The numerical signs ʹ and ͵ redirect here. For the accent, ´, see Acute accent.

Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals (from Miletus in Ionia), Alexandrian numerals, or alphabetic numerals (in common with other alphabetic numerations). In modern Greece, they are still used for ordinal numbers and in situations similar to those in which Roman numerals are still used elsewhere in the West. For ordinary cardinal numbers numbers, however, Greece uses Arabic numerals.

History[link]

Originally, before the adoption of the Greek alphabet, Linear A and Linear B had used a different system, called Aegean numbers, with symbols for 1, 10, 100, 1000 and 10000 operating with the following formula: | = 1, – = 10, ◦ = 100, ¤ = 1000, ☼ = 10000.^[1]

The earliest alphabet-related system of numerals used with the Greek letters was a set of the acrophonic Attic numerals, operating much like Roman numerals (which derived from this scheme), with: Ι = 1, Π = 5, Δ = 10, Η = 100, Χ = 1000, Μ = 10000; and with 50, 500, 5000, and 50000 represented by composites of Π and a tiny version of the applicable power of ten.^[1] The acrophonic system was replaced by a new alphabetic system, sometimes called the Ionic numeral system, from the 4th century BCE.

Description[link]

This section's factual accuracy is disputed. Please help to ensure that disputed facts are reliably sourced. See the relevant discussion on the talk page.

Greek numerals in a Byzantine mathematical manuscript of Hero of Alexandria's Metrika, c.1100. The first line contains the number "͵θϡϟϛ δʹ ϛʹ", i.e. "9996 ⁴⁄₆". It features each of the special numeral symbols: sampi (ϡ, = 900), Koppa (ϟ, = 90, and two instances of digamma (ϛ, = 6), in their minuscule forms.

Each unit (1, 2, …, 9) was assigned a separate letter, each tens (10, 20, …, 90) a separate letter, and each hundreds (100, 200, …, 900) a separate letter. This requires 27 letters, so the 24-letter Greek alphabet was extended by using three obsolete letters: digamma ϝ for 6, qoppa ϟ for 90, and sampi ϡ for 900. Digamma is today most often written in its modern form ϛ, which is also called stigma; in Greece it is often replaced by the letter combination στ/ΣΤ.^[2] To distinguish numerals from letters they are followed in modern print by the keraia (Greek κεραία, "hornlike projection"), a symbol ( ʹ ) similar to an acute sign ( ´ ) but with its own Unicode character (U+0374). In ancient and medieval manuscripts, number signs were written with a horizontal line above.

This alphabetic system operates on the additive principle in which the numeric values of the letters are added together to form the total. For example, 241 is represented as σμαʹ (200 + 40 + 1). A famous example is 666 (the number of the Beast), which is represented as χξϛʹ (600 + 60 + 6) in medieval manuscripts of the Book of Revelation.

To represent numbers from 1,000 to 999,999 the same letters are reused to serve as thousands, tens of thousands, and hundreds of thousands. A "left keraia" (Unicode U+0375, ‘Greek Lower Numeral Sign’) is put in front of thousands to distinguish them from the standard use. For example, 2011 is represented as ͵βιαʹ (2000 + 11).

In modern Greek, uppercase letters are preferred, as in Φίλιππος Βʹ = Philip II.

Higher numbers[link]

To represent greater numbers, the Greeks also used the myriad from the old Attic numeral system in their notation. Its value is 10,000; the number of myriads was written above its symbol (Mʹ). For example (keraias replaced for technical reasons):

Failed to parse (Missing texvc executable; please see math/README to configure.): \stackrel{\text{,}\delta\phi\pi\beta}{\Mu}\psi\theta' = 4582\times 10,000+709 = 45,820,709. \,

Other forms are also possible. When that didn't suffice the myriad myriad (one hundred million, symbol: ΜΜʹ) was used.^[3]

In his text The Sand Reckoner the natural philosopher Archimedes gives an upper bound of the number of grains of sand required to fill the entire universe, using a contemporary estimation of its size. This would defy the then-held notion that it is impossible to name a number greater than that of the sand on a beach, or on the entire world. In order to do that, he had to devise a new numeral scheme with much greater range.

Hellenistic zero[link]

Hellenistic astronomers extended alphabetic Greek numerals into a sexagesimal positional numbering system by limiting each position to a maximum value of 50 + 9 and including a special symbol for zero, which was also used alone like our modern zero, more than as a simple placeholder. However, the positions were usually limited to the fractional part of a number (called minutes, seconds, thirds, fourths, etc.) — they were not used for the integral part of a number. This system was probably adapted from Babylonian numerals by Hipparchus c. 140 BC. It was then used by Ptolemy (c. 140), Theon (c. 380), and Theon's daughter Hypatia (died 415).

In Ptolemy's table of chords, the first fairly extensive trigonometric table, there were 360 rows, portions of which looked as follows:

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{array}{ccc} \pi\varepsilon\varrho\iota\varphi\varepsilon\varrho\varepsilon\iota\tilde\omega\nu & \varepsilon\overset{\text{'}}\nu\vartheta\varepsilon\iota\tilde\omega\nu & \overset{\text{`}}\varepsilon\xi\eta\kappa\omicron\sigma\tau\tilde\omega\nu \\ \begin{array}{|l|} \hline \pi\delta\angle' \\ \pi\varepsilon \\ \pi\varepsilon\angle' \\ \hline \pi\stigma \\ \pi\stigma\angle' \\ \pi\zeta \\ \hline \end{array} & \begin{array}{|r|r|r|} \hline \pi & \mu\alpha & \gamma \\ \pi\alpha & \delta & \iota\varepsilon \\ \pi\alpha & \kappa\zeta & \kappa\beta \\ \hline \pi\alpha & \nu & \kappa\delta \\ \pi\beta & \iota\gamma & \iota\vartheta \\ \pi\beta & \lambda\stigma & \vartheta \\ \hline \end{array} & \begin{array}{|r|r|r|r|} \hline \circ & \circ & \mu\stigma & \kappa\varepsilon \\ \circ & \circ & \mu\stigma & \iota\delta \\ \circ & \circ & \mu\stigma & \gamma \\ \hline \circ & \circ & \mu\varepsilon & \nu\beta \\ \circ & \circ & \mu\varepsilon & \mu \\ \circ & \circ & \mu\varepsilon & \kappa\vartheta \\ \hline \end{array} \end{array}

Each number in the first column, labeled περιφεριῶν, is the number of degrees of arc on a circle. Each number in the second column, labeled ενθειῶν, is the length of the corresponding chord of the circle, when the diameter is 120. Thus πδ represents an 84° arc, and the ∠' after it means one-half, so that πδ∠' means 84.5°. In the next column we see π μα γ, meaning 80 + 41/60 + 3/60². That is the length of the chord corresponding to an arc of 84.5° when the diameter of the circle is 120. The next column, labeled ὲξηκοστῶν, for "sixtieths", is the number to be added to the chord length for each 1° increase in the arc, over the span of the next 12°. Thus that last column was used for linear interpolation.

The Greek sexagesimal place holder or zero symbol changed over time. The symbol used on papyri during the second century was a very small circle with an overbar several diameters long, terminated or not at both ends in various ways. Later, the overbar shortened to only one diameter, similar to our modern o macron (ō) which was still being used in late medieval Arabic manuscripts whenever alphabetic numerals were used. But the overbar was omitted in Byzantine manuscripts, leaving a bare ο (omicron). This gradual change from an invented symbol to ο does not support the hypothesis that the latter was the initial of ουδέν meaning "nothing".^[4][5]

Some of Ptolemy's true zeros appeared in the first line of each of his eclipse tables, where they were a measure of the angular separation between the center of the Moon and either the center of the Sun (for solar eclipses) or the center of Earth's shadow (for lunar eclipses). All of these zeros took the form 0 | 0 0, where Ptolemy actually used three of the symbols described in the previous paragraph. The vertical bar (|) indicates that the integral part on the left was in a separate column labeled in the headings of his tables as digits (of five arc-minutes each), whereas the fractional part was in the next column labeled minute of immersion, meaning sixtieths (and thirty-six-hundredths) of a digit.^[6]

See also[link]

• Attic numerals
• Gematria
• Greek numerals in Unicode (acrophonic, not alphabetic, numerals)
• Isopsephy

References[link]

External links[link]

Wikimedia Commons has media related to: Greek numerals

• The Greek Number Converter

v t e Greek language · Eλληνική γλώσσα History Proto-Greek (c. 3000–1600 BC) Mycenaean (c. 1600–1000 BC) Ancient Greek (c. 1000–330 BC) Koine Greek (c. 330 BC–AD 330) Medieval Greek (330–1453) Modern Greek (from 1453) Alphabet Archaic alphabets Orthography Diacritics History Romanization Greeklish Numerals Linear B Cypriot syllabary Letters Alpha Beta Gamma Delta Epsilon Zeta Eta Theta Iota Kappa Lambda Mu Nu Xi Omicron Pi Rho Sigma Tau Upsilon Phi Chi Psi Omega Obsolete: Digamma Heta Koppa Stigma San Sampi Phonology Ancient Greek (accent) Koine Greek Modern Greek Grammar Ancient Greek (tables) Modern Greek Dialects Cappadocian Cretan Cypriot Chalkidiki Demotic Greek-Calabrian Griko Katharevousa Misthiotica Pontic Tsakonian Yevanic Literature Ancient Greek Byzantine Modern Greek Related topics Greek Wikipedia Exonyms Morphemes Terms of Endearment Place names Proverbs Greek language question Graeco-Armenian Graeco-Aryan Pre-Greek substrate Promotion and study Hellenic Foundation for Culture Center for the Greek language

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Friedrich A. Kittler (June 12, 1943 – October 18, 2011) was a literary scholar and a media theorist. His works relate to media, technology, and the military.

Biography[link]

Friedrich Adolf Kittler was born in 1943 in Rochlitz in Saxony. His family fled with him to West Germany in 1958, where from 1958 to 1963 he went to a natural sciences and modern languages Gymnasium in Lahr in the Black Forest, and thereafter, until 1972, he studied German studies, Romance philology and philosophy at the Albert Ludwigs University of Freiburg in Freiburg im Breisgau. During his studies, he was influenced by Jacques Lacan's and Michel Foucault's writings.

In 1976, Kittler received his doctorate in philosophy after a thesis on the poet Conrad Ferdinand Meyer. Between 1976 and 1986 he worked as academic assistant at the university's Deutsches Seminar. In 1984, he earned his Habilitation in the field of Modern German Literary History.

He had several stints as a Visiting Assistant Professor or Visiting Professor at universities in the United States, such as the University of California, Berkeley, the University of California, Santa Barbara and Stanford University.

From 1986 to 1990, he headed the DFG's Literature and Media Analysis project in Kassel and in 1987 he was appointed Professor of Modern German Studies at the Ruhr University. In 1993 he was appointed to the chair for Media Aesthetics and History at the Humboldt University of Berlin. Between 2005 and 2011 he was a professor at the European Graduate School in Saas-Fee, Switzerland.^[1]

In 1993, Kittler was awarded the "Siemens Media Arts Prize" (Siemens-Medienkunstpreis) by ZKM Karlsruhe (Zentrum für Kunst und Medientechnologie, or "Centre for Art and Media Technology") for his research in the field of media theory.^[2]

He was recognized in 1996 as a Distinguished Scholar at Yale University and in 1997 as a Distinguished Visiting Professor at Columbia University in New York. Kittler was a member of the Hermann von Helmholtz Centre for Culture and the research group Bild Schrift Zahl ("Picture Writing Number") (DFG). He died in Berlin. His last words were reportedly "Alle Apparate auschalten", which translates, referring to the machines which were keeping him alive, as "switch off all apparatuses".^[3]

Work and its importance[link]

Friedrich Kittler is seminal in the new approach to media theory that grew popular starting in the 1980s, new media (German: Technische Medien, which translates roughly to "technical media"). Kittler's central project is to "prove to the human sciences [...] their technological-media a priori" (Hartmut Winkler), or in his own words: "Driving the spirit out of the humanities",^[4] a title that he gave a work that he published in 1980.

Kittler sees an autonomy in technology and therefore disagrees with Marshall McLuhan's reading of the media as "extensions of man": "Media are not pseudopods for extending the human body. They follow the logic of escalation that leaves a written history behind it. (Kittler in Geschichte der Kommunikationsmedien. In: Jörg Huber, Alois Martin Müller (publishers): Raum und Verfahren).

Consequently, he sees in writing literature, in writing programmes and in burning structures into silicon chips a complete continuum: "As we know and simply do not say, no human being writes anymore. [...] Today, human writing runs through inscriptions burnt into silicon by electronic lithography [...]. The last historic act of writing may thus have been in the late seventies when a team of Intel engineers [plotted] the hardware architecture of their first integrated microprocessor." (Kittler, Es gibt keine Software. In: ders.: Draculas Vermächtnis. Technische Schriften).

See also[link]

• Media influence
• Paul Virilio

Notes[link]

Publications[link]

• 2009: Musik und Mathematik. Band 1: Hellas, Teil 2: Eros. Wilhelm Fink Verlag, Paderborn.
• 2006: Musik und Mathematik. Band 1: Hellas, Teil 1: Aphrodite. Wilhelm Fink Verlag, Paderborn.
• 2004: Unsterbliche. Nachrufe, Erinnerungen, Geistergespräche. Wilhelm Fink Verlag, Paderborn.
• 2002: Zwischen Rauschen und Offenbarung. Zur Kultur- und Mediengeschichte der Stimme (as publisher). Akademie Verlag, Berlin
• 2002: Optische Medien. Merve: Berlin. ISBN 3-88396-183-3 (English edition: Optical Media, with an introduction by John Durham Peters. Polity Press 2010)
• 2001: Vom Griechenland (with Cornelia Vismann; Internationaler Merve Diskurs Bd.240). Merve: Berlin. ISBN 3-88396-173-6
• 2000: Nietzsche – Politik des Eigennamens: wie man abschafft, wovon man spricht (with Jacques Derrida). Berlin.
• 2000: Eine Kulturgeschichte der Kulturwissenschaft. München
• 1999: Hebbels Einbildungskraft – die dunkle Natur. Frankfurt, New York, Vienna
• 1998: Zur Theoriegeschichte von Information Warfare
• 1998: Hardware das unbekannte Wesen
• 1997: Literature, Media, Information Systems: Essays (published by John Johnston). Amsterdam
• 1993: Draculas Vermächtnis: Technische Schriften. Leipzig: Reclam. ISBN 3-379-01476-1 Essays zu den "Effekten der Sprengung des Schriftmonopols", zu den Analogmedien Schallplatte, Film und Radio sowie "technische Schriften, die numerisch oder algebraisch verfasst sind".
• 1991: Dichter – Mutter – Kind. Munich
• 1990: Die Nacht der Substanz. Bern
• 1986: Grammophon Film Typewriter. Berlin: Brinkmann & Bose. ISBN 3-922660-17-7 (English edition: Gramophone, Film, Typewriter, Stanford 1999)
• 1985: Aufschreibesysteme 1800/1900. Fink: Munich. ISBN 3-7705-2881-6 (English edition: Discourse Networks 1800 / 1900, with a foreword by David E. Wellbery. Stanford 1990)
• 1979: Dichtung als Sozialisationsspiel. Studien zu Goethe und Gottfried Keller (with Gerhard Kaiser). Göttingen
• 1977: Der Traum und die Rede. Eine Analyse der Kommunikationssituation Conrad Ferdinand Meyers. Bern-Munich

Literature[link]

Secondary literature on Friedrich Kittler:

• Frank Hartmann: Friedrich Kittler. In: Information Philosophie 25 (1997) 4, S. 40-44.
• Josef Wallmannsverger: Friedrich Kittler. In: Helmut Schanze (publisher): Metzler Lexikon Medientheorie/ Medienwissenschaft, S. 162 f. Stuttgart 2002.
• Geoffrey Winthrop-Young: Friedrich Kittler zur Einführung, Hamburg: Junius Verlag 2005.

Lectures[link]

• The Relation of Art and Techne, European Graduate School
• Friedrich Kittler. Ein Medienphilosoph, European Graduate School
• Die Endlichkeit der Algorithmen
• Aphrodite mit Stefan Münker
• Farben und/oder Maschinen denken
• Vom Gott der Diebe zum gerechneten Raum
• Kittler liest Gedichte von Sappho und spricht über die Liebe
• Blitz und Serie, Ereignis und Donner
• Ontologie der Medien

External links[link]

• Friedrich Kittler Faculty page at European Graduate School. Biography, bibliography, articles and video lectures
• Friedrich Kittler in the German National Library catalogue (German)
• Auf dem Weg in den Maschinenpark - Rezension Friedrich Kittler: Eine Kulturgeschichte der Kulturwissenschaft - von Frank Hartmann, 28 November 2000
• Telepolis: Friedrich Kittler meets Stephan Schambach von Stefan Krempl, 26. Mai 2000
• Telepolis: Vom Sündenfall der Software - Medientheorie mit Entlarvungsgestus: Friedrich Kittler - von Frank Hartmann, 22 December 1998
• Telepolis: Nicht Cyborg, sondern Affe 17 April 2005
• "Rock me, Aphrodite!" - Interview mit Kittler auf Telepolis, 24 May 2006.
• "Hegel is dead. Miscellanea on Friedrich A. Kittler (1943-2011)" - Obituary on Kittler, Telepolis, 17 November 2011.
• The Sigmund H. Danziger, Jr. Memorial Lecture in the Humanities (Sigmund H. Danziger, Jr Lecture 1993-1994
• "We only have ourselves to draw upon"" - An interview by Andreas Rosenfelder

Notes[link]