Tag Archive: numerals

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 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 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.


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.


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


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:


[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.




A Linear B Tablet listing 50 swords

A Linear B Tablet listing 50 swords (CLICK to enlarge):

Linear B Tosa Pakana

This small Linear B tablet clearly illustrates the accounting system adopted for Linear B. Once again, we see an Ideogram, which is tagged with an asterisk (*).  It may seem rather odd that on this particular tablet the scribe actually supplemented the word for sword, “pakana” with its ideogram, which sounds counter-intuitive, given what I just said in the last post, that the whole idea of the Linear B accounting system was to save space on the tablets, not waste it. But in fact, such is not the case. The explanation is simple: in this particular case, the scribe is making certain that no one mistakes what he is counting, by not only writing out the word but also inscribing its ideogram right beside it.  It’s almost as if he were self-auditing. This makes the Linear B accounting system even more coherent and consistent than it might otherwise have been. We will see that this practice of writing the word for the total number of items accounted for + its ideogram recurs frequently in Linear B tablets. However, the downside of this is that some Linear B scribes were apparently either lazy or in a rush or simply felt that the ideogram alone more than sufficed in tabulating accounting lists. Thus, on some (but far from all) Linear B tablets, accounting lists give only the ideograms for the items in the list(s), which means that unfortunately for us, we have to learn all the major ideograms if we are to be in a position to decipher all the accounting records.  We cannot count on finding both the words and the ideograms for each item being listed in all Linear B tablets.


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