AR52. 29 May 2007.
Copyright 2007 by Kevin Sharpe and Leslie Van
Gelder. All rights reserved.
To appear in Semiotica.
Paleolithic Finger Flutings
as Efficient Communication: Applying Zipfs Law to Two Panels in
Kevin Sharpe
Graduate College, Union Institute & University,
Harris
ksharpe@ksharpe.com
www.ksharpe.com
and
Leslie Van Gelder
leslievg@ksharpe.com
ABSTRACT.
Two fluted panels in
KEY WORDS.
Finger flutings, notation, Paleolithic communication,
prehistoric art,
CONTENTS.
Introduction
Our research centers on the study of Paleolithic finger
flutings (lines fingers make on a soft surface), especially those found in the
French caves of Rouffignac, in the
We notice subjectively that some panels in some caves look
chaotic, random, or perhaps more accurately haphazard, while others fluted and engraved on walls, rocks, and
portable objects look highly structured or ordered.
Compare, for example, Figure 1 with Figures 2 and 3. The flutings of the panel
in Figure 1 look haphazard; it comes from the Zone of Crevices in
Given the visual orderliness of the panels depicted in Figures 2 and 3, we would go so far to ask whether their fluter(s) intended the panels to convey thoughts and ideas (as opposed to only passing on feelings and sensations, perhaps in Figure 1). Is it possible objectively to establish that such a communication intention lay behind the fluting of the two panels? To help answer this, we use a method derived from communications theory called Zipfs Law, which can establish whether data represent efficient communication or are random (Zipf 1949).
Figure 1. Flutings on
the ceiling of the Zone of Crevices,
Figures 2a and 2b.
Two views of the left hand side of the panel of flutings in
Figures 3a, 3b, and
3c. Three views from left to right of the panel of flutings in Chamber G of
Rouffignac Cave that includes a Rhinoceros Horn (on the left of Figure 3b) and
that subjectively appear to have a highly ordered structure. Approx. 6.8 m long
(Barrire 1982: 27).
Figure 4. Plan of
Rouffignac Cave contains over 500 square meters of flutings (Plassard 1999: 62), made into moonmilk (a white and potentially soft precipitate from limestone comprising aggregates of fine crystals of varying composition usually of carbonate materials, e.g., calcite, hydromagnesite, and gypsum). Traditional scholars consider the art in Rouffignac, including the flutings, to be 13-14,000 years old based on stylistic considerations, though it could date up to 27,000 years (Sharpe and Van Gelder 2006c: 180). It has yet to receive any absolute datings.
Zipfs Law
The law of George Zipf (1949) proposes a constant and inverse relationship between the order of a word in a frequency list and the frequency with which the text uses it. The relationship obtains regardless of the author, subject matter, or any other linguistic variable (Crystal 1997: 87). The method draws on information theory, one of whose planks differentiates the informational content of a message from its meaning. Writes Steve Nadis:
The first step in information theory is to confirm that a communication signal is carrying information and is not just random noise.Zipf counted the number of times different letters appeared in representative English texts. He then logarithmically plotted the frequency of occurrence of these letters in descending order. The resulting slope had a gradient of -1.Chinese text also yielded a -1 slope, as did most written and spoken languages. This relationship, Zipfs Law, held true, moreover, for words, letters, characters and phonemes perceptually distinct units of speech.
For an entirely random string of letters that contained no encoded information, the slope would be flat, or zero, because every character occurs equally often. There would be no rhyme nor reason to it, no way of anticipating what will come next. The other extreme would be a vertical line on the left-hand axis representing, for example, speech with just one sound replayed continuously. In between are countless possible lines of negative slope, centered around -1, indicating that some elements of a signal are used more frequently than others. A -1 slope is a sign of optimized communications: it is more efficient because elements that occur frequently can be coded to be shorter than those that are used less often. In English, for example, common words like a and the take fewer letters and syllables than less familiar terms like antidisestablishmentarianism (Nadis 2003: 37).
The communication goes between members of the same species and social group as the communicator or at least from someone or something that knows how the social group communicates. The communications can comprise information about thoughts and ideas and not merely feelings or sensations. The above idea of optimized or efficient communications for a -1 sloped Zipf graph needs emphasizing because it relates to how modern languages convey thoughts and ideas. Researchers use the law to try finding the communication content of animal noises, such as dolphin whistles, and of signals coming from outer space (McCowan et al. 1999; Nadis 2003).
Methodology
In brief, the corner-stones of our methodology include multiple examinations of the flutings under investigation, experimentation, and the initial setting aside of questions of meaning (assumptions as to meaning can determine what investigators then see in the flutings). The physical data in the flutings themselves are what we seek: how their fluters constructed them, how they functioned with respect to one other and, if possible, how they functioned for the fluters. Francesco dErrico points out (1992: 95) that his similar approach to markings on portable artifacts makes it possible to look beyond the incised lines to the sequence of motions employed by the prehistoric artists. Our methodology too emphasizes the process of creating the flutings as opposed to just viewing the final results.
We employ a terminology (Sharpe and Van Gelder 2006a: 282-283) to help with the study: a fluter makes a fluting by sweeping his or her fingers across a soft surface; a unit comprises flutings drawn with one sweep of one hand or finger; the profile of a unit or a fluter comprises the silhouette of the finger tops left in the medium from the fluting; a cluster comprises an isolatable group of units that exhibit a unity, for instance because they overlay each other; and a panel comprises a collection of clusters that appears geographically or otherwise distant from other clusters or on a surface of reasonably uniform orientation.
In terms of our field methodology, we become familiar with a cluster and then carry out an Internal Analysis of it (Marshack 1972), specially noting the directions of the flutings and their overlays (which provide the temporal sequence of the flutings). We have also developed a further method for obtaining data (Sharpe and Van Gelder 2006a: 293), what we call a Forensic Analysis. It notes such things for a unit as the width of the flutings of the three central fingers when held together and the profile. Such data suggest the age group, sex, and individuality of the fluter.
We make a methodological assumption that especially shows in this paper. With engravings, the individual mark constitutes the basic element, suggesting for flutings the taking of each individual finger line as the foundational element. The basic unit we assume and usually work from for flutings, however, comprises the lines drawn with one sweep of a hand. We argue that the fluter makes one hand of finger lines at a time, matching the engraver who makes one line, notch, or microcupule at a time. This methodological assumption does not lie in the Internal Analysis because that deals with individual finger lines, especially their overlays. Neither does it belong to the Forensic Analysis proper because that focuses on the fluters physiology. Rather, it comes before both analyses and rises to application at various relevant points.
Thus we recommend two analyses: an internal one and a forensic one. Now we add a third way to study a collection of flutings, a Zipf Analysis. This requires (McCowan et al. 1999: 411):
1. selecting a significant observable to use as the variable in the analysis (we discuss this choice below);
2. dividing up the collection of flutings by this variable and recording the number of units for each value of the variable;
3. ranking this list in decreasing order of incidence (also called frequency);
4. graphing the log10 values of the order of decreasing incidence (1, 2, etc.) against the log10 incidence for it; and
5. noting the slope of the resultant graph.
A slope of -1 indicates that efficient communication was taking place with the fluted panel.
One of the challenges in using Zipfs Law involves
ascertaining significant variables. In our application of the law to the two
panels in
We now perform a Zipf Analysis on the Mammoths of Discovery
and the Rhinoceros Horn panels in
Results
The fluted units in the Mammoths of Discovery Panel, from left to right, showing the number of fingers used for each unit, are:
1 1 2 2 1 2 2 4 4 4 4 4 4 3 3 2 3 3 3 3 3 3 3 4 3 3 3 3 3 1 3 3 2 1 1 1 3 3 1 3 4 3 2 3 3 3 4 4 3 4 4 4 3 4
Incidence of 1-finger units = 8
Incidence of 2-finger units = 7
Incidence of 3-finger units = 25
Incidence of 4-finger units = 14
Incidence of 5-finger units = 0
Variables: Number of fingers used per unit, 1-4
|
Order of Decreasing Incidence |
Log10(Order) |
No. Fingers |
Incidence |
Log10(Incidence) |
|
1 |
0 |
3 |
25 |
1.39794 |
|
2 |
0.30103 |
4 |
14 |
1.146128 |
|
3 |
0.4771213 |
1 |
8 |
0.90309 |
|
4 |
0.60206 |
2 |
7 |
Figure 5. A graph of the Zipf Analysis of the Mammoths of Discovery
Panel according to the number of fingers used to flute each unit. The resultant
trendline has a gradient of
-0.96, whereas the dashed line has a gradient of -1.
The fluted units in the Rhinoceros Horn Panel, from left to right, showing the number of fingers used for each unit, are:
2 3 1 3 2 5 4 4 4 1 4 2 4 3 3 3 3 5 5 3 1 3 2 3 3 5 3 3 3 2 4 3 3 2 3 4 4 2 4 4 3 4 4 4 2 4 3 4 1 1 3 4 1 1 5 4 4
Incidence of 1-finger units = 7
Incidence of 2-finger units = 8
Incidence of 3-finger units = 19
Incidence of 4-finger units = 18
Incidence of 5-finger units = 5
Variables: Number of fingers used per unit, 1-5
|
Order of Decreasing Incidence |
Log10(Order) |
No. Fingers |
Incidence |
Log10(Incidence) |
|
1 |
0 |
3 |
19 |
1.278754 |
|
2 |
0.30103 |
4 |
18 |
1.255273 |
|
3 |
0.4771213 |
2 |
8 |
0.954243 |
|
4 |
0.60206 |
1 |
7 |
0.845098 |
|
5 |
0.69897 |
5 |
5 |
0.69897 |
Figure 6. A graph of the Zipf Analysis of the Rhinoceros Horn Panel according to the number of fingers used to flute each unit. The resultant trendline has a gradient of -0.86, whereas the dashed line has a gradient of -1.
Discussion
Because they produce graphs with gradients closely approximating -1, the two panels appear to constitute efficient communication, given the accuracy of Zipfs Law and our observations of the flutings. We intend with these preliminary and indicative Zipf Analyses to introduce the issue and type of study for artifacts such as these two fluted panels, and to form a basis for further investigations. The analyses provide suggestive preliminary results rather than definitive proofs.
Many continuing points for discussion arise, on the theoretical and data sides, and having to do with meaning.
Theoretical Issues
Some people might ask about the applicability of Zipfs Law. To what extent and under what circumstances might fields like rock art apply communications theory? Or the critic might inquire whether the result of -1 comes about from something else for example, the consistent use of a specific numbers of fingers for convenience or ease rather than from the flutings use for communication.
Another discussion provisionally accepts the -1 result and focuses on the implications of this for a supposed notational nature (or related terms) of the fluted panels.
The Archaeology Dictionary defines (2007) notation in the Paleolithic context as: deliberate markings madeto count objects or remember events in a sequence. With engravings, such markings include successions of single-stroke lines (produced by single movement of the tool tip), notches produced by a back-and-forth movement of the cutting edge), and microcupules (produced by a rotation or pressure of the tool tip) on stone, bone, antler, ivory, and amber (dErrico 1992: 95). We differentiate between the dictionarys two-sense elaboration of the word. The first way, to count objects, refers we say to tallies made at one time and that do not record any sense of time passing. We use the word tally and not notation for this. The second sense, to remember events in a sequence, requires, we say, the recording in some manner of the time-passing element of the sequence. The line marker(s) made them at various junctures over a period of time. We at first restrict the word notation to this usage.
In a tally, explains Denise Schmandt-Besserat (1997: 91), each mark represents one item to keep track of, entered in a one-to-one correspondence. But, she continues (1997: 92), only the tallier and perhaps a few others knew the meaning of the notches because the objects of the tally remained enigmatic to other people. Other people might try to reconstitute the meaning, but their ideas remain hypothetical.
A similar conclusion applies to engraved artifacts that display patterns made at one time, were possibly not tallies, but yet whose marks had significance to their makers. DErrico writes from his (1994) study of markings on Azilian pebbles:
We found that they had always been made by rapid, repeated tool movements. In addition, most of the neighboring marks were made by the same tool, while in many cases all the marks on a given pebble had been produced by the same tool in a single series of operations.One is thus tempted to conclude that prehistoric [people were] more interested in the overall result.The actions that produced them seem to be the expression of a repeated pattern (dErrico 1989: 117; see also Lewin 1989).
Unfortunately, the tally interpretation keeps appearing in the literature (e.g., Bullington and Leigh 2002) without appreciation of the complexity of the situation. The body of artifacts defies a single let alone a simple interpretation.
The two panels studied from
Consider a putative notational artifact. Its marks, either individually or in groups, slowly accumulated to represent cultural or natural events from different times (dErrico in Marshack and dErrico 1989: 498). Several observable factors could indicate this: repeated changes of tool, variations in marking techniques, in the arrangement of marks [e.g., as in distinguishable subsets] and in mark morphology (dErrico 1998: 22). On the other hand, if the marks on an artifact appear indistinguishable, they provide very little informational content and the investigator cannot assure their time-dependency notational nature.
DErrico wrote (1997; regarding Sharpe and Lacombe 2003) several years ago about the possibility of flutings as notations: The problem is how to create a theoretical and analytical tool able to verify whether they are or not. In part, the Zipf Analysis attempts to answer this challenge. We showed above that the two panels studied in Rouffignac are not haphazard, decoration, or time-independent tallies. They probably do not constitute time-dependent notations either though the units in the panels appear distinguishable. We say this because the fluters probably made all the marks at the same time. The full internal and forensic analyses of the panels will help clarify this issue because they will show whether the same or a series of different people fluted the units at one or at several times. In the mean time, initial results indicate that a small group of fluters fluted at one time. Thus the question becomes whether the fluted panels comprise notations in another sense of notation or whether they constitute something else altogether.
How many types of notation can humans develop? asks dErrico (1998: 20). How many of them will we be able to identify among the archaeological material? He at first incorporates the time element in his understanding of notation. By the mid 1990s, however, he seems to have dropped this aspect as essential (rather, he seems to consider it only one type of notation) and adopts a more general understanding of the term. He produced the following model, though still provisional, and in part answers his questions about the types of notation. He suggests three kinds, in which, respectively:
(1) the elements constituting the system differ from each other; (2) the elements themselves are identical but can be differentiated by their distribution on the surface (e.g., organization by groups); (3) the marks cannot be differentiated (identical and equidistant elements) (dErrico 1994: 194-195).
What other categories than tally and notation might apply to the Rouffignac panels? Protowriting? Writing? In his Blackwell Encyclopedia of Writing Systems, Florian Coulmas defines (1996: 376; see also Sharpe and Lacombe 2002) protowriting as: an array of visual signsused for information storage and communication. They include decorations on objects such as pottery vessels, message sticks, clay pebbles, knotted cords, and seal impressions marking property, among others. He also defines (1996: 560) a writing system as a set of visible or tactile signs used to represent units of language in a systematic way, with the purpose of recording messages which can be retrieved by anyone who knows the language in question and the rules by virtue of which its units are encoded in the writing system. Writing visibly records a language, ideally all of its words or sounds.
Note that writing, protowriting, and notations can exist side by side; one does not necessarily replace or evolve from either of the others. Writing can also form notational systems, writes Coulmas (1996: 356), though, he adds (1996: 377), a systematic relationship between the symbol inventory and linguistic unitsdistinguishes writing from other visual recording devices.
Despite this overlap, scholars usually distinguish prehistory from history, defining history as the advent of writing. Cave paintings and the petroglyphs of prehistory may appear the precursors of writing, but do not constitute writing because they do not directly represent language. This draws an arbitrary, nonempirical value judgment, however; whether the artifacts did represent language requires knowing something of the original language spoken. For Rouffignac, no one knows how or what the fluters spoke. Many scholars would also probably not consider the fluted panels writing in the full sense of modern forms of writing, thinking of writing as rather complex and the Paleolithic markings as very simple. This may only come from a modern bias. The problem remains of identifying coherent and non-arbitrary criteria by which methodologically and evidentially to distinguish protowriting, writing, and notation (Coulmas 1996: 376).
The Zipf Analysis may help by pointing to something so-far
overlooked in the investigation of flutings potential as protowriting or
writing. However, though the Rouffignac panels give a -1 Zipf gradient, they
may not support sufficient complexity to represent a physical form of speech.
Distinguishing grammatical variables (see point 4 below) in addition to the
number of fingers in each unit may help adjudicate this potential. The
Four years after he introduced his notational model, dErrico uses (1998) the idea of artificial memory systems rather than notations. This could prove a fruitful ideational class to cover some of the artifactual phenomena under discussion, but it will not resolve the need for coherent and non-arbitrary criteria for making the distinctions because it does not seem to cover protowriting and writing. Overall, the above discussion on decorations, time-independent tallies, time-dependent notations, artificial memory systems, protowriting, and writing shows a blurring between the various terms and their relationships, and renders the preconceived categories inconsistent, artificial, and perhaps out of touch with the data dErrico, his colleagues, and we are discovering. It seems pointless to tinker with the old interpretations and categories. The issues they raise may even direct research on Paleolithic engravings and flutings into futile directions. The study of the markings needs, rather, to focus on the data in the artifacts. A more useful approach than dErricos new model and term for notational systems, for instance, would create a fresh terminology based on the different phenomena seen in the record of the artifacts.
Data Issues
Several matters concerning the data used for this study beckon exploring, besides the need for continual vigilance about the data collected and the means for ascertaining and interpreting them.
1. The study requires a full Internal Analysis of the panels, especially showing the overlays and thereby the temporal sequence of the flutings. Did the fluter(s) of the Mammoths of Discovery Panel, for instance, make it from left to right? Do the few horizontals move in the same direction? Such data may require adjustments to the Zipf Analyses.
2. The study also requires a Forensic Analysis on the panels and to follow its effects through to the Zipf graphs. Forensics could isolate the various fluters of each panel, differentiating them by age group and sex. Were all their flutings part of the panel under consideration? It could help determine the fluting period of the panels. It could, in addition, help evaluate dErricos statement that older members of the community, initiated individuals, or bards, probably specialized in memory storage (the fluted panels functioning as instruments for such), and thus probably were those who created, transmitted, and eventually modified artificial memory systems both in their artifactual reality and in the organization of their codes (dErrico 1998: 47).
3. The
use of gauges like the
Primitive communications, such
as chemical signaling systems employed by cotton plants, dont go beyond
first-order
4. The study requires further exploration of the variables that separate, differentiate, or group the units and that therefore transfer information and distinguish the flutings from random marks. We need to break the panels into components and work out, writes Nadis (2003: 37), where one discrete segment ends and the next begins. Our first attempt, the one employed in this paper, involves the obvious natural break into hand units and the different number of fingers each uses. Zipfs Law can help find more such variables, if they exist. The investigator need only isolate a potential variable for example, the diagonal units under the vertical ones and then test using the law to see if it holds significance for efficient communication. Finding these variables is tantamount to finding the grammatical structure of the system behind the fluted panels.
5. Zipf Analyses need attempting for other examples of line markings not only fluted on the cave walls in Rouffignac (e.g., the Patriarch Panel in Chamber J, other panels in Chamber G such as the Henri Panel, and the various clusters in Chamber E) and elsewhere, but also engraved on bones and stones. Doing this calls upon and could supplement the work of dErrico and his colleagues.
6. DErricos results from portable objects offer hypotheses and directions for the fluted panels and invite further data research to help evaluate them. For example:
a. Codes based on the combination of two and possibly three factors (morphology, spatial distribution, and accumulation over time) appearfrom the beginning of the Upper Paleolithic (dErrico 1998: 46).
b. Does a formal distinction exist between marks juxtaposed on a single alignment and ones that rely on the semiological technique of spatial grouping (dErrico 1998: 46)?
c. Emblems (such as drawings of animals or signs) occur on some portable artifacts in association with the series of marks (dErrico 1998: 46). Both of the fluted panels studied in Rouffignac include images of animals (mammoths or rhinoceroses), plus in the case of the Rhinoceros Horn Panel, a tectiform.
Meaning
If the two panels studied here indeed constitute efficient communication, the issue remains as to what they mean or at least meant to their fluters. We state that no one now may ever know this and that no one now should expect to know it.
Previously we pointed out (e.g., Sharpe and Van Gelder
2006c) inadequacies in several attempts (e.g., the shamanic, phosphene, and
pseudohallucination hypotheses) to provide the meaning or origin of so-called
geometric flutings such as the panels under consideration. Studies of these
artifacts, we would add, must use the tools available: including the Internal,
Forensic, and Zipf Analyses, with a
Conclusions
The research challenge raised at the beginning of this paper asks for a way to establish objectively that a thoughts-and-ideas communication intention lay behind the fluting of the two studied panels, and to rule out their representing activities that predominantly produce haphazard-looking flutings. Zipfs Law seems to help distinguish random or haphazard markings from efficient communication, and hence possibly answers the challenge.
Note that we have not shown the haphazard or random nature of the Gargas fluted panel in Figure 1. Random could in some instances relate to mainly aesthetic or tactile intentions, and have its own sense of order but not the strong communication sense surmised as inherent in the structure of the two fluted panels in Rouffignac. On the other hand, we have not looked for a variable for the Gargas panel that might in fact lead to a -1 Zipf plot.
The -1 plots from the Zipf Analyses of the two fluted panels suggest that a higher cognitive function may exist for lines previously ignored or considered unimportant in comparison to animal figures.
Acknowledgements
Several individuals have helped in this research: Jean,
Marie-Odile, and
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