Tuesday, March 20, 2012

An Indus Syntax?

Detail from seal M-38 with inscription: 2 POSTS / BLANKET / MAN HOLDING DEE-SLASH / TRI-FORK /
CROSSROADS EX // POT (double slashes indicate division of the inscription into parts -- prefix, medial
segment, and terminal -- while "+" indicates the signs on either side form a close pair or triad).

This post is a discussion of an article published last year by S.Sinha, A.M. Izhar, R.K. Pan, and B.K. Wells (2010: 1-17).  The title of their work indicates they have performed network analysis of Indus inscriptions and found syntactic organization.  My first reaction to the title was that such “syntactic organization” had been found previously, on more than one occasion.  G.L. Possehl describes a number of analyses that made such claims (1996).  G.R. Hunter as early as 1929 noted the function of the POT and COMB as final elements – or terminal signs to use M. Korvink’s terminology (Possehl 1996: 85).  Similar conclusions come from the work of Father H. Heras (p. 110-112), a Soviet Russian team of scholars headed by Yu. V. Knorozov (p. 115-122), a Finnish team including A. Parpola (p. 124), and others.  M. Korvink’s analysis, which I have referred to repeatedly, came after the publication of Possehl’s review, but also notes such organization (2008).

In their preliminary discussion, Sinha et al note that the ancestral scripts that later became Mesopotamian cuneiform, Egyptian hieroglyphs, and Mayan writing had limited connections to spoken language (2010: 2).  They state, “In almost all cases, a writing system became more or less capable of expressing spoken language only after centuries of development....”  This is certainly correct for cuneiform and hieroglyphs (my knowledge of Mayan writing is too limited to assess the accuracy of the statement).  However, the earliest hieroglyphs may not be true writing, but rather proto-writing (O’Connor 2009: 144-147).  Proto-cuneiform, like proto-Elamite, is also considered not closely tied to speech (Englund 2001: 1-43).  The first tablets contain only numerical symbols, at the second stage containing ideographs as well, representing “owners” (people and/or institutions) and commodities.  When speaking of a symbol system that eventually evolved into a fully developed writing system, it is common to extend the term “writing” to the earliest examples of the script.  But that does not really demonstrate that the earliest inscriptions are indeed true writing.  Thus, the fact that the Indus script shares characteristics of the earliest proto-cuneiform, proto-Elamite, and hieroglyphic scripts may well suggest that the Indus script itself is proto-writing rather than a fully developed writing system (as noted in several previous posts).
A long bead of lapis lazuli from Mari in Syria, dating to the Early Dynastic IIIB period,
2400-2250 BCE, with a short inscription in early cuneiform: "For [...], Mesanepada, king of
Ur, the son of Meskalamdug, king of Kish, has consecrated [this bead]" (after Aruz 2003: 143). 

That caveat aside, the analysis of Sinha et al is quite interesting.  They begin by defining the corpus they use which is based on Wells’ database (2010).  This includes the inscriptions from all three volumes of the corpus, as well as some unpublished data (Sinha et al 2010: 3).  These inscriptions come from 3,896 artifacts, from which a subset of 2,393 are selected as being complete, unbroken, and legible.  From this a further subset is taken for analysis, comprising inscriptions that occur on a single line.  The selected sequences contain from 1 to 13 signs, with a median length of 4 signs.  As a comparison set, the authors created randomized variations on each inscription, in which the signs were combined in every possible order, with statistical measures averaged.  If the signs of the Indus script are arranged purely randomly, the statistics from the comparison set would match the statistics from the actual corpus.  The fact that results generally differ between the two sets is the evidence the authors cite for syntactic organization.

To begin with, the authors note 21 signs that only occur individually, as 1-sign inscriptions (2010: 4).  They then identify 128 signs that only occur at the beginning of an inscription, a group they term “beginners.”  The third group of 43 signs, which appears only at the end of inscriptions, is referred to as “enders.”  This leaves 401 signs, some of which sometimes occur at the beginning, some of which sometimes occur at the end, but all of which also occur in other positions.  Out of this large group, the authors isolate 127 signs that are never initial or final.  By comparison, the randomized set shows very different beginners and enders, far fewer beginners but considerably more enders.  “We observe that four beginners in the empirical set...and two enders...never occur as beginners and enders (respectively) in the 100 randomized trials we carried out.  It implies that the occurrence of these signs always at the beginning or end of a sequence (and never in any other position) may be highly significant, and certainly not a result of simple chance” (2010: 5).

One troubling feature of the three lists and of the conclusion drawn from this analysis is the large number of singletons.  As noted in previous posts, one of the striking characteristics shared by proto-cuneiform, proto-Elamite, and the Indus script is the very large proportion of signs that occur only once in the corpus.  Of approximately 1,900 proto-Elamite signs (not including numerals), over 1,000 are singletons (Dahl 2002: 1-2).  Around 300 additional signs occur only twice, while the vast majority – 1,700 in all – appear fewer than 10 times.  This leaves a relatively small core of 200 “common” signs, out of which just 20 occur 100 or more times.  What effect does this characteristic have on the three lists provided by Sinha et al?  As it happens, of 21 signs that occur solo, 10 are singletons in the entire corpus and only one appears 9 times.  Thus, all are rare.  In addition, of the 128 “beginners,” 66 are singletons.  A similar proportion are singletons among the “enders” – 26 out of 43 signs.  It seems misleading to say that a singleton is found only at the beginning or end of an inscription.  If it is a singleton, it only occurs once, which is not enough to establish a rule! 
An administrative text in proto-cuneiform from Jemdet Nasr, dated to 3000-2900 BCE
(from Aruz 2003: 41, copy by author).  The inscription includes around 20 symbols that
are separated into compartments.  It concerns distribution of grain as represented by
the signs resembling ears of barley or wheat.  No Indus inscription has four occurrences
of a single sign in such non-contiguous arrangement, i.e., not side by side.

After comparing the number of sequences begun or ended by these signs, the authors observe that “most of the beginner signs appear in only 1-3 distinct sequences” with a maximum of 8 sequences, while “a particular ender sign can appear at the end of a maximum of 4 distinct inscriptions” (2010: 5).  With such small numbers, the results may not be random but they do not seem particularly robust either.

Sinha et al also look at the distribution of the number of links each sign has (its degree) and the strength of these links (2010: 5-6).  The authors describe their results concerning the degree as indicating that “the variation of sign relations is much more restricted in the empirical sequences than would be the case had each of the sequences been put together randomly” (2010: 6).  Their graph indeed shows a difference of degree between the real or empirical set and the randomized set, but that difference does not appear particularly great.  When it comes to strength, the authors must agree that the results are almost the same between the two data sets, inasmuch as “this is governed by the frequency of occurrence of individual signs” (2010: 6).  Clearly, a common sign will have links with more signs than will a rare sign, whether or not their arrangements are random.

Thus, the 10 most frequent signs in the empirical set have the most links.  These signs include POT, BI-QUOTES, FISH, 2 POSTS, COMB, WHISKERED FISH, SPEAR, TRI-FORK, 3 POSTS, and VEE IN DIAMOND.  Arrows in one of the figures show in which direction the links occur among these signs.  For example, VEE IN DIAMOND precedes but does not follow POT; POT both precedes and follows WHISKERED FISH and COMB; FISH precedes but does not follow SPEAR, while SPEAR precedes but does not follow 2 POSTS.  The profusion of arrows is hard to interpret, but the description summarizes the situation: “about half of all potential connections [are] present” (2010: 6).

When Sinha et al discuss medial signs, they seem to be on firmer ground.  The intersection of two sets of signs – those with the most connections with preceding signs and those with the most connections with following signs – yields an inner core of 26 signs most likely to appear in medial position (2010: 7).  Of these, only 5 occur less than 100 times apiece, so the statistical measures are more convincingly robust.  Further statistical manipulations of the data yield a group of 35 signs forming the “core lexicon” (2010: 7-8).  They include medial signs: SINGLE QUOTE, BI-QUOTES, 3 QUOTES, 3 POSTS, WINGED MAN, HAIRY HUNCHBACK, FISH, MAKRED FISH, FISH UNDER CHEVRON, WHISKERED FISH, TRI-FORK, RAKE, MALLET, CUPPED POST, POT, CRAB, CIRCLED FORK.  They also include signs that are most likely to precede this medial group: SINGLE POST, PINCH, CROSSROADS EX, POTTED ONE, TRI-FORK TOPPED POT, CIRCLED E-FORK, CIRCLED VEE, CARTWHEEL, OVERLAPPING CIRCLES, VEE IN DIAMOND, BOAT (and three others occurring slightly fewer than 100 times each).
An Egyptian amuletic circle of gold and silver dating to 2000-1800 BCE (after
Pinch 2006: 111).  Most of the symbols are hieroglyphs, including wedjat eyes,
djed pillars, the ankh knot, and possibly the face (shown en face!).  But this is
not writing -- each symbol communicates its own message independently of position.

The authors then focus on determining which signs occur in pairs by comparing the probability of a given pair’s occurrence in the empirical data versus the probability in the randomized data set (2010: 9).  They find some groupings that Korvink and others identified previously: FOOTED STOOL + PINWHEEL; MALLET + FORK; CUPPED SPOON (or CUPPED POST) + 3 POSTS; 3 POSTS + SPEAR; STACKED 7 + EF TOPPED EXIT; 2 POSTS + FISH; PRAWN + ZEE; ZEE + CROSSROADS EX; CROSSROADS EX + POT; TRI-FORK TOPPED POT + POT; POT + MAN; POT + COMB; CIRCLED VEE + BI-QUOTES; VEE IN DIAMOND + BI-QUOTES; CARTWHEEL + BI-QUOTES; CARTWHEEL + PINCH; BOAT + PINCH; FAT EX + PINCH.  They also find some groupings that seem unintuitive by Korvink’s analysis, including BI-QUOTES + CIRCLED FORK; BI-QUOTES + WHISKERED FISH; BI-QUOTES + FISH UNDER CHEVRON; FAT CEE + POT. 

Here I have underlined the signs identified as terminals by Korvink and placed his prefix elements in italics.  Thus, the reader can see that where Korvink divides the inscriptions into three segments – prefix, medial portion, and terminal – Sinha et al simply note which combinations are most frequent.  The signs that occur most frequently at the beginning of the medial segment will thus seem to form pairs with the most frequent prefix constant (i.e., the final sign in the prefix).  The signs that occur most frequently at the end of the medial segment will similarly seem to form pairs with the most frequent terminals.  Now, how does one determine whether or not this type of – perhaps fortuitous – occurrence is significant?  Following the method of Sinha et al, one constructs a control group of fake sequences in which signs occur in random order.  Then one points to the differences between the set of random sequences and the real sequence, concluding that this difference indicates syntactical organization.  I suppose I am suggesting that there is organization all right, but not necessarily any syntax behind that organization. 

The main source of my discomfort with the study’s conclusions lies in the final section where the authors construct segmentation trees for the longest 33 inscriptions, each containing 10 or more signs.  The second tree they show is M-38 (see illustration above): 2 POSTS / BLANKET / MAN HOLDING DEE-SLASH / TRI-FORK / BI-QUOTES / FISH UNDER CHEVRON / WHISKERED FISH / 2 POSTS / FISH / PRAWN / ZEE / CROSSROADS EX / POT.  They find a strong sign pair to be 2 POSTS + FISH and another, equally strong, is PRAWN + ZEE.  So far, I would agree. 

Sinha et al find a third pair that I find problematic: FISH UNDER CHEVRON + WHISKERED FISH.  Further, they link this pair fairly strongly with the preceding BI-QUOTES, forming a triad.  In Korvink's analysis, BI-QUOTES belongs with the first four symbols, all five together forming the prefix.  Korvink also notes that the various "fish" signs tend to occur in a semi-standardized order (2008: 37), with FISH UNDER CHEVRON typically the first of any series, followed by FISH, WHISKERED FISH, DOT IN FISH, MARKED FISH in that order (though no inscription contains all of these).   He also notes the pair 2 POSTS + FISH, which may precede the otherwise standard sequence (2008: 38).  In M-38, though, this pair follows the other "fish." 

Sinha et al further show a strong link between the pair PRAWN + ZEE on one side and the following sign, CROSSROADS EX (2010: 11).  This seems clear enough.  But then they link this triad to the final symbol, the terminal POT.  This link with POT is stronger, in their view, than that between the symbols preceding BI-QUOTES, all elements of the prefix according to Korvink's analysis.  Thus, Sinha et al would divide the prefix between an initial "phrase" of four signs on one side, and the prefix constant along with the first two elements of the medial segment on the other side.  I find this segmentation tree -- as well as the other two shown -- to be unconvincing.

The authors’ description of their first example (with my sign names substituted for their numerical designations) reads thus:

The 3-sign cluster “LOOP ARMED MAN-DOUBLE BOATS-SPEAR” at the beginning of the sequence is the initial phrase, and is separated from the rest by sign SQUARE AY.  The medial sequence is broken into two parts “VEE IN DIAMOND-BI-QUOTES-FISH UNDER CHEVRON” and “DOT IN FISH-CUPPED POST-3 POSTS.”  The sequence ends with the terminal phrase “2 POSTS-FAT EX IN DIAMOND-POT.”  We observe that each of these four sub-sequences obtained by this analysis also  occur as units in other inscriptions in the WUCS dataset, thereby verifying the accuracy of the segmentation procedure (2010: 11, emphasis added).

Let us examine this type of verification, seeking the sign pairs in the corpus that Sinha et al designate.  I find 10 examples of 2 POSTS + BLANKET in the concordance of Koskenniemi and Parpola (1982: 101-102).  In two of these other than the cited sequence, BLANKET is followed by the MAN HOLDING DEE-SLASH (KP2027, M-119, M-1188).   There are other examples of this "man" followed immediately by one or the other FORK (14 instances in KP, 1982: 33).  Five of these place the FORK just before BI-QUOTES.  Interestingly, other instances have this apparent pair at or near the end of the inscription rather than in the prefix.  Since BI-QUOTES is one of the most frequent signs, it is not surprising that it often occurs immediately preceding FISH UNDER CHEVRON.  But if this prefix constant is joined with the pair, FISH UNDER CHEVRON + WHISKERED FISH, then the occurrences are fewer (6 examples in KP, 1982: 45-46).  There are multiple examples of 2 POSTS + FISH (66 examples in KP, 1982: 99-100).  Equally compelling is the link between PRAWN + ZEE (45 examples in KP, 1982: 53).  Of these 45 pairs, many but not all are followed by CROSSROADS EX (27 examples).  Two of these include another sign or two between CROSSROADS EX and the terminal (POT in each case).  In two inscriptions, the sign following CROSSROADS EX is either missing or illegible.  Thus, I find Korvink's description more convincing as it separates the terminal from the medial signs.  It seems to me that the "link" between CROSSROADS EX and POT is essentially fortuitous and due to the fact that POT is the most frequent sign by far.

In conclusion, I am not any more impressed with this article than I was by the work of Yadav et al (2008: 39-52).  Sinha et al, like the previous team, demonstrate that there are some patterns in the sequences of Indus signs.  But neither group seems to have developed a way to determine which of these patterns are likely to be syntactic and which are the result of other characteristics, such as frequency.  That is, if one finds that feature X correlates with feature Y, this may indicate a direct link between the two.  On the other hand, it may only be a clue that some other (unobserved) feature Z directly links with both and thus the apparent link between X and Y is really an indirect one.
A proto-cuneiform inscription on the so-called "Blau" monument shaped like a scraper (after
Aruz 2003: 39, drawing by author).  The "scraper" is from Jemdet Nasr in Mesopotamia and dates
to 3000-2900 BCE.  The text records an economic transaction with land exchanged for such goods
as wool, silver, goats, and (most importantly?) beer.  Note that there are over 30 signs, more than
on any known Indus artifact, though this is proto-writing. 

The conclusion of Sinha et al is tempered by their recognition that there is still no generally accepted sign list; where Mahadevan lists 417 signs, Wells enumerates over 700 (2010: 12).  They state that “an important open issue that needs to be settled is the robustness of these results with respect to the sign list being used” (loc. cit.).  Part of this open issue can easily be settled, though.  For example, among the “beginners” that appear only in initial position are some that would not be included if Wells had not classified them as independent signs rather than variants.  For example, Wells always distinguishes multiples of a sign from the same sign’s individual occurrences: DOUBLE SKEWERED CHEVRONS, QUADRUPLE TRI-FORK, DOUBLE CHEVRONS, DOUBLE EF TOPPED EXITS, DOUBLE CUPS, TRIPLE BOATS.  Each of these signs, when found individually, occurs in non-initial positions.  Wells also distinguishes reversed signs from their mirror images, something not all other list-makers do (unless the reversed sign appears in an inscription along with its mirror image).  If we remove both of these types of examples and remove all the rare signs (those that occur only once or twice in the corpus), then we are left with a much smaller inventory. 

In fact, if we require a sign to occur at least five times – which is still far too rare for meaningful statistics – the list of “beginners” would be significantly reduced.  If this reduced list were to be compared to sign lists of other researchers, even fewer would remain.  For example, Wells has ODD STACKED 7 appearing in initial position only.  But there are non-initial examples in the KP list where all variants of ODD STACKED are conflated (1982: 96).  MAN WITH WING might remain on the list of beginners, but KP show one instance where this sign is final (M-1054).  This fact is not noted by Sinha et al because they analyze only complete, unbroken inscriptions and M-1054 shows an initial sign to have been broken off.  CAGED MAN HOLDING POST is a singleton in KP’s concordance although Wells gives it a frequency of 5 (1982: 33).  FIGURE EIGHT WITH LADDER indeed appears only initially, but the similar BEE WITH SLASH, possibly a variant, is medial (1982: 56).  The BED is only a beginner if one separates the variants according to the number of legs; the one with 6 legs occurs initially as Sinha et al observe, but other variants appear both medially and finally (1982: 148).  SKEWERED CIRCLE is probably a variant of SKEWERED DONUT, which appears medially in 3 inscriptions (1982: 70). 
Inscription from a foundation figure of Lugalkisalsi, dating to the Early Dynastic IIIB period,
2400-2250 BCE (after Aruz 2003: 65, drawing by author).  It reads: "For Namma [a goddess],
wife of An [a god], Lugalkisalsi, king of Uruk and king of Ur, erected this temple of Namma."
Note that with 12 or 13 symbols, this is equivalent in length to some of the longest Indus
inscriptions, but with three non-contiguous repetitions of LUGAL, "king," it shows features
quite rare to Indus script.

SHISH KEBAB IN TRIANGLE is almost certainly a variant of BISECTED STRIPED TRIANGLE (1982: 22).  The latter sign occurs at least as often in medial position as initially.  Besides this fact, KEBAB IN TRIANGLE only occurs in a single inscription that is duplicated multiple times on tablets, as far as I can tell.  The duplicate inscriptions should be removed from the frequency count per Sinha et al's stated procedure (2010: 3).  STRIPED BOWTIE WITH EXTRA RIBBON occurs once in medial position (Kd-8).  REVERSED FOOTED STOOL is non-initial at least 6 times (Koskenniemi and Parpola 1982: 131).  BLANKET has a number of variants with differing numbers and arrangements of inner strokes or “ticks.”  Wells’ version with 8 “ticks” may well be a beginner, but other variants certainly occur medially and even once in final position (1982: 138-140).  Wells divides ASTERISK UNDER TABLE into two signs, one with an eight-legged star resembling the keyboard asterisk, the other showing the “X” form with extra strokes only between the upper and lower “legs,” not across the middle.  Presumably the KP list subsumes the two into one group with all in initial position (1982: 132).  The similar EX UNDER TABLE is always final except for one instance which is initial – perhaps this one instance was an error for ASTERISK UNDER TABLE!  The version of POTTED 3 with slashes cross the sign may be initial, but other variations are medial (1982: 178).  Two examples with slashes appear in what may be final position on a broken seal (H-689).  CRAB IN STRIPED LEAF TOPPED POT is another sign that is most likely a variant of several others, one of which occurs medially (L-11).  VEE & TRI-FORK IN DIAMOND appears in both medial and final position according to KP (1982: 201). 

It is rather tedious to examine each symbol in this way, but the point should be clear.  If researchers use the KP list, the same statistical measures would yield results that differ from those reported for Sinha et al using Wells’ list.  Lest the reader think my objection applies only to beginners, I will quickly note the enders as well.  If we remove signs occurring fewer than 5 times, this group would then be reduced to PANTS (one variant only since the KP list, which groups together all variants, shows 2 examples in initial position), EF PRONGED CHEVRON UPON STACKED 6 IN POT (which KP show as occurring in only 2 distinct inscriptions), CAGED SLASHES IN OVERLAPPING CIRCLES, SEPTUPLE STACKED ROOFS (which KP show as a singleton), and RAINY CARTWHEEL.
The foundation figure of Lugalkisalsi, bearing inscription (after Aruz 2003: 65).

At the end of their paper, Sinha et al address some of the problems of assuming Indus script is true writing.  Clearly they would prefer to define writing very generally, terming it “a system of intercommunication by means of conventional visible marks” (2010: 12, following Gelb 1963: 11).  Even so, they admit that “often writing tends to be narrowly defined as a means of efficiently encoding speech” (loc. cit.).  What they fail to note is that even Gelb went further with his definition and separated what he called the semasiographic stage from the phonographic stage of writing (1963: 12).  In today’s terminology (at least the terms I use), he separates proto-writing from true or fully developed writing.  In other words, early “writing” is often loosely connected to speech.  A given sequence of symbols may be expressed in a number of ways in speech.  At this point, those who define writing narrowly would not term the symbol system writing. 

There is good reason for defining writing narrowly in this way, since not all communication systems that use visible marks qualify as writing even to the most generous.  Gelb gives examples of such, including carvings and paintings on stone such as those in caves at Lascaux, petroglyphs in Africa and the Americas, mason’s marks from Anatolia, the Nsibidi system used in Nigeria (similar to the Adinkra symbols I referred to in some earlier posts), and so on.  We could also include Navaho sand paintings.  They are visible and they communicate – at least to those who know enough of the Navaho culture to interpret them.  But they are not writing and not intended to be writing.  In a similar way, we can point to symbols in our own culture that are not part of a writing system – the conventional hearts that appear on Valentines, the cross, star of David, and star and crescent that represent major religious faiths, the icons on computer screens, some simple depictions found on traffic signs, etc.  These communicate and they are symbols.  But they are not writing.

When scholars study proto-cuneiform, they may not always distinguish between the semasiographical stage, or proto-writing, on the one hand and the phonetic stage on the other.  After all, the symbols gradually evolved from proto-writing into true writing.  The same may be true of Egyptian hieroglyphs – the earliest symbols found on pre-dynastic tags mostly evolved into later glyphs with specific phonetic realizations.  But not all early writing systems continued to evolve in this way.  We know, for example, that proto-Elamite failed to evolve into true writing, dying out instead.  After a lapse of centuries, it was replaced by Linear Elamite, which is phonetic writing.  Similarly, the Indus script did not evolve continuously into a fully developed writing system used later on.  Instead, it died out and after a lapse of several centuries was replaced by clearly phonetic writing.

The authors note another problem, namely the fact that the inscriptions are so short (2010: 12).  They want to counter this by claiming that “many early writing systems exhibit such brevity,” citing early Sumerian and early Egyptian.  Early proto-cuneiform (if that is what they mean by early Sumerian) does include very brief texts.  Oddly enough, though, even in proto-cuneiform there are some that are longer than any Indus inscription (see tablets dating to Uruk III phase in Nissen, Damerow and Englund 1993: 22-23).  For example, a single tablet listing pigs bears 30 or so sections, each containing a single wedge (here functioning rather like the bullets in a modern bulleted list) and one or more non-numerical symbols (fig. 26).  And this is just on one side!  Even if we count symbols occurring on multiple sides of objects from the Indus Valley, there are no inscriptions with 30 signs.  So, while some brief texts are understandable in early proto-cuneiform economic documents, others are longer without necessarily containing phonetic writing.  The same is probably true of Egyptian hieroglyphs, as noted previously.
An ancient Chinese inscription from a bronze vessel (after Wieger 1965: 372).
Wieger interprets this to mean "In the presence of the Ancestor, after libation,
offering of jade wine and tow, by the son, a grandson having recently been born."
But for the first phrase, "in the presence of the Ancestor" there is just one symbol,
the character second from the bottom on the left which resembles the Indus MAN.
There may have been no simple, one-to-one correspondence between symbol and word
at this stage of (proto-?) writing.

In their effort to show Indus script to be nothing unusual, the authors go as far as to cite early Chinese, specifically symbols found on bronze vessels from Anyang that may predate even the Shang oracle bones (though the exact date depends on who is doing the dating).  “The majority of these inscriptions comprise only a clan sign and an ancestor dedication,” they say.  If clan signs and symbols (early Chinese characters) representing specific ancestors are the only types of signs, then this would also be better characterized as proto-writing.

An Egyptian tag from the pre-dynastic period (after O'Connor 2009: 145).
Archeologist G. Dreyer reads this two hieroglyphs, the elephant 3b and the
triple mountain peaks dw, thus spelling the name of Abydos.  O'Connor thinks
this represents the name of a town, though not necessarily Abydos.  Neither
seems to address the third element, a schematic tree.  (The circle upper left is a hole).

Perhaps early (proto) writing is always brief, the authors suggest, because “the main use of writing was as a mean[s] of maintaining accounts, list and other economic records” (loc. cit.).  But this is mainly true in the Near East.  In China, the oracle bones record divinations rather than economic transactions.  Among the Maya, early writing records astronomical and ritual information.  Mesoamerican proto-writing such as that used by the Mixtecs includes symbols for dates – which include numerals – and the names of persons.  There are also semi-conventionalized methods for indicating specific places and few other items of information.  The earliest Egyptianglyphs are also mainly indications of specific persons and places.  Thus, writing does not always serves first as an economic account and therefore we cannot assume that this is the reason for the brevity of Indus texts.

In one way, it does not matter what definition one uses.  One can still study a “script” even though it is not fully developed writing.  Several scholars now focus mainly on proto-cuneiform or proto-Elamite, for example, and they have been able to make considerable progress in interpreting the early, enigmatic accounts.  They do not try to excuse the difficulties of their documents by changing definitions to suit them.  Neither should scholars of the Indus script.  It is whatever it is because the people who once used it found it sufficient for their purposes.  In the end, then, is there syntactic organization in the Indus script?  I am not convinced we know, although the signs are not completely random.


Aruz, J. 2003. Art of the First Cities: The Third Millennium BC from the Mediterranean to the Indus. New York: Metropolitan Museum of Art and Yale University Press.
Dahl, J.L. 2002. “Proto-Elamite Sign Frequencies” in Cuneiform Digital Library Bulletin 1: 1-3.  Available online at http://cdli.ucla.edu/pubs/cdlb/2002/001.html
Englund, R. 2001. “The State of Decipherment of Proto-Elamite” available online at http://cdli.ucla.edu , to be published in S. Houston, ed., First Writing. Cambridge: Cambridge University Press.
Gelb, I.J. 1963. A Study of Writing. Chicago: University of Chicago Press.

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.
Nissen, H.J., P. Damerow, R.K. Englund. 1993. Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East. Paul Larsen, transl. Chicago and London: University of Chicago Press.

O’Connor, D. 2009. Abydos: Egypt’s First Pharaohs and the Cult of Osiris. London: Thames & Hudson.
Pinch, G. 2006 and 1994. Magic in Ancient Egypt. London: The British Museum.
Possehl, G.L. 1996. Indus Age: The Writing System. Philadelphia: University of Pennsylvania.

Sinha, S., A.M. Izhar, R.K. Pan, B.K. Wells. 2010. “Network analysis of a corpus of undeciphered Indus civilization inscriptions indicates syntactic organization” available online at arXiv:1005.4997v1
Wells, B.K. 2010. Epigraphic Approaches to Indus Writing. Cambridge, MA: Oxbow Press.

Wieger, Dr. L. 1965. Chinese Characters: Their Origin, Etymology, History, Classification and Signification. A Thorough Study from Chinese Documents. New York: Paragon and Dover (reprint of 1927 edition by Catholic Mission Press, originally printed 1915).

Yadav, N., M.N. Vahia, I. Mahadevan, H. Jogelkar. 2008.  “A statistical approach for pattern search in Indus writing” in International Journal of Dravidian Linguistics, 37 (1): 39-52.

Friday, March 9, 2012

A Comparison of Kudurru Symbols and Indus Signs

A kudurru from the prehistoric period (Seidl 1989: 21, fig. 1, no. 5).
Note the sun, moon, and star in the top row on left, the snake in row 4.

In Science magazine, R.P.N. Rao and colleagues published a study of the conditional entropy in the Indus script (Rao et al 2009: 1165).  That is, they examine the likelihood that a given sign will be followed by any other given sign.  They also compare the conditional entropy of the Indus script with that of various linguistic and non-linguistic systems.

In this article, the authors state that symbols of deities found on kudurru – or Mesopotamian boundary stones – follow a rigid sequence that reflects the hierarchy of the deities.  In contrast, they say, Indus signs exhibit some regularity of sequencing but also evince flexibility similar to that of linguistic symbols.  In part, they conclude that this is evidence that the Indus script encodes a language. 

Their graphs show the Indus script to have a conditional entropy similar to that of known languages (Sumerian, Old Tamil, Sanskrit, and English).  But a major criticism of the study is that some of the non-linguistic data are inaccurate.  Specifically, the authors did not actually sample data on symbols of Mesopotamian gods from real boundary stones.  Relying on the “fact” that kudurru symbols are rigidly sequenced, they created an artificial data set reflecting this “fact” (based on a statement from Black and Green 1992).
Another kudurru from the prehistoric period (Seidl 1989: 23, fig. 2, no. 9).
Note star, moon, sun sequence at the top, the snake at the bottom.

But the real fact is that sequences of kudurru symbols are not as rigid as presented in the article.  This post examines the types of sequences that do occur on real kudurru, based on descriptions and illustrations of these stones (Seidl 1989).  According to Rao et al, such a reanalysis of the non-linguistic symbols on kudurru should not alter the conclusions of their study because this data set served only as a control (Rao et al 2010).  Let us see whether that is, in fact, the case.

Seidl lists 110 specific kudurru, providing either a drawing, a photo, or a description of the vast majority (1989: 19-63).  She examines 66 symbolic representations (anthropomorphic and zoomorphic symbols, depictions of objects, and scenes) through 10 time periods from the prehistoric to the Achaemenid era.  The symbols fall into various categories: astral objects (sun, moon, stars, lightning), man-made objects, plants, animals, objects bearing the head and sometimes the forelimbs of an animal (objects with protomes), hybrid beings that are composites of various animals or partly human, anthropomorphs, unidentifiable objects, and scenes.

Of the 66 representations, 21 occur in nearly periods.  This core of very frequent symbols includes the following: crescent moon (moon god Sin), sun disk (sun god Shamash), single star (Venus as the goddess Ishtar), lightning fork (thunder god Adad, Marduk, or Buriaš), spade (Marduk in another role or Šulpa’e), lamp (Nusku, god of fire and light), pedestal or base (usually with another symbol on top), horned crowns (high/sky gods Anu, Enlil, and sometimes Aššur), stylus (Nabu, the scribe god), dog (Gula, goddess of healing), striding bird (Papsukkal, a messenger or vizier among gods), snake (Nirah and/or Ištaran, formerly known as Sataran), scorpion (the goddess Išhara in the Kassite period), turtle (Ea, the water god), lion-headed staff (Nergal, god of war, or Meslamta’ea, whose function seems to be guarding doors), staff with double lion heads (Nergal, same as the previous, or else the obscure Šar-ur), eagle-headed staff (among the Kassites, Zababa, again a war god, but Šar-gaz otherwise), ram-headed staff (Ea again), snake-dragon (Marduk or Nabu), goat-fish (Ea yet again), and an item resembling the Greek letter omega (Ω) (mother goddess). 
A kudurru from the early historic period (Seidl 1989: 27, fig. 3, no. 26).
Note there are no visible astral symbols and no snake here.

Some symbols are quite rare, appearing only in a single period.  Such “singletons” include a shrine, boat, plow, dagger, twig or branch, cat, equid (horse or donkey), horse head, waterbird, woman with bird legs, scorpion-man, winged bull, cross, standard, and a scene of divinities in procession.  Other symbols may occur in only a few periods or in several, their frequency often peaking in one period while they appear only occasionally or not at all during other periods.

There is a certain amount of regularity in the positions in which the symbols occur.  Astral symbols generally appear at the top of a kudurru, although this varies somewhat.  On several of the later kudurru, the astral symbols decorate the top edge, while the same symbols appear over the other symbols elsewhere, on the same side of the stone.  Among these, the crescent moon, sun disk, and star are the most frequent.  The lightning fork may occur with the other astral symbols but it may also stand on a pedestal or base, lower down and among other symbols on bases.  The last of the astral symbols, a grouping of seven small stars probably representing the Pleiades, only characterizes a few kudurru of the two latest periods.  Seidl considers the position of the astral symbols to be due to their character, not the rank of the deities symbolized.  That is, the sky is above and the earth below, so astral symbols stand above items and beings that are earth-bound.
A kudurru from the Mesilim period (Seidl 1989: 31, fig. 4, no. 40).
Notice the snake coiled on top, with astral symbols by its head, the
moon here combined with the star (?), the sun beneath.

Man-made objects most often stand on bases, but this is not a hard and fast rule.  The lamp, for example, often seems to float in mid-air over another symbol.  During some early periods, objects seem to rise out of the back of one of the hybrid animals.  And at times a hybrid bears a pedestal on its back, with an object perched on the pedestal. 

One particularly frequent object, the horned crown – which does not appear during the first, prehistoric period – is usually duplicated, but in a few cases there are three of these side by side.  As these crowns represent high gods, they often occur immediately below the astral symbols, reflecting the divine hierarchy.  Immediately after the crowns on their bases there is often a symbol for the water god, Ea.  This may be a goat-fish (the ancestor of Capricorn), a turtle, a ram-headed staff, or a combination of two of these (sometimes including a pedestal, sometimes not).  The “omega” sometimes appears among the symbols of high-ranking gods, probably representing the mother goddess Nintu (Black and Green) or Ninhursag/Ninmah (Seidl).  Generally speaking, the sequence of other symbols appears to be less standardized.
A kudurru from the Ur I period (Seidl 1989: 39, fig. 8, no. 62).
Note the moon, sun, and star at the top and snake at the bottom.

A snake is very commonly depicted, for example, but its position is not codified.  There may be a snake coiled on the top of the kudurru, one crawling up one or the other side, or the body of the snake may underlie a whole row of symbols, sometimes with the snake’s head rising up to stand among the ther other symbols.

To better demonstrate the variability, I present images of several kudurru (my artwork based on drawings or photos in Seidl 1989).  The first comes from the earliest period when kudurru were made, the prehistoric period (1989: 21, fig. 1, no. 5).  The top row on one side bears the astral symbols (an apparent four-pointed star representing the sun, the crescent moon in its typical lazy position, and a five-pointed star for Venus).  The second row or register includes a reclining animal or hybrid, a seated dog, and a bird.  The third row has a hybrid, part man and part animal, standing upright on the far left.  Next to him seems to be the spade followed by the stylus, though it is hard to be sure of these.  The “U” shape with rumpled sides is a lightning bolt.  Next to it stands an anthropomorphic figure, perhaps a deity.  The fourth row of symbols includes a standing animal (a jackal?), a snake, a scorpion, and the lion-headed staff.  The bottom row bears a double lion-headed scepter, what seem to be two arrows or knives, two birds – one stacked upon the other – and a cross.  There are also a few symbols on an adjacent side, over the text of the inscription.  These include an unidentified animal, a peculiar symbol that Seidl terms a bundle, and a turtle, beneath which there are three birds, one on a staff.
A kudurru from the Ur III period (Seidl 1989: 47, fig. 13, no. 79).
The moon, sun, and star are more or less beside the snake here.

The second illustration is clearer, showing a disorderly grouping of symbols that are not lined up in neat rows.  Symbols include a six-pointed star (Venus), the crescent moon, and the sun disk on the upper right.  Beneath these are a lamp, turtle, and scorpion.  And below these there is a ram-headed staff, a spade, a bird on a staff or perch, a seated dog, a possible jackel over a crouching ram.  A snake holds its head up before the ram, the snake’s body lying beneath the ram and partly below the dog.  In front of the snake is a bird with the lightning bolt above it as well as a lion-headed staff.  Note that several symbols from the first example are not included in the second.  There is no standing hybrid, no anthropomorph, no double lion-headed scepter, and no arrows or knives.  Also note that the sequence of astral symbols at the top differs, although the moon is in the center in both cases.

The next kudurru comes from the second period, the early historic period (Seidl 1989: 27, fig. 3, no. 26).  Here, there seem to be no astral symbols, but much of the top of this stone has broken away.  So the sun and moon may once have adorned this kudurru as well.  What is visible is a lightning bolt in the center with a lamp to its right.  Below, there is a standing anthropomorph with one foot upon a winged snake-dragon (one of the most common hybrids).  There may be a bundle on the lower right, partly broken away.  Thus, many symbols appear to be missing, but due to the condition of the stone, it is not clear which ones never were present and which have been obliterated by time.

From the following Mesilim period comes the next example (1989: 31, fig. 4, no. 40).  The snake that was so small in the first example (fourth row) and stretched beneath some symbols on the second is here coiled on top with its head extending down among the symbols.  The text indicates that the snake is wound around a cow or bull.  Next to the snake’s head are the astral symbols, the moon taking up the lower part of a circle containing a seven-pointed star, with an eight-pointed star below.  To the left of these are two horned crowns on pedestals, representing the high gods Anu and Enlil (or Ellil).  To the left of these is the goatfish before a base with a ram protome on top, together symbolizing the god Ea.  To the left again is the “omega” on a base, representing a goddess, perhaps Nintu or Ninhursag.  Beside this is a hybrid being called snake dragon before a base with a spade on it (Marduk) followed by another such dragon before a base bearing a rectangle.  The next base has no creature associated with it and holds a triangular object adorned with dotted circles.  There follow a winged lion dragon, a lion-headed staff, a bird looking backward, an eagle-headed staff, and another winged lion-dragon, this one with apparent horns.  A second lion-headed staff is partly covered by the head of the snake.  Several symbols make their appearance here that did not occur on the previous examples: the horned crowns, the goatfish, and the “omega” are very common from this period forward.
A fragmentary kudurru from the Neo-Babylonian-Assyrian period
(Seidl 1989: 56, fig. 19, no. 97).  The sun and star are visible
on the right, with a possible fragment of the moon further right. 
The snake is possibly on the left, itstail or nose appearing alongside a break.

The next example is from the fourth or Ur I period (1989: 39, fig. 8, no. 62).  Like the first kudurru shown here, it is characterized by rows or registers of symbols, though not all are neatly linear.  Above the first row are the astral symbols, this time in the sequence moon, sun, star.  A lamp appears to the right of them despite the fact that this is not an astral symbol.  Beneath are the eagle- and lion-staffs, the seated dog, and a scorpion that floats above the baseline.  To the right of this are probably an “omega” on a base with a bird above it, though these are nearly worn away, making identification somewhat uncertain.  The second row includes a bird on a perch, a calf with the lightning bolt rising from its back, a snake dragon with a spade rising from its back, and another dragon, very small this time, with a stylus rising from it.  The last hybrid is in front of a large stepped pyramid.  The bottom row depicts the snake, whose body underlies the other symbols – this serpent sporting horns.  A goatfish with a ram-staff rising from it lies over the snake and a winged lion-dragon strides upon the serpent as well.  It is significant for our purposes to note that the snake is at the bottom rather than the top and that the goat-fish does not immediately follow any horned crowns (which are not present at all).

Skipping the poorly attested fifth period, we move on to an example from the sixth, the Ur III or Isin period (1989: 47, fig. 13, no. 79).  Some kudurru from this period have symbols neatly arranged in rows or registers, but this one does not.  The snake’s head is on top, but the creature is not coiled.  Instead, its body stretched up the side of the stone.  Beneath the snake’s head and part of its body are the three astral symbols (moon, sun, star), with two horned crowns on bases beneath them.  To the right of the crowns is a turtle over a base, representing Ea who appeared as a goat-fish elsewhere.  Further to the right is a scepter and a bird.  To the left of the horned crowns is the lightning bolt, a bird on a perch, and an arrow (moving from right to left).  These are followed by a seated dog and an “omega” without a base.  There are two horned snake-dragons – or rather the protomes of such dragons – next to bases bearing the stylus and spade.  A double lion-headed scepter floats above the second hybrid, a scorpion above the first.
A kudurru from the Neo-Babylonian-Assyrian period (Seidl 1989: 58,
fig. 21, no. 100).  The star, sun, and moon appear here on the top of
the stone.  There is no snake on this boundary stone.

Ignoring the Old and Middle Babylonian-Assyrian periods for the moment, we come to the ninth Neo-Babylonian-Assyrian period (1989: 56, fig. 19, no. 97).  This example is broken into several pieces, with some parts entirely missing.  Only two astral symbols are visible, the star to the left of the sun.  The moon may once have been further to the right but is gone now.  What is most interesting is the appearance of two very small stars to the left of the scorpion.  These small orbs are probably part of an original group of seven, representing the Pleiades (a rare symbol).  Beneath these are an eagle-staff, a scepter, a lion-staff, and two horned crowns on bases.  There may have been a stylus on a base to the right, now mostly broken away.

A more complete example from the ninth period has symbols on the top edge and down one side (1989: 58, fig. 21, no. 100).  The top bears the three astral symbols: star, sun, moon.  The lightning bolt is also there, standing on a pedestal, as well as the seated dog.  Down the side are a spade on a base, the double lion-headed staff on a base, and a lion-staff on a base.  The other side also has a single symbol, the stylus on a base.  Notice that the high gods, Anu and Enlil, are missing completely as there are no horned crowns.  Ea is also missing as there is neither a goat-fish nor a turtle.  And while the lion-staff is present, its usual companion, the eagle-staff, is missing.
The side of the same kudurru as shown above (Seidl 1989: 58, fig. 21, no. 100).

The last example shown here comes from the tenth and last period, the Late Babylonian / Achaemenid period (1989: 60, fig. 22, no. 103).  The snake lies across the top of this stone with the astral symbols beside its tail: moon, sun, star, and Pleiades (all seven stars present this time).  The scorpion is next followed by the lamp and the bird.  Beneath these are two horned snake-dragon protomes before bases, the first bearing a spade, the second a stylus.  The “omega” floats above the second hybrid’s head.  There follows the goat-fish – protome only – before a base that holds the ram-staff, both symbols of Ea.  After these hybrids there are lion- and eagle-staffs and the two horned crowns on bases.  The head of the snake on the top of the stone hangs down onto one edge, over a lightning bolt.  Beside this there is a scepter.  There are also symbols on the back of this kudurru, including the seated dog, three standards with ribbons hanging down, and three anthropomorphic figures.  The first of these apparent human holds a bow and is accompanied by a reclining snake-dragon with wings.  The second holds her (?) hands out before her and has no accompanying creature.  The third holds a ring and has a reclining lion at his (her?) feet.

A kudurru from the Late Babylonian-Achaemenid period (Seidl 1989: fig. 22, no. 103).
On the top of the stone are the astral symbols, moon, sun, and star, as well as the snake.

Thus, it is clear that the number of symbols varies from kudurru to kudurru.  Some are quite common, appearing on stones from the early to the late periods, while others appear at some point and then disappear.  The particular symbols even vary when a single god is represented.  For example, Ea may be included in the form of a turtle, a goat-fish, a ram-staff, or some combination of these – with or without a pedestal or base.  Where the horned crowns appear, they stand side by side.  But there seems to be no hard and fast rule about what stands next to them.  It is sometimes a representation of Ea (1989: 50, fig. 16, no. 84 as the ram-staff on base; p. 47, fig.13, no. 79 as the turtle); sometimes the paired eagle- and lion-staffs (1989: 60, fig. 22, no. 103); and elsewhere something different (p. 46, fig. 12, no. 75 right beside the three astral symbols).  The astral symbols tend to occur above the other symbols, but there is no fixed order within this set.  The moon may be on the left (fig. 13, no. 79), in the middle (fig. 2, no. 9), or on the right (mostlikely fig. 19, no. 97).  The eagle- and lion-headed staffs tend to occur together, but this is not an invariable rule either.  On kudurru no. 97 (in Seidl’s list), we see eagle-staff, scepter, lion-staff; on no. 98 the sequence is lion-staff, eagle-staff, scepter.

If we describe these regularities in the same terms as are used for the Indus script, we might say that there are "prefixes" here (the astral symbols).  But there seem to be no "terminals" since the end of the symbol groupings is less standardized than the beginning.  There may be some "sign pairs" such as the eagle- and lion-staffs, but these symbols also occur alone.  Some symbols may be doubled, especially the horned crowns, which recalls the doubling of certain Indus signs (such as the DOUBLE BLANKETS).  We might even describe the appearance of symbols on pedestals or bases as a kind of "ligature" -- this type of variation sometimes appearing and sometimes not.  Like signs in a true script, the kudurru symbols sometimes line up very neatly, as well, a feature that often impresses people as indicating writing.  These symbols are quite definitely not signs in a form of writing, though, and the fact that they often appear in non-linear arrangements is not surprising in view of this.  I do not think there is enough material here to repeat the statistical test that Rao et al used.  And I lack the competence to do it in any case.  But it is clear, at least, that kudurru symbols do not provide an example of rigidly sequencing of nonlinguistic elements.


Black, J. and A. Green. 1992. Gods, Demons and Symbols of Ancient Mesopotamia: An Illustrated Dictionary. Austin: University of Texas.

Rao, R.P.N., N. Yadav, M.N. Vahia, H. Joglekar, R. Adhikari, I. Mahadevan. 2009. “Entropic Evidence for Linguistic Structure in the Indus Script,” in Science (324) 5931: 1165 (doi: 10.1126/science.1170391).

_____. 2010. “Probabilistic analysis of an ancient undeciphered script” in IEEE Computer online at http://www.cs.washington.edu/homes/rao/ieeeIndus.pdf and http://www.cs.washington.edu/homes/rao/IndusResponse.html
Seidl, U. 1989. Die Babylonischen Kudurru-Reliefs: Symbols Mesopotamischer Gottheiten. Göttingen: Universitätsverlag Freiburg Schweiz, Vandenhoeck & Ruprecht (reprint, orig. 1969).

Saturday, March 3, 2012

Complex Signs in Proto-Elamite and Indus Script

Handmade replica of a proto-Elamite tablet.  Repeated symbols are numerical.
The third from the bottom on the left shows a symbol between "less than" and
"greater than" signs, a form of ligature also found in the Indus script (A + B + A).

I recently reread J.L. Dahl’s article on complex graphemes (or signs) in proto-Elamite and noted how often this author’s remarks also apply to the Indus script.  For example, he begins by noting that, although proto-Elamite was clearly inspired by proto-cuneiform, the Iranian system “exhibits a high degree of independent development of both sign repertoire and text structure” (2005: 1).  Similarly, the Indus script arose around the time that contact between the Indus Valley and Mesopotamia is documented in cuneiform, so it is quite reasonable to suggest that cuneiform (and perhaps Linear Elamite from Iran) influenced the development of the Indus script (see dates in Parpola 1994: 18).  However, even if the idea for the Indus script came from outside – from Iraq or Iran – the forms of the signs and the patterns of their use differ, indicating that same “high degree of independent development” cited by Dahl for proto-Elamite.

Dahl divides the complex signs of proto-Elamite into two basic types, with further subdivisions.  The first category is formed by the placement of a numeral in, on, or next to a non-numerical sign.  He terms these Complex Capacity Signs (CCS).  While we cannot tell whether Indus signs represent symbols for capacity, there are signs resembling CCS’s in this script.  For example, the POT acts as a terminal marker when there is nothing inside it.  But when an almost identical sign contains an apparent numeral (one to four “quotes”), the result is a ligature that behaves quite differently.  POTTED ONE, POTTED TWO, and so on are medial signs, not terminals.  Similarly, the CUP sometimes contains an apparent numeral, so there is a CUPPED TWO and a CUPPED THREE (KP signs 311 and 312). 
Seal H-76 with inscription, using a proto-Elamite transcription method, as described in this post:
(Note that the addition of a "quote" inside the "pot" changes the sign's position from terminal to medial).
In a discussion of the BLANKET sign in a previous post, I noted the hypothesis of W. Fairservis that the differing numbers of “ticks” inside the rectangle might have significance (1992: 100-101).  There are BLANKETS with 4, 5, 6, 7, 8, and 10 short strokes (“ticks”) attached to the inner top and bottom.  In addition, sometimes those with 4 such strokes also have additional strokes in the center, usually two (“dashes”).  Occasionally, the sign contains “ticks,” “dashes,” and an additional “C” shaped mark attached to one side.  Fairservis thinks it possible these represent various weights.  However, he consider it unlikely that the CUP and POT containing “numerals” represent quantities (1992: 87). Without claiming to know the purpose of such “numerical” inclusions, I merely point out the existence of Indus ligatures containing both “numerical” and “non-numerical” elements.

The second type of complex grapheme in proto-Elamite is that containing two non-numerical symbols, according to Dahl (2005: 1).  These can be subdivided into three groups, the first of which is termed framing (written A + B + A).  The second subtype is formed by placing one symbol inside another (written A x B).  The third is simply the grouping of two symbols in close proximity, one after the other (A + B).  We can symbolize several Indus ligatures in a similar fashion.  The CEE symbol, for example, can appear singly (CEE) or doubled (CEE + CEE).  Additionally, a different sign may stand between two CEES (e.g., CEE + WINGED MAN + CEE).  Since there is also a reversed CEE (BACK CEE), a symbol can also be framed by “parentheses” (CEE + BIRD + BACK CEE).  In some cases, the positions of the “parentheses” seem to be reversed (BACK CEE + SKEWERED CHEVRON + CEE).  Less frequently, one sign appears inside another (MALLET x FOOTED STOOL).  Using the same type of notation, we can rewrite POTTED ONE as POT x SINGLE QUOTE (or, more briefly, as POT x 1Q). 
Detail of seal fragment M-1106 with partial inscription, now transcribed:

Not all types of ligatures can be written with these symbols, when it comes to the Indus script.  In some cases, the choice of one transcription system over another must be purely subjective.  For example, “caging” is a relatively common qualification of an Indus sign.  If we wish to define this as framing, then CAGED MALLET consists of three signs: STACKED 2 + MALLET + STACKED 2.  But if we wish to define this as enclosing one sign in another, then the same sign becomes STACKED 4 x MALLET (because the MALLET is inside STACKED 4).  Where a POST is attached to another element by a slanted line, we might choose to “read” the group from left to right on seals, from right to left on tablets (e.g., KP 31 is MAN + SINGLE POST, or more succintly, MAN + 1P; KP 74 is 1P + PRAWN).  Alternatively, it might be better to ignore the side an attachment is on, instead always writing the name of the dominant element first, followed by the (often smaller) attached portion (MAN + 1P, PRAWN + 1P).

Indus ligatures sometimes add an element above or below the main sign as well, something not demonstrated for proto-Elamite.  We could press the symbol for division into service to represent this relationship, placing the upper element first in the “equation,” followed by the lower element.  Thus, FISH UNDER CHEVRON would become CHEVRON ÷ FISH.  Since this symbol is not on the standard keyboard, this is not convenient, however.  Since the percentage sign resembles the mathematical division sign, I suggest we use it instead: CHEVRON % FISH; TABLE % EX.
Seal L-45 with inscription, now transcribed: BLANKETx8Q / POTx1Q / FISH /

In proto-Elamite, the third type of complex grapheme consists of two signs placed side by side.  The result is not a true ligature, but “it can be established that they form a distinct semantic unit that can be replaced by a CG of the second type” (Dahl 2005: 1).  In other words, a single concept is sometimes written A x B (with B inside A) and sometimes A + B (with B next to A).  This kind of replacement of a sign pair by a ligature cannot be demonstrated for the Indus script.  Thus, it is not a good idea to write the pair with the same “+” sign used in examples of attached elements.  Instead, we can pull the equal sign into use for this.  Thus, the common pair TWO POSTS plus FISH can be rewritten as 2P = FISH.

Another complication introduced by the Indus script is the combination of three elements in a single ligature.  For example, using notation similar to that for proto-Elamite, we can rewrite CIRCLED FORK as CIRCLE x FORK.  But if CAGED CIRCLED FORK is a FORK inside a CIRCLE inside a STACKED 4, how do we write it?  It seems reasonable to simply extend the system, writing the outermost element first and proceeding toward the inside: STACKED FOUR x CIRCLE x FORK (or more succintly 4S x CIRCLE x FORK).  Similarly, CARTWHEEL IN FAT EX IN DIAMOND can be shortened to CARTWHEEL x FAT EX x DIAMOND.  Or the BOXED BI-RAKE WITH EAR can be rewritten as (BOX x BI-RAKE) + EAR, using parentheses to show that the EAR is not attached to the BI-RAKE inside the “box” but to the BOX (the outer symbol containing the BI-RAKE).  When the attachment is inside, the position of the parentheses can show this as well.  Thus, TRI-FORK & VEE IN DIAMOND becomes DIAMOND x (VEE % FORK) – the VEE and FORK touch one another, both being inside the DIAMOND, with the VEE above the FORK (KP 390).  Where the FORK attached on the outside of the DIAMOND and the VEE is inside (KP 392), the transcription differs: (DIAMOND x VEE) + FORK – the FORK is attached to the outside of the DIAMOND, which encloses the VEE.
Detail from seal M-831 with inscription, now transcribed: COMB$MAN / CIRCLEx1Q.

Occasionally, one element is placed right on top of another element, so that the two overlap.  This is sometimes seen in Egyptian hieroglyphs, where a long but short glyph crosses the median of a tall and thin glyph, e.g., D59, where the arm, D36, forms the horizontal portion of a sort of cross shape and the leg, D58, forms the vertical portion.  Often such a ligature is read as if one glyph sat next to the other.  This type of ligature appears in the Indus script in the COMB BELTED MAN, where a horizontal “comb” seems to lie right on top of the MAN’s waist.  To represent this type of combination, I suggest using the dollar sign which itself resembles the letter “S” with a vertical stroke drawn right through it ($).  Thus, the COMB BELTED MAN becomes COMB $ MAN.  The signs I term “skewered” show this type of combination as well: SKEWERED CHEVRON is thus rewritten 1P $ CHEVRON.  This same character framed by inverted parentheses (formerly SKEWERED CHEVRON BETWEEN BACK CEE & CEE) can now be rewritten thus: BACK CEE + (1P $ CHEVRON) + CEE.

In some cases, though, it may be preferable to continue referring to a complex symbol with a simple name.  The BEARER, for example, might be seen as a ligature of MAN with two CIRCLES and possibly the TABLE (as the shoulder yoke).  But BEARER is much briefer and clearer than CIRCLE + (TABLE $ MAN) + CIRCLE.  When doing so shortens some of the clumsier designations, the use of symbols +, x, =, %, $, and parentheses is useful.  When the use of such symbols obscures the unity of a sign or becomes cumbersome, a simple name is preferable.

As a final note, Dahl observes that while proto-Elamite scribes shared a common stock of symbolic elements, the system was not fully standardized, a characteristic that “allowed the scribes who wrote the proto-Elamite tablets to generate signs in an ad hoc manner when needed, usually relying on a set of basic signs” (2005: 7).  This same situation characterized proto-cuneiform as well.  It seems quite likely that it was true of the Indus script, too.  This may be the reason that (1) there are so many rare signs (they were invented on the spot and used only for a short period by a small number of “scribes”) and (2) so many signs are vanishingly rare (the vast majority occur in the Corpus fewer than 100 times).


Dahl, J.L. 2005: “Complex Graphemes in Proto-Elamite” in Cuneiform Digital Library Journal (3): 1-15. http://cdli.ucla.edu/pubs/cdlj/2005/cdlj2005_003.html

Fairservis, W.A. 1992. The Harappan Civilization and Its Writing: A Model for the Decipherment of the Indus Script. Leiden: E.J. Brill.
Parpola, A. 1994 and 2009. Deciphering the Indus Script. Cambridge: Cambridge University.