Thomas H. Lewis 2602 East DesertCove, Phoenix,Arzona 85028

Counts,Coups, and :Evidence of Notational Systemsin the Pictographic/PetroglyphicRecord

Abstract

Count marks or tallies are connon in the iock art oflh€ Northern Plains.Analysis of eighteensites on the niddle Yello{stone Riv€r, including somepehoglyphic r€cordsof considerableconplexity, is consist€ntwith a notntionalsysten ofunits and pairs. No int€rnal evidence of ordering, sequencing,or furiher aithn€tical evolution is yet discernibje.

lntroduction setsof 20 (vegesimal),or can other cornbinatory methodsbe descried?As an initial effort. 87 oic- Rock art on the Northern High Plains has been tographipe troglyph sites were recorded in deiail. describedas symbolic or representational,bio- Of thesel8 had count marksof somekind. graphic,or ceremonial.That it may alsobe nota- tional and ideographichas receivedlirtle atten- The Tally Mark and the Originsof tion, Iargely becauseof the lack of a sufficient amount of comparative material. A survey of The keeping of counts has been a human con- knownand newly-discoveredsites in south-central c€rn acrossrnillennia. Perhapswhat began an "how Montanain l98l-1984 alleviatesthis scarcityand aide-memoirand an anslverto the question leadson to problemsin interpretalion. many," becamean end and a pleasurein itself, a mental product with a magic and reality all irs Rock art productions frequently include a own. Cultures became reflected in what was "counts," "coups," "tallies" series of or counted and what waEnot. Marshak (1972)de- associatedwith a representationalor symbolic scribedengraved count marks on bodeand antler theme.These tallies may be obscureand easily from the EuropeanPaleolithic and found thern overlooked,or they may be clearly delineated congruent with lunar observation.The Maya, although enigmatically related to the other preoccupiedwith time and its divisions,elabor- glyphs.When associatedwith battle scenesrhey ated with dot ("one") and far ("five") into a might, for example,signify coup markers,kills, numerical systemwith conceptsof completion or enemiesinyolved. When associatedwith hunt- and zero.the ability to calculatein time units ing, animals,or symbolicglyphs, other numerical of 64,000,000precise lunar-solar-venusian calen- evaluationsare possible.With little justification drics, a numericalfoundation for the component tallies havebeen called day counts,year counrs, namesof men and deities, and intricate books moon calendars,or astronomicalnotations. The of divinationbased on dates(Thompson l9?l). marksmay haverepresented some non-arithmeti- Modern Europeanmathematics seems to have cal idea,but the cultural provenanceof manypic- begun with the stick ("tally") ard sim- "sets" tographsand petroglyphsis unknown,and there ple (scores,hundreds, etc.), as Shake- are no coevalterls, Thus. their meaningmay speareremembers in Henrl VT(2)Act 4 Scene7, never be establishedby external data, We are "our ancestorshad no otherbooks but the score limited to such internal information we can and tally." The Perriar. ar'd chimpu, us- discernin the glyphsthernselves. This discussion ing knotsor beads,achieved a similaraccount- is basedupon the presumptionthat countmaiks ing systembased on units,tens, hundreds, and may be arithmetic.A minimal interpretationrule thousandswhirh scrved the needs of an empire suggeststhat perhapsa notationalsystem of some (Menninger1969). The addition of a wrre on kind is beingrepresented. and on examination which beads could slide and a mechanismfor of a numberof examplesmay allow somehypoth" keepingtrack of setsas well as units produced esesabout aboriginal numerical ideas-for in- the versatileabacus. Much encouragementthat stance,are counts unitary, , or basedon count or tally marksin pictographsmight reflect

Counts,Coups, and Tally Marks in Pictographic/PetroglyphicRecord 243 "counts." alr arithmetic notational systemcomes from the seriesof l2 Adjacentpanels, now dim, meticulous analysis by Glossen and Marshak have many barely-discernibleseries of parallel (1974)of a Chamulacalender board on which the arrowsand guns, and a seriesof 35 vertical "tallies" day counters,vertical lines of equallength and eachabout 60 cm. long. spacing,are arrangedin horizontal series,much Anothercombat between a mountedman and "tallies" like thoseat 245T560in our sample. one afoot at 24GV557(Fig. 2) has 13 pattern.A hand-to-hand In order that the descriptive material from arrangedin a slanting 24YL4lB(Fig. 3) hasa superscript the Yellowstonesites may receive principal at- encounterat deeply-carved"tally marks." At 24YL70 tention in this discussion,a review of the con- of three (Fig.4) armedmen standbefore a double tinental or world-widepictographic record is three of count marks,joined at the endsby vertical deferred.The varietyof presentationand inter- set (Fig.5) large count marks pretationpresents a majortask in synthesisand lines. At 24ST403 smallfigures engaged in bearhunting suggeststhat an intensiverather than com- dominate 24\L434 (Fig. 6) a group prehensiveapproach may be moreilluminating. and horse-riding.At men ride towarda tallyseries. At Alsodeferred is the complexissue of the cultural of four armed the cliffsbear a profusionof painted affiliation of rhe artists who producedthe draw- 24ML563 incisedglyphs in severalstyles. Interspersed inss we vill examine.More than a scoreof tribes and setsof "tally marks," alsoin several ar; knor'ento havehunted acrossthe Northwest' areseveral styles(Fig. 7). ern Plains(Ewers 1968). A summaryof picto- graphipetroglyphchronologies is providedby The bearpanel at 24YL4l9 (Fig.8)contains Sundstrorn(I984 p. 137-140).In the geographic almost-terminally-erodedbears and shield' boundsof our study,namely the middlereaches bearingmen mixedrrith othersthat appeallo of the YellowstoneRirer. several invesligalors be later,almost-fresh additions. There is an ad' "superscripr" have addressedcounls and counting.Mulloy joining panelfilled with faintly (1958 p. 139) illustrated without discussion visiblecount marks (not figured). the top series "coup several series" of marks and glyphs. with tenvertical bars, each 20 cm.,in a horizon' Secrist(1960 p. 8) describeda seriesof figures tal series.Below is a sirnilarrow of22 marks,each which may ultimately be shown to have an 30 cm.tall, with a crudelyoutlined bear's head. arithmeticalsignificance. Conner and Conner At Pillar Creek(Fig. 9) a man (inverted)wirh (1971p. 27-34)were among the first to discuss a lance standsbeside two smaller figures and a lhe o.currenceof rounls and figures-in-series. continuingrow of2l objectswhich look like guns. Keyserand Knight (1976p. 608)noted that tally Just above, four figures, two of which are in- markswere the mostcommon pictographic motif completeand anotherwhich lookslike a death "hair- in westernMontana and describeddot seriesand bundle are in horizontal serieswith four their possiblemeaning. Keyser and Sundstrom pin" (count rnarksconnected at the top in pairs) (1984)give many excellent reproductions of count and elevencount marks(pairs and units?).A red seriesin the BlackHills and a brief discussion pictographat 24C8630(Fig. l0) showsmore of tally marks (p. l9). Beyond the presumption clearlyan effort to usesets. Series of 16 dots, that count markswere somehow numerical these placedhorizontally on an alcovevall is then authorsavoided an anallsisof meaning. repearedin 8 paireddots. Below 4 dotsare placed plus shapedfig- What werethe nomadichunters of rhe Plains in a vertical line, tto half-moon perhaps?indicating a lunar count. countingif that is what they weredoing? How ures, "heraldry" elaboratedid their systembecome? Are their A panelof incisedpetroglyphs at petroglyphmarks recordinganything more than 24YL4l9 (Fig. I l) is of countand symbolinterest. "one countequals one thing"? Let us beginto At bottom left are two men in combat.Associated Iookfor answersin whatseem to be the simpler are two horizontalseries and 37 lance-likeob' examples.A battle sceneat 24YL600(Fig. l) jects and one gun, Somefew of theseare un- looksout over the YellovstoneRiver. Three rnen adorned,but the rest have modifying details, with shieldsare assailed by guns,spears, and ar' noneof which are identical.These include ornate "tally "fans," "feathers," rows.0n the left are 75 marks" associated projectilepoints, varied' with two enigmatic marks.On the right is a shape pendants, and perhaps individual

Lewis "medicine" or clan markers.The overalleffect 24\L4O2, 24yL600, 24yL1190 arLd 24YL419, to the moderneye is of a hand-to-handcontest wherethey wind through the "action" of the in the presenceof a host of namedindividual scene,and at 24yL'704where they are depicted observers,something like a heraldictourney or in squaredgroups. the panoplyof the Field of the Cloth of Gold. The pictograph at 245T560, as noted, sug- In any case,the glyphic paneldoes concern itself gestsa solarnotation, while that at 24C8630on with an accounting,of somekind, of similarbut similarlyIimited grounds, provokes question of recognizablyindividual objects. a lunar record.Another, 24CB4l6 (Fig. l7 photo- A deepalcove 245T560 in the upperreaches graph)was pointed out by a landorvnerwithin the "The of Big CouleeCreek has a panelof blackcount former rese ation boundary. Crowused marks(Fig, l2) which,are well-protectedfrom the to call it a mooncalendar," he said.The glyph weatherand exposedto sunlight only at the mo- seemedto be a numberrecord laboriously pecked mentof sunset,and givean impressionof antiq- into extremelyhard sandstone. It wascomposed "units" uity. The panel is 276 crn. long, with 46 vertical of of regular,carefully-formed, carefully- bars,each 30 cm. Somehave an enlargedhead, spaced,short, double,horizontal lines. These others a bent foot. They were painted in black, werein two verticalseries, beginning 1.35 cm. evenly,without drip or run. The "brush" may abovethe cliffbase.One series, extending 90 cm., havebeen a fingertip,or an implementof com- had 23 of the double-horizontalunits. The other parablesize, The regularityof rendition suggests series,inclined slightly from the vertical,has l7 "units." that they weredone in one "sirting," (i,e.they Belowwas a serpentinepecked figure do not seemto be accumulatedover time).Small which seemedto representa horneddancer. interstitial figures include five tailed circles, seven"horse hoof-marks" twenty-four "dots," Discussion four open squaresor circles.Aboye are fourteen "Tally" or "count" marks are common in the X marks,this seriesbeing interupted by water Plainsperroglyphic record. Do they indeedrepre- damageand possiblybeing eighteen in sentan arithmeticalnotation and the mentalpro- originally. The "coefficient glyphs" or "sub- cesseswhich adumbrate it, or is the artist il- sidiarynotations" are enigmatic,as are permuta- lustratingsome other idea,quite unknovn to us? tions of 46 and 14 or 46 and 18. The cave If they are counts, what is being counted and overhangshades this giyph panel all day until rhy? In someglyphs the intendedcommunica- ju6t at sunset,and a rounded treelesshill due tion seemsto be "how many" tipis or gunsor west cuts off the sunlight a few moments later men, but there is no evidenceyet discernedof (on l0 September1983). No sighting mark r,vas ord,eringor sequencilrgof units, the next expect- evidentto suggestthat solarequinoctial declina- ablestep in a number system.A third expectable tions werebeing observed,although the position step,a grouping of tumbers, seemsto be shown wasexcellent for that purpose.The accompany- in two of our samplesby wayof pairsor "count- ing (alsoblack) pictographs,some meters away, ing by two's." It is unfonunatefor the hypothesis includea pair of humansin copulation,a man of a notationalsystem that proof most likely will with spearand shield,a verticalseries of eleven come, if at all, from internal evidenceof the horizontal count marks, and a very nearly glyphsrhemselves. We can,so far, only presume obliteratedmounted spear-bearer. for working purposesa rudimentarycounting de- Someancient artists, instead of single-marks vice of one mark for one object, with no further or tally strokes,used a seriesof depictionsof the conceptualevolution, as in Mesoamerica,of nota- objectsthemselves. At 24ML562(Fig. l3) men are tional sophistication;i.e., sets more complexthan "counted" by presentingrows of conventional- pairs, glyphic number conventions,calendric ized man-figures.At 24yL82 (Fig. 14) a super- ideas,narning sequences, phonetic equivalents scriptabove a spiritedbattle is a row of eleven or time units.The very large number ofsites yet tipis.At 24YL4l7(Fig. l5) a groupof scvenguns to be analyzed,dated, and understood,and in- hangsover another battle scene.Ro\ys of horse deed yet to be discovered,may alter this hoofprints, perhaps counts, perhaps trails or appraisal. directionindicators, occur at 24YL1189(Fig. l6),

Counts,Coups, and Tally Marks in Pictographic/PetroglyphicRecord Sites Described 24CB4l7 Kraus 24\L434 Horse-House 24CB630 Bear Two Shield 24\LB2 Manual Lisa 24YL4l7 Doctordic 24\L419 Nordstrom-Bowen 24YL704 Chief Joseph 24YL\190 Pillar 24\L402 Alkali Creek South 24CV557 Northside 24YLll89 CanyonCreek 24ST403 Molt 24YL600 Custer 245T560 Weppler #2 24YL4IB Castle 24ML563 Signal Mountain 24YL70 Rossell 24ML562 30 Mile Station LlteratureCited

Conner, S. W., and B. Conner. 1971. Rock art of th€ Monrana lligh Plains. University of California Press,Santa Barbara. Ewerc,J. C. I 7. Vas There a Northwesre.nPlsins Subculture? An EthnographicalAppraisal. Plains Anrhropologist 12{36):167-174. Go$en, G. H. 1974.A Chamula Calendar Board fron Chiapas,Mexico. 1n Ncnan Hanmon (ed.)Meso-Anerican Archeology: New Approaches.1972. University of Texas Pr€ss,Ausrin. Pp. 2t7.254. Keyser,J. D., and G. C. Knishr. 19?6.The RockArt of WesternMontana. Plains An*ropolosist 2l(71):t-12. Keyser,J. D., and L. Sundstron. 1984.RocI Art ofVesrern South Dakota:The North CaveHills and rhe southernBlacl Hills. Spec. Publ. South Dalola Archeological Society,No. 9, pp. 142. Maller/, G. 19?2.Picture Writing of $e American Indians. Dover PublicationsReprinl of loth Annual Reporr of tbe Bureau of tunerican f,thnolosy. Marshak, A. 1972. Upper Pal€olithic Notation and Symbolisn. Science178:81?,28 . l9?2. The CharnulaCalendar Board: Ar internal and comparativeanalysis. /r Norman Hammon(ed.) Meso-Amencan Archeology: New Approach€s,1972. Uniyersity of Texas Press,Austin. Pp. 255-270. M€nninger, K. W. 1969.Number Words and Number Synbols: A culrural hisrory of nunbers. M.I.T. Press,Boston. Pp. 480. Mulloy, W. 1958.A Preliminary Historical outline for the NorihwesternPlains. Universiry of Wyoning Publications,Laramie. Secrisi,K. G. 1960.Pictographs in Central Montana, Parr l. Anthropologicaland Social PapersNo. 20. Uniyersiiy of Monrana, Missoula. Thompson,J. E. S. I971. Maya HieroglyphicWriting. Cirilization ofthe Anedcsn Indian Series,Vol.56, UniversiryofOklahoma Press,Nornan. Pp. 343.

Receiued9 August 1985 Acceptedfor publication 26 December 1985

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Counts,Coups, and Tally Marks in Pictographic/PetroglyphicRecord 249