until 13xx A.D.: The Human Age of Information Processing

• 2,000,000 BC: first wave of hominides leaves Africa to settle Eurasia.
• 172,000 BC: last common predecessors of all modern humans (calculated from comparison of mitochondrial DNA). These predecessors are in Africa, from where they spread over the entire world (the Out-of-Africa theory).
• 130,000 BC: oldest fossiles of homo sapiens (Africa).
• 40,000-30,000 BC: homo sapiens replaces homo neanderthaliensis in Near East and Europe; palaeolithic revolution.

• Not much can be known for sure about pre-historic human calculating capabilities. Presumably numbers were first represented by 1:1 correspondence.
  • Encod. + Aide: Man's ever-present fingers came handy as the first aide for calculation with 1:1 representation for 0 to 10.
  • Aide: «As the need to represent larger numbers grew early man employed readily available materials for the purpose. Small stones or pebbles could be used to represent larger numbers than fingers and toes, and had the added advantage of being able to easily store intermediate results for later use. Thus, it is also no coincidence that the word "calculate" is derived from the Latin word for pebble.» [Maxmon]
  • Principle: «Early man counted by means of matching one set of objects with another set (stones and sheep). The operations of addition and subtraction were simply the operations of adding or subtracting groups of objects to the sack of counting stones or pebbles.»
  • Notat., 20,000 - 30,000 (western Europe)[>]: Bones with carved-in notches (1:1 number notation, cf. fingers[<]) are the oldest documented calculation aides.
    Especially: first evidence of tallying with groups of five (Czechoslovakia)
    At the same time: first appearance of Cro-Magnon man.
• Notat., 15,000 BC[>]: The earliest cavedrawings [AITL]

Neolithicum

• Theory, 8500 BC (Africa): prime numbers 11, 13, 17, and 19 on a bone.
• Notat., 8000 BC (Mesopotamia) [<>]: shapes written into clay are used in large numbers. They are are pictograms, i.e. they look like what they mean.
• Symbols, 7000 BC: rock paintings with wusum (painter's signature) in Bir Hima, Southern Saudi Arabia [Geo, 12/2002]
• Notat., 4000 [AITL] - 3400 BC (Sumeria) [<>]: A greatly elaborated set of clay shapes formed a pictographic system.
  3400 BC: Sumerian scribes invented the practice of writing cuneiforms on clay tablets with styluses.
  The switch to pointed styluses makes cuneiforms more stylized (requiring to learn the script to read it [AITL]).
• Notat., 3100 BC [<>]: Shapes on clay tablets are now unambiguously related to the Sumerian language, constituting a logographic system (a limited system of notation suitable for recording particular events; generally adequate to economic and administrative purposes), made of some 1,200 symbols representing (not only the concepts of, but the words for [AITL]) numerals, names, and such material objects as cloth and cow. Graphs for numerals were geometric shapes, while those for objects were often stylized pictures of the things they represented.
• Notat., 3000 BC[<>]: Chinese script - icons for words and syllables.
• Notat., 3000 BC[<>]: Egyptians write hieroglyphs [AITL], icons for words and syllables (including 24 symbols for (the names of) consonants) See some hieroglyphs. Further development of Egyptian glyphs: [>]
•  Notat., 3rd millennium BC[>]: The first syllabic system: Akkadians (Babylonias, and Assyrians) adopt Sumerian cuneiforms [<]: to (unsystematically) represent their syllables [and also some word-symbols] -- they are phonographic symbols with no visual connection. From these "Semitic syllabries" the writing of many languages evolves (Persian (600-400 BC), Urdu, Hindi etc) [AITL].
• Glyphs, ca 2200 BC [<>>]: hieratic script (for Egyptian words and syllables), a stylized writing of hieroglyphs on papyrus.
• Principle, before 2000 BC / first appeared around 1900 to 1800 BC [>]: The Babylonians calculated in a sexagesimal system, the first known place-value number system.
  Notat.[<>] Numbers were written by accumulating, per position, the two digits 1 and 10 (with the values 1, 60, 60*60 ...), a space "represented" the zero "digit".
• Principle. [when?] [<>]: Egyptians used a duo-decimal (base-12) system (12 finger-joints on one hand!)
  On the other hand, Egyptian multiplication[>] implicitly uses binary arithmetics.
  Notat.[<>]: But Egyptians also a non-positional base-10 numbers: 1 = "|"; 10 = "O"; 100 = coiled rope; 1,000 = lotus blossom; 10,000 = pointing finger; 100,000 = tadpole; 1,000,000 = man.

Notat., when?[

Second Millenium BC

• Theory, betw. 1900 and 1600 BC: The oldest number theory document in existence: a Babylonian tablet on Pythagorean triples, i.e. numbers a, b, c with a² + b² = c².
• Principle, 1650 BC: Ahmes/Ahmose's (Egypt) "Rhind Papyrus" based on work of about 2000 BC shows calculations with fractions and a multiplication procedure based on binary arithmetics (but without binary notation!) to achieve multiplication by additions [<>]
•  Notat., 1800/1600/1400 BC [<>]: Linear A, a syllabic script, attested in and around Crete since 1850BC. Linear B adapted 1600BC by Mycenaean Greeks from Linear A, attested since 1400BC, is a strictly syllabic script, exclusively used for economic administration.
•  Notat., 1500 BC [<>]: The Phoenicians' West-Semitic consonantal alphabet is the first alphabet, i.e., a writing system of sounds instead of words/syllables [AITL]. The plethoria of (symbols for) possible syllables ka, ke, ki, ... is folded to simply one symbol 'k' by 'acrophony' [dtv].
  Glyphs[<>]: The glyphs of this alphabet are derived from Egyptian hieroglyphs whose name begins with that sound. They are written right-to-left (the oldest Greek texts are also still right-to-left; cf. 5th cent. BC Latin text 'lapis niger' with lines alternating left-to-right and right-to-left). [dtv]
  - Most/All? known consonant and alphabetic scripts were derived from this alphabet: Greek[>] (Roman, ...), South Arabian, Aramaic. Aramaic replaced cuneiforms in Mesopotamia around 1 cent. BC, and evolved to alphabet for Hebrew, Arabian, Persian, Indian, Uiguric, ...). [AITL,dtv]
• Encod. + Principle + Aide, 14th century BC, China: First record of the suan pan (in Greece "abacus" from sand/dust) [<>]:
  Abacus is a method for performing arithmetics by stepwise manipulation (increment/decrement) of numbers in a positional notation (commonly decimal, with zero!).
  Abacus as an aide (mechanical storage device allowing direct manipulation) orignally was a «a flat stone covered with sand (or dust) into which numeric symbols were drawn».
  1000 - 500 BC: abacus invented by the Babylonians (or was it 3000 BC?).
  «Over time the stone was replaced by a wooden frame».
  Encod. [when?]: «[M]ost popular became those based on the bi-quinary system, which utilizes a combination of two bases (base-2 and base-5) to represent decimal numbers».
  In its modern form since 13th century AD China.

First Millenium BC

•  Notat., 1000 BC [<>]: the Greek alphabet of (and glyphs for) consonants and vowels, derived from the Phoenician constonantal alphabet & glyphs [<].
  Glyphs[>>]: The Greek inventory of sounds and glyphs was adapted by many European cultures:
  750 BC: Etruscians adapted Greek and/or Phoenician alphabet.
  500 BC: Romans adapted Etruscan and/or Greek alphabet to the Latin alphabet
  Other derivates of Greek alphabet: runes, Cyrillic. [AITL].
• Glyphs, ca. 700 BC [<]: demotic script (for Egyptian words and syllables), a more fluent form of hieratic script (used up to 500 AD).
• Notat., 6th cent. BC: Greeks use letters to represent notes [>]
• Pythagoras of Samos' (569-475) school: abstract concept of numbers and geometric figures; geometrical algebra; discovered irrationals. They believed that all relations could be reduced to number relations.
• Syntax[>]: Panini (uncertain: 520-460, India), most influential Indian grammarian, describes the grammar of Sanskrit by 4000 rules and a list of gound forms (uses symbols and abbreviations) [EML].
  Grammar[>]: The Indian tradition knows 12 schools of linguistic theories. Indian linguistics distinguish noun (subject) : verb (predicate) : preposition : particle. In India, unlike Europea, linguists investigated phonetics and morphology (word structure).

  Grammar[<>]: Protagoras' (one of 5th cent.'s oldest and most influential sophist) distinction of three genera in Greek [EML]

  Linguistics[>]: Greek philosphers were undecided whether language is a social convention or is derived from the nature of things [EML]

  Meaning[>]: «Very early in traditional grammar the question about the connection between the word and the `thing', to which it refered or which it `denoted', was raised». Notably the Greek philosphers of the time of Sokrates and, after him, Platon. [EML 412].

  Model[>]: The atomists «claimed that what exists fundamentally is material atoms and the void, and all change or alteration, such as motion, combustion, or the growth and decay of living things, is merely the rearrangement of atoms in the void» [x].

  Plato (429-347).
  - Grammar[<>]: He distinguishes nouns:verbs (where ``verbs'' includes adjectives) as (main) parts of speech: nouns can be subjects, ``verbs'' describe activities or properties [EML]
  - Model[<>]: Based on the inherent difference between subjects and predicates, Plato's Theory of Forms distinguishes ``ideal'' Forms (exist independently from objects) and their Instances (have obtained their form from a Form).

  Technology (Automaton): fine mechanics [next: relays] was advanced enough so that Archytas of Tarent (430-345) could build a flapping pigeon figure, the first automaton (according to ancient litarature) [Mey]. Other achievements of Archytas: represented tone intervals by proportions of numbers; started theoretical mechanics.

• Meaning[<>], from 300 BC onwards: The Stoic school of philosophers was founded in Athens ca 300 BC [x]. Philosophy was divided into three parts, one of which was called `logic'. The stoicists distinguished in logic the (study of) form (that which `signifies', the refering), from the (study of) meaning (that what is `signified', the refered) [EML].
  - Grammar[<>]: «The work of Chrysippus (280-207 BC) and his pupil Diogenes of Babylon (c. 240-152 BC) is particularly important in the development of the system of parts of speech; also of case, tense, and other semantic categories» [x].
  Stoicists made progress in flexion, introduce the term "case", distinguish verbs into completed:progressing aspect, active:passive mode, transitive:intransitive Early Stoicists distinguished nouns:verbs:conjunctions:articles where nouns include adjectives (both declinated). Later, nouns were separated into appelativa:proper names. [EML].

• Axiomatization [>]: Euclid's (Alexandria; uncertain: 326-265) "Elements", the first logical treatment, by axiomatization of a branch of mathematics: geometry.
  Euclid's algorithm for the greatest common divisor.
• Notat., around 300 BC[<>]. The Sumerian sexagesimal positional numbers are augmented by a special sign for the zero digit (but still no concept of 0 as a number).
• 3rd century BC: Assumed origin of "Chiu-chang Suan-shu", a Chinese mathematics textbook with negative numbers and square equations.
• Meaning, 3rd cent. BC [<>]: Eubulides of Megara's masked man fallacy is concerned with referentially opaque contexts: 'You say you know your brother, but that masked man is your brother, and you did not know him' [x].
  He is also an early propounder of the liar paradox 'I am lying' [x].
• Algorithm: Archimedes (287-212, Syracuse) perfected an exhaustion-based method of integration.
• Algorithm: Eratosthenes' (276-194, Alexandria) Sieve of Eratosthenes for finding prime numbers.
• Linguistics, 2nd cent. BC [<>]: Dispute whether language is primarily regular ("analogists") or irregular ("anomalists") [EML].
• Grammar[<>]: Dionysius Thrax's (late 2nd cent. BC Alexandria, pupil of Aristarchus (ca 217-145 BC) x]) first comprehensive and systematic grammatical description of the occident (except for syntax) (only first half authentic? [x]). He distinguishes noun:verb:conjunction:article:adverb:particip:pronoun:preposition. (Greek syntax was described less systematically by Appolonius Dyscolus 2nd cent. AD) [EML]
• Published reports on musical automata reach back to 2nd century BC [Mus].
• Theory: Geminus (130-70, Rhodos) deals with the logical subdivisions of mathematics, considers the concepts of 'hypothesis', 'theorem', 'postulate', 'axiom', 'line', 'surface', 'figure', 'angle' etc.

• Theory: Nicomachus of Gerasa (60-120, Jordan) treated arithmetic as a separate topic from geometry (but gives no abstract proofs of his theorems, like Euclide). Contains the first multiplication table in a Greek text. Contains Arabic numerals, not Greek ones.
• Algorithm, 3rd century AD: Diophantos of Alexandria's (200-284) "Arithmetica" gives numerical solutions of determinate and indeterminate (linear and square[Math]) equations.
• Principle, 499 AD (India) [<>]: Decimal positional number system and arithmetics[<>] used by Aryabhata the Elder (India, 476-550) (Gurjara inscription 595) [HN].
  Notat.[<>]: Ten digits including zero "o" for the empty position (Gualori inscription 876) [Math].
  Brahmagupta (India, 598-670) calculates with the zero as a number and with fractions [Math].

 Glyphs[<>] in the Roman Empire [dtv]:

Originally, Latin is written as majuscles, perfected in form of the capitalis quadrata during the Emperors' time.

4th cent.: uncial script, a rounded majuscle script, appeared and prevailed over capitalis quadrata in the 5th cent.

4th - 5th cent.: the long-in-use cursive script for faster writing of Latin develops into a minuscule script (going above and below the base line).

800: newly developed rounded Carolingian minuscles, spread over Europe (reaching the Vatican in mid-11th cent.)

• Reprod, 618-907 (China): block printing, the first practical method of reproducing writing mechanically was developed during the T'ang dynasty [next: types] (explanation).
• Notat., 8th cent.: documented use of Byzantian neumens [Mey] to casually express pitch and tone duration [<>]

Muhammad ibn-Musa Al-Khowarizmi (780-850, Tashkent cleric/mathematician, professor in Baghdad): Notat.: His "Arithmetics" introduces to Arabia decimals (integers and ratios) and the four basic arithmetic operations on them [Math]. 830: Developed the concept of a written process to be followed to achieve some goal. Published in "[Al Kitab al muktasar fi] hisab al-jabr w'al-muqabala" [Short Book on Calculation of Restoration and Reduction, latinized: "Algebra et Almuqabala"] about quadratic equations and geometric squares describes formalized, step-by-step procedures for calculations [known as algorithms, from his name "Al-Khowarizmi"]. Also: rules for determining square roots, and sine tables.

• Notat., 9th/10th cent. (W/M Europe): Latin neumens [<] for unisonic liturgia (course of the melody, no rhythm) [Mey]
  Ca. 1000: Guido of Arezzo's (Benedictine monch) writes neumens into four-fold lines fixing the pitch.
  Neumens evolve to choral notation with squares as note symbols [>]
• Algorithm, 1030: Guido d'Arezzo's table lookup procedure for assigning vowels to pitches. (Similar: 1130 Affiligemensis's rules) [Mus].
• Reprod, about 1041-48 (China): Pi Sheng's (iconographic) movable types [^block/_Gutenberg] (not followed up in China, but in Korea).

1096-1275: The Cruzades. Europe regains access to Aristotle's texts through the Arabs.

Logic, early 12th cent. [<>]: Peter Abelard composed an independent treatise on logic: conversion, opposition, quantity, quality, tense logic, reduction of de dicto to de re modality, ...

• Linguistics[<>]: The area of "speculative grammar": Scholastic philosophers believed in universal common categories of logic, grammar and metaphysics. They believed that language is a product of reason, mirroring a logical system. Roger Bacon (1214-94): «Grammar is, except for accidental variations, substantially the same in all languages» [EML].
• Grammar[<]: Scholastic philosophers distinguished noun:adjective:verb.
• Meaning, late 12th cent. [<>]: Scholastic philosophers, like Stoicists before, were interested in language as a means for analyzing reality -- hence their interest in meaning (``modis significandi'') [EML]. «In course of the development of traditional grammer it became common to distinguish between the meaning of a word and the `thing' or `things' which the word `names'. This distinctions was expressed by medieval grammarians as follows: The form of a word (the vox-component of a dictio) means `things' due to the `concept', which is connected with the form of a word in the mind of the speaker of a language; and the 'concept' ... is the meaning of the word (the significatio).». [EML 412]. Philosophers developed supposition theory to specify the reference of a term in various propositional contexts [x] - first phase in the middle of the thirteenth century [x].

Glyphs, 12th cent. [<>]: Gothic script is formed, breaking the rounds of uncials as capitals and Carolian minuscles as small letters (cf. the breaking of round Romanic arches to pointed Gothic arches) [dtv]
Notat., 12th cent.: modal notation
13th cent.: mensural notation shows tone duration (for coordinating part singing) [<]
Notat.: Li Jan' [China, when?] writes decimal fraction part as index [HN]. In 1202 Leonardo Fibonacci's (1170-1250, Pisa) "Liber Abaci" introduces the Indian ``Arabian'' digits (including 0) to Europe. In the 12th/13th century, Al-Hassar and Leonardo di Pisa (ca 1170-1240) use the fraction bar for division of numbers [HN]. Jordanus Nemorarius (1225-60, Germany) used letters to replace (known?) numbers. In 1261/75 Yang Hui (1238-98, China) uses decimal fractions in the modern form.

Notat.[<>] / Symbolism[>]: Ramon Llull (philosopher, 1235-1316, Mallorca) is a precursor of combinatorics. He tried to prove Christian dogmas using logic and complex mechanical techniques ... involving symbolic notation and combinatory diagrams to relate all forms of knowledge, including theology, philosophy, and the natural sciences. 1272 Llull invented the idea of a machine that would produce all knowledge, by putting together words at random. He even tried to build it. He rotates concentric disks with words on them to generate sentences. His 1274 Ars Magna is one of the few wholly worked through and finished systems in the history of formalization of knowledge and language Influenced Leibniz, rejected by Swift.

• (Automaton): 13th century Netherlands [Mus]: Carillons in church towers generate chromatic sequences of tones at every quarter of an hour.
  Around 1300: Jaquemarts, automated bell figures performing some action during the chiming, became popular [Mey] (e.g. in the Netherlands 1381 and 1383).

13xx-1820: Invention of Special Purpose Devices

• 1303: Chu Shih-Chieh's (1270-1330, China) transformation method for solving equations (used up to degree 14).
• Meaning, 14th cent. [<>]: «Supposition theory is developed extensively in its second phase by logicians such as William of Ockham, Jean Buridan, Gregory of Rimini, and Albert of Saxony.» [x].
• about 1340: William of Ockham formulates Ockham's razor, the epistemologic principle that entities should not be multiplied beyond necessity when trying to explain things [x].

• Al-Kashi (1390-1450, Persia) uses fixed-point iteration to solve a cubic equation.

Glyphs in the 15th century[<>]:

Ca. 1500: Fracture script proper was designed in Augsburg (Germany) on order of Emperor Maximilian I.

Notat. in the 15th century: Mid 15th century in France and Italy: "p" and "m" (with or without a tilde on them) for plus and minus. In Germany "+" evolved from "&" for "et" (Latin and) and "-" from the tilde on "mio" (minus) [e.g. Johannes Widman 1489 [TEP]]; used in whole Europe since the late 16th century [HN]. Johann Müller Regiomontanus (German mathematician and astronomer, 1436-76) introduces the multiplication dot "^." [HN]. In 1484, Nicolas Chuquet (1445-88, France) uses (free standing!) elevated numbers for the different powers of a unique variable in formulas [HN]. He is also the first to use (unpublished) negative numbers as coefficients, exponents and solutions. In 1492, Pellos introduces the decimal point [HN].

•  Notat. [<]: King Sejong of Korea (reign 1419-1450) designes a featural writing system: 10 vowel symbols (straight lines) and 14 consonant symbols (suggesting the articulation point), blocked to syllables.
  Much later: encoded as triple 6-bit code, official South Korean standard 1992.
• 1434 (Korea): The first self-striking water clock.
• Reprod, 1440/50 (Germany): Gutenberg disects text into letters, pointation marks, ligatures, etc, and prints from movable types [^types/_linotype].
• Calculator?: Leonardo da Vinci (1452-1519, Italy) draws a calculating device or ratio machine in "Codex Madrid" (similar to one in "Codex Atlanticus"). Its function is uncertain [replica built in 1968]. [pictures]. [next: Schickard's calculator].
• Theory: Michael Stifel (1487-1567) invented logarithms.
  Notat.: Invented the square root symbol "".

Notat. in the 16th century: In 1557, Robert Recorde (Britisch medician, 1510-58) invents the equivalence symbol "=" [TEP]. In 1585, Simon Stevin (Dutch merchant and engineer, 1548-1620) makes decimals (decimal fraction [Math]) popular in Europe, and promotes decimal decimal coinage and measures. He introduces a notion for real numbers (= scientific notation with E ?), taken up by Napier[>]. And Thomas Harriot (1560-1621) invented "<" and ">", recognised negative roots and complex roots. In 1591[?], François Viète or Vieta (France, 1540-1603, advisor of Henry IV of Navarre) is one of the first to use systematically (single) letters for known and unknown quantities (vowels for unknowns, consonants for known quantities; Descartes uses letters near the beginning of the alphabet for known and near the end for unknown quantities) and uses the fraction bar for all divisions [HN]. In 1600, Adriaan van Roomen (1561-1615, Belgium, Germany) uses variable names with an elevated number for their exponentiation [HN]. (Also used by James Hume 1636 [TEP]).

Encod. + Crypto, 1605: A 5-bit (``five-level'') code [>] «used for cryptography by Sir Francis Bacon as far back as 1605» [Article about revised ASCII]

Non-algorithmic aides to arithmetics begin to appear:

• John Napier (1550-1617, Scottish mathematician):
  Theory: 1614: "Rabdologia" (re)invented logarithms (approach different to Stifel) reducing multiplication to addition of table entries.
  Principle + Aide: Bones [^abacus/_{slide rule}]: non-algorithmic digital aid to reduce multiplication to addition, and taking square roots and cube roots.
  Automaton[?]: chessboard calculator [details?].
  Notat.: Uses decimal notation for fractions. He takes up Stevin's[<] notation for real numbers.
   Notat.[<>]: Proposed binary numbers "a" = 1, "b" = 2, "c" = 4 ... [HN] --- not a positional system!
• Aide: Slide Rules [prev.: bones]:
  1620: Edmund Gunter (1581-1626, England) plotted a logarithmic scale along a single ruler.
  1622: William Oughtred's (1574-1660, private tutor in Oxford) described the slide rule.
  [continued]

1622: Invention of the Mechanical Calculator Machine Type: Calculator [processors/generators]. 1622/23, William Schickard's (1592-1635, Germany) first adding machine [da Vinci's try/Pascalene] allowing more easy multi-digit multiplication, used by Kepler. These calculators are non-programmable, mechanical devices realizing a built-in set of algorithms for arithmetic operations based on the primitive of incrementing (counting) numbers in decimal representation. Classification of adders and calculators with pictures. Their construction. How to operate them (for example, to multiply a number by 125, the user would enter the number and turn the crank 5 times, shift the carriage into the 10s position, crank 2 times, shift the carriage into the hundreds position and crank once to yield an answer). Java Applet of the 1885 Felt & Tarrant Comptometer adding machine. From these first experimental calculators it took until 1820 for commercial production to start. Mechanical calculator were in use until the 1960's when the were replaced by electronic calculators. Calculator are still found in current computers as the ALU (arithmetic-logical unit) of the Von-Neumann architecture.

• Aide: [continued from]
  1624: "Gunter's scale" to multiply based on logarithms.
  1630: Richard Delamain publishes his circular slide rule.
  1632: Oughtred's circular slide rule based on two Gunter rulers aids addition, multiplication etc. Analog, accuracy about 3 digits.
  A 1654 slide rule. Slide rules were used up into the 20th century. [Java applett] How to use.
• Notat., 1631: Oughtred [prev. episode] introduces the multiplication cross "×" [TEP] (John Wallis 1656(?) uses "×" between numbers, and no symbol between variables) [HN].
• Notat., 1639: Stampioen de Jonghe (1610-90, Netherlands) writes "A:B = C:D" for proportions; since then "=" prevails on the continent [HN]. (Did he introduce ":" for proportions?)
• Calculator, 1642-45: Blaise Pascal's (France, 1623-62) Pascalene [^Schickard's/_Leibniz's] to help tax collecting work adds and subtracts with automatic carry-over (ignorant of Shickard; French patent request (1645) and grant (1649)).
• Notat., 1659: Johann Heinrich Rahn (Swiss) introduces ``Pell's division symbol'' "÷" [TEP] (prevails in the English world since Pell's translation 1668).
• Linguistics, 1660[<>]: Revival of speculative grammar. The teachers of Port Royal (France) publish their grammar to prove that the structure of language is a product of reason. (1637: Richelieu founded the Académie Française to regulate vocabulary and grammar of French [EML].
•  Notat., 1668 [<>]: Dalgarno's Characteristica Universalis or Generalis [HSem]: E.g. 'tan' = conscientia, 'tam' = ingenium, 'taf' = curiositas where 't' is for the genus of intellectual accients, and 'a' for the species of actus intellectus primi. And from 'ska' = religion: 'skaf' = worship and 'skan' = good luck. But no complete semantic decomposition.
•  Notat., 1668 [<>]: John Wilkins' (Dean of Ripon, later Bishop of Chester) Real Characters on demand of the Royal Society as a universal script for all languages:
  • defines a systematic way to construct symbols for noun(root)s (similar to facette-based archiving). 40 superconcepts (e.g. stone) by first two letters @ up to 9 subconcepts (e.g. gem) by a consonant @ 9 species (e.g. turkis) by a vowel.
  • + derivational / flexion particles and phonetic symbols.
  • Adjectives and verbs are constructed by modification from nouns.
  Had a great impact on decyphering and understanding of ancient scripts. [Maurice Pope: The Story of Decipherment; Thames and Hudson, 1975]

Gottfried Leibniz (1646-1716, Germany). Calculator, 1673: presents Leibniz's Wheel [Pascalene/Hann's] to the Royal Society (London). It is the first four function calculator (add, sub, mult, div): multiplication by automatic repeated addition in accumulator. Technology: 1694: stepped drum mechanical technology [next: pin wheel] in (another?) machine by Leibniz. Notat.[<] + Principle[<>]: 1666-1679 (published 1701) he developed and strongly advocated positional binary numbers [<] and binary arithmetics influenced by a (misunderstood) Llull.  1666[HSem], Notat.[<>]: Characteristica Universalis or Generalis, or Lingua Generalis - his universal ideographic script. He set out to invent a perfect writing system which would reflect systems of thought directly and thereby be readable by all human beings regardless of their mother tongues. Symbolism[<>]: Leibniz persued the symbolism idea that that (correct) thoughts can be reduced to calculations. For his Ars Combinatoria, he encoded concept hierarchies into numbers to enable reasoning by calculation. «Leibniz used prime numbers to represent conceptual primitives and multiplied them together to make composite concepts. ... if one concept's number is divisible by that of a second concept. then the first concept is subsumed by the second (i.e. it is more specific)» [Ellis, Lehmann: Exploiting the induced order on type-labeled graphs for fast knowledge retrieval; in: Conceptual Structures: Current Practices; LNAI 835, 1994] Quote from a letter of the old Leibniz [TEP]: «Ich möchte eine Methode finden ... mit deren Hilfe sich alle Wahrheiten des Verstandes auf eine Art Rechnung zurückführen lassen. Diese könnte gleichzeitig eine Art Sprache oder allgemene Ausdrucksform sein, die sich jedoch von allen bis heute vorgeschlagenen unerscheidet, da die Zeichen und selbst die Wörter den Verstand leiten und es sich bei Fehlern (außer den Fehlern der Wirklichkeit) nur um Rechenfehler handeln würde. Zwar wäre es sehr schwierig, diese Sprache oder diese Merkmale zu erstellen oder zu erfinden, doch man könnte sie sehr einfach ohne Wörterbücher erlernen.» Notat.: 1675 he introduces the " f(x)" notation for his integrals (in print 1686). (Isaac Newton wrote about his integrals introducing the dot notation in 1671, published 1736. Babbage[>] promotes Leibniz' notation in Britain). 1678/79: He uses the proportion symbol ":" generally for divisions (prevails in continental European). 1698: Leibniz favors multiplication dot over cross [HN].

• Model, 1689[<>]: John Locke (England, 1632-1704) is the person «normally credited with introducing» the concept of abstraction by which Universals are made (cf. Aristotle). Locke: «[D]oes it not require some pains and skill to form the general idea of a triangle, ... for it must be neither Oblique, nor Rectangle, neither Equilateral, Equicural, nor Scalenon; but all and none of these at once. In effect it is something imperfect, that cannot exist; and Idea wherein some parts of several different and inconsistent Ideas are put together». Therefore abstraction is a feature of human thought [MRW].
• Notat., 17th century Germany: The decimal comma[!] prevails at school and in buisness (also used by Lagrange 1808) [HN].
• Notat., 1706: Greek letter "" used for the diameter:circumfence proportion by William Jones [TEP].
• Writer, 1714: Henry Mill's patent on a writing machine (typewriter); no keyboard, never built [next: typographer]
• Processor, around 1725: a paper strip was used to control mechanical processes in weaving mills. In that strip of paper, punch holes were positioned according a certain system. By a scan mechanism, these punch holes were transferred into mechanical movements [<>].

• Symbolism/Society, 1726[<>]: In Gulliver's Travels Jonathan Swift makes fun of (the symbolistic idea of) a machine for writing texts in philosophy, poetry etc.

• Notat., about 1862[>]: Leonhard Euler (1707-83) uses set diagrams to visualize logical inclusions. Extended by Venn 1880 and then called Venn diagrams.
• Classific., 1749(35/37/53)[<>]: Carl Linné's (Swedish botanist, 1707-1778) binomial nomenclature for plants and animals: generic name + specific name [xx]. He grouped genera to classes, and classes to orders [x].
• Processor, 1752: J F Unger's and J Hohlfeld's (Germany) processor of piano rolls (Père Engramelle's keyboard transcriptions on paper) (= punched paper?) drives a harpsichord [Mus] [<>].
• Technology, 17xx-1761: For determining longitudes at sea, the British Longitude Act rewards the first clock that deviates less than 0.2 sec. per day on a ship at sea.
  John Harrison (-1776) develops clocks H1, H2, H3 (1756?, demonstration canceled because of war), H4 (1761, deviates 5 sec. in 81 days, 8750 pounds reward).
• Calculator, 1770: Philip Mathäus Hahn (priest near Stuttgart) presents his Staffelwalzen (stepped drum) calculator (``for the spreading of the evangelii'') [Leibniz's/<sub>Arithmometer</sub>]. An original calculator on display e.g. in the Artihmeum, Bonn (Germany). [Zahlenrausch; bild der wissenschaft 11/1999; DVA 1999]
  == (?) the improved machine of ``Phillip Hann'' in 1774 [hpmuseum] (?)

1775-1783: American Revolution [Encarta]. Colonial population at that time: approx. 2.5 million people. Black slaves: more than 500,000 (roughly 22%), Scots-Irish: ca. 250,000, Germans: ca. 200,000.

2nd Age of Linguistics[<>]: Comparative Philology (1786-1906) Comparative philology establishes linguistics as a discipline separate from philosophy & logic (e.g., linguistic vs. logic categories [x]). Linguistics, 1786[<>]: William Jones (British orientalist), among others, discovers the surprising similarity between old Sanskrit (India) and ancient Greek. Classific.[<>]: Similarities of (European) languages were explained as result of their evolution from a common (often unknown) ancestor by different laws of sound shifts. Languages are grouped to families based on their ancestrial relationships [EML].

• Algorithm: Several methods of automatic composition, e.g. 1791: Mozart's "Musikalisches Würfespiel".
• Reprod, 1797: Alois Senefelder's (1771 - 1834) first book printed with lithography (based on fat v. water).
•  Processor, 1801: Joseph-Marie Jacquard's (France) devises punched cards (as opposed to paper strips, patented in 1804), enabling the creation of the fully automated loom: it processes punch cards describing patterns in rugs and clothings [^{piano rolls}/_Componium]. Bitmap encoding: which of the two weaving threads should go on top?
•  Calculator, early 1800s[>]: Charles Earl of Stanhope's (scientist, statesman) Stanhope Demonstrator, the first real logic machine: «a small box with a window in the top, along with two different colored slides that the user pushed into slots in the sides» (published 1879).