Monday, May 10, 2010

How many Linear A signs do we have?

My next post will be a bit of "return to basics". I have been dodging this matter for long enough, but now we really need to put some systematics into our work. What I attempt right now is to establish a 'minimal set' of Linear A signs, in the hope that this will shed light on previously undetected features of the underlying language. Of course, the only thing we are interested in, are the phonetic signs. There are zounds of logograms in both Linear A and B (and in Hieroglyphics, too), but I leave their analysis to the economists: for it is the language that interests us, not the goods Cretans produced or paid for. And this is when we need to work out a good way how to separate the two. This what my current post is about.

The base set of the Linear A system encompasses about 55 signs. These signs are all well-attested in Linear A, in phonetic use, and have a more-or-less ascertained reading thanks to their Linear B counterparts. You can see them all on the table below:

(I put an asterisk onto Lin AB *85 = AU because of its special value - it might have also been *hu or *wu instead of *au)

Unfortunately, not all signs attested in Linear A have such clear readings. We also have a couple of signs in the next group I shall term the extended set. The criteria for a sign to fall into this set are simple: (1) It cannot be a hapax (occurring once in the entire Linear A corpus) and (2) it should be featured at least two times in a certainly non-logogrammatic situation (the same word two times does count). I also included signs that (1) occur only once as phonetic characters, but (2) have clear Linear B counterparts with well-established reading. Using these relatively stringent criteria I could count about 27 additional phonetic signs. Most of them have very dubious readings - see them on the table below (warning: the list is very long - and it took quite some time to comply):

(I would like to express my thanks to John Younger, as his site provided invaluable references as well as corrected transcriptions of most phrases, and visual images of all the rare signs)

Even so, we are not finished yet. When searching for the signs of the 'extended set', I disqualified a number of signs that did not satisfy the appropriate criteria. Some Linear A signs are clear precursors of well-known Linear B ones, yet they are only and exclusively used as logograms. A good example is Linear A *122, the 'olives' (OLIV) logogram, that is exactly the same as Linear B *33 = RA3, with a phonetic value of rai or lai. Another example is the case of the Linear B *20 = ZO sign, that has a clear Linear A ancestor in Lin A *304. The only problem is - and that is a major problem - that Lin A *304 is exclusively a logogram, and never used as a phonetic sign. The Linear B *87 = TWE sign is attested too, but only as a mere logogram. In these cases, one can suspect that either these syllables were extremely rare in the Minoan language, or were perhaps already covered by existing signs; or even that the phonetic reading of these signs changed over time.

Other signs look like phonetic ones, but they are only attested once. This goes for examples like Lin A *342 (only in PA-*341-I), Lin A *349 (A-TO-*349-TO-I) and Lin A *361 (A-KU-TU-*361). Unfortunately, we have very little chance to ascertain their phonetic use, to exclude the possibility of graphic variants and - of course - to find the true phonetic value. Because all these troubles, I did not even attempt to make a list of this group. A clear-cut list might be impossible to comply, because of the nasty tendency of certain scribes (especially those at Phaistos) to heavily deviate from well-established sign-shapes, or to use logograms for phonetic purposes as 'shorthand notes' or even 'puns' (when used in names).

Clearly, we should not forget about the fact that no matter how many tablets we have found so far, there is no guarantee that these feature all the possible signs. Yet there is some correlation between the completeness of our syllabaries and the size of corpus. An exact calculation of sign-set size was first proposed by Alan Mackay, back in 1965, when he attempted to estimate the size of sign-set behind the Phaistos Disc. His formula was quite simple: The total number of signs, T = L*(1 - L/(L-A)), where A = the number of attested signs, and L is the total length of the sample. While this formula works well with alphabetic signs (just give it a try in English), it performs more poorly on texts that are either very repetitive or of sign-sets with very skewed distribution (e.g. ideogrammatic or complex scripts). Though I'm afraid the method won't pass a bootstrap analysis, let's try it on a subset of Linear A texts: the Haghia Triada inscriptions! In roughly 2000 non-logogrammatic characters, it attests 77 of the 80-85 known phonetic Linear A signs. Mackay's formula would predict 80 characters. So it isn't that bad after all. We shouldn't forget though, that Linear A signs actually have a very skewed distribution towards zero frequency, so what Mackay's formula gives is an underestimation. Perhaps - if I'll have ample time in the future, I shall put some effort into developing a better mathematical model...

Because of such reasons we should not forget about those signs that are only attested in Linear B, without any known single Linear A precursor. Although some of these signs might be novel inventions, such as QO (*32) from Mycenean *qous = 'cow', PTE (*62) from Greek pteros = 'wing' (looks like the 'horns of consacration') or DWO (*90) from the numeral *dwo = '2'; the rest might be Minoan heritage. Some signs may have evolved to yield more than one offspring: a possible example is the Lin B *90 = DWO sign with its twin Lin B *83 (possibly ZI). A truely peculiar case is what we find at the Linear B signs WE and NO. There are signs that resemble them in Linear A, the problem is, they remain assigned to another group (the Lin B *75 = WE closely resembles certain occurrances of Lin A *53 = RI). Either some of these Linear A signs are mis-assigned, or we deal with a quite complex evolution. Especially problematic is the case of the Linear A 'I'-group. In this case, there are not only two but three linear B counterparts: I (*22), AI (*43) and NO (*52) ! This matter is so complicated I would like to deal with it in a separate post. But up to this date, the available evidence is still more suggestive of the main Linear A signs being correctly aligned, thus the ancestors of these Linear B signs being missing. A collection of these missing signs - along with those whose identification in Linear A is not universally accepted - I put on our last table:

Now, what was this fuss worth at all? With more-or-less precise numbers on our hands, we can immedietely go and check some theories about the phonetic system of Minoan language. For example, it was proposed by Beekes, that the language underlying the Minoan system should have had two additional series for most consonants: a palatalized and a labialized one. However, looking at the number (and the expected maximal number) of signs in Linear A, it quickly becomes clear that it is sheer impossibility to reconstruct a complete palatalized-labialized system. With 5 vowels, and 24 or more series of consonants, the quantity of signs would be far too high versus the attested sign-set, which is reasonably small (82 according to our tables). Even with the O-series discounted (4 vowels only), we would get a really bad overestimation.

In my opinion, the highest possible number of full consonantal series (based on 5 vowels) is about 18. The first table already featured 16 probably full or almost full series - if we add the less-well established DW- and SW- series, we are done. And there are no normal-palatalized-labialized triads, not even with T (or at least there cannot be a complete series). This estimation would give 90 signs as a theoretic maximum, and we were not far from that when counting all the 'uncertain' signs. Since certain syllables were likely very rare (as in any other language), I do not expect to ever see the full system. And - of course - we shouldn't forget about the presence of superfluous 'shorthand' signs: removal of these lower the number of possible regular signs even further!

Some other would-be decipherers of Linear A go with a different assumption: if the limited number of signs make their hypothesis impossible (as they assume too many consonants), they lower the number of vowels instead. While there do exist languages with just 3 vowels (Arabic comes to my mind), it requires painstaking 'reassignment' of a high number of signs, with an otherwise perfect reading in E or O. These "reconstructions" thus create much more problem than they solve. The only thing I could view as acceptable (though certainly not with my approval), is the removal of the O-series from the list. This series has the lowest number of confirmed signs; and some Linear A words even seem to testify an O - U ambiguity (e.g. compare A-MI-DA-U [ZA10] and A-MI-DA-O [PH31]). However, anyone who would have his hands itching to obliterate the O-column from the table with a single scratch should stop for a second. Because they really need to explain why the PO, TO and RO (=LO) signs borrowed into Cypro-Minoan (and ultimately Linear C) have exactly the same phonetic value as the Linear B ones!


  1. I notice that in your graphic above, you assign the value /t/ to the d-series and /θ/ to the t-series. I've already explained my reasoning which now happens to be the exact opposite of yours. Why not simply evaluate "t" as /t/ as it was actually used in Linear B?

  2. What I wrote in the table with question marks, are an attempt to resolve the D/T problem according to D W Packard (see it in his book). I am aware that other solutions are also possible. I preferred the *t/*th one because of some words in Linear A with parallels in other scripts and other languages point to this direction. For example, take the place-name WI-NA-DU that is WI-NA-TO = *Winatos in Mycenean Greek, or the name A-RA-U-DA, that is Eleuthia (likely the same stem as in Etruscan lautni = 'freedmen' or Greek eleutheros = 'free, easy'). The signs themselves are another interesting clue: The Lin A *79 resembles an eye, and if the value is indeed DO, than it becomes easy to explain from an Aegean word for 'eye' (Luwian dawa, Etruscan tva), derived via the route *tawa -> *twa -> *to:. The same would apply to the Lin AB *05 = TO sign, derived from the Hiero bull-head *11 (not identical to the "bovine head in profile" [*12?=MU]), if we supposed the development *thawr -> *thaur -> *tho:r. (Thus it could indeed stand for 'bull'- notice that in Etruscan, it also stands with th- [thevru].) I am still gathering evidence for this, so far I only found a small number of words and phrases (e.g. Minoan O-RA2-DI-NE ?= Greek rhétiné [resin], A-DI-KI-TE- ->Dikté [mount Dikti] and KU-DO-NI = Greek Kydonia [town Hania]). These would show that the D-series signs could have had values in *t/*d as the difference between 'd' and 't' was probably non-phonemic. On the other hand, the difference between T- and D-series could have been based on aspiration or stress that was likely phonemic in Minoan, but not elsewhere in the Aegean (i.e. Cypriot made the two series collapse into one - taking DA and DU but TE, TI and TO into a single series).

  3. Oh my god. I had absolutely *no* clue about Luwian tawa- 'eye' in connection with my reconstruction of Etruscan *tau (based on presentive tva) and my translation of 'to see, behold'!

    And upon further research I notice that some Indo-Europeanists have connected this Luwian word to Latin tueor 'to look' as well! This is a *perfect* match for Etruscan tva and suggests a potentially fascinating Aegean wanderword. I'll have to investigate this alleged Indo-European root *teu- because I've already reconstructed an Aegean root *tau in my personal offline database. Alot to think about. Brilliant!

    I'm off for now but I'll certainly have to ponder your other insights. Great job.

  4. Okay, so as I said, I'm impressed with the Etrusco-Latin connection you lead me to between tueor and tva but I think your value for L79 may need work.

    I've reviewed my data and also thought through your clever switcheroo of the values for the D- and T-series. It's certainly had me thinking but here's a possible counterargument...

    In inscription HT Zd 156, Olivier suggests TAYA means 'five'. If so, it surely is a borrowing from Egyptian *ṭīya(w) (> Sahidic ⲧⲓⲟⲩ) but the initial stop in Egyptian appears to be an ejective while plain t is aspirated. A sound *ṭ would not correlate as well with a theta as it would with a plain t. So I conclude based on the Egyptian phonetics and based on the Linear A spelling then that the Minoan numeral must be read tia.

    In general too, I find that Minoan 'D', whatever its value, appears mirrored by Etruscan z. In terms of the structure of the phonological system, I also see that velar Q (= /kx/) aligns nicely with dental D (= /tθ/) as part of an affricate series.

    I'm skeptical that L79 is properly DO (or even, per John Younger, ZU) but a connection with Etruscan tva and Lydian tawa- would, in my mind, motivate a value TO.

    With this value, KA-U-*79-NI ~ KU-*79-NI becomes KA-U-TO-NI ~ KU-TO-NI (for *Kautonia = 'Kydonia [town]').

  5. Thanks for your comments, Glen! You contributed many times before to the posts here with valuable notes. It is so unfortunate that when Google decided to block your blog, they immediately deleted all the comments you made in any other blog (this time irrevocably).

    It is interesting that you too, suggest that the Minoan TA-JA (HT Zd154) is derived from the Egyptian language. I came to the same conclusion after checking all the Afroasiatic, Indo-European, Caucasian and any other languages that were possibly spoken in nearby territories. I can confirm, that there is only one single match, and that is a good match: t'iyaw = '5' from Egyptian. Does this mean that the Minoan has borrowed so extensively from Egyptian, that even their numeral system is partly Egyptian? This warrants many new interesting studies.

    I don't want to rush ahead (because my next post in preparation will cover the topic), but it seems like I might have found a further example of the usage of the LinAB *79 sign (or rather, the corresponding Hiero 'eye' sign). One of the Minoan gold rings contains an inscription - beside the figure of a goddess, that might very putatively read as PI-PI-*79-NA. Although there are many uncertainties, if it is correct, then it could prove a clue for reading this sign - as Lin B had the theonym PI-PI-TU-NA.

    In the meantime - when searching for possible counter-examples for the t/th reading (to check it from a critical perspective), I came across the term TU-RU-SA, that was read by J. Younger as Tylissos. I was starting to believe that the T-series could have denoted a simple *t in some cases, but then I found a derivation of the word above in the form A-TU-RI-SI-TI. This could only mean that the stem-word was at best *tursa or *tulsa. Even with a 't'-reading, this obviously cannot the ancestor of the place-name Tylissos (where did the -i- come from?). So the question is still left open.

    I must admit, if my derivation of the Lin A *79 is peculiar, then the theory on the 'TO' sign must sound straightforwardly strange. It is an 'I don't have any better idea' type of theory. Because Hieroglyphics features a sign: 'bovine head in front', that is not even uncommon, it must have a Linear A descendant. But if one checks it - based on shape, frequency and distribution - there are only two viable candidates: TO or DI. While I could not remove sign DI from the list of possible readings, it is only the TO sign that admits a good etymology. If we go with the reading DO (from *tau) for the 'eye', then a clearly parallel derivation would be the value TO for the 'bull' sign (from *thaura). I only thought of this second one, because it could prove a regular development of *aw diphtongs in Minoan into *o. Unfortunately, I could not meaningfully analyse the PO sign (as I don't know what it depicts), or the RO sign. On the other hand, the KO sign might depict a coriander seed, but we cannot approach it from an etymological direction (as the origins of the word coriander [Lin B KO-RI-JA-DA-NA] are obscure).

    Otherwise, if we don't accept the reading DO for Lin A*79, we could still try a similar value like DWA. That would not invalidate the etymology, and could give a solution for the pressing problem of having two Linear B signs when Lin A had just one.

  6. Here is the continuation of the previous comment (broken in two due to length restrictions).

    I also tried playing with other members of the D and T-series to see if they can help. The DA and TA signs, for example, admit a relatively clear derivation from objects like 'branched twig' (sometimes looks almost like a glove) and 'a pair of teats' in Hieroglyphics. As far as I know, the words for 'wood' or 'teats' are not yet known from Etruscan, but the Hittite taru = 'wood' (PIE *deru) and Greek thélé = 'nipples' (PIE *dhela) suggests to me (if Minoan possessed related IE-like stems) that the t/th reading might not be as bad as it seems. Of course, this 'etymology' is worth close to nothing until we can find at least one similar word in any Aegean language to check their correctness. I did not even attempt to check the pictorial origins of DE, TE, DI, TI, DU or TU signs, these are one of the hardest nuts to crack up to date.

    On the other hand, there is something that might dicredit the D=*l theory further. The only real cornerstone of that theory is the word DA-PU-RI-TO-JO in Linear B (Labryntheion). But I discovered that there is a Middle-Eastern word for 'axe', that is tabar (used in Persia and India). Unfortunately, I could not get a concise report if it has a clear etymology, but one cannot avoid the thought if this is the same word the Greeks also used for double-axe: labrys. If we could prove this, it would immediately imply that the writing DA-PU-RI-TO-JO is entirely correct, with a reading *daburinthoio, and that the *d->*l phonetic change clearly happened in the post-Mycenean age.

    To end this discussion: this is a hard task to find good examples of reading for the D and T series, but if anyone is up to that task, I really welcome any examples or counterexamples you can provide!

  7. As I said, Google can go suck it. ;o) When online we sadly need to adopt the philosophy of "easy come easy go" and actively backup what we intend to keep despite any incompetency around us. I'm a fan of self-sufficiency anyway. If the comments are gone, it doesn't take away the fact that information has been shared. There's a lot to comment on here but I'll try to be brief.

    To me, Egyptian substrate in Minoan is more than expected considering the close ties between Egypt and "Kaftiu". However, there are also numerals of Semitic origin here, at least if we go by Etruscan where śar 'ten' and zathrum '20' seem to go back to *azáro (cf. Ugaritic ʕaṣāru) and *θa-θaroma (cf. Ugaritic ʕiṣrūma). If the Minoan numeral is correct, Etruscan's corresponding numeral maχ deviates from this and yet may be equally ancient.

    Concerning the duality you note in TA/DA signs, I've already been suspecting Minoan *θa '2' based on Etruscan zal and other interesting factoids.

    As for the 'double-axe' caper, I interpret DAPURITOJO as a reflex of Minoan *θaperu. It's perfectly natural that the Indo-European languages in Anatolia, lacking theta, would approximate the sound with /t/ instead. If the initial sound in Minoan weren't something odd like theta, it's hard to simultaneously explain Greek λάβρυς. Remember that this is not the only d/l set in existence (nb. Odysseus and Ulysses).