Happy New Year to everyone! I hope you enjoyed my last post about hard-to decipher Linear A tablets. Now we shall examine some even more mysterious ancient documents: those ones that can only be understood if we analyse not just the names - but the numbers standing beside them. It is now time for some mathematics!
The most obvious problem one can encounter when reading Minoan clay tablets is the lack of knowledge about the transaction terms themselves. After all, how can we understand anything about Cretan accounting, if we do not even know if the goods mentioned were actually collected or - on the contrary - distributed? Our path is clear: to understand more of the meaning of the tablets, we have to analyse the quantities of wares.
Let our first specimen to study be the clay tablet HT8 (see figure). This tablet is fortunately complete, and written with easily readable characters. But it still somehow lacks in clarity. Judged from the absence of any totalling term (KU-RO), it likely lists outgoing goods: the headers seem to list the total stockpile of oil (OLE+KI) to be distributed. The modifier 'KI' might point to a type of "scented oil" (e.g. rose-scented or sage-scented) that was sent to sanctuaries of gods all across the land on certain annual festivals - if we can believe the Linear B tablets already deciphered by Ventris and Chadwick. The distribution patterns on HT8 are quite intriguing on their own, and may admit more than one possible solution. At least some of the entries must be transaction terms, otherwise the numbers would not work. The most trivial solution to the problem was found by Brent Davis & John Younger. But this is not the only possible one. You shall also see my rival hypothesis on the same figure.
The main strength of the original solution is the ability to interpret both sides of the tablet as complete and integrated entity. However, Davis & Younger needed to assume two transaction terms to achieve this goal - both the sole 'PA' syllabogram and the hapax word SU-PU2-*188. Although a single 'PA' returns on other documents, no other tablet supports their reading as transaction terms. On the other hand, most names clearly recur on other tablets, such as PA-JA-RE [HT29, HT88, ZA10], TE-WE [HT98] or QA-*310-I [HT85, HT122]. HT85 even features a similar single-syllable 'PA' term. However, on the toponym list HT85, 'PA' probably abbreviates PA-I-TO, the name of Phaistos. It is tempting to believe that the same applies to the place-name list on HT10, where a toponym tied to KU-NI-SU (Knossos?) is contrasted to a list headed by 'PA' (tributaries to Phaistos?). To remedy the situation, I played around the numbers to find an even better solution to this tablet. As you can see on the figure, if we split the document into two almost-separate lists (with 15 units of oil to distribute, instead of 10), we only have to assume the existence of a single transaction term on side B. KA-PA is a more-or less obvious candidate: it also returns on the headers of tablets HT6, HT94, HT102 and HT105. On HT11 and HT140 we also find a counting term 'KA' (abbreviation, KA-PA?) that frequently stands beside large quantities without any names mentioned. KA-PA is likely related to another word: KA-PE [HT9], that is undoubtedly a transaction term, and stands as contrasted to SA-RO2 on the same tablet. Note that KA-PA itself can form a single expression with SA-RA2 (as on HT102), but it never-ever joins up with A-DU (another common term alongside SA-RA2).
To understand the complementarity and mutual exclusivity of these transaction terms, we must make some assumptions on their meanings first. SA-RA2, one of the most common transaction terms on the Haghia Triada tablets could be cautiously translated as "supplies" (note that it almost always stands before a list of consumables, most typically GRA [wheat]). I chose the word "supplies" to avoid any explicit implications to incoming or outgoing transactions - that are often difficult or impossible to guess. As for A-DU, after a thorough study, I find the reading of John Younger (A-DU = "assessed") really enticing. Now, if KA-PA would mean something like "leftover", "remaining", we could now explain entire phrases: A-DU • SA-RA2 [HT99] = "assessed supplies", TE • A-DU [HT92, HT133] = "give (as) expected" KA-PA • SA-RA2 [HT102] = "remaining supplies", SA-RO2 = "supplied", in contrast to KA-PE = "of what remains". KA-PA can be used with a wide variety of goods, even people [HT94, HT105], in which case, they are counted by type (profession) and not by provenience. On HT102, KA-PA stands before a very substantial number of GRA: 976 units - that would be about 32,000 litres of wheat if measured by volume - likely the whole stockpile of an entire settlement. There is even a Classic Greek word: κάπηλος of prehellenic origins, meaning "local wholesale merchant" (i.e. who dealt in the surplus goods a community produced), that could possibly be connected with KA-PA / KA-PE.
It is also important to examine the dual 'PA3' syllables that start each sub-list. Since the tablet completely lacks word-dividers, these particles might form separate words. Unlike 'PA', the abbreviation 'PA3' (whose reading as a member of the P-series is only weakly supported in Linear B) is a well-attested transaction term (HT9, HT34, HT103, HT132). Its occurrance on HT103 in particular, suggests a reading like 'delivery'.
Tablet HT8 is also interesting because of a completely different reason: it features the rare sign Lin A *188 twice. While *188 also stands as a separate word (abbreviation of a name?) on several documents (HT15, HT56, HT103, HT123, HTWc3014, HTWb229), not just on HT8, here it also recurs as part of a longer word: SU-PU2-*188. This is particularly intruguing because of the phonological character of 'PU2'. That is quite a special syllabogram, as its use in words DA-PU2-RI-TO-JO (Lin B *daburinthoyo) and DU-PU2-RE (Lin A *duphre?) shows: unlike the ordinary 'PU', its consonant might have been at least partially voiced, possibly due to external triggers [clustering with thrills or nasals]. This realization may imply sign *188 being of the the N-series. Interestingly, the N-series has a very obvious hole in it in Linear A: the ancestor and Minoan counterpart of Linear B *42 ('NO') has not yet been identified. Now we have a plausible candidate - but this topic clearly deserves its own post, so I shall leave it to later. Nevertheless, a reading SU-PU2-NO (*suphnú) speaks for itself, and even resembles to the modern name of the island Siphnos - known to be an important economic center (thanks to its precious metal mines) of the Cyclades in the Bronze Age and later. Though it is also true that the naval distance between southern Crete and Siphnos is substantial, so a direct identification is questionable at best.
Now, let us turn to our attention to another piece of numeric riddles. Tablet HT103 offers an equally difficult puzzle as our previous one was. Although HT103 is slightly damaged at its right edge (rendering some signs only partially legible), it is preserved well enough to enable a clear reading without major reconstructions. The first sign on the header is abraded, but - if we can believe the reconstruction of J. Younger (that I also find plausible) - the first word was probably U-TA2. Note that a tablet written by the same scribal hand (HT26) features a very similarly shaped 'U' sign that we reconstructed here. U-TA2 would be a hapax term, albeit it resembles to both an alternative reading of KN10 (inital word: TA-NU-TA2-TI) and to the supposed Eteocretan term 'utat'. Potential tyrrhenian parallels (Etruscan *ut-/*uth- = "to deliver") would indicate a transaction term, having to do something with distribution of goods. Indeed, the header continues with the logogram 'NI' (figs) and a number of 40. Since there is no totalling term anywhere below (although we have KI-RA for missing units), and all the numerals on the tablet are considerably smaller than 40, it appears to be recording the act of distribution.
The key to understanding is provided by the obervation that practically all quantities recorded are multiples of 6.5: Number 13 (third line) is the double of this base portion, and the single unit mentioned in the last line also gives 1+5.5 = 6.5, if we add the missing 5.5. The tablet apparently records an attempt to distribute the initial 40 units of figs into 6 smaller, equal units. This gave a standard unit (with the qualifier DA-KU-SE-NE) of 6.5, and the double unit (qualifier: *188) of 13. Since 40 = 6 x 6.5 + 1, the remaining 1 unit of fruits is distributed as a portion , with the premise that 5.5 would be paid later. The initial segment of line two has broken off, but - judged from the inclination of signs - a syllabogram must have been there before the number, probably 'TI' (c.f. DA-KU-SE-NE-TI [HT104]). DA-KU-NA appears to be just another grammatic case of DA-KU-SE-NE, with a defective writing (*DA-KU-SA-NA) - this points to DA-KU-SE-NE being something like *takusne.
Now we have seen that - with ample effort - many of the tablets can be given a fairly meaningful reading. Unfortunately, I lack the time and resources to continue on this path and examine each tablet separately, but I promise to come up with other Cretan topics soon. Including the revision of some of my earlier theories.