Here we continue the discussion of signs comprised of three strokes. In the Indus script, THREE QUOTES, THREE POSTS, and STACKED THREE all contain three straight vertical lines. The “quotes” and “stacked” versions sometimes seem more like dots when viewed from a distance because they are so short. Lines and dots are both among the basic phosphenes or entoptic forms I have mentioned in previous articles. The original journal article on these 15 forms was written by Max Knoll and J. Kügler (1959: 1823-1824). I have not seen it as yet, only many references to it (e.g., in Leone 2009). In Knoll and Kügler’s list as presented by Leone, lines are the fourth most common entoptic form. This much-reproduced drawing includes five lines, but I have never seen that many. My own experience has been that there are never more than three self-generated forms of any kind.
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| Medieval finger counting (from Menninger 1969: 215) |
There is one exception to this rule and that involves after images. If I look at a bright light and close my eyes, I “see” a colored dot in the darkness. This is an after image. It can also be seen with open eyes by turning and looking at a blank, pale surface such as a white wall. Now, if I move my head while looking at the bright light, then close my eyes, I will “see” a neatly arranged row of colored dots. The row matches the direction in which I moved. If I move fast enough, the colored dots merge into a line. If there are several lights, the pattern becomes more complex.
But the only way I have been able to induce a neatly ordered pattern of lines as an after image, one which resembles tally marks, is to enter a darkened room where I can see a bright light from the edge of a door slightly ajar. I stare at this bright edge for a few moments, moving my head, then either close my eyes or turn away toward the darkest area of the room. Only then do I see a neat row of colored lines as an after image. I never see such tally marks during migraines or when feeling faint. It would be interesting to know whether others do and to know how many they see. As I said earlier, I do not see more than three except very briefly, as after-images. It is the same with the dots. Three seems to be my limit, pretty much.
Knoll and Kügler apparently obtained their list of entoptic forms by stimulating their subjects’ brains with electrical current, which may make a difference. Other authors have proposed that in ancient times, shamans ingested hallucinogenic substances (such as peyote, datura, etc.) in order to obtain visions. These authors hypothesize that there is a direct connection between shamanic visions and art, in particular Paleolithic art (Clottes and Lewis-Williams 1998; Lewis-Williams 2002). If this hypothesis is correct, the earliest art was not intended to represent things in the physical world, but rather the visions of the shaman. Thus, we should expect to see many entoptic forms, including (1) curves similar to the parenthesis, but oriented in a variety of directions and nested in other curves; (2) rayed circles similar to the standard Western representation of the sun; (3) parallel wavy lines or zigzags (the usual list shows four horizontal wavy lines, stacked one over the other); (4) parallel straight lines (five vertical lines are shown in the standard list); (5) “irregular shapes” (shown as a star-like shape with six points); (6) concentric circles (a circle in a circle in a circle is shown); (7) dots (shown as very tidy rows and columns, 6 x 5); rhombs (i.e., diamonds); (9) labyrinths or indefinable shapes (shown as something like the outline of an amoeba); (10) spirals (one with three coils is shown); (11) crosses (an “X” shape is shown); (12) grids (one tilted to create multiple diamonds is shown); (13) triangles (the apex is shown at the top); (14) the shape of digits (although I would have guessed this drawing was supposed to be fire); (15) and the shape of cherries (a small circle with a curved line attached).
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| Tallies (from Menninger 1969: 241) |
Knoll is said to have done his experiments in the 1930’s in Germany. As a result, I find myself wondering whether his thousand or so subjects could have been truly representative of the whole human race. I first wonder about native Australians. Were any queried in his study? When I first mentioned this thought to someone else, she immediately asked about Eskimos. Did Knoll study any? From there, the little group I was in collectively wondered whether any San from southern Africa were included in any of the phosphene studies? Had the people of Tierra del Fuego (at the tip of South America) seen cherry shapes or triangles?
My roundish and longish floaters do sometimes come together, which perhaps might be thought of by somebody else as cherry-like. But I have to admit to a certain skepticism about triangles, rhombs, crosses, digits, or labyrinths since I see none of them. My entoptic shapes are generally not sharp at the edges but rounded, so these all seem suspiciously cleaned up. And on another note, I see a different shape when I have migraines, a chevron that grows into something like the Indus FLAIL which is not on the list at all. Why isn’t my shape in there if this list is universal? Aren’t I part of the universe? If we sampled a few Australians, might they not have a shape or two that is not on the list as well?
Leaving that alone for now, there is another little difficulty with the phosphenes-as-art hypothesis. More than one author cites Rachel Kellogg next to Max Knoll, in this connection. Kellogg studied preschoolers, not cave folk. She noted that in the scribblings of little tykes going to daycare in San Francisco, there were a lot of dots and lines and circles, quite a few zigzags, a rayed circle here and there, and perhaps a “cherry” or two, maybe even a “rhomb” or “digit.” I have been unable to access her paper either, although it too is referenced often. But I have seen a few hundred toddler-produced masterpieces, in my day. In fact, I still have a few boxes full of them in my garage and I’ve tossed at least that many in the trash when the toddlers who produced them weren’t looking, sad to say. They decked my refrigerator for a few years (the masterpieces, not the toddlers). I have a pretty good idea of what a toddler draws.
But I also have a pretty idea of what the tot is thinking, too, because I was with the tot at the time. She was first capable of two basic movements while making her masterpieces. She could beat on the paper with an up and down movement of the arm. This tends to make dots, although holding the crayon or marker at the wrong angle causes a more glancing blow, yielding a short line. Our sweet tot can also swing her arm from side to side. This may make more of a long line, or rather a whole series of lines. But, of course, at first she mostly doesn’t raise the crayon from the paper while she’s doing this. That means the lines become all one line, sort of a series of connected ovals as her arm swings back and forth, back and forth. As she gets carried away with the fun of marking up the paper, her swinging arm makes wilder swings and pretty soon the back and forth is becoming more of a round and round movement.
In essence, we have three basic possibilities for marks, here at the beginning of “baby art.” There is still the up and down movement which yields dots, more or less. And there is the back and forth which yields lines, again more or less (mostly less). Then this round and round movement yields circles (again mostly less). But these all tend to merge into one another. And she doesn’t know when to stop, so the paper gets more marks than it can handle, the marks run off the edge onto the table, and if the paper isn’t very sturdy it’s liable to rumple up and become shredded along the way. This may or may not bother the tot. It may not even slow her down. She may be just as happy to mark up the table top and forget about the dinky little old paper altogether. She has virtually no control over the marks she’s making and doesn’t really care to have any. She’s just having fun swinging her arm about and banging. She isn’t the least bit concerned with making a particular image. If I ask her what she’s drawing, she may or may not give me an answer. She hasn’t thought about that. Suppose she does give me an answer. If I ask the same question five seconds later, she may give me another answer, completely different from the first answer.
When my older tot made one such a scribble at two years, I asked – as I usually did – “What is it?”
Boobeleh pondered for a second and then announced, “A kangaroo!”
I was pleased that she knew the word although I doubted that she knew what a kangaroo was. So I wrote her name on the corner of the page, the date, and the word, ‘kangaroo.’ I fastened it on the refrigerator. The next day I pointed to it and noted that her kangaroo was there.
Boobeleh screwed up her little face and said, “That’s not a kangaroo, that’s Papa’s belt!” It was as much a belt as a kangaroo. The next minute it was Cheerios. Still later it wasn’t her drawing at all and she wanted a cookie and some cheese for her doll’s lunch. Such is the toddler’s mind.
In fact, the following day, while dotting the paper happily, the same tot got carried away again and started dotting the table beside the paper, noted that little Bubby beside the table was undotted, and began dotting his shoulder. Bubby objected with a satisfying squeak and the two of them went squawking and chirping down the hallway, she dotting him madly all the way. Later, Mama found dots on the kitchen table, dots on Bubby, lines on the wall in the hallway, a few dots and lines on the arm of the chair in the living room, some more dots and lines on the tiles of the hearth beside the chair, Boobeleh’s first neatly controlled circle on the window ledge next to the edge of the hearth, and a few more dots beside that circle. Mama also found Bubby sitting under the window with its marked up ledge, the marker in his hand, ignoring the dots on his shoulder, adding careful, little lines to his knees.
Don’t tell me those kids were illustrating their phosphenes. I know better. They were simply delighting in marking. This was a great exercise in discovery for them. The thoughts in those two little brains were these: ‘Will it mark on this? Will it mark on that? Will he make another interesting noise if I mark him again?’ Boobeleh probably tried marking the linoleum floor of the hallway and it just didn’t show up. I’ll bet you money she tried it on the rug in the living room, too, but the mark was too faint to be satisfying. She probably made a few marks on the TV screen and couldn’t see them worth a darn. Once she started marking on the window ledge, Bubby probably wrestled the thing away from her. I believe I heard louder screaming along about that time....
At a later stage of development, Boobeleh purposely drew more controlled shapes, included what looked to me like suckers, a circle on a post. These, she told me, were “bwooms.” I spent at least 10 minutes suggesting various possible interpretations of that enigmatic word – blooms, brooms, vacuums, vrooms, plumes? None were correct. It eventually turned out that she was saying “balloons.” I suppose that if one wished to take a crowbar and beat the phosphene hypothesis hard enough, little Boobeleh’s “bwooms” could be forced into category 15, “like cherries.” Knoll might still be pleased with his list. I am a bit dubious about the preschooler connection.
Boobeleh also got around to drawing more or less circular objects with lines coming out, items which one might consider examples of the “rayed circle” (Knoll’s 2nd phosphene). I thought of these as looking like Humpty Dumpty. But to Boobeleh they were early attempts at depicting regular people. She put dots and/or lines inside the roundish portion most of the time, intending to depict faces. To begin with, her idea of how many limbs and facial features did not quite match mine. But she liked me to draw things on her paper and came to match my drawings more and more exactly, as time went on.
We bought her a coloring book during this early phase. She soon colored in all of the eyes of the people and animals. She then announced that she had finished the book and was ready for another. Nothing could convince her that anything else was worth coloring. When I gave her instead what I considered scratch paper, blank on one side and with typing or writing on the other side, she never wanted to use the blank side. She inevitably drew or colored on the side with writing on it. In fact, she preferred to color right over the writing! In doing this, she was writing too, she said, just like Mama. The point of this long digression is that hypotheses are all well and good, whether concerning a connection between phosphenes and art in the preschool child or any other. But it is not enough to make the hypothesis by looking at data. We must also do a bit of testing of our hypotheses, now and then. It is a vital part of the scientific method. And be forewarned. There is always a Delta of Dirty Data out there somewhere. It is waiting for even the loveliest of hypotheses.
I mentioned earlier that 3 seems to be a sort of limit in my own phosphenes (or entoptic forms). In one study of hand prints and negatives in a Paleolithic cave, four or five seems to be a different type of limit (Clottes and Courtin 1996: 69-79). A “print” is made by putting paint on the hand and pressing it against the rock, while a negative or, in the authors’ terminology, a stencil, is made by placing the bare hand on the rock and blowing paint over it. The authors note how many hand marks there are in Cosquer cave, where, in what color, whether a print or a stencil, and how many fingers are shown. The thumb always appears in these, so the fact that not all fingers are shown is most unlikely to be pathological (i.e., lost due to disease, frostbite, or accidents). If it were, the thumb would also sometimes suffer. Thus, one or more fingers were sometimes folded under. In some cases, later on, marks were added over the hand stencil or nearly the whole thing was cut out of the wall. These are the figures for the seven categories of hand configurations as found in the cave (1996: 77):
Whole hand with all fingers intact, left 10
Whole hand with all fingers intact, right 3
Left hand, little finger folded 2
Left hand, little & ring finger folded 15
Left hand, little, ring, & middle finger folded 6
Left hand, 4 fingers folded (not thumb) 1
Right hand, 4 fingers folded (not thumb) 1
Note that only contiguous fingers are folded or held upright. In contrast, in Texas we make a different sort of hand gesture, holding up the index finger and the little finger, folding under the thumb, middle, and ring fingers. This means, “Hook ‘em horns,” indicating support for the University of Texas Longhorns, a football team. Essentially the same gesture once fended off the Evil Eye, according to one of my folklore professors (although I can’t quite remember who since I learned this in graduate school in the ‘70s). The point is, since many possible hand gestures do not appear in Cosquer, the hands look to me like simple counting. In fact, in the ESL classes I taught (English as a Second Language), most students counted in just this way, folding the little finger for “one,” the ring finger for “two,” and so on. My students considered Americans to be quite odd for starting with the thumb.
Another item of note is that the most common configuration in the hands at Cosquer is where 3 digits are up (i.e., little finger and ring finger are folded). Three is a significant number in European folklore, as evidenced by our tales of three pigs, three bears, and many in which three brothers are featured or someone gets three wishes. Of course, this configuration represents 3 only if we count the thumb, a point on which I am uncertain since the thumb is never folded under in any of the stencils. If we disregard the thumb, the same hand configuration would represent 2. That would mean that a maximum of four fingers could be held up at one time.
It is possible that “four” was the limit of counting in the Paleolithic, difficult as that may be to believe. There still exist a few languages that have no number words beyond “three” or “four” and in earlier times this may have been true of all languages. The Warlpiri, an Australian people, count only to three (Dehaene 1997:93). The Abipone, a native American people, once had words only for the first three numbers as well (Menning 1969: 10-11). Such groups have words that mean, in effect, “one,” “two,” and “many.”
This state of linguistic evolution may be reflected in the grammar of classical Greek, Biblical Hebrew, and classical Arabic which have singular, dual, and plural number for nouns. Even in Chinese, which has no noun inflection, there is a distinction in the pronouns between singular and plural and, in the first person, a third distinction. For example, “I” (wo3) is rendered plural by the addition of men (wo3-men, “we”). “You” (singular) is pluralized with the same morpheme (ni3 “you”; ni3-men “y’all”). Ta1 (“he, she, it”) is pluralized in the same way (ta1-men). In the dictionary, za2 is defined as “we (you and I); za2- men “we, us;” and only with the addition of liang as “we two” (Fenn and Tseng 1940: 536). But my Chinese friends inevitably define za-men as “both of us” or “you and me.” This division into three is not universal, however. Cherokee has a four-fold grammatical division, with singular, dual, triad, and general plural used with the fourth person or object (Holmes and Smith 1976: 313).
Nowadays, it is rare for a language to make do with such limited number words. Stanislas Dehaene and Jacques Mehler examined the frequency of number words in written texts in various modern languages. They looked at French, English, Dutch, Spanish, Japanese, and Kannada, the last a Dravidian language of southern India and Sri Lanka (Dehaene and Mehler 1992: 1-29). Regardless of the type of literature and despite cultural and geographic variation in this sample, the results were quite regular: “The most striking pattern is a regular decrease of frequency with numerical magnitude, with reproducible local increases for 10, 12, 15, 20 and 100” (1992: 20). In other words, the number “one” appears considerably more often than any other number. “Two” appears more often than all larger numbers, but less often than “one.” “Three” occurs less often than “two,” but more often than all larger numbers, and so on. The only departures from the pattern of steadily decreasing frequency occur for 10, 12, 15, 20, and 100. Converted to a graph, we see small spikes for each of these last numbers. Otherwise, it is a pretty regular downward slope.
There is another sort of pattern to be found, though. This appears in folklore. In traditional ballads and folk tales, as well as in mythological tales, certain culturally significant numbers appear considerably more often than the frequency data of Dehaene and Mehler would predict. In my study, I counted the appearance of number words in various folktale and folksong collections as part of my master’s thesis, long ago. I will present that data in Table 2 alongside data on the frequency of apparent numerals in the Indus script. Readers will then be able to judge whether the Indus “numerals” follow the normal pattern (i.e., the pattern of steady decrease in frequency with increasing magnitude of the “number,” as described by Dehaene and Mehler), or whether the pattern is more of a folklore pattern.
Before doing so, though, I must make a few preparatory remarks concerning Indus “numerals.” There are five possible types of numerals in the Indus script, the apparent numeral three being included in each type:
First, there are the short vertical strokes in a horizontal row, which I term “quotes.” In the case of three, this is III1, THREE QUOTES (also KP123a, W197, not shown as a sign in Fairservis). Second, there are long vertical strokes in a horizontal row, which I term “posts.” In the case of three, this is III2, THREE POSTS (also KP123b and KP147, W194 who gives its frequency as 140, Fairservis O-3, giving its frequency as 314). Third, there are short strokes which are stacked over one another in various configurations. In the case of three, there are two strokes over one, STACKED THREE, III3. This is KP139, W206, Fairservis P-13 (seen as a proper name). Fourth, the ROOF symbol which appears on copper objects is repeated, stacked vertically. THREE ROOFS appear in the script, a 6-stroke sign (my VI 76, KP133, not shown in Wells, Fairservis O-18). Fairservis calls it a fingernail marking, suggesting it may be an enumerator of metals and pottery, but I have no frequency data on this symbol. The fifth and last type of possible numeral is the least likely, the ligature. There are CUPS with one to four short strokes inside, for example. I term these CUPPED ONE, CUPPED TWO, and so on. In the case of these ligatures, it is not at all clear whether the included “quotes” or “posts” should be considered enumerative even if one thinks that they normally serve this function as independent symbols.
Some of the apparent numerals appear in all five forms while some only appear in one or two. Table 1 presents data on frequencies of apparent numerals in the Indus script in POST, QUOTE, STACKED, and ligatured form, drawn from Wells (1998: 136-285). Table 2 takes the totals from this and compares it data on the frequency of number words drawn from my folklore study (Gainer 1993).
Numeral | Post | Quote | Stacked | Ligatured | TOTAL |
One | 42 | 82 | -- | 333 | 457 |
Two | 115 | 481 | 2* | 45 | 643 |
Three | 140 | 75 | 11 | 35 | 261 |
Four | 4 | 34 | 1 | 83 | 122 |
Five | 15 | 21 | 4 | 2 | 42 |
Six | 2 | 1 | 21 | -- | 24 |
Seven | 0 | 4 | 38 | 19 | 61 |
Eight | 0 | 0 | 10 | 4 | 14 |
Nine | 0 | 1* | 2 | 1 | 4 |
Ten | 0 | 0 | 1* | 0 | 1 |
Twelve | 0 | 0 | 30 | 0 | 30 |
Dbl.Twelve | 0 | 0 | 9 | 0 | 9 |
Table 1. Frequencies of Apparent Numerals in the Indus Script
The data in Table 1 is amended by information from Korvink where there is an asterisk (2007: 60). As may be observed, there is some disagreement about whether 9 QUOTES or STACKED TEN ever appears, and whether the STACKED TWO truly exists (I believe the latter shows up clearly enough on the pot shard Rhd-19, more disputably on Rhd-18). Wells’ data differs from that of Korvink, but the latter took his information from a concordance while the former counted the symbols as they appeared in the Corpus. Personally, I think no two people will agree precisely. Many of the vertical strokes themselves are not entirely clear. They are often three-quarter sized and thus classifiable as either “quotes” or “posts” as the viewer judges. When it is a matter of such strokes alone on pot shards, how can one distinguish them at all?
Note that POSTS only appear for numerals from 1 through 5, with 2 and 3 being the most common, by far. Looking only at this form of apparent numeral, one would think “three” was the Harappans’ favorite number. QUOTES occur for a wider range, 1 through 7 at least and perhaps 9. Since the CUP appears so often in company with one to four POSTS, Wells once hypothesized that the CUP was a numeral. It superficially resembles the Roman numeral for “five.” But it would be astonishing if it actually meant the same thing. However, as can be seen here, there are many instances of 5 POSTS and 5 QUOTES, even if not nearly as many as there are fours, threes, twoes, and ones. There are also a great many more fives in the stacked form, usually as three strokes over two. If the CUP meant “five,” there should not be so many other forms of what appear to be clearer representations of that number. We have to admit the hypothesis of the CUP as the numeral “five” is not confirmed.
The ligatures are interesting, though. Fairservis lists the SINGLE POST twice, once as a numeral and once as a simple stick. No one else does this. But this symbol occurs more often in ligatures than in other forms. It could be that as a ligature it has some stick-associated meaning. If some person in the Indus Valley carried a staff of office, for example, the attachment of a representation of this staff might carry non-enumerative meaning associated with this office. Korvink also demonstrate that the SINGLE QUOTE is non-enumerative, a “prefix” of some sort (2007: 22-28). This is the case with the DOUBLE QUOTE as well. If these three symbols are not numerals, we must consider the possibility that others are not either.
Table 2 contains data on number word frequency from various collections of folklore: volumes one and two of Francis James Child’s five-volume work, English and Scottish Popular Ballads (1965; 113 ballads or songs that tell a story, the first variant of each assessed); German folktales (Ranke 1966; 83 tales); Russian fairy tales (Afanas’ev 1973; 178 tales); Lakota Sioux tales (Walker 1983; 13 tales); Yurok tales from California (Kroeber 1976; 156 tales), and medieval Japanese tales (Ury 1979; 62 tales). More recently, I added information from ancient Canaan (Coogan 1978, four poetic myths) and one very long Navaho mythological tale (Newcomb and Reichard 1975). Figures are in percentages, rounded to the nearest tenth of a percent. Asterisks point up departures from the normative pattern observed by Dehaene and Mehler.
Number | English | German | Russian | Lakota | Yurok | Japan | Navaho | Canaan | Indus |
One | 8.8 | 6.6 | 4.0 | 7.8 | 15.2 | 7.4 | 7.35 | 12.0 | 13.9 |
Two | 23.4 | 21.1 | 21.8 | 21.7 | 30.2 | 21.8 | 19.12 | 30.2 | 50.2 |
Three | 33.1* | 38.4* | 40.2* | 15.7 | 9.1 | 14.8 | 16.18 | 19.5 | 19.0 |
Four | 3.89 | 5.4 | 4.4 | 45.2* | 4.8 | 9.3 | 37.5* | 6.9 | 3.3 |
Five | 2.8 | 3.5 | 3.3 | 4.4 | 10.8* | 7.9 | 7.35 | 8.0 | 3.4 |
Six | 1.7 | 6.6* | 4.4* | 0 | 1.2 | 6.5 | 2.94 | 8.0 | 2.0 |
Seven | 11.3* | 5.7 | 2.1 | 0.9 | 2.4 | 9.3* | 0.7 | 12.6* | 3.5* |
Eight | 2.2 | 0.3 | 0.4 | 2.6* | 1.7 | 4.6 | 1.5* | 3.8 | 0.5 |
Nine | 1.7 | 1.9 | 3.9* | 0 | 2.4 | 1.9 | 0.7 | 0 | 0.2 |
Ten | 3.6 | 2.2 | 5.5 | 0.9 | 18.9 | 5.6 | 0 | 0 | 0.1 |
Eleven | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Twelve | NR | NR | NR | NR | NR | NR | 6.6 | 0 | 4.0 |
Table 2. Frequencies of number words in folklore (expressed as percentages) compared to frequencies of apparent numerals in Indus inscriptions (“posts,” “quotes,” and “stacked” forms combined, expressed as percentages).
Although I failed to note occurrences of the number 12 in my earlier study, it did appear. Interestingly enough, “eleven” did not, just as no apparent “elevens” occur in Harappans inscriptions. While I cannot give frequency data, I do recall that “twelves” were more common in the English and Scottish ballads than any other number higher than “seven.” For example, in The Unquiet Grave, the weeping maiden sits on her true love’s grave for a year to roust his spirit. But this isn’t how she sings it. She croons, “I would sit and mourn all on his grave / For a twelvemonth and a day” (Child 1965: 237, Vol. II, Ballad 78). The occasional doubling of this number occurs as well. In Lord Thomas and Fair Annet (Vol. II, No. 73, p. 183), we hear: “Four and twanty gay gude knichts / Rade by Fair Annet’s side, / And four and twanty fair ladies, / As gin she had bin a bride.” (In other words, 24 happy, good knights rode by Pretty Annette’s side, and 24 pretty ladies, as if she had been a bride – which she wasn’t. Shocking!)
Occurrences of an apparent 24 appear in the Indus inscriptions, accounting for some of the discrepancies between Wells’ and Korvink’s frequency data. The STACKED TWELVE is doubled in some cases (not always with any spacing, so it looks like three rows of eight). It is anyone’s guess what to make of this. If these apparent tally marks are really numerals, this would make 24. But since there is no numeral between 12 and 24, it seems unlikely that they actually function as numerals. There are a great many other oddities, too, some of which we will have to point out at in another post, as this one is far too long already.
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