Wednesday, September 15, 2010

The Mystical, Magical Number Three (Part I)

This post begins by considering the Indus signs that are made with three strokes.  The first of these, to which I assign the numerical designation III1, is THREE QUOTES or TRIPLE QUOTES.  I am ambivalent about the terminology for the apparent numerals in the Indus script precisely because these signs appear to be numerals.  If they are indeed numerals it would seem best to reflect that in the terminology.  In that case, I would reconsider previous names including SINGLE POST, SINGLE QUOTE, DOUBLE POSTS, STACKED TWO, and BI-QUOTES.  However, as noted in previous posts on these symbols, there are reasons to consider at least some of the apparent numerals to be non-enumerative.  In particular, Korvink has shown the SINGLE QUOTE and BI-QUOTES to be “prefixes” (2007).  Or, rather, the single short stroke and the double short strokes cause others to precede them at the beginning of inscriptions.  For example, the combinations VEE IN DIAMOND + BI-QUOTES and CARTWHEEL + BI-QUOTES are commonly found in initial position.
Even if we delete the “single quotation” and “double quotation” (as Korvink terms them) from consideration, the other apparent numerals are not necessarily enumerative either.  As noted previously, other ancient writing systems sometimes use strokes in non-enumerative ways.  In Egyptian hieroglyphs, Z2 is Gardiner’s designation for three vertical strokes, for example.  This collection of strokes is a determinative for plurality, used from Dynasty IX onwards.  Earlier, three glyphs often indicate plurality. 
Lady 4 Death gives birth (Mixtec proto-writing from Nuttal codex)

For example, if a scribe wished to denote the plural of the ka (one of the Egyptian souls), he would write the ka glyph three times.  By Dynasty VI, he was substituting the ka glyph (two raised arms joined by what appear to be shoulders without a head) followed by three little circles.  Three circles were an early plural marker, in other words.  By Dynasty IX this became the ka glyph followed by three vertical strokes.  Since the sound of the plural involved the semi-consonant w, by the time of Middle Egyptian the same three vertical strokes also could indicate that sound even when it was not part of the plural.  The triple strokes appear most often in a horizontal row but also occur in a vertical column, or, in my terms, as a “stacked three.”

Egyptian numerals (left); Roman numerals (right) (from Menninger 1969: 42)
In Old Chinese, three horizontal strokes represent the numeral three and the word, san1.  This numeral has not changed in modern Chinese except that in business style the strokes can become vertical (Fenn and Tseng 1940: xxxv).  There is no grammatical plural in the language, but three items are often grouped together to convey an abstract notion of plurality in a compound character in a non-enumerative symbol.  For example, three stacked slashes represent hair, feathers, etc. in shan1, the 59th radical (Wieger 1965: 162).  The character pin3 comprises three symbols for the mouth, one over two in a line, and is described thus: “Disposition by order and degrees, graphically represented by the disposition of three elements, taken for a multitude.  [The mouth] is used as a sign and has no meaning” (Wieger 1965: 182).  The same three mouths “repeated three times in the same line,” is ling2, “Noise of voices” (op cit.).  A character including three trees, one over two, is shen1, “a great number of trees, and by extension, a great number in general” (Wieger 1965: 279).  Two trees in a single character, side by side, is lin2, “a forest, a clump of trees” (1965: 278). 
In Chinese, it is thus common to find a single element repeated within a character as many as four times without enumerative meaning.  That seems to be the limit, though.  An exampleis yu4, a park, including four trees in stacked position, two over two, inside a square divided by a vertical and horizontal (that is, four trees inside a symbol resembling the Indus WINDOW).  There are four mouth characters, stacked again two over two, in the character qi1, “many mouths, clamours” (Wieger 1965: 183).  Three repetitions appear to be more common than four and two more common than three, but I have not made a systematic count.  When I do, I will report it in a later blog.  There are no instances of five repetitions of an element in a single character, to my knowledge.
Both proto-cuneiform and proto-Elamite include various representations of the number three.  In these cases, it is certain that numerals are indeed intended.  An in-depth study of ancient accounting in the Near East reveals a variety of enumerative symbols and complexities that I will not attempt to go into here (Nissen, Damerow, and Englund 1996).  Suffice it to say that scribes used straight lines as numerical symbols but also many other types of signs.
In Mixtec proto-writing, the smaller numerals are represented by circles rather than lines.  The circles are ubiquitous in codices where they appear in people’s names.  The most common type of name was essentially a birthday.  The Mixtecs followed a calendar including 20 “months” of 13 days each.  The 20 “months” are as follows: Alligator, Wind, House, Lizard, Serpent, Death, Deer, Rabbit, Water, Dog, Monkey, Grass, Reed, Tiger, Eagle, Vulture, Movement, Flint, Rain, and Flower (Smith 1973: 24-25).  A person was named according to the number of the day and the name of the “month” on which he or she was born.  Thus, an individual might be called 6-Lizard, 8-Deer, 12-Water, etc.  The number in this combination is represented by the appropriate number of small circles, as shown in the accompanying illustration.  The other part – the lizard, deer, or water – is depicted in a non-standardized manner by something approaching a hieroglyph.  Often an animal is represented by its head alone.  But on occasion the whole animal is shown.  Elements such as water, wind, and movement are not as recognizable because of the highly stylized manner of representation.  For someone familiar with the norms of this tradition, presumably there would have been little difficulty in interpreting even these more abstract glyphs.
In the illustration shown, a detail from the Nuttall Codex, Lady 4-Death, also known as “Jewel” is giving birth to little Sir 13-Dog, later also known as “Eagle-Venus Sign” (Smith 1973: 223c).  The four circles in the upper left relate to the mother’s birthday while her birth “month” is part of her headdress.  Her bouncing baby boy’s numerical symbol is not shown here.  The curlicue between Mama’s face and her four is a representation of speech, although the specifics of her conversation on this occasion are not known.  I suspect she was saying the Mixtec version of “Owie!”  In connection with the number three, note that little 13-Dog has only three fingers on his left hand.  This anomaly occurs on occasion in these codices.  Feet, hands, and footprints (the latter indicating journeys and visits) generally have the appropriate five digits.  But occasionally they sport an additional one or two digits and just as occasionally they are missing one or two.  Thus, while the Mixtecs evidently could count, as shown by their numerical names/birthdays, it seems that they didn’t always bother. 
I note this with a certain warmth of feeling because, once upon a time, certain preschoolers of my acquaintance adorned their Humpty-Dumpty-like drawings of people with the same semi-accurate numbers of digits.  The egg-like people generally had only an approximately correct number of fingers, with sometimes one or two too many, sometimes lacking one or two.  At the time, the budding artists could not count, unlike the Mixtecs.
Let us move on to the rock art of the Americas further north.  Here, we find that lines which seem to be tally marks appear fairly often.  In the collection from Texas, I see what appears to be a group of three over a row of 14 shorter strokes (Newcomb 1996: 94, Pl. 53, no. 1).  There may actually be a fourth stroke just to the left of these, very faint.  There is also a more clearly grouped set of three vertical strokes to the left of a hut-like object (1996: 96, Pl. 54, no. 1).  Further west, the same motif appears quite clearly (Heizer and Baumhoff 1984: 188, fig. 125i).  Lines are common in Australian rock art but it is difficult to state with certainty that any particular number go together as opposed to other elements.  There are also sets of dots that appear to be lined up.  Dotted lines also occur as an engraved motif at Sundown Point in northwest Tasmania (Flood 1997: 233).  In both areas, Australia and Tasmania, the impression I get is that these lines and dots are not tally marks (for what that is worth).

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