Ligatures in the Indus Script: Part I

Seal M-1921 with FORK & EF TOPPED DUBYA (center), a ligature.

In the hieroglyphic writing of ancient Egypt, on occasion two independent glyphs are written together, i.e., as a ligature.  In Gardiner’s list of Middle Egyptian glyphs, for example, D59 is a combination of the lower leg with foot (D58) and the forearm with hand (D36).  Separately, these represent the sounds transliterated b (D58) and ‘ (D36).  Together, the ligature represents these two sounds, ‘b, as in the word for “horn” (Gardiner 1976: 458).   

Egyptian glyph D59, a ligature of D36 (forearm) and D58 (leg).

 Following this example from a known script, we could hypothesize that Indus symbols form ligatures in the same way.  We may designate this type of ligature as “simple addition,” in which symbol A, with meaning x, combines with symbol B, with meaning y, to give the ligatured symbol AB, with meaning x + y.  The ligature AB would then serve the same function in the script as the sequence A + B.  More succinctly, the hypothesis is that ligature AB = sign A + sign B.  Korvink’s note on FORK & EF TOPPED DUBYA (M-1921) implies just such a hypothesis: “As a side note, POT and FORK-TOPPED POT, may be expressed in the abbreviated sign FORK & EF TOPPED DUBYA” (2008: 30).

Seal M-1908 with inscription: SINGLE POST (?) / FORK TOPPED POT / POT (over rhino).

To test whether this is the case, we will examine the inscriptions, seeking to compare sequences of A + B with occurrences of the ligature AB.  For the POT-HATTED BEARER (designated more briefly as POT BEARER), this means that this ligatured symbol should appear in the same contexts as sequences of POT + BEARER.  As it happens, the sequence POT + BEARER appears in eight inscriptions in the concordance of Koskenniemi and Parpola (henceforth referred to as KP; 1982: 23-24).  In five of these, the combination occurs at the end of the inscription (KP 5061, K-8, M-209, M-733, L-140).  In one case, this sign pair forms the whole inscription (L-184).  In the other two instances, the combination is followed by one to four additional signs (KP 5035 and the duplicates M-494 and M-495A).  This evidence tends to support the hypothesis.

Tablet M-495A with inscription (right to left): CIRCLED FORK / CRAB / HAIRY HUNCHBACK / POT / BEARER / TRIPLE CUPS / FORK (?).

Note further that there are no occurrences of either *DOUBLE POT or *DOUBLE BEARER (the asterisk indicates that it is not attested).  Thus, if POT BEARER = POT + BEARER, there should be no occurrences of *POT + POT BEARER or *BEARER + POT BEARER.  In fact, POT BEARER appears at the end of 51 inscriptions.  In the other 35 inscriptions, this sign is followed by one to four additional signs (KP 1982: 24-25).  Among the inscriptions that include POT BEARER, there are, as expected, no sequences of *POT + POT BEARER or *BEARER + POT BEARER.  This evidence is consistent with the hypothesis that ligature AB (here, POT BEARER) is equivalent to the sequence A + B (POT + BEARER). (Gulf seals bearing Indus signs may show DOUBLE POT: BM1883_1116_1 ends with this doubling; cf. M-1792 with three non-contiguous POTS along with the singleton DUCK IN POND.)

Gulf seal BM 1883.1116.1 with inscription: PLOW / CRAB / SINGLE QUOTE / DOUBLE POTS.

But other apparent ligatures do not provide the same evidence.  MAN HOLDING QUOTE appears to be a ligature of MAN + SINGLE QUOTE.  MAN appears most often at the end of an inscription (60 times out of 102 inscriptions or 59% in KP 1982: 29-30).  This fact leads Korvink to analyze MAN as a terminal sign (2008: 28-29).  In contrast, SINGLE QUOTE functions as the “constant” and final part of a prefix (2008: 22).  As such, it seldom occurs in final position in inscriptions (11 instances in KP 1982: 84; about 6% of the total of 191 occurrences 2011:166).  Since the medial section of an inscription usually separates prefix and terminal, sequences of MAN + SINGLE QUOTE are not expected.

Detail from seal L-2 with inscription: MAN HOLDING QUOTE / TRI-FORK / PINCH / MARKED FISH / CRAB (FOOTED STOOL?) / PINWHEEL / SINGLE QUOTE / CORN HOLDER.

When these two signs are ligatured, forming MAN HOLDING QUOTE, the result is neither a prefix constant nor a terminal.  Of 16 inscriptions featuring this ligature, the sign appears in final position only once (KP 2751; although Kd-9 includes it as one of only two signs, so that it might be in final position, depending on the direction of reading).  It appears as part of the variable portion of the prefix in 7 instances (M-71, L-2, KP 9551, Laursen 26/KP 9907, M-1052, L-1, and duplicates M-519 through M-521 and M-1470 through M-1472).  In the other 8 inscriptions, it appears as part of the medial segment (C-40; Kd-9; H-660; duplicates M-547-549 and -1555-1560; duplicates M-2053 and -599; M-425; M-403; and M-428).  

Seal M-1918 with partial inscription: FORK / MAN / SINGLE QUOTE / ... / TRIPLE BRICK.

Prefixes, medial elements, and terminals appear in distinct contexts, so it is not surprising that the same kind of evidence as in the first example is lacking (POT BEARER as POT + BEARER, all three terminals).  Indeed, MAN and SINGLE QUOTE rarely occur in sequence: in M-1918, MAN immediately precedes SINGLE QUOTE, while in KP 9701 SINGLE QUOTE immediately precedes MAN (inscriptions in the KP 9000 series are Gulf seals with Indus symbols, a group that shows a number of differences from true Indus inscriptions, as noted in Laursen 2010: 96-134).  This is insufficient evidence to support the hypothesis of “simple addition” for MAN HOLDING QUOTE.

Similarly, MAN HOLDING POST (37 occurrences; e.g. H-72 and M-282) is medial, occurring 6 times in initial position, twice as the variable portion of the prefix (H-241 and M-1686), never in final position.  MAN does not appear alongside SINGLE POST, so there is no data for comparison.  It may be significant that all the modifications of the basic MAN are medial signs except for the BEARER types (BEARER, CHEVRON-HATTED BEARER, POT-HATTED BEARER).  This complicates the test of the “simple addition” hypothesis.  

Seal H-72 with inscription: MAN HOLDING POST / DOUBLE GRIDS.

But the change from terminal to medial sign suggests that modification itself may have a significance other than simply the addition of the meaning of the ligatured elements.  In other words, virtually any modification of MAN being modified changes it from a terminal to a medial sign.  Does this happen to other terminal signs?  This does not seem to be the case for the BEARER.  The changes in the top of this sign from a straight vertical line to a chevron (CHEVRON HATTED BEARER) or to POT (POT HATTED BEARER) do not change these signs’ “syntactic” function.  They remain terminals.  So it is not a general rule that ligatures must be medial signs.  

 

Tablet H-967 with inscription (right to left): ODD STACKED / 2 POSTS / POT / COMB.

But modifications to POT do change its function.  The addition of a SINGLE QUOTE, BI-QUOTES, THREE QUOTES, or FOUR QUOTES changes the terminal POT to a medial sign (POTTED ONE, POTTED TWO, etc.).  Korvink is somewhat vague on this point.  He notes that inscriptions may contain more than one terminal sign, in the following sequence: (1) FORK-TOPPED POT, (2) COMB, (3) SPEAR, (4) POT, (5) MAN, (6) CHEVRON-HATTED BEARER, (7) POT-HATTED BEARER, (8) BEARER, (9) COMB (and this final COMB may be duplicated) (2008: 29).  (Note that every sign in this sequence is optional and no inscription contains all of these.)  To determine the relative placement of MAN and the various types of BEARER in this sequence, Korvink uses what he calls “variants” of MAN, including MAN BETWEEN POSTS, MAN WITH EAR, and MAN HOLDING POST (2008: 31).  He explains that he uses the term “variant” here not to suggest that these signs all mean the same thing but “to infer a similar syntactical function of the sign” (2008: 30).   

Tablet H-1934 with inscription (right to left): QUADRUPED / POTTED 1 / HAIRY HUNCHBACK / POT / MAN.

While it is clear why MAN should be considered a terminal sign, it is not so clear with these proposed “variants.”  MAN BETWEEN POSTS always immediately precedes a terminal sign, either one of the BEARERS or the COMB (although in KP 1141 the sign or signs following MAN BETWEEN POSTS are illegible).  Thus, it might be analyzed as a terminal itself.  But such an analysis would make a fair number of inscriptions anomalous in containing nothing but a terminal of two signs (M-716, M-915, M-1816, M-1839; M-197; M-830, and the duplicates H-543 and 544).  MAN WITH EAR occurs three times (out of a total of 6 inscriptions) in the prefix, which would be unusual for a terminal sign (though not without parallel).  Further, while MAN HOLDING POST often immediately precedes a terminal (17 times), it also occurs immediately after the prefix (8 times), as part of the prefix (3 times), and often in combination with DOUBLE GRIDS (14 times), which is not a terminal.  Thus, it appears to be a medial element rather than a terminal.

In contrast to this subsuming of MAN’s “variants” in his discussion of terminal signs, Korvink clearly differentiates POT, as terminal, from its apparent variants, POTTED ONE, POTTED TWO, POTTED THREE (2008: 35, fig. 18).  

Sign	Solo	Initial	Medial	Final	Total
POT (terminal)	3	1	420	971	1395
POTTED 1	0	20	152	5	177
POTTED 2	3	4	26	2	35
POTTED 3	0	25	24	2	52

Positional Distribution of POT, POTTED-ONE, -TWO, and -THREE (Korvink 2008: 35).

Here, it is clear that POT most often occurs in final position.  When it appears in medial position, it is usually because another terminal follows it (e.g., H-967: ODD STACKED EIGHT / TWO POSTS / POT / COMB).  In other cases, POT occurs medially as the end of the first unit of information in a long inscription, followed by another unit of information (e.g., H-58: FISH UNDER CHEVRON / DOT IN FISH / FLANGE-TOPPED POT / POT / PLOW / CIRCLED FORK / POT BEARER).  The insertion of one or more “quotes” changes the POT to a medial sign.  As such, the ligatured sign may occur in initial position as part of the prefix or as a medial sign where there is no prefix.  In rare cases, it ends an inscription when there is no terminal.  Inscriptions containing both POT and POTTED ONE/POTTED TWO reveal the difference in these signs most clearly (e.g., H-1934 with POTTED 1; M-304 with POTTED 2; for the latter, compare M-258 with the sequence POT / TWO POSTS).  Thus, Korvink concludes: “Using pictographic similarity to infer a similarity in meaning is a highly speculative approach” (2008: 36).

Seal M-304 with inscription: MAN HOLDING STOOL (?) / FAT STOOL / POTTED 2 / FISH / POT // MAN.

In other words, the hypothesis that ligature AB = sign A + sign B is not confirmed as far as modifications of MAN and POT are concerned.  Now, although I began this post by referring to an Egyptian ligature, this type of “simple addition” does not apply to all Egyptian ligatures either.  In Egyptian, some glyphs are phonetic symbols.  They represent one, two, three, or occasionally more consonants.  The ligature of two phonetic glyphs does follow the “simple addition” pattern.  In addition to the example cited at the beginning of this post, there is S 30, a combination of S 29, a folded cloth, and I 9, a horned viper.  Phonetically, s + f = sf.  But not all glyphs are phonetic.  A great many serve as ideographs or determinatives, or both.  For example, the most common anthropomorph is A1, a man seated with his left leg under him and the right knee up, both arms bent at the elbow.  As an ideograph, it may occur alone or with the vertical stroke (which indicates that a glyph is an ideograph), meaning “man” (Gardiner 1976: 442).  Also ideographically, it may represent the first person pronoun, “I, me.”  In either case, it may be accompanied by phonetic glyphs, s for “man,” and i, wi, ink, or kwi as “I, me.”  When the seated man holds a basket steady on his head, this is A9, determinative in 3tp “load,” f3i “carry,” or k3t “work” (1976: 443).  When the seated man holds an oar in his right hand, this is the determinative in sķdw “sail.”  So it goes.  Modifications of the basic man are almost always determinatives and/or ideographs.  An exception, an upright man with legs spread, is A27, phonetic in “by” (1976: 445).

Chinese characters from oracle bones: bao yi (upper left); bao (upper right); bao bing (lower left); bao ding (lower right) (after Keightley 1985: 185).

Chinese characters from oracle bones: two variants of wang "king" (after Keightley 1985: 216).

 In Egyptian writing, the determinative comes at the end of a noun or verb.  In this way determinatives are similar to the Indus terminals.  However, virtually all phonetic glyphs in Egyptian can also act as determinatives or ideographs (or both).  So the two classes of glyph are not mutually exclusive.  In fact, all originally were ideographs and their phonetic function was due to the rebus principle (the same principle by which English speakers use the numeral 2 as an abbreviation for “to” in texting). 

Egyptian glyph A1, the basic seated man (after Gardiner 1976: 544).

Glyphs A9 (left) and A10 (right), which resemble ligatures of A1 with a basket (W10) and oar (P10).

Similarly, in the earliest Chinese writing on oracle bones, there are ligatures, combinations of two or more elements in a single character.  For example, there is a squared off “C” shape similar to the square bracket “]” with longer horizontals, bao.  The insertion of the character yi, similar to the Indus ESS, inside the bracket bao creates the name Bao Yi (Keightley 1985: 185).  If, instead, a small square is inserted in the bracket, this is the name Bao Ding.  One estimate is that 27% of the oracle bone characters are made up of two components, a radical and a phonetic (1985: 68, f. 49).  

In some cases, modifications of these early Chinese characters are not meaningful, representing simply variant writings.  For example, the character wang “king” appears sometimes as a stick figure upon a horizontal base, at other times as the same stick figure on the same base but with an additional horizontal across the top, and in still other cases as three stacked horizontals joined by a single vertical (1985: 216).  Other modifications are indeed meaningful.  The variants of wang appear to be modifications of the simple stick figure, which represents da “big, great” (1985: 119).  The first variant of wang resembles da “big” plus yi “one” as the base.  However, in this case the meanings of the two characters apparently ligatured in wang (“big” + “one”) do not provide its true meaning (“king”).  The addition of a horizontal across the top – which seems to place the stick figure between the strokes of erh “two” – does not derive the ligature’s meaning from its apparent components (“big” + “two”) either.  Thus, as Korvink noted concerning Indus symbols such as POT and POTTED ONE, etc., assuming a semantic relationship between symbols based only on graphic similarity is speculative and may be misleading.  

Thus far, it seems that one cannot automatically assume that a complex symbol is a ligature simply because it looks like a combination of two (or more) simpler symbols.  Nor can one assume that an apparent ligature serves as an abbreviation for its component parts.  In other words, it is only sometimes true that ligature AB = sign A + sign B in a sequence.  I will return to this theme in my next post.

REFERENCES

Gardiner, Sir A. 1976 (1927). Egyptian Grammar: Being an Introduction to the Study of Hieroglyphs. Oxford: Ashmolean Museum and Griffith Institute.

Joshi, J.P. and A. Parpola. 1987. Corpus of Indus Seals and Inscriptions. 1. Collections in India. Helsinki: Suomalainen Tiedeakatemia.

Keightley, D.N. 1985 (1978). Sources of Shang History: The Oracle-Bone Inscriptions of Bronze Age China. Berkeley: University of California.

Korvink, M.P. 2008. The Indus Script: A Positional Statistical Approach. Gilund Press (Amazon).

Koskenniemi, K. and Parpola, A. 1982. A Concordance to the Texts in the Indus Script. Helsinki: Department of Asian and African Studies, University of Helsinki.

Parpola, A., B.M. Pande, and P. Koskikallio. 2010. Corpus of Indus Seals and Inscriptions. 3. New Material, Untraced Objects, and Collections Outside India and Pakistan. Helsinki: Suomalainen Tiedeakatemia.

Shah, S.G.M. and A. Parpola. 1991. Corpus of Indus Seals and Inscriptions. 2. Collections in Pakistan. Helsinki: Suomalainen Tiedeakatemia.

Wells, B.K. 2011. Epigraphic Approaches to Indus Writing. Oxford & Oakville: Oxbow Books.

'Phrase Structure Rules' in Indus Script

Phrase structure tree of the English sentence, "The dog bites the cat."

 

In English, as in other languages, speech consists of words put together into phrases, which, in turn, are put together into sentences.  (This sequence is neither the beginning nor the end of the things put together, but it is all we need for now.)  Using transformational grammar, linguists analyze sentences into their constituent phrases and the phrases into their constituent words, in the form of phrase structure trees.  To diagram the sentence, “The dog bites the cat,” I began the tree at the top with “S,” which stands for sentence.  I divide this into two constituent parts, a noun phrase (NP) on the left and a verb phrase (VP) on the right.  The initial NP is further divided into its constituents, the article “the” (Art) on the left and the noun “dog” (N) on the right.  The second element in the sentence, the VP, is also further subdivided, into the verb “bites” (V) on the left and another NP, “the cat,” on the right.  At the base, the final NP subdivides into another sequence of Art + N.  (Additional details can be included, but I chose to simplify the diagram.)

The Indus inscriptions are amenable to a similar type of analysis, although I cannot relate the various elements of the script to any specific linguistic elements.  In other words, no one yet knows whether each sign represents a phonetic element (eg., a sound, a syllable), a semantic element (e.g., a word or affix), or neither one.  Nevertheless, several researchers have demonstrated that there is some structure in the inscriptions.  The following discussion is my attempt to describe the structure using a tree similar to that found in linguistics for phrase structure.  My analysis is based upon Korvink’s statistical positional analysis of the Indus script, although he does not use the tree diagram (2008).

Korvink’s analysis demonstrates the existence of three possible subdivisions or subclasses of an inscription, which I have often discussed in previous posts:

1.       Prefix, typically in initial position, consisting of one or more signs (variables) followed by one of three “constants,” either SINGLE QUOTE, BI-QUOTES, or PINCH (in rare cases by two constants);

2.       Medial section, typically following any prefix and/or preceding any terminal, consisting of one or more signs;

3.       Terminal, typically in final position, consisting of one or two terminal signs, POT, FLANGE-TOPPED POT, FORK-TOPPED POT, COMB, MAN, BEARER, CHEVRON-HATTED BEARER, POT-HATTED BEARER, SPEAR, or PINWHEEL.

An inscription may include one, two, or all three of these segments, which I will term ‘phrases’ in the following (without implying that they are linguistic phrases).  Based upon Korvink’s discussion, I originally assumed the basic structure could be expressed in the following manner, where parentheses indicate an element that is optional:

First approximation to phrase structure tree for an Indus inscription.

This would indicate that the M phrase is always present and thus obligatory.  Before M, a P phrase optionally occurs.  After M, a T phrase optionally occurs.  This is what Korvink’s analysis suggests, providing a testable hypothesis.

If it is correct that the M phrase is obligatory, there should be no inscriptions consisting only of a P phrase or of a T phrase.  On my first pass through my own database, I did find some P-only and T-only inscriptions, although not many.  Of course, I had to eliminate from consideration all inscriptions on broken objects where another element may originally have appeared.  While this winnowing process leaves over 100 M-only inscriptions, I found just 16 examples containing only a P phrase. 

Seal B-7 with inscription containing only a P phrase: CIRCLED VEE / BI-QUOTES.

Of these 16, 10 appear on seals from Mohenjo daro, Harappa, Kalibangan, and Banawali; 3 examples plus one duplicate are on tablets from Harappa; and 3 examples appear among the graffiti on pot shards and an ivory stick.  All of the graffiti examples are dubious: either one or more symbols are close to a break or difficult to identify.  For this reason, I will ignore the graffiti category for now.  This leaves 13 inscriptions.  In these, the P phrase consists of 2 to 6 signs.  Shorter types outnumber longer ones: 8 inscriptions consist of a 2-sign P, 2 each of a 3-sign and 4-sign P, and 1 each of a 5-sign and a 6-sign P.  Thus, the length of the apparently independent ‘prefix’ is much the same as that of the P in inscriptions that include one or more other elements.

Button seal Dmd-1 with inscription containing only a T phrase: POT.

I found even fewer inscriptions containing only the T phrase, 8 in all.  Only 1 instance appears on a seal – specifically a button seal from Daimabad.  The other 7 examples occur in graffiti on pot shards and a bangle fragment.  Again, it seems wise to discard the data from graffiti for now.  With only one counter-example, I conclude that the button seal with only a POT is an anomaly, that the hypothesis that T is optional is essentially confirmed.  But I must revise my original assessment somewhat as regards M.  There are in fact a few inscriptions consisting only of P and I cannot easily explain away or discard this.  So while the M phrase is almost always present, it too is optional in some cases.  While P is clearly optional, being absent in many cases, its status appears somewhat stronger than that of T.  We will come back to this later.

For now, although my initial analysis is not entirely accurate, I will continue using it since it describes the bulk of the data.  The reason for the occasional absence of M is not at all clear at this point, but that is something to investigate further in a future post.

Detail from seal H-43 with inscription containing only an M phrase:
TWO POSTS / ASTERISK / QUAD-FORK.

In examining the M-only inscriptions, I found many examples demonstrating greater variety of form than in the other two phrases.

Number of signs in M-only inscription	No. of examples including graffiti	No. of examples excluding graffiti
1	47	31
2	72	54
3	79	71
4	35	2 (+3 Gulf seals)
5	19	1 (+2 Gulf seals)
6	6	0 (+2 Gulf seals)
7	6	0
8	4	0
TOTAL:	268	159 (excluding Gulf)

After excluding such dubious examples as M-only inscriptions on broken objects (the vast majority), on graffiti, and on seals from the Persian/Arabian Gulf, my search yielded 159 good examples.  These contain between 1 and 8 signs, with most examples being at the shorter end (true of the Indus inscriptions as a whole).

Given that an inscription can be M alone – in rare cases P alone – the next step is to determine which combinations of phrases occur.  First, let us consider the possibility of repetition of a single phrase.  Since M can appear alone, if repetition is possible then we would also see MM.  Since the P occurs alone, we might also expect to see PP.  Since T essentially does not appear alone (except for dubious cases), we would not expect to see TT.  Which 2-phrase sequences do occur?

I found two possible examples of a PP phrase within a longer inscription, both of which are better analyzed as PMT.  Analysis of the first example, M-706, depends upon the identification of the initial sign.  Looking only at the relative sizes of the signs themselves, this inscription reads: SINGLE QUOTE // VEE IN DIAMOND / BI-QUOTES // WHISKERED FISH / BI-RAKE WITH ATTACHED TRI-FORK // POT.  This could be analyzed as PPMT, although that would be quite anomalous in that the variable(s) in the first P is missing.  The icon on this seal is the unicorn, however, and its long horn cramps the first sign, causing it to become smaller than the other signs.  Thus, this is better analyzed as SINGLE POST / VEE IN DIAMOND / BI-QUOTES // WHISKERED FISH / BI-RAKE WITH ATTACHED TRI-FORK // POT.  Analysis then becomes a straightforward PMT.

The second possible example is more problematic, since the inscription takes up two lines (Ns-9).  Reading both lines from left to right, I could transcribe the inscription as follows:

CIRCLED DOT WITH EAR / STRIPED TRIANGLE / CORN HOLDER / PANTS / BUD / BI-QUOTES //

X / POT // (WINGED?) MAN HOLDING POST / PINCH.

(Here, “X” represents an ambiguous element at the left end of the second row of signs, where the bottom of the element is lost with the broken off corner.  I am assuming this element is not a sign but the top of the tail of the tiger body of the icon.)  This would yield an anomalous analysis as PTP.  Thus, it seems better to read the second line in the opposite direction from the first line, right to left (a ways of reading termed boustrophedon, “as the ox plows”):

CIRCLED DOT WITH EAR / STRIPED TRIANGLE / CORN HOLDER / PANTS / BUD / BI-QUOTES // (L-R)

PINCH // (WINGED?) MAN HOLDING POST // POT (R-L).

This provides a normal analysis of PMT (possibly with a rare appearance of two constants, one at the end of line 1, the other at the beginning of line 2).

Seal C-17 with inscription analyzable as MT (or MTT):
 WINGED MAN // POT / MAN.

Since we can analyze the apparent PP sequences in these two examples in more normalized fashion, I tentatively conclude that PP does not occur.  A similar process yields the same result for TT.  There are infrequent examples where two terminal signs appear together on one line.  In two such cases, one might conclude that a terminal sign appears in one part of the inscription and a second terminal appears in another part of the same inscription, yielding a TT phrase.  The first example is C-17, where there are two signs above the iconic unicorn (WINGED MAN // POT) and a third sign below the head of the animal where the cult stand usually appears (MAN).  We could analyze this as MT-T (in other words, two phrases, one MT and the other simply T), due to the spatial separation of POT and MAN.  However, if we assume that the final sign took this unusual position only because of crowding at the top or for stylistic reasons, we can group the 3 signs together in a less anomalous form as indicating simply MT (where T includes two signs). 

The other example is from the Gulf, showing a somewhat odd POT on the left and another on the right, on either side of the iconic animal.  Again, due to their separation, the signs could be analyzed as T-T (two phrases, each simply T).  Other Gulf inscriptions show sequencing and positioning of signs not found in Indus inscriptions.  So, again, it is best simply not to group this inscription with authentic Indus inscriptions.

Since PP and TT do not occur, we must ask whether MM appears.  If it does not, then we can express all three non-occurrences with a single rule: a phrase cannot duplicate the previous phrase type.  If an inscription appears on two lines and each line is an M phrase, then there are indeed MM (or rather, M-M) inscriptions.  Since one cannot know, at the outset, whether an inscription on two lines contains one or two independent messages, I have analyzed each line separately.  But I have not yet attempted to demonstrate whether this is accurate.  For now, I have assumed MM is possible, leaving the test of this assumption to another time.  No other duplication of phrase type is allowed for contiguous phrases.

Based on the postulated (P)M(T) sequence, I expect just two kinds of two-phrase sequences, namely, PM and MT.  That is, I would not expect to find MP, TM, PT, or TP.  In a first pass, I find PM (without any additional elements) in 6 Gulf seals and 1 Mesopotamian example (to be temporarily discarded from further analysis) alongside 235 Indus examples.  Narrowing the search to the first volume of the corpus and to inscriptions that are clear and complete on seals and tablets, I find 72 examples.  This clearly demonstrates the occurrence of PM as a complete inscription.

If the P phrase can occur alone, even if rarely, we would expect a few phrases with 2 constituents to lack M, yielding PT.  As it happens, I do find a few instances of PT, either as a complete inscription or as part of one:

1.       M-1177 (seal):  CIRCLED VEE / BI-QUOTES / SINGLE QUOTE // TRI-FORK TOPPED POT / POT (PT).

2.       H-829 (tablet):  CARTWHEEL / BI-QUOTES // MAN // (B side) QUAD-FORK / 2 POSTS / CUP (PT-M; although this seems to appear in the KP concordance as CARTWHEEL / BI-QUOTES // MAN BY CHEVRON, which yields analysis as PM).

3.       M-257 (seal): BOAT / PINCH // POT // RECTANGLE (PT-M).

4.       M-267: EX UNDER TABLE / BI-QUOTES // POT-HATTED BEARER // BLANKET // POT (PT-MT).

5.       M-1591 (graffiti): BI-QUOTES // POT (PT?)

6.       M-311 (seal): COIL / STRIPED FAT LEG LAMBDA / BI-QUOTES // DOUBLE COMBS (PT).

7.       M-394 (bar seal): CUPPED SPOON / 3 POSTS / SINGLE QUOTE // FLANGE-TOPPED POT / POT (PT).

8.       Laursen 23 (Gulf seal): AY OVER QUOTES / CRAB / SINGLE QUOTE // DOUBLE POTS (PT?).

We can safely discard number 8, the Gulf seal, since this group is often anomalous.  As my notes indicate, we can also probably discard number 2, assuming my original reading was wrong and the KP concordance is correct.  The 5^th example appears as graffiti on a pot shard and can also be discarded.  This still leaves 5 examples, 3 PT alone (M-311, M-394, and M-1177, colored yellow above) and 2 with PT followed by something else, PT-M (M-257), and PT-MT (M-267) (colored blue above).  These last two will be dealt with in a later post, when I consider longer inscriptions.  It is interesting that all 5 come from Mohenjo daro, which hints at geographical variation in phrase structure rules.  However, much more material comes from Mohenjo daro than from any other site, so this may only be an accident of preservation.

Seal M-311 with rare inscription containing PT phrases (shown reversed):
COIL / STRIPED FAT LEG LAMBDA / BI-QUOTES // DOUBLE COMBS.

My conclusion thus far is that PP does not occur; PM is common; PT occurs but rarely.

Moving to sequences beginning with M, we expect to find MT, but not MP.  My search yielded no examples, so I conclude that MP does not occur.  There are a number of inscriptions that appear on two or more lines, or on two or more sides of an object.  One cannot determine whether this spatial separation is meaningful or not.  So I have coded each line separately, in case each is a separate message.  By this criterion, there are indeed MM sequences.  This should not be taken as a definitive finding, though, by any means.

As expected, MT is common, even more so than PM.  I find a total of 609 occurrences not counting Gulf seals or Indus graffiti with this pattern.  Again, narrowing the field to the first volume of the corpus and discarding all broken and unclear examples, the number shrinks but remains high with 136 examples.

In conclusion, MP does not occur; MM appears to be common; MT is very common.

Let us move now to sequences with T.  Since this is a terminal element, it should not occur in initial position (except after a break).  Thus, there should be no TP, no TM, and no TT.  Indeed, not counting broken objects which probably contained M originally, there are no instances of TP or TM.  The only example of TT is the Gulf seal mentioned earlier (Laursen 56).  I noted already that PT is rare and MT very frequent.

TP does not occur; TM does not occur; TT does not occur.

That is enough for now.  My next post will take up the occurrences of inscriptions with three phrases.

REFERENCES

Korvink , M.P. 2008. The Indus Script: A Positional-Statistical Approach. Gilund Press.

Koskenniemi, K. and A. Parpola. 1982. A Concordance to the Texts in the Indus Script. Helsinki: Department of Asian and African Studies, University of Helsinki.

Laursen, S.T. 2010. "The westward transmission of Indus Valley sealing technology: origin and development of the 'Gulf type' seal and other administrative technologies in Early Dilmun, c. 2100-2000 B.C." in Arabian Archaeology and Epigraphy 21: 96-134.  (available online at academia.edu)