Tag Archive: counting



The ancient Greek alphabetical numeric system:

ancient greek numerals

This chart illustrates both the ancient Greek acrophonic and alphabetical numeric systems. However, the acrophonic system, used primarily in Classical Athens ca. 500 – 400 BCE, came much later than the alphabetical system. So in effect we must resort to the only Greek numeric system we can use to represent numbers in Mycenaean Greek numbers, i.e. the alphabetical system. The alphabetical numbers are displayed in the second column after the modern numbers, 1 – 100,000 in the following chart. Here are some examples of alphabetic numbers representing Mycenaean numbers: 

mycenaean numbers followed by their alphabetic greek equivalents




Derivation [D] of Linear B Numerics: 1-10 20 100 & 200 [Click to ENLARGE]:

1-200

Derivation [D] of Linear B Numerics: 1-10 20 100 & 200 as reconstructed in Progressive Linear B Grammar:

Explanation of the Table of Numerics:

The Principle of Derivation [D] as applied to the reconstruction of the orthography of numerics in Linear B. Even though there are very few attested [A] examples of numbers spelled out on Linear B tablets, I believe that we can safely derive them with a considerable degree of confidence, if we strictly apply the spelling or orthographic conventions of Linear B, which are available online here:

NOTES:

[1] These numbers are all spelled identically in Linear B and in ancient alphabetic Greek.

[2] The linear B number QETORO [4] is obviously a variant of the Latin “quattro”. There is nothing unusual whatsoever about the parallelism between Linear B & Latin orthography, since linguistically speaking, Q or QU are interchangeable with T.  First, we have the spellings of 4 in Greek (te/ssarej te/ttarej).  Though it will come as a surprise to many of you that the Linear B spelling for 4 QETORO would eventually morph into (te/ssarej te/ttarej) in ancient Greek & then back to “quattro” in Latin, there is a perfectly logical explanation for this phenomenon. This is why you see a ? to the left of the Greek for 4, because it is all too easy to fall into the trap of erroneously concluding that Linear B QETORO cannot have been a ancestor of the ancient Greek spellings for 4, when in fact it is. In order to put this all into proper perspective, Latin spells 4 as “quattro” for the simple reason that “tattro” would simply not do. All this boils down to a single common denominator, the principle of euphonics, meaning the alteration of speech sounds, hence orthography, such that any word in any language sounds pleasing to the ear to native speakers of that language (not to non-speakers, i.e. anyone who cannot speak the language in question). Every language has its own elemental principles of euphony, but some languages place far more stress on it than others. Greek is notorious for insisting on euphony at all times.

? The masculine for the number 1 is missing for the exact same reason that the 2nd. person singular is missing from my paradigm for the present tense of Linear B verbs. I find it impossible to accurately reconstruct any Greek word ending in eij for the simple reason that it not possible for any word to end in a consonant in Linear B. So why bother? This handicap will return to haunt us over and over in the Regressive reconstruction of all the conjugations and declensions and parts of speech in Linear B Progressive grammar, leaving gaping holes all over the place.

Orthography of Numerics In Linear B:

At a glance, we can instantly see that the spelling of several numerals in Linear B is identical to that of their later Greek alphabetic counterparts, with the exception of marking initial aspirates & non-aspirates, which Linear B was unable to express with just one exception, the homophone for HA. This speaks volumes to the uniformity of the spelling of numerics over vast expanses of time, as in this case, from ca. 1450 BCE (Linear B) – ca. 100 AD and well beyond. In fact, some numbers are still spelled exactly the same way in modern Greek, meaning that the orthography of the Greek numeric system has remained virtually intact for over 3,400 years!

Linear B’s Conspicuous Reliance on Shorthand:

Since the Mycenaeans used Linear B primarily for accounting, agricultural, manufacturing & economic purposes, they almost never spelled out numbers, for the obvious reason that they needed to save space on tablets that were small, because they were baked, hence fragile, and not only that, destroyed at the end of every “fiscal” year, to make room for the following year’s statistics. Their habitual use of logograms for numbers was in fact, (a type of) shorthand. Keep this in mind, because Linear B makes use of shorthand for various annotative purposes – not just for numerals. This is hardly surprising, considering that the tablets were used almost exclusively for accounting. So if we think shorthand is a modern invention, we are sorely mistaken. The Mycenaeans & Minoans were extremely adept in the liberal use of shorthand to cram as much information, or if you like, data on what were, after all, small tablets. But there is more: every extant single tablet is a record of the agricultural, manufacturing & economic activities for one single year. It also means that there is no way for us to know which, if any, of the tablets from one site, for instance, Knossos, where the vast majority of tablets have been found, represent accounting statistics for exactly the same year as any of the others. So we have to be extremely careful in interpreting the discrepancies in the quasi-chronology and even reverse-chronology of the data found on the tablets. There are several other reasons why we need to exercise extreme caution in interpreting the data on extant tablets, but since these are of a different nature, I shall not address them here.

Richard

 

 

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