Thomas H. Lewis
2602 East DesertCove, Phoenix,Arzona 85028
Counts,Coups,and Tally Marks:Evidenceof Notational
Systemsin the Pictographic/Petroglyphic
Record
Abstract
Count marks or tallies are connon in the iock art oflh€ Northern Plains.Analysisof eighteensites on the niddle Yello{stone
Riv€r, including somepehoglyphic r€cordsof considerableconplexity, is consist€ntwith a notntional systen ofunits and pairs.
No int€rnal evidence of ordering, sequencing,or furiher aithn€tical evolution is yet discernibje.
lntroduction
Rock art on the Northern High Plains has been
describedas symbolic or representational,biographic,or ceremonial.That it may alsobe notational and ideographichas receivedlirtle attention, Iargely becauseof the lack of a sufficient
amount of comparative material. A survey of
knownand newly-discovered
sitesin south-central
Montanain l98l-1984 alleviatesthis scarcityand
l e a d so n t o p r o b l e m si n i n t e r p r e t a l i o n .
Rock art productions frequently include a
series of "counts," "coups," or "tallies"
associatedwith a representationalor symbolic
theme.Thesetalliesmay be obscureand easily
overlooked,or they may be clearly delineated
although enigmatically related to the other
glyphs.When associatedwith battle scenesrhey
might, for example,signify coup markers, kills,
or enemiesinyolved.When associatedwith hunting, animals,or symbolicglyphs,other numerical
evaluationsare possible.With little justification
tallies have been called day counts,year counrs,
moon calendars,or astronomicalnotations.The
marksmay haverepresentedsomenon-arithmetical idea,but the cultural provenanceof many pictographsand petroglyphsis unknown,and there
a r e n o c o e v a lt e r l s ,T h u s .t h e i r m e a n i n gm a y
never be establishedby external data, We are
limited to such internal information we can
discernin the glyphsthernselves.
This discussion
is baseduponthe presumption
that countmaiks
may be arithmetic.A minimal interpretationrule
suggeststhat perhapsa notationalsystemof some
k i n d i s b e i n gr e p r e s e n t eadn. d o n e x a m i n a t i o n
of a numberof examplesmay allow somehypoth"
esesabout aboriginal numerical ideas-for instance,are countsunitary,decimal,or basedon
setsof 20 (vegesimal),or can other cornbinatory
methodsbe descried?As an initial effort. 87 oictographi
petroglyphsiteswererecordedin deiail.
Of thesel8 had count marks of somekind.
The Tally Mark and the Origins of Arithmetic
The keeping of counts has been a human conc€rn acrossrnillennia. Perhaps what began an
aide-memoirand an anslverto the question"how
many," becamean end and a pleasurein itself,
a mental product with a magic and reality all irs
own. Cultures became reflected in what was
counted and what waEnot. Marshak (1972) describedengravedcount markson bodeand antler
from the EuropeanPaleolithic and found thern
congruent with lunar observation.The Maya,
preoccupiedwith time and its divisions,elaborated with dot ("one") and far ("five") into a
numerical systemwith conceptsof completion
a n d z e r o .t h e a b i l i t yt o c a l c u l a t e
in timeunits
of 64,000,000preciselunar-solar-venusian
calendrics, a numericalfoundationfor the component
names of men and deities, and intricate books
of divinationbasedon dates(Thompsonl9?l).
Modern Europeanmathematicsseemsto have
begun with the counting stick ("tally") ard simple "sets" (scores,hundreds, etc.), as Shakespeareremembers
in Henrl VT(2)Act 4 Scene7,
"our ancestors
had no otherbooksbut the score
and tally." The Perriar. quipu ar'd chimpu, using knotsor beads,achieveda similar accounting systembasedon units,tens,hundreds,and
t h o u s a n dws h i r hs c r v e dt h e n e e d so f a n e m p i r e
(Menninger1969).The addition of a wrre on
which beads could slide and a mechanismfor
keepingtrack of setsas well as units produced
the versatileabacus.Much encouragement
that
count or tally marksin pictographsmight reflect
Counts,Coups,and Tally Marks in Pictographic/Petroglyphic
Record
243
"counts." Adjacentpanels,now dim,
seriesof l2
have many barely-discernibleseriesof parallel
arrows and guns, and a seriesof 35 vertical
"tallies" each about 60 cm. long.
Anothercombatbetweena mountedman and
"tallies"
one afoot at 24GV557(Fig. 2) has 13
arrangedin a slantingpattern.A hand-to-hand
In order that the descriptive material from
encounterat 24YL4lB(Fig.3) hasa superscript
the Yellowstonesites may receive principal at"tally marks." At 24YL70
of three deeply-carved
tention in this discussion,a review of the con(Fig.4)
men
standbeforea double
armed
three
tinental or world-widepictographicrecord is
joined at the endsby vertical
marks,
of
count
set
and interdeferred.The varietyof presentation
lines. At 24ST403(Fig.5) large count marks
pretationpresentsa majortaskin synthesisand
dominatesmallfiguresengagedin bearhunting
comsuggeststhat an intensiverather than
and horse-riding.At 24\L434 (Fig. 6) a group
prehensive
approachmay be moreilluminating.
of four armedmen ride towarda tally series.At
Alsodeferredis the complexissueof the cultural
24ML563the cliffs bear a profusionof painted
affiliation of rhe artists who produced the drawand incisedglyphsin severalstyles.Interspersed
a
score
of
tribes
More
than
inss we vill examine.
"tally marks," alsoin several
are severalsetsof
ar; knor'ento have hunted acrossthe Northwest'
styles(Fig. 7).
ern Plains(Ewers1968).A summaryof pictoThe bear panelat 24YL4l9 (Fig.8) contains
provided
by
graphipetroglyphchronologiesis
bears and shield'
almost-terminally-eroded
(I984
geographic
p.
In
the
137-140).
Sundstrorn
bearingmen mixed rrith othersthat appeallo
boundsof our study,namelythe middlereaches
additions.Thereis an ad'
o f t h e Y e l l o w s t o nRe i r e r .s e v e r ailn v e s l i g a l o r s be later,almost-fresh
"superscripr" panel filled with faintly
joining
Mulloy
have addressedcounls and counting.
v i s i b l ec o u n tm a r k s( n o tf i g u r e d )t.h e t o p s e r i e s
(1958 p. 139) illustrated without discussion
"coup series" of marks and glyphs.
with ten verticalbars,each20 cm.,in a horizon'
several
tal series.Belowis a sirnilarrow of22 marks,each
Secrist(1960p. 8) describeda seriesof figures
30 cm. tall, with a crudelyoutlinedbear'shead.
an
to
have
which may ultimately be shown
arithmeticalsignificance.Conner and Conner
At Pillar Creek(Fig. 9) a man (inverted)wirh
(1971p. 27-34)were amongthe first to discuss
a lance standsbesidetwo 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 inmarkswerethe most commonpictographicmotif
completeand anotherwhich lookslike a death
"hairin westernMontanaand describeddot seriesand
bundle are in horizontal serieswith four
their possiblemeaning.Keyserand Sundstrom
pin" (count rnarksconnectedat the top in pairs)
(1984)givemany excellentreproductionsof count
and elevencount marks(pairs and units?).A red
seriesin the Black Hills and a brief discussion
pictographat 24C8630(Fig. l0) showsmore
of tally marks (p. l9). Beyond the presumption
clearlyan effort to use sets.Seriesof 16 dots,
that count markswere somehownumericalthese
placed horizontallyon an alcovevall is then
a u t h o r sa v o i d e da n a n a l l s i so f m e a n i n g .
repearedin 8 paireddots.Below4 dotsare placed
in a vertical line, plus tto half-moonshapedfigWhat werethe nomadichuntersof rhe Plains
ures,perhaps?indicatinga lunar count.
countingif that is what they were doing?How
A "heraldry" panel of incisedpetroglyphsat
elaboratedid their systembecome?Are their
(Fig. I l) is of count and symbolinterest.
24YL4l9
petroglyphmarks recording anything more than
"one count equalsone thing"? Let us begin to
At bottom left are two men in combat.Associated
are two horizontalseriesand 37 lance-likeob'
Iookfor answersin what seemto be the simpler
jects and one gun, Somefew of theseare unexamples.A battle sceneat 24YL600(Fig. l)
adorned,but the rest have modifying details,
looksout over the YellovstoneRiver. Three rnen
noneof which are identical.Theseincludeornate
by guns,spears,and ar'
with shieldsare assailed
"fans," projectilepoints, "feathers," varied'
"tally marks" associated
rows.0n the left are 75
shape pendants,and perhaps individual
marks.On the right is a
with two enigmatic
alr arithmetic notational systemcomesfrom the
meticulous analysis by Glossen and Marshak
(1974)of a Chamulacalenderboard on which the
day counters,verticallinesof equallength and
spacing,are arrangedin horizontal series,much
like thoseat 245T560in our sample.
Lewis
"medicine" or clan markers.The overalleffect
to the moderneye is of a hand-to-hand
contest
in the presenceof a host of namedindividual
observers,
somethinglike a heraldictourneyor
the panoplyof the Field of the Cloth of Gold.
In any case,the glyphic panel doesconcernitself
with an accounting,
of somekind, of similarbut
recognizablyindividualobjects.
A deepalcove245T560in the upperreaches
of Big CouleeCreekhasa panelof black count
marks(Fig, l2) which,are well-protected
from the
weatherand exposedto sunlight only at the moment of sunset,and givean impressionof antiquity. The panel is 276 crn. long, with 46 vertical
bars,each30 cm. Somehavean enlargedhead,
others a bent foot. They were painted in black,
evenly,without drip or run. The "brush" may
havebeena fingertip,or an implementof comparablesize,The regularityof rendition suggests
that they weredonein one "sirting," (i,e.they
do not seemto be accumulatedover time).Small
interstitial figures include five tailed circles,
seven"horse hoof-marks" twenty-four "dots,"
four open squaresor circles.Aboye are fourteen
X marks,this seriesbeing interupted by water
damageand possiblybeing eighteenin number
originally. The "coefficient glyphs" or "subsidiary notations" are enigmatic,as are permutations of 46 and 14 or 46 and 18. The cave
overhang shadesthis giyph panel all day until
ju6t at sunset,and a rounded treelesshill due
west cuts off the sunlight a few moments later
(on l0 September1983).No sighting mark r,vas
evidentto suggestthat solar equinoctialdeclinations were being observed,althoughthe position
wasexcellentfor that purpose.The accompanying (also black) pictographs,some meters away,
includea pair of humansin copulation,a man
with spearand shield,a verticalseriesof eleven
horizontal count marks, and a very nearly
obliteratedmountedspear-bearer.
Someancientartists,insteadof single-marks
or tally strokes,useda seriesof depictionsof the
objectsthemselves.
At 24ML562(Fig. l3) men are
"counted" by presentingrowsof conventionalized man-figures.At 24yL82 (Fig. 14) a superscript abovea spiritedbattle is a row of eleven
tipis.At 24YL4l7(Fig. l5) a groupof scvenguns
hangs over another battle scene.Ro\ysof horse
hoofprints, perhaps counts, perhaps trails or
directionindicators,
occurat 24YL1189(Fig.l6),
24\L4O2, 24yL600, 24yL1190 arLd 24YL419,
where they wind through the "action" of the
scene,and at 24yL'704where they are depicted
in squaredgroups.
The pictograph at 245T560, as noted, suggestsa solarnotation,whilethat at 24C8630on
similarlyIimited grounds,provokesquestionof
a lunar record.Another,24CB4l6 (Fig. l7 photograph)waspointedout by a landorvnerwithin the
former rese ation boundary."The Crow used
to call it a moon calendar,"he said.The glyph
seemedto be a numberrecordlaboriouslypecked
into extremelyhard sandstone.
It wascomposed
of "units" of regular,carefully-formed,
carefullyspaced,short, double,horizontallines. These
were in two verticalseries,beginning1.35cm.
abovethe cliffbase.Oneseries,extending90 cm.,
had 23 of the double-horizontalunits. The other
series,inclinedslightlyfrom the vertical,has l7
"units." Belowwasa serpentinepeckedfigure
which seemedto representa horneddancer.
Discussion
"Tally" or "count" marks are common in the
Plainsperroglyphicrecord.Do they indeedrepresent an arithmeticalnotationand the mentalprocesseswhich adumbrate it, or is the artist illustratingsomeother idea,quite unknovn to us?
If they are counts, what is being counted and
r h y ? I n s o m eg l y p h st h e i n t e n d e dc o m m u n i c a tion seemsto be "how many" tipis or guns or
men, but there is no evidenceyet discernedof
ord,eringor sequencilrgof units, the next expectablestepin a number system.A third expectable
step,a grouping of tumbers, seemsto be shown
in two of our samplesby wayof pairsor "counting by two's." It is unfonunatefor the hypothesis
of a notationalsystemthat proof most likely will
come, if at all, from internal evidence of the
glyphsrhemselves.We can,so far, only presume
for working purposesa rudimentarycountingdevice of one mark for one object, with no further
conceptualevolution,as in Mesoamerica,
of notational sophistication;i.e.,setsmore complexthan
pairs, glyphic number conventions,calendric
ideas,narningsequences,
phoneticequivalents
or time units.The very largenumberofsitesyet
to be analyzed,dated,and understood,and indeed yet to be discovered,may alter this
appraisal.
Counts,Coups,and Tally Marks in Pictographic/Petroglyphic
Record
Sites Described
24CB4l7
24CB630
24YL4l7
24YL704
24\L402
24YLll89
24YL600
24YL4IB
24YL70
Kraus
Bear Two Shield
Doctordic
Chief Joseph
Alkali Creek South
CanyonCreek
Custer
Castle
Rossell
24\L434
24\LB2
24\L419
24YL\190
24CV557
24ST403
245T560
24ML563
24ML562
Horse-House
Manual Lisa
Nordstrom-Bowen
Pillar
Northside
Molt
Weppler #2
Signal Mountain
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.nPlsinsSubculture?An EthnographicalAppraisal.PlainsAnrhropologist12{36):167-174.
Go$en, G. H. 1974.A Chamula Calendar Board fron Chiapas,Mexico. 1n Ncnan Hanmon (ed.)Meso-AnericanArcheology:
New Approaches.1972. University of Texas Pr€ss,Ausrin. Pp. 2t7.254.
K e y s e r ,J . D . , a n d G . C . K n i s h r . 1 9 ? 6 .T h e R o c k A r t o f W e s t e r nM o n t a n a .P l a i n sA n * r o p o l o s i s t2 l ( 7 1 ) : t - 1 2 .
Keyser,J. D., and L. Sundstron. 1984.RocI Art ofVesrern South Dakota: The North Cave Hills 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. Science 178:81?,28
. l9?2. The CharnulaCalendarBoard: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.Pictographsin 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
246
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Counts,Coups,and Tally Marks in Pictographic/Petroglyphic
Record
247
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Counts,Coups,and Tally Marks in Pictographic/Petroglyphic
Record
249