primarily by astronomers, and in software for easily calculating elapsed days between two events.

<span class="mw-page-title-main">Coptic calendar</span> Egyptian liturgical calendar

The Coptic calendar, also called the Alexandrian calendar, is a liturgical calendar used by the Coptic Orthodox Church and also used by the farming populace in Egypt. It was used for fiscal purposes in Egypt until the adoption of the Gregorian calendar on 11 September 1875. This calendar is based on the ancient Egyptian calendar. To avoid the calendar creep of the latter, a reform of the ancient Egyptian calendar was introduced at the time of Ptolemy III which consisted of adding an extra day every fourth year. However, this reform was opposed by the Egyptian priests, and the reform was not adopted until 25 BC, when the Roman Emperor Augustus imposed the Decree upon Egypt as its official calendar. To distinguish it from the Ancient Egyptian calendar, which remained in use by some astronomers until medieval times, this reformed calendar is known as the Coptic or Alexandrian calendar. Its years and months coincide with those of the Ethiopian calendar but have different numbers and names.

A solar calendar is a calendar whose dates indicate the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as a standard in the world, is an example of a solar calendar. The main other types of calendar are lunar calendar and lunisolar calendar, whose months correspond to cycles of Moon phases. The months of the Gregorian calendar do not correspond to cycles of the Moon phase.

List of Christian liturgical calendars, calendars used by predominantly Christian communities or countries, and calendars referred to as the "Christian calendar."

<span class="mw-page-title-main">Zoroastrian calendar</span> Religious date system

Adherents of Zoroastrianism use three distinct versions of traditional calendars for liturgical purposes, all derived from medieval Iranian calendars and ultimately based on the Babylonian calendar as used in the Achaemenid empire. Qadimi ("ancient") is a traditional reckoning introduced in 1006. Shahanshahi ("imperial") is a calendar reconstructed from the 10th century text Denkard.

The epact used to be described by medieval computists as the age of a phase of the Moon in days on 22 March; in the newer Gregorian calendar, however, the epact is reckoned as the age of the ecclesiastical moon on 1 January. Its principal use is in determining the date of Easter by computistical methods. It varies from year to year, because of the difference between the solar year of 365–366 days and the lunar year of 354–355 days.

The history of calendars covers practices with ancient roots as people created and used various methods to keep track of days and larger divisions of time. Calendars commonly serve both cultural and practical purposes and are often connected to astronomy and agriculture.

The Ethiopian calendar, or Ge'ez calendar is the official calendar of Ethiopia. It is used as both the civil calendar and an ecclesiastical calendar. It is the liturgical year for Ethiopian and Eritrean Christians belonging to the Orthodox Tewahedo Churches, Eastern Catholic Churches, and Eastern Protestant Christian P'ent'ay Churches. The Ethiopian calendar is a solar calendar that has much in common with the Coptic calendar of the Coptic Orthodox Church of Alexandria and Coptic Catholic Church, but like the Julian calendar, it adds a leap day every four years without exception, and begins the year on 11 or 12th of September in the Julian calendar. A gap of seven to eight years between the Ethiopian and Gregorian calendars results from an alternative calculation in determining the date of the Annunciation.

The Era of the Martyrs, also known as the Diocletian era, is a method of numbering years based on the reign of Roman Emperor Diocletian who instigated the last major persecution against Christians in the Empire. It was used by the Church of Alexandria beginning in the 4th century AD and it has been used by the Coptic Orthodox Church of Alexandria from the 5th century until the present. This era was used to number the year in Easter tables produced by the Church of Alexandria.

Mesori is the twelfth month of the ancient Egyptian and Coptic calendars. It is identical to Nahase in the Ethiopian calendar.

The intercalary month or epagomenal days of the ancient Egyptian, Coptic, and Ethiopian calendars are a period of five days in common years and six days in leap years in addition to those calendars' 12 standard months, sometimes reckoned as their thirteenth month. They originated as a periodic measure to ensure that the heliacal rising of Sirius would occur in the 12th month of the Egyptian lunar calendar but became a regular feature of the civil calendar and its descendants. Coptic and Ethiopian leap days occur in the year preceding Julian and Gregorian leap years.

<span class="mw-page-title-main">Ancient Roman units of measurement</span> System of measurement used in Ancient Rome

The ancient Roman units of measurement were primarily founded on the Hellenic system, which in turn was influenced by the Egyptian and the Mesopotamian systems. The Roman units were comparatively consistent and well documented.

<span class="mw-page-title-main">Enkutatash</span> Ethiopian and Eritrean New Year holiday

Enkutatash is a public holiday in coincidence of New Year in Ethiopia and Eritrea. It occurs on Meskerem 1 on the Ethiopian calendar, which is 11 September according to the Gregorian calendar.

<span class="mw-page-title-main">Geʽez script</span> Script used for languages in Ethiopia and Eritrea

Geʽez is a script used as an abugida (alphasyllabary) for several Afro-Asiatic and Nilo-Saharan languages of Ethiopia and Eritrea. It originated as an abjad and was first used to write the Geʽez language, now the liturgical language of the Ethiopian Orthodox Tewahedo Church, the Eritrean Orthodox Tewahedo Church, the Eritrean Catholic Church, the Ethiopian Catholic Church, and Haymanot Judaism of the Beta Israel Jewish community in Ethiopia. In the languages Amharic and Tigrinya, the script is often called fidäl (ፊደል), meaning "script" or "letter". Under the Unicode Standard and ISO 15924, it is defined as Ethiopic text.

<span class="mw-page-title-main">Adoption of the Gregorian calendar</span> Transition to "New Style" dating system

The adoption of the Gregorian Calendar was an event in the early modern history of most cultures and societies, marking a change from their traditional dating system to the modern dating system – the Gregorian calendar – that is widely used around the world today. Some states adopted the new calendar from 1582, some did not do so before the early twentieth century, and others did so at various dates between. A few still have not, but except for these, the Gregorian calendar is now the world's civil calendar universally, although in many places an old style calendar remains used in religious or traditional contexts. During – and for some time after – the change between systems, it has been common to use the terms "Old Style" and "New Style" when giving dates, to indicate which calendar was used to reckon them.

References

  1. 1 2 3 4 5 6 7 8 PANKHURST, RICHARD (1970). "A Preliminary History of Ethiopian Measures, Weights and Values - (Part 3)". Journal of Ethiopian Studies. 8 (1): 45–85. ISSN   0304-2243. JSTOR   41965801.
  2. ↑ Tadesse Tassew Alemayehu (17 July 2022). "Application of Linear Body Measurements for Live Body Weight Estimation of Highland Sheep in Tigray Region, North-Ethiopia".
  3. ↑ "The counter-balance weight for a steelyard. Drawing by T. Erwin and S. Pulak". 17 July 2022.
  4. ↑ "Systems of Measure in Ethiopia". abyssiniagateway.net. Retrieved 2022-07-17.
  5. ↑ "Ethiopian Astronomy/Zodiac". An Ethiopian Journal. 2008-09-14. Retrieved 2022-07-17.
  6. ↑ "Ethiopia: Talisman Zodiac With Visual Performance". allafrica. 17 July 2022.
  7. ↑ "Numerology". www.geez.org. Retrieved 2022-07-17.
  8. 1 2 3 4 5 6 7 Mekonnen, Yohannes K. (April 2013). Ethiopia: The Land, Its People, History and Culture. New Africa Press. ISBN   978-9987-16-024-2.
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