Attic numerals

The Attic numerals are a symbolic number notation used by the ancient Greeks. They were also known as Herodianic numerals because they were first described in a 2nd-century manuscript by Herodian; or as acrophonic numerals (from acrophony) because the basic symbols derive from the first letters of the (ancient) Greek words that the symbols represented.

The Attic numerals were a decimal (base 10) system, like the older Egyptian and the later Etruscan, Roman, and Hindu-Arabic systems. Namely, the number to be represented was broken down into simple multiples (1 to 9) of powers of ten — units, tens, hundred, thousands, etc.. Then these parts were written down in sequence, in order of decreasing value. As in the basic Roman system, each part was written down using a combination of two symbols, representing one and five times that power of ten.

Attic numerals were adopted possibly starting in the 7th century BCE, and were eventually replaced by the classic Greek numerals around the 3rd century BCE. They are believed to have served as model for the Etruscan number system, although the two were nearly contemporary and the symbols are not obviously related.

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Detail of stela showing tributes paid by allies of Athens in the League of Delos. The amounts are in Attic numerals, using the drachma sign "𐅂" instead of the geenric unit sign "Ι". Some amounts are "𐅄" = 50, "ΗΗΗ" = 300, "𐅅ΗΗΗ" = 800, "ΔΔΔ𐅂𐅂𐅂" = 33, "Χ" = 1000, and "Χ𐅅𐅄Δ𐅂𐅂"? = 1562?.

The system

Symbols

The Attic numerals used the following main symbols, with the given values:

Value Symbol Talents Staters Notes Etruscan Roman
1 Ι Tally mark? 𐌠 I
5 Π 𐅈 𐅏 Old Greek: ΠΕΝΤΕ [pɛntɛ] Modern: πέντε 𐌡 V
10 Δ 𐅉 𐅐 Old Greek: ΔΕΚΑ [deka] Modern: δέκα 𐌢 X
50 𐅄 𐅊 𐅑 "Δ" in "Π": 10 × 5 = 50 𐌣 L
100 Η 𐅋 𐅒 Old Greek: ΗΕΚΑΤΟΝ [hɛkaton] Modern: ἑκατόν 𐌟 C
500 𐅅 𐅌 𐅓 "Η" in "Π": 100 × 5 = 500 ? D
1000 Χ 𐅍 𐅔 Old Greek: ΧΙΛΙΟΙ [kʰilioi] Modern: χίλιοι ? M
5000 𐅆 𐅎 "Χ" in "Π": 1000 × 5 = 5000 ? V
10000 Μ 𐅕 Old Greek: ΜΥΡΙΟΝ [myrion] Modern: μύριον ? X
50000 𐅇 𐅖 "Μ" in "Π": 10000 × 5 = 50000 ? X

The symbols representing 50, 500, 5000, and 50000 were composites of an old form of the capital letter pi (with a short right leg) and a tiny version of the applicable power of ten. For example, 𐅆 was five times one thousand.

Special simbols

The fractions "one half" and "one quarter" were written "𐅁" and "𐅀", respectively.

The symbols were slightly modified when used to encode amounts in talents (with a small capital tau, "Τ") or in staters (with a small capital sigma, "Σ"). Specific numeral symbols were used to represent one drachma ("𐅂") and ten minas "𐅗".

The symbol for 100

The use of "Η" (capital eta) for 100 reflects the early date of this numbering system. In the Greek language of the time, the word for a hundred would be pronounced [hɛkaton] (with a "rough aspirated" sound /h/) and written "ΗΕΚΑΤΟΝ", because "Η" represented the sound /h/ in the Attic alphabet. In later, "classical" Greek, with the adoption of the Ionic alphabet throughout the majority of Greece, the letter eta had come to represent the long e sound while the rough aspiration was no longer marked.[1][2] It was not until Aristophanes of Byzantium introduced the various accent markings during the Hellenistic period that the spiritus asper began to represent /h/, resulting in the modern Greek spelling ἑκατόν. In modern Greek the /h/ phoneme has disappeared altogether, but the accent on the is retained in the standard spelling.

Simple multiples of powers of ten

Multiples 1 to 9 of each power of ten were written by combining the two corresponding "1" and "5" digits, namely:

Units Ι II III IIII Π ΠI ΠII ΠIII ΠIIII
1 2 3 4 5 6 7 8 9
Tens Δ ΔΔ ΔΔΔ ΔΔΔΔ 𐅄 𐅄Δ 𐅄ΔΔ 𐅄ΔΔΔ 𐅄ΔΔΔΔ
10 20 30 40 50 60 70 80 90
Hundreds Η ΗΗ ΗΗΗ ΗΗΗΗ 𐅅 𐅅Η 𐅅ΗΗ 𐅅ΗΗΗ 𐅅ΗΗΗΗ
100 200 300 400 500 600 700 800 900
Thousands Χ ΧΧ ΧΧΧ ΧΧΧΧ 𐅆 𐅆Χ 𐅆ΧΧ 𐅆ΧΧΧ 𐅆ΧΧΧΧ
1000 2000 3000 4000 5000 6000 7000 8000 9000
Tens of thousands Μ ΜΜ ΜΜΜ ΜΜΜΜ 𐅇 𐅇Μ 𐅇ΜΜ 𐅇ΜΜΜ 𐅇ΜΜΜΜ
10000 20000 30000 40000 50000 60000 70000 80000 90000

Unlike the more familiar Roman numeral system, the Attic system used only the so-called "additive" notation. Thus, the numbers 4 and 9 were written ΙΙΙΙ and ΠΙΙΙΙ, not ΙΠ and ΙΔ.

General numbers

In general, the number to be represented was broken down into simple multiples (1 to 9) of powers of ten — units, tens, hundred, thousands, etc.. Then these parts would be written down in sequence, from largest to smallest value. For example:

  • 49 = 40 + 9 = ΔΔΔΔ + ΠΙΙΙΙ = ΔΔΔΔΠΙΙΙΙ
  • 2001 = 2000 + 1 = ΧΧ + I = ΧΧΙ
  • 1982 = 1000 + 900 + 80 + 2 = Χ + 𐅆ΗΗΗΗ + 𐅄ΔΔΔ + ΙΙ = Χ𐅆ΗΗΗΗ𐅄ΔΔΔΙΙ
  • 62708 = 60000 + 2000 + 700 + 8 = 𐅇Μ + ΧΧ + 𐅅ΗΗ + ΠIII = 𐅇ΜΧΧ𐅅ΗΗΠIII.

Attic numerals are available in Unicode in the Ancient Greek Numbers block (U+10140 to U+1018F).

See also

Notes and references

  1. ^ Woodhead, A. G. (1981). The Study of Greek Inscriptions. Second Edition. Cambridge: Cambridge University Press. p. 18. ISBN 0-521-23188-4.
  2. ^ Smyth, Herbert Weir; Messing, Gordon M. (2002) [1920]. Greek Grammar. Revised Edition. Cambridge, MA: Harvard University Press. p. 10 (§14). ISBN 0-674-36250-0.
Acropolis of Athens

The Acropolis of Athens is an ancient citadel located on a rocky outcrop above the city of Athens and contains the remains of several ancient buildings of great architectural and historic significance, the most famous being the Parthenon. The word acropolis is from the Greek words ἄκρον (akron, "highest point, extremity") and πόλις (polis, "city"). Although the term acropolis is generic and there are many other acropoleis in Greece, the significance of the Acropolis of Athens is such that it is commonly known as "The Acropolis" without qualification. During ancient times it was known also more properly as Cecropia, after the legendary serpent-man, Cecrops, the supposed first Athenian king.

While there is evidence that the hill was inhabited as far back as the fourth millennium BC, it was Pericles (c. 495–429 BC) in the fifth century BC who coordinated the construction of the site's most important present remains including the Parthenon, the Propylaia, the Erechtheion and the Temple of Athena Nike. The Parthenon and the other buildings were damaged seriously during the 1687 siege by the Venetians during the Morean War when gunpowder being stored in the Parthenon was hit by a cannonball and exploded.

Ancient Greek dialects

Ancient Greek in classical antiquity, before the development of the common Koine Greek of the Hellenistic period, was divided into several varieties.

Most of these varieties are known only from inscriptions, but a few of them, principally Aeolic, Doric, and Ionic, are also represented in the literary canon alongside the dominant Attic form of literary Greek.

Likewise, Modern Greek is divided into several dialects, most derived from Koine Greek.

Attic Greek

Attic Greek is the Greek dialect of the ancient city-state of Athens. Of the ancient dialects, it is the most similar to later Greek and is the standard form of the language that is studied in ancient Greek language courses. Attic Greek is sometimes included in the Ionic dialect. Together, Attic and Ionic are the primary influences on Modern Greek.

Brahmi numerals

The Brahmi numerals are a numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). They are the direct graphic ancestors of the modern Indian and Hindu–Arabic numerals. However, they were conceptually distinct from these later systems, as they were not used as a positional system with a zero. Rather, there were separate numerals for each of the tens (10, 20, 30, etc.). There were also symbols for 100 and 1000 which were combined in ligatures with the units to signify 200, 300, 2000, 3000, etc.

Cycladic culture

Cycladic culture (also known as Cycladic civilisation or, chronologically, as Cycladic chronology) was a Bronze Age culture (c. 3200–c. 1050 BC) found throughout the islands of the Cyclades in the Aegean Sea. In chronological terms, it is a relative dating system for artefacts which broadly complements Helladic chronology (mainland Greece) and Minoan chronology (Crete) during the same period of time.

Demonax

Demonax (Greek: Δημώναξ, Dēmōnax, gen.: Δημώνακτος; c. AD 70 – c. 170) was a Greek Cynic philosopher. Born in Cyprus, he moved to Athens, where his wisdom, and his skill in solving disputes, earned him the admiration of the citizens. He taught Lucian, who wrote a Life of Demonax in praise of his teacher. When he died he received a magnificent public funeral.

Greece in the Roman era

Greece in the Roman era describes the period of Greek history when Ancient Greece was dominated by the Roman Republic (509 – 27 BC), the Roman Empire (27 BC – AD 395), and the Byzantine Empire (AD 395 – 1453). The Roman era of Greek history began with the Corinthian defeat in the Battle of Corinth in 146 BC. However, before the Achaean War, the Roman Republic had been steadily gaining control of mainland Greece by defeating the Kingdom of Macedon in a series of conflicts known as the Macedonian Wars. The Fourth Macedonian War ended at the Battle of Pydna in 148 BC and defeat of the Macedonian royal pretender Andriscus.

The definitive Roman occupation of the Greek world was established after the Battle of Actium (31 BC), in which Augustus defeated Cleopatra VII, the Greek Ptolemaic queen of Egypt, and the Roman general Mark Antony, and afterwards conquered Alexandria (32 BC), the last great city of Hellenistic Greece. The Roman era of Greek history continued with Emperor Constantine the Great's adoption of Byzantium as Nova Roma, the capital city of the Roman Empire; in AD 330, the city was renamed Constantinople; afterwards, the Byzantine Empire was a generally Greek-speaking polity.

Greek Dark Ages

The Greek Dark Ages, Homeric Age (named for the fabled poet, Homer) or Geometric period (so called after the characteristic Geometric art of the time),

is the period of Greek history from the end of the Mycenaean palatial civilization around 1100 BC to the first signs of the Greek poleis (city states) in the 9th century BC.

The archaeological evidence shows a widespread collapse of Bronze Age civilization in the Eastern Mediterranean world at the outset of the period, as the great palaces and cities of the Mycenaeans were destroyed or abandoned. At about the same time, the Hittite civilization suffered serious disruption and cities from Troy to Gaza were destroyed and in Egypt the New Kingdom fell into disarray that led to the Third Intermediate Period.

Following the collapse, fewer and smaller settlements suggest famine and depopulation. In Greece, the Linear B writing of the Greek language used by Mycenaean bureaucrats ceased. The decoration on Greek pottery after about 1100 BC lacks the figurative decoration of Mycenaean ware and is restricted to simpler, generally geometric styles (1000–700 BC).

It was previously thought that all contact was lost between mainland Hellenes and foreign powers during this period, yielding little cultural progress or growth, but artifacts from excavations at Lefkandi on the Lelantine Plain in Euboea show that significant cultural and trade links with the east, particularly the Levant coast, developed from c. 900 BC onwards. Additionally, evidence has emerged of the new presence of Hellenes in sub-Mycenaean Cyprus and on the Syrian coast at Al-Mina.

Greek numerals

Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used elsewhere in the West. For ordinary cardinal numbers, however, Greece uses Arabic numerals.

Grotta-Pelos culture

The Grotta-Pelos culture (Greek: Γρόττα-Πηλός) refers to a "cultural" dating system used for part of the early Bronze Age in Greece. Specifically, it is the period that marks the beginning of the so-called Cycladic culture and spans the Neolithic period in the late 4th millennium BC (ca. 3300 BC), continuing in the Bronze Age to about 2700 BC.

The term was coined by Colin Renfrew, who named it after the sites of Grotta and Pelos on the Cycladic islands of Naxos and Milos, respectively. Other archaeologists prefer a "chronological" dating system and refer to this period as the Early Cycladic I (ECI).

Kastelli Hill

Kastelli Hill (also Kasteli; Greek: Λόφος Καστέλλι or Καστέλι) is a landform at the city of Chania on the island of Crete in the present day country of Greece. The Minoan city of ancient Cydonia was centered on Kastelli Hill, which later was selected by the Romans as the site of an acropolis.

Members of the Delian League

The members of the Delian League/Athenian Empire (c. 478-404 BC) can be categorized into two groups: the allied states (symmachoi) reported in the stone tablets of the Athenian tribute lists (454-409 BC), who contributed the symmachikos phoros ("allied tax") in money, and further allies, reported either in epigraphy or historiography, whose contribution consisted of ships, wood, grain, and military assistance; proper and occasional members, subject members and genuine allies.

Numerals in Unicode

Numerals (often called numbers in Unicode) are characters or sequences of characters that denote a number. The Hindu-Arabic numeral system (base-10) is used widely in various writing systems throughout the world and all share the same semantics for denoting numbers. However, the graphemes representing the numerals differ widely from one writing system to another. To support these grapheme differences, Unicode includes encodings of these numerals within many of the script blocks. The decimal digits are repeated in 22 separate blocks. In addition to many forms of the Hindu-Arabic numerals, Unicode also includes several less common numerals such as: Aegean numerals, Roman numerals, counting rod numerals, Cuneiform numerals and ancient Greek numerals. There is also a large number of typographical variations of the Arabic numerals provided for specialized mathematical use and for compatibility with earlier character sets, and also composite characters containing Arabic numerals such as ½.

Numerals invariably involve composition of glyphs as a limited number of characters are composed to make other numerals. For example, the sequence 9–9–0 in Arabic numerals composes the numeral for nine hundred ninety (990). In Roman numerals, the same number is expressed by the composed numeral Ⅹↀ or ⅩⅯ. Each of these is a distinct numeral for representing the same abstract number. The semantics of the numerals differ in particular in their composition. Hindu-Arabic digits are positional-value compositions, while the Roman numerals are sign-value and they are additive and subtractive depending on their composition.

Numerical digit

A numerical digit is a single symbol (such as "2" or "5") used alone, or in combinations (such as "25"), to represent numbers (such as the number 25) according to some positional numeral systems. The single digits (as one-digit-numerals) and their combinations (such as "25") are the numerals of the numeral system they belong to. The name "digit" comes from the fact that the ten digits (Latin digiti meaning fingers) of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal (ancient Latin adjective decem meaning ten) digits.

For a given numeral system with an integer base, the number of digits required to express arbitrary numbers is given by the absolute value of the base. For example, the decimal system (base 10) requires ten digits (0 through to 9), whereas the binary system (base 2) has two digits (e.g.: 0 and 1).

Paideia

In the culture of ancient Greece, the term paideia (also spelled paedeia) (; Greek: παιδεία, paideía) referred to the rearing and education of the ideal member of the polis. It incorporated both practical, subject-based schooling and a focus upon the socialization of individuals within the aristocratic order of the polis. The practical aspects of this education included subjects subsumed under the modern designation of the liberal arts (rhetoric, grammar, and philosophy are examples), as well as scientific disciplines like arithmetic and medicine. An ideal and successful member of the polis would possess intellectual, moral and physical refinement, so training in gymnastics and wrestling was valued for its effect on the body alongside the moral education which the Greeks believed was imparted by the study of music, poetry, and philosophy. This approach to the rearing of a well-rounded Greek male was common to the Greek-speaking world, with the exception of Sparta where a rigid and militaristic form of education known as the agoge was practiced.

Phylakopi I culture

The Phylakopi I culture (Greek: Φυλακωπή) refers to a "cultural" dating system used for the Cycladic culture that flourished during the early Bronze Age in Greece. It spans the period ca. 2300-2000 BC and was named by Colin Renfrew, after the settlement of Phylakopi on the Cycladic island of Milos. Other archaeologists describe this period as the Early Cycladic III (ECIII).

Prehistoric numerals

Counting in prehistory was first assisted by using body parts, primarily the fingers.

This is reflected in the etymology of certain number names, such as in the names of ten and hundred in the Proto-Indo-European numerals, both containing the root *dḱ also seen in the word for "finger" (Latin digitus, cognate to English toe).

Early systems of counting using tally marks appear in the Upper Paleolithic.

The first more complex systems develop in the Ancient Near East together with the development of early writing out of proto-writing systems.

Roman numerals

Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Modern usage employs seven symbols, each with a fixed integer value:

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more convenient Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day.

One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XIIThe notations IV and IX can be read as "one less than five" (4) and "one less than ten" (9). On most Roman numeral clock faces, however, 4 is traditionally written as IIII.Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. MCM, signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is written MCMXII. For this century, MM indicates 2000. Thus the current year is MMXIX (2019).

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