Tag Archive: numbers



Translation of  Knossos Linear B tablet KN 552 R o 03 by Rita Roberts:

knossos linear b tablet kn 552 r o 03


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




So-called Cretan hieroglyphs are not hieroglyphs at all. Example 1

Cretan symbolic writing ideograms a

These 2 palm-leaf tablets incised with Cretan symbols are the first example of why so-called Cretan hieroglyphs are not hieroglyphs at all. We note right off the top that there are only 6 symbols, all of which are in fact ideograms or logograms. The numeric symbols, 40 and 100 on the fist tablet and 50, 10 & 80 on the second, do not conform to Linear A and B standards. In Linear A & B, decimals to the tens (10…90) are represented by horizontal bars, 1 for 10, 2 for 20, 8 for 80 etc. It appears instead that the dots on these tablets represent decimals to the tens. This is partly because the figure for 100 on the first tablet accords with Linear A & B practice, making it more likely that the dots are indeed in the tens.

Some other symbols are clearly identifiable. No. 1. is definitely the ideogram for an adze or labrys, which in Linear A and B is metamorphosed into the syllabogram for the vowel A. 2. is more likely to represent olive tree(s) rather than olive(s), for reasons which will become apparent in upcoming examples. 5. is very likely the ideogram for helmet, because it is very similar to same ideogram in Linear B.

So what are these palm-leaf tablets about? The first appears to be primarily military, te second primarily agricultural, with the sole exception of the ideogram for helmet, which appears out of place. But perhaps it is not. Perhaps the olive tree crops are being defended by the military. We shall never know.


Linear B numerals 100, 1k and 10k are atemporal, like those in the movie. Arrival:

It is quite clear from the following illustration of the numbers 1-12 in the Heptapod circular language, which correspond to the number of ships landing on earth, that their numbers, occurring in a circle, are similar to the numerals for 100, 1k and 10k in Mycenaean Linear A. This correspondence reveals an intriguing characteristic of these Linear B numerals, namely, that they can serve as ideograms for extraterrestrial communication. In other words, just as the Heptapod numbers serve to communicate from the extraterrestrials, the Linear B numerals can serve to communicate with them or any other extraterrestrial civilization.

movie Arrival heptapod 12 and Linear B 100 1k 10k

 


Partial conjectural decipherment of Linear A tablet HT 6 Haghia Triada (VERSO):

Haghia Triada Linear A tablet HT6 VERSO

If there is any Linear A tablet which has proven a real headache, it has to be this one. The surface of the VERSO of HT 6 (Haghia Triada) is so badly damaged that experts such as Andras Zeke of the Minoan Language Blog and Prof. John G. Younger cannot even agree on a few syllabograms in the text, while I myself disagree with them on some of the same. Additionally, there is no consensus on the values of Linear A fractions. Interpretations by Andras Zeke and Prof. John G. Younger of the smaller fractional values often do not agree. So I am unwilling to add fuel to the fire. I simply choose whichever value (either that of Zeke or of Younger) seems more convincing to me. At any rate, no one today can determine with any degree of accuracy numeric values in Minoan Linear or Mycenaean Linear B, since both syllabaries are so historically remote as to preclude any convincing readings.

As for the syllabograms on this tablet, once again, Andras Zeke and John G. Younger do not agree on the values of at least 3 of them. And I find myself at odds with their own interpretations. This is the result of the shoddy scribal hand and the less than ideal condition of the tablet itself. As for maridi, I find myself obliged to read it as if it were meridi, since the interpretation wool (mari) is utterly out of the question in the context of this tablet, whereas reading it as meridi = “honey” makes much more sense contextually. As for sama, it may be the Minoan equivalent of Mycenaean Linear B samara = mound/hill”, but once again, this interpretation is conjectural. I have previously tentatively deciphered Old Minoan (OM) pa3nina (painina) as “an amphora for the storage of… ”, but here again, I have gone out on a limb. Nevertheless, the interpretation once again suits the context. Once all of fig and pomegranate juice (RECTO) and the drops of wine and honey (VERSO) are accounted for, we can see that this tablet may deal with a recipe for a sweet alcoholic beverage, which with these ingredients would indeed be delicious.

Consequently, any convincing decipherment of the VERSO of HT 6 is beyond our reach. We simply have to muddle through it and come up with the best alternatives we can for each apparently decipherable word. However, by fully taking into account the much more accessible text on the RECTO of HT 6, I believe I have been able to rescue a small portion of the significance of the text on the VERSO by placing it in its proper context with the RECTO. See the previous post for my fuller decipherment of the RECTO.


Partial decipherment of Linear A inscription PH 1 (Arkalochori Axe):

Linear A tablet PH 1 Arkalochori Axe

My decipherment is partial. The only candidate for Mycenaean derived vocabulary is the word uro = entire, whole, i.e. total, a synonym of kuro = reaching, attaining, i.e. total.
The  word jaku obviously refers to the cargo. 


Comparison of the Merits/Demerits of the Linear B, Greek & Latin Numeric Systems:

Linear B:

As can be readily discerned from the Mycenaean Linear B Numeric System, it was quite nicely suited for accounting purposes, which was the whole idea in the first place. We can see at once that it was a simple matter to count as far as 99,999. Click to ENLARGE:

Mycenaean Linear B Numeric System and Alpha

In the ancient world, such a number would have been considered enormous.  When you are counting sheep, you surely don't need to run into the millions (neither, I wager, would the sheep, or it would have been an all-out stampede off a cliff!)  It worked well for addition (a requisite accounting function), but not for subtraction, multiplication, division or any other mathematical formulae. Why not subtraction, you ask?  Subtraction is used in modern credit/deficit accounting,  but the Minoans and Mycenaeans took no account (pardon the pun) of deficit spending, as the notion was utterly unknown to them. Since Mycenaean accounting ran for the current fiscal year only, or as they called it, “weto” or “the running year”, and all tablets were erased once the “fiscal” year was over, then re-used all over for reasons of practicality and economy, this was just one more reason why credit/deficit accounting held no practical interest to them. Other than that, the Linear B numeric accounting system served its purpose very well indeed, being perhaps one of the most transparent and quite possibly the simplest, ancient numerical systems.

Of course, the Linear B numerical accounting system never survived antiquity, since its entire syllabary was literally buried and forgotten with the wholesale destruction of Mycenaean civilization around 1200 BCE (out of sight, out of mind) for some 3,100 years before Sir Arthur Evans excavated Knossos starting in early 1900, and successfully deciphered Linear B numerics shortly thereafter. This “inconvenient truth” does not mean, however, that it was all that deficient, especially for purposes of accounting, for which it was specifically designed in the first place. 

Greek:

Greek alpha-numeric
On the other hand, the Greek numeric system was purely alphabetic, as illustrated above. It was of course possible to count into the tens of thousands, using additional alphabetic symbols, as in the Mycenaean Linear B system, except that the Greeks were not anywhere near as obsessive over the picayune details of accounting, counting every single commodity, every bloody animal and every last person employed in any industry whatsoever.  The Minoan-Mycenaean economy was hierarchical, excruciatingly centralized and obsessive down to the very last minutiae. Not surprisingly, they shared this zealous, blinkered approach to accounting with their contemporaries, the Egyptians, with whom the Minoan-Mycenaean trade routes and economy were inextricably bound on a vast scale... much more  on this later in 2014 and 2015, when we come to translating a large number of Linear B transactional economic and trade records.

However, we must never forget that the Greek alphabetic system of numeric notation was the only one to survive antiquity, married as it is to the universal Arabic numeric system in use today, in the fields of geometry, theoretical and applied algebra, advanced calculus and physics applications. Click to ENLARGE:

geometry with Greek and English algebraic annotation 
It would have been impossible for us to have made such enormous technological strides ever since the Renaissance, were it not for the felicitous marriage of alphabetic Greek and Arabic numerics (0-10), which are universally applied to all fields, both theoretical and practical, of mathematics, physics and technology today. Never forget that the Arabians took the concept of nul or zero (0) to the limit, and that theirs is the decimal system applied the world over right on through to computer science and the Internet.

Latin (Click to ENLARGE):

Latin 1-1000

When we come to the Roman/Latin numeric system, we are at once faced with a byzantine complexity, which takes the alphabetic Greek numeric system to its most extreme. Even the ancient Greeks and Romans were well aware of the convolutions of the Latin numeric system, which made the Greek pale in comparison. And Roman numerics are notoriously clumsy for denoting very large figures into the hundreds of thousands. Beside the Roman system, the Linear B approach to numerics looks positively like child's play. Thus, while major elements of the alphabetic Greek numeric system are still in wide use today, the Roman system has practically fallen into obscurity, its applications being almost entirely esoteric, such as on clock faces or in dating books etc. And even here, while it was still common bibliographic practice to denote the year of publication in Roman numerals right on through most of the twentieth century, this practice has pretty much fallen into disuse, since scarcely anyone can be bothered to read Roman numerals anymore. How much easier it is to give the copyright year as @ 1998 than MCMXCVIII. Even I, who read Latin fluently, find the Arabic numeric notation simpler by far than the Latin. As for hard-nosed devotees of Latin notation, I fear that they are in a tiny minority, and that within a few decades, any practical application of Latin numeric notation will have faded to a historical memory.

Richard

Sir Arthur Evans‘ successful decipherment of the Numeric Accounting System in Linear B (Click to ENLARGE):

Scripta Minoa Arthur Evans Numerics pp. 51-52

as published in Scripta Minoa (Oxford University Press, 1952), the very same year that Michael Ventris finally deciphered the entire Linear B syllabary as well as a large number of its ideograms. Sir Arthur Evans had, of course, deciphered the numeric system years before.

SCRIPTA MINOA Oxford 1952


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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