AR53. 9 June 2008
Copyright © 2008 by Kevin Sharpe and Leslie Van Gelder. All rights reserved.
In process. Zipf #2. **For Nature/Science or Antiquity/CAJ/Phil. Trans. of Royal Society of London**

 

Using Zipf’s Law to Demonstrate the Notational Nature of Prehistoric Art

Using Zipf’s Law to Demonstrate the Notational Nature of Some Prehistoric ‘Art’

 

by

Kevin Sharpe

Graduate College, Union Institute &University, Cincinnati, Ohio, USA
Harris Manchester College, Oxford University, UK
 
 10 Shirelake Close, Oxford OX1 1SN, United Kingdom
ksharpe@ksharpe.com
www.ksharpe.com

 

and

Leslie Van Gelder

College of Education, Walden University, Minneapolis, Minnesota, USA
 
10 Shirelake Close, Oxford OX1 1SN, United Kingdom
leslievg@ksharpe.com


ABSTRACT.

KEY WORDS.

CONTENTS.

Introduction. 3

Notation. 3

Zipf’s Law.. 12

Ogham.. 12

Discussion. 12

Writing. 12

Translation. 13

Conclusions. 13

Other Applications. 13

Variables. 13

Other Communication Measures. 14

Acknowledgements. 14

References. 14


 

·         Where do I want to take this?

o       After panels in Rouffignac.

o       After panels and baton in Gargas.

·         I really want other people to take this up.

·         Could do a more thorough analysis of all these panels, with different variables, i.e., grammars, etc. With forensics where possible and helpful.

·         Espouse a greater study of notation. Move to engraved severines.

·         Issues of translation.

·         Look at possible application to Koonalda.

·         Animal scratches: should have a different result. Maybe this is an important difference. But theoretically, given the number of fingers or claws, should there be any difference or significance? Maybe this relates to the issue of whether Zipf can apply to flutings when fingers per unit is the variable; i.e., maybe it is purely a chance phenomenon (in which case for animals or humans, there should be a flat graph).

·         The translation stuff is where I wanted to go initially (i.e., after Koonalda) and perhaps I just want to lay down these possibilities.

·         As a book, this work might have greater influence.

Introduction

Similar to AR52: some panels look structured (Gargas bones look the same); versus some looking haphazard. Therefore notation? See d’Errico on this. AR52: some notational stuff indicated using a Zipf analysis.

·         Paul Bahn, 'Cracking the Easter Island...,' New Scientist 15 June 1996, pp.36ff. Translating the written language of the island.

·         The places where the lines form a maze: would this be writing? How to disentangle them: u/v light?

·         Go through other works and ideas to see if anything relevant.

·         Can’t assume they mean the same thing as the styles, forms, etc., are so different.

·         Some seem to be meaning in the production – i.e., it’s the act of fluting that’s meaningful. So the question is to do with the flutings where the act of making them isn’t as much as perhaps the look of the final product.

·         Do structural/internal and forensic analyses first.

·         This might work with Kirian lines as well as Rugolean ones.

Notation

Could make this a focus of this paper. Empirically redefine the categories (decoration, tally, notation?, … protowriting, writing…maybe use different words). The writing types may be defined by -1 Zipf slopes but differentiated by amounts of Shannon entropy. Note these are tactile/visual records as opposed to sounds.

Lots of literature review on d’Errico.

The following is the full length version of the first Zipf paper now drastically cut.

Another discussion provisionally accepts the -1 result and focuses on the implications of this for the ‘notational’ nature – and related purposes – of the fluted panels. The -1 rules out their purely decorative character.

The American Heritage Dictionary of the English Language defines this sense of ‘notation’ as: ‘A system of figures or symbols used in a specialized field to represent numbers, quantities, tones, or values.’ The Archaeology Dictionary elaborates (2007): ‘Paleolithic notation is the term used by archaeologists for deliberate markings made by our ancestors to count objects or remember events in a sequence.’ This applies to sequences 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’ (d’Errico 1992: 95). In the way we use the elaboration of the word ‘notation’ in the Archaeology Dictionary, the first of the uses, ‘to count objects,’ refers to the making of tallies and need not record any sense of time passing. They are independent of time. The second sense, to ‘remember events in a sequence,’ can require, and to separate it from the first meaning we assume it does require, the recording in some way of the time element of the sequence.

Denise Schmandt-Besserat writes (1997: 91) of such marks first being symbols of magical or religious significance. Then, later in the development of mind, they became tallies, ‘each notch representing one item of which to keep track…entered according to the basic principle of one-to-one correspondence,…matching each unit of the group to be tallied with one notch.’ She thus thinks (1997: 91) of ‘the notches as signs promoting the accumulation of knowledge for specific ends…the storing and communicating of concrete information.’

The tallies remained, however, a rudimentary device. For one thing, the notches were unspecific and could suggest an unlimited field of interpreta­tions. Marshack postulates that the signs stood for phases of the moon; others have hypothesized that they served to keep a tally of animal kills. But there is no way to verify their meaning. In fact, the notched bones were limited to recording quantitative information concerning things known by the tallier but remaining enigmatic to anyone else (Schmandt-Besserat 1997: 92).

The actual meaning of the tally has become lost, though someone might try hypothetically to reconstitute it.  ??? this Azilian example actually isn’t about tallies but about designs ??? As an example, d’Errico 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 (d’Errico 1989: 117; see also Lewin 1989).

Unfortunately, the tally interpretation keeps being raised (e.g., Bullington and Leigh 2002) without appreciation of the points above and below. The body of artifacts is complex and defies a single let alone a simple interpretation as time-independent tally marks recording or counting by ‘the repeated addition of one unit’ at a time (Schmandt-Besserat 1997: 114). In particular, the two panels studied from Rouffignac Cave are not tallies because if so they would not produce a -1 gradient in a Zipf plot, but rather a point. The variable that produced the plot for the Rouffignac panels, the number of fingers per unit, would not have mattered if they were tallies.

The tally interpretation corresponds to the Archaeological Dictionary definition of notation as ‘to count objects,’ without a record of time. One can imagine a piece of bone on which were simple tally-like incisions ‘made by repeated actions, with no lapse in continuity, using the same tool.’ But, continues d’Errico (Marhsack and d’Errico 1989: 498), ‘because to the naked eye all the lines appear identical,’ they cannot actually constitute a notational system. If, on the artifact, there is no way to distinguish between the marks, there is no way of gaining informational content from them. This is more than Schmandt-Besserat’s point of a loss of meaning because the tally makers and users have died out. D’Errico’s point is that, to an outsider, the set of marks could have little meaning because the differentiation between the constituents of the sequence is lost or did not exist. Thus a lunar calendar only of identical incised markings and produced in one sitting to chart a woman’s menstrual cycle (Boroneant et al. 1979: 606) may well be a counting tally, but is neither a calendar nor notational. Similarly, ‘lunar calendars, cyclic notations, “marques de chasse,” or kill scores envisaged in the past are devoid of practical foundation,’ writes d’Errico (1989: 117), unless their creation involved ‘several distinct operations over a relatively long period and in all probability the use of more than one tool.’ ‘To recover information in notations ‘based on serial markings requires patterns allowing a visual and/or tactile discrimination of the signs,’ writes d’Errico (1998: 25).

This leads to the second notational approach – in the Archaeological Dictionary as to ‘remember events in a sequence.’ Here, to think of the portable bones and stones with lines and other marks engraved on them are considered time dependent – the mark compilations noticeably made over time and not, as with a tally, all in one sitting – i.e., as containing the information d’Errico requires. Time-dependent ‘notation’ usually holds preeminence in usage over the tally sense, but, it turns out, many artifacts do not necessarily support it. A ‘slow accumulation’ of identical marks on an artifact, where ‘each of them or a group of them represented, for prehistoric people, an event, whether natural or cultural,’ from different times, writes d’Errico (Marshack and d’Errico 1989: 498), ‘would have to have been made at intervals over a period of time.’ If so, they were probably made ‘with more than one tool’ (d’Errico 1992: 94). Several observable factors could indicate this: for example, ‘repeated changes of tool, variations in marking techniques, in the arrangement of marks and in mark morphology….When marks are created by stone tools, for example, a change of tool will probably take place between each new stage of marking if the periods stages are relatively long’ (d’Errico 1998: 22). Sometimes the marks were made in subsets. Discriminating between the signs ‘implies a certain degree of isomorphism of the signs and their arrangement in a way which would enable them to be “read.”’ For the modern investigator, it is a matter of ‘understanding the variability of the operational chains that produced similar motifs by trying to identify the elements that most interested prehistoric people’ (Marshack and d’Errico 1989: 499; see also d’Errico 1994: 185-186).

D’Errico thus builds his case against Marshack’s notational interpretations, including the idea of Paleolithic lunar calendars. Marshack, the father of the study of notation in the archaeological context (starting at least with his 1964 paper), writes (1998: ¶2): ‘Pre-agricultural record-keeping and notations…were not ‘linguistic’ or arithmetic….They were records of elapsed time, of the periodicities observed in nature, including the months and seasons.’ D’Errico disputes elements of both Marshack’s method and conclusions. (D’Errico refers especially to his study of Azilian pebbles, but Marshack states [1989; see also his 1995] that he too previously concluded the Azilian pebbles are not notational.)

The dispute is instructive (d’Errico 1989; 1998: 20; Lewin 1989; Marshack 1989; 1995; 1997; Marshack and d’Errico 1989). Marshack writes (Marshack and d’Errico 1989: 491) that ‘the primary test for the presence of notation’ with engraved marks is ‘that they be carefully made and accumulated linearly and sequentially.’ While d’Errico disagrees (Marshack and d’Errico 1989: 498) with this ‘primary test,’ the main issue he has with Marshack’s work is that one of Marshack’s methods to demonstrate the test is flawed (Marshack and d’Errico 1989: 495-497). Marshack thinks he shows his ‘calendars’ are time-dependent in their construction because he detects changes in the cross-sections of the marks, hence of tools, hence of the time periods for the engraving, and hence they could be notational. But d’Errico shows Marshack’s studies do not necessarily find these changes. D’Errico’s disagreement with Marshack’s ‘primary test’ in fact has to do with differentiating between the marks, the issue in distinguishing between tallies and notations, which Marshack thinks he does but which d’Errico shows he does not.

 ??? This area has three mentions of the use of different tools over time (d’Errico)

The only systematic effort to disprove [my] studies, by F. d’Errico, of France,’ recounts Marshack  (1998: ¶2; see also his 1995), ‘recently admitted that his more recent studies had confirmed the presence of notation in the Upper Paleolithic, though he does not as yet know why they should have been kept or what the mode of notation consists of.’ Time appears to have come down on d’Errico’s side as to the unknownness of the meaning of the notations and the shortcomings of Marshack’s techniques, but still there remains support for Marshack’s insistence on some of the objects he studied being notational. To assist him in his research, d’Errico carries out investigations with a scanning electron microscope, and he reproduces the artifacts to see the results that might be achieved by engraving in various ways. Working and pioneering 2-3 decades earlier, Marshack depends on a regular optical microscope at best and does little reproductive work. Bednarik says (2007: ¶4) Marshack relies ‘essentially on visual judgment acquired from close familiarity with the materials.’ His primary method of analysis to recognize notational markings, in fact, ‘cannot furnish conclusive evidence for or against interpretation as notation’ (Bednarik 2007: ¶8).

D’Errico wrote to one of us (KS) about flutings and notations several years ago (1997; regarding Sharpe and Lacombe 2003), specifically about the possibility of flutings being notations: ‘The problem is how to create a theoretical and analytical tool able to verify whether they are or not.’ This is what this Zipf analysis attempts. The two panels studied in Rouffignac pass the test of Zipf and therefore are not random or decoration, but efficiently transfer communication at least through their structure around the variable of the number of fingers used per unit. Further, they are probably not time-independent tallies or time-dependent or notations because all the units in each were probably all made at the same time and yet are differentiable. The full internal and forensic analyses of the panels may help explain this further because they should show whether the same or a series of different people fluted the units. Initial results, however, show a small group of fluters were involved at one time. Are the fluted panels notational in another sense of ‘notation’?

‘How many types of “notation” can humans develop?’ asks d’Errico (1998: 20). ‘How many of them will we be able to identify among the archaeological material?’ Marshack theoretically has the time element in his understanding of ‘notation’ and d’Errico at first has it too. By the mid 1990s, however, d’Errico seems to have dropped this element as essential (rather, it seems to have become only one type of notation) and he adopts a more general understanding of ‘notation.’ He produced the following model, though still provisional, and in part answers his questions about the types of notation. It

considers three types of notation: (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).

In the last case, two possibilities arise: (3a) the elements of the notation were produced at the same time (in this case, after a certain lapse of time it becomes impossible for the engraver or other group members to differentiate one element from another); (3b) the elements were added over the course of time. To each event (or events) corresponds the addition of one or more new elements. If made with a lithic tool, it is probable that numerous tool changes were involved in this last type of notation. To be able to clearly distinguish sets made by the same tool from sets made by several tools is thus a major aspect of this research (d’Errico 1994: 194-195).

This might empty the word notation. It might be better to use different terms for the different types, i.e., allow the data to dictate the types. Four years later, d’Errico adopts (1998) the idea of ‘artificial memory systems’ for these Paleolithic artifacts. This may prove a fruitful category because, for one thing, it may broaden the idea of ‘notation.’ It appears even more based on the markings themselves rather than on preconceived interpretations and categories.

What other of these categories than ‘notation’ may apply to the Rouffignac panels? Protowriting? Writing? In his Blackwell Encyclopedia of Writing Systems, Florian Coulmas defines (1996: 376) ‘protowriting’ as (see also Sharpe and Lacombe 2002): ‘an array of visual signs…used 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.’

Coulmas 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 language, its words or sounds. Its makes its norm phonemic and it attempts to symbolize every significant sound in the language.

Note that writing, protowriting, and notations can exist side by side; one does not necessarily replace or evolve from either of the others. ‘When we drive to an airport,’ Michael Stitt explains (2007), ‘the road signs constitute a protowriting system of pictograms, and if the airport is in a country whose language we do not speak, we navigate through the airport by means of another protowriting system.’ Writing systems can also be viewed as notational, writes Coulmas (1996: 356), ‘since by representing languages they at the same time function as descriptions of languages which single out certain aspects rather than others.’ But he adds (1996: 377) that ‘a systematic relationship between the symbol inventory and linguistic units is what distinguishes writing from other visual recording devices.’ He also says (1996: 376), ‘the theoretical problem is…to identify non-arbitrary and coherent criteria which distinguish protowriting from writing proper.’ Herein lies an active research issue in itself (see, e.g., Damerow 2006), and one perhaps pertinent to the Rouffignac panels.

Historians usually distinguish between prehistory and history, however, defining history as the advent of writing. Cave paintings and the petroglyphs of prehistory may be considered precursors of writing, but not writing because they do not directly represent language. This appears an arbitrary, nonempirical value judgment; whether they did represent language means knowing something of the original language spoken. We do not know how or what the Rouffignac fluters spoke. Many scholars would probably not consider the fluted panels writing in the full sense of our modern forms of writing, being rather complex and thinking of the supposed Paleolithic varieties as very simple. But is this only our modern bias?

How from the artifacts might we distinguish protowriting and writing from notation? What is the move methodologically from distinguishing notation from protowriting and from that to writing, or from evidence of notation to evidence of protowriting to evidence of writing?

Turning to the Zipf results, how do the panels as efficient communication relate to notation, protowriting, and to writing? Since flutings like these, along with other line markings, are usually considered notational or candidates for notation, what has been overlooked in the seeing of them as protowriting or even writing? On the other hand, though they give a -1 Zipf gradient, they may not be complex enough to represent a physical form of speech, unless distinguishing the grammatical variables (see the discussion below) can provide substantial insight. If they do have sufficient complexity to consider them a form of writing, we might research the type of writing they constitute: alphabetic, featural, logographic, or syllabic. Ideographic forms (symbols for ideas) never developed sufficiently to represent language. Pictographic forms insufficiently represent language on their own, but often form the core of logographies.

The above discussion on decorations, time-independent tallies, time-dependent notations, artificial memory systems, protowriting, and writing blurs the relationship between the various terms, and renders the categories artificial and perhaps out of touch with the data d’Errico, his colleagues, and we are discovering. The above questions, in fact, may direct research on Paleolithic engravings and flutings into futile directions. Whatever the study of them, it needs to focus on data in the artifacts and not try to fit them into preconceived category or set of categories with inconsistent and apparently artificial meanings. We may need to continue studying the artifacts and then create the categories – maybe drawing on some aspects of the current collection – out of the empirical data found.

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.

The first matter requires performing a full internal analysis, especially showing the overlays and thereby the temporal sequence of the flutings. Was the panel made from left to right? How would the sequence of fluting change the data derived from the panels for a Zipf analysis? D’Errico writes about (1992: 96) some of the Azilian pebble engravers adding their new lines by ‘aligning each new incision to the right of the preceding one’

i.e., in the manner natural for a right-­handed person. Some of the neighboring marks also turned back on or criss-crossed each other. The same effect could be produced experimentally by making marks with no particular intention of making each one an individual creation….Some pebbles had a further set of incisions superimposed on a previous set, an arrangement that defies ready interpretation. The idea that these marks are a form of writing must surely be rejected. It is impos­sible to attach a meaning to any single incision (1989: 117).

This does not seem because of the right-handedness of the engraver, d’Errico reflects, but from the symbolic meaning of the engraving (1992: 100). It will be interesting to see how d’Errico’s judgment here relates to the method used by the Rouffignac fluter(s) of the panels. For one thing, the flutings are variable by the number of each unit, different from the ‘single incisions’ on the pebbles.

Second, we need to perform a forensic analysis on the panels and see how this affects the Zipf analysis. It would differentiate the various fluters of each panel and inform our understanding of the period over which the panels were fluted.

The third matter involves exploring the use of gauges like the Shannon entropy analysis for the panels to measure the complexity of the communication contained in the panels (McCowan et al. 1999; Nadis 2003).

The fourth involves further exploration of the variables that separate or differentiate the units and that therefore transfer information and differentiate it from random marks. Nadis writes:

This is fairly straightforward when the language in question has detailed spelling and grammar rules. In English, for example, ‘e’ is the most commonly used letter, and ‘q’ is almost always followed by ‘u.’ Similar rules dictate word usage and frequency. So searching for statistical correlations between words, letters and other symbols provides a way to work out what is being conveyed (Nadis 2003: 37).

We need to break the panels into components, ‘working out where one discrete segment ends and the next begins’ (Nadis 2003: 37). Our first attempt as used in this paper involved identifying natural breaks in the system, probably the most obvious one being the separation into units and their obvious differences namely the number of fingers used in each unit.

Zipf’s Law can help find these variables. One can select a variable and test it using Zipf’s Law to see if it is significant for the efficient communication supposedly occurring with the phenomenon being studied.

For example, if Morse code is analyzed one dot or dash at a time, the line on the Zipf plot is almost flat. At first glance, this would not seem like a promising signal. But if the dots and dashes are taken two at a time, the slope goes up. When dots and dashes are examined in groups of four, roughly the size of letters [words], the slope approaches -1. ‘Then you know you’ve sampled correctly because a -1 slope cannot occur by chance,’ Doyle says. So if you want to work out the correct units, simply tinker with a Zipf plot, trying different combinations (Nadis 2003: 38).

Zipf’s law helps determine if any old observable is significant communications wise. Finding these variables is tantamount to finding the grammatical structure of the system behind the fluted panels. Another potential significant variable might involve the diagonal units under the vertical ones: perhaps they qualify the meaning context.

A further data issue that we would like to resolve concerns the dating of the flutings in Rouffignac Cave. As mentioned above, the issue is not settled with a stylistic comparative date being far more recent that what other scholars suggest for instance because of the animals depicted. However, carbon is trapped between two layers of fluted clay in Chamber E or the cave (Sharpe and Van Gelder 2006c: 187) and offers a chance of absolute dating. If this does produce a much older date than is usually accepted, the two fluted panels discussed above could make an interesting contribution to the current discussion on the origin of modern human behavior, evidence for this being pushed further and further back because of finds, for instance in southern Africa: ‘modern behavioral traits, such as the use of external symbols, developed gradually over a couple of hundred thousand years…“widespread in Africa far earlier than in Europe”‘ (Holden 2004; see also Balter 2006; Henshilwood et al. 2001; 2002; 2003; 2004; Vanhaeren et al. 2006).

The sixth potential exploration is to try to use a Zipf analysis on other examples of line markings (what we call ‘severines’ [Sharpe and Van Gelder 2006a]) not only fluted on 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. In this it may well as a technique supplement the careful and indispensable work being done by d’Errico and his colleagues by very close examination and replication techniques on portable artifacts.

The results of d’Errico’s work offer hypotheses on the fluted panels and a seventh direction for further data research. He writes (1998: 46) from his research on portable objects, that ‘codes based on the combination of two and possibly three factors (morphology, spatial distribution, and accumulation over time) appear to be present from the beginning of the Upper Paleolithic.’ How much the evidence from the fluted panels augments this will be interesting. Also interesting will be how the evidence from the panels interacts with other of d’Errico’s general observations and conclusions, for instance whether there is a ‘formal distinction between marks juxtaposed on a single alignment, or [ones that] rely on the semiological technique of spatial grouping’ (d’Errico 1998: 46). Both of the fluted panels studied here include images of animals (mammoths or rhinoceroses), plus in the case of the Rhinoceros Horn Panel, a tectiform. These might be classified as ‘emblems’ as d’Errico uses the term, a feature in common with many of the portable artifacts that associate emblems with markings (d’Errico 1998: 46). On the other hand, fluted walls and engraved portable objects appear to show a significant difference, namely between the number of fingers in a fluted unit versus a single marking in an engraved, notched, or microcupled unit. This offers another interesting twist to the discussion.

Several of d’Errico’s speculations may be open to investigation from the fluted panels here investigated or to be investigated. He writes:

the increase in the number of marks and sets appearing at the end of the Upper Palaeolithic might signal an increase in the volume of stored information. This increase coincides with the use of marking techniques producing many marks on a reduced surface, and with a more systematic adop­tion of visual perception in the process of recovering information....This [may also be] the moment when complex codes based on the hierarchical organiza­tion of information, and the use of formally differen­tiated marks, are systematically adopted.

These elements of continuity might imply that, during the European Upper Palaeolithic, the pro­duction and use of artificial memory systems took place in similar social contexts. It is possible that only a few individuals were fully aware of the more complex codes, and that this competence was only one element of the role that these individuals played within Paleolithic societies. Individuals specialized in storing memory among preliterate human groups, such as older mem­bers of the community, initiated individuals or ‘bards,’ are the best candidates for being those who created, transmitted, and eventually modified artificial memory systems both in their artifactual reality and in the organiza­tion of their codes (1998: 47).

Our forensic research in Rouffignac will help ascertain who were the individuals who created the fluted panels.

Meaning and Intention

If the two panels studied here are indeed efficient communication (whether notation, protowriting, or writing), the issue remains as to what they mean or at least meant to their fluters. This may never be known and should not be expected to be known. Suppose the results provided in this paper do hold up to further theoretical and data scrutiny. Are the panels still notation or has a step been made toward their being shown to be writing, albeit probably an ‘unsophisticated’ form of protowriting in comparison to our own? An exploration of Shannon entropy may help answer this. If they are a form of writing, then the issues of meaning and intention rise even more starkly than if they are not.

Previously we published (e.g., Sharpe and Van Gelder 2006c) on the inadequacy of several attempts at saying what is the meaning, intention, or the origin of so-called ‘geometric’ flutings such as the panels under consideration, including the shamanic, phosphene, and the pseudohallucination hypotheses. We can at present only study such artifacts with the tools available – which provide information on the panels’ structure and on the fluters who made them, then whether the flutings are random or intentionally structured – and, given the latter, their grammar (finding the variables that provide a -1 slope on a Zipf analysis) and their level of sophistication (using the Shannon entropy). Future methodological advancements may add to these possibilities, but they may well not include meaning. The current tools and future ones as well, however, do and may even more so rule out various meaning proposals (e.g., the Desbordes Panel in Chamber A1 of Rouffignac Cave includes flutings by young children aged about 5 and this tends to rule out several potential meanings for them such as their having to do with male initiation ceremonies [Sharpe and Van Gelder 2006b-c]).

Finally, we need to revisit the research challenge raised at the beginning of this paper, namely to find a way to distinguish between random and intentionally structured panels of finger flutings. The result of our approach is the possibility of saying the panels are notation/protowriting/writing, but that was not the initial issue. Zipf’s Law can help distinguish random from intentionally structured, and it goes further to decide on communication and grammar. It seems too powerful a method for merely distinguishing between random and intentionally structured panels; there may be other ways to merely distinguish intentional structure without going so far as efficient communication. On the other hand, Zipf’s Law being a heavy hitter may not matter.

Note that we have not shown the random nature of the Gargas fluted panel in Figure 1. ‘Random’ could relate to purely aesthetic or tactile reasons, and this could relate to intention. In this case we have random but intentioned though not structured.

The application of a Zipf’s analysis to fluted panels provides the possibility that a higher cognitive function exists for lines previously ignored or considered relatively unimportant, usually in favor of fluted figures such as of animals and that these were given the higher cognitive function.

Zipf’s Law

Full on Zipf, including critique.

·         Does Zipf’s law help determine if an observable is significant communications wise?

Ogham

Applying a Zipf analysis to Ogham.

·         Re Ogham lines – look like Rugolean (without the base line).

·         Could Ogham help us? With Ogham, even if we find the letter equivalents, what about the words? I suppose there’s some way of translating these. If the flutings were a form of Ogham, I wonder if we have anything more than names (as in Ogham, supposedly)?

·         Does Zipf’s law work for Ogham?

·         Look at the history of Ogham, its source, and translations. Similarly, the history of the Celts. Where did they come from?

Discussion

Writing

Writing?

·         Can we break a cluster of structured units into ideational units (called motifs or something)? If so, how do the ideational units of one cluster compare with those of another cluster? (Maybe this is as close as we can get to meaning.)

·         Are there repetitions of structures?

·         The biggest question I face is whether the markings are structured culturally or individually. There is a certain amount of cultural consistency, but how much? Only further consistent stucturalisms will answer that.

·         Suppose they are communications; then what is the alphabet and what is the grammar? The alphabet seems to be: # fingers, angle, existence of horizontals, of base lines (see their existence in tectiforms), of verging into a line (very much like Ogham). A case for this can be made from Ogham. Look also at the Easter Island script. Writing space bounded up and below; respect for white space: part of grammar.

·         Show they are communications.

Translation

Translation i.e., meaning?

Can we get it by using Ogham as a model?

·         Are there repetitions of structures?

·         How do the symbols function (not what they might mean).

·         The old myth of the rain fertilizing the ground -- in dark

                                                                    -- in the ground (ie., in a cave)

Cutting the rock to make the old man bleed (Mulvaney in Kenneth site of rainbow snake -- rainmaking).

·         The big challenge now is to ask the MEANING OF THE LINES.

·         Treat them as Ogham as a way of to understand them (like a model without saying this is exact).

·         Could we treat or assume these are only names (as in Ogham?)? There’s a case for people doing this in caves (contemporary graffiti).

·         Can a writing system remain the same more or less for tens of thousands of years? Upper Paleolithic to the Celts, etc.

Conclusions

Other Applications

Many other potential applications from prehistoric ‘art.’

·         Numbers of lines grouped together matter like the number of fingers per unit in Rugolean seem to matter.

·         Do a Zipf’s law job on the Öküzini pebble, and see if we can extend this work to mobiliary artifacts.

Variables

Different variables. With a Zipf analysis, to see if any are significant.

·         Are there any other significant variables? Do a list of all possible variables and why in this cluster some are significant and others are not.

·         One of the characteristics that seems to apply to all the possible notational clusters we've seen (in Rouffignac and Gargas) are horizontals going through or under some of the verticals. I think this might also apply to the Gargas engraved bones. Check out Ogham because I think this applies also to some of its letters or meanings.

·         The question, given the desire to look for repeating or informative structures, is to find variables in the lines that might give this. One is the number of lines used in a unit. (There are potentially many others – does this provide a basic method for looking at many of the severines – i.e., they may not all have the same significant variables, decide on those that may be significant.)

·         It looks as though the number of lines in a unit does vary.

·         Need to run our variables through Zipf’s law. What are some other meaning-giving variables? (Angle, direction, length.) Apply Zipf’s law to them.

·         Look at diagonals as a potential qualifier of context.

·         Check against short hand: there are evidently also a lot of lines here. // Shorthand also evidently uses emphases such as darker lines as opposed to lighter ones to indicate different meanings: can we use this too for severines, e.g., is the depth of a line a significant observable?

·         Is there an equivalent to the base (as in Ogham?)?

·         Do certain marks (e.g., curls at the tops or dots) take on a new significance as indicators (as in Ogham?)?

·         (Aquitaine Museum) There's really no time between Paleolithic and Neolithic, therefore should expect little change in art and writing.

·          Analogy with Ogham (includes looking for structural clues)

·         Apply Zipf’s law in various ways according to what may be significant variables.

Other Communication Measures

Other information content measures.

Other Matters

·         Is there anything else besides Zipf and Ogham to help with getting at writing? I was before looking for structural consistencies.

 

Acknowledgements

 

References

Archaeological Dictionary. 2007. http://archaeology.about.com/od/nterms/Glossary_N_Terms.htm, accessed 25 April.

Balter, Michael. 2006. First Jewelry? Old Shell Beads Suggest Early Use of Symbols. Science 312:5781 (23 June), p. 1731.

Barrière, Claude. 1976. L’Art Pariétal de la Grotte de Gargas: Paleolithic Art in the Grotte de Gargas. BAR Supplementary Series, no. 14; Mémoires de l’Institut d’Art Préhistorique de Toulouse, no. 3. Oxford: British Archaeological Reports.

_________. 1982. L’Art Parietal de Rouffignac: La Grotte aux Cent Mammouths. Paris: Picard.

Bednarik, Robert G. 2007. Scientifically Based Interpretation. http://mc2.vicnet.au/home/interpret/web/science.html, accessed 15 April.

Boroneant, V., Boris Frolov, and Alexander Marshack. 1979. On Upper Paleolithic Symbol Systems. Current Anthropology 20:3 (September), pp. 604-608.

Bullington, Jill and Steven R. Leigh. 2002. Rock Art Revisited. Science 296:5567 (19 April), p. 468.

Coulmas, Florian. 1996. The Blackwell Encyclopedia of Writing Systems. Oxford: Blackwell Publishers.

Crystal, David. 1997. The Cambridge Encyclopedia of Language. 2nd edn. Cambridge: Cambridge University Press.

Damerow, Peter. 2006. The Origins of Writing as a Problem of Historical Epistemology. Cuneiform Digital Library Journal 2006:1. http://cdli.ucla.edu/pubs/cdlj/2006/cdlj2006_001.pdf, version 28 January 2006, accessed 22 April 2007.

d’Errico, Francesco. 1989. Paleolithic Lunar Calendars: A Case of Wishful Thinking? Current Anthropology 30:1 (February), pp. 117-118.

_________. 1992. Technology, Motion, and the Meaning of Epipaleolithic Art. Current Anthropology 33:1 (February), pp. 94-109.

_________. 1994. L’Art Gravé Azilien de la Technique à la Signification. Supplément à ‘Gallia Préhistoire,’ no.  ??? also for IBID. Paris: CNRS Éditions.

_________. 1997. Pers. Comm. 1 July.

_________. 1998. Paleolithic Origins of Artificial Memory Systems: An Evolutionary Perspective. In Colin Renfrew and Chris Scarre, eds., Cognition and Material Culture: The Archaeology of Symbolic Storage (Cambridge: McDonald Institute for Archaeological Research), pp. 19-50.

_________ and Carmen Cacho. 1994. Notation versus Decoration in the Upper Paleolithic: A Case-Study from Tossal de la Roca, Alicante, Spain. Journal of Archaeological Science 21:2 (March), pp. 185-200.

Henshilwood, Christopher S., Francesco d’Errico, Curtis W. Marean, Richard G. Milo, and Royden Yates. 2001. An Early Bone Tool Industry from the Middle Stone Age at Blombos Cave, South Africa: Implications for the Origins of Modern Human Behavior, Symbolism, and Language. Journal of Human Evolution 41:6 (December), pp. 631-678.

_________, Francesco d’Errico, Marian Vanhaeren, Karen van Niekerk, and Zenobia Jacobs. 2004. Middle Stone Age Shell Beads from South Africa. Science 304:5669 (16 April), p. 404.

_________, Francesco d’Errico, Royden Yates, Zenobia Jacobs, Chantal Tribolo, Geoff A. T. Duller, Norbert Mercier, Judith C. Sealy, Helene Valladas, Ian Watts, and Ann G. Wintle. 2002. Emergence of Modern Human Behavior: Middle Stone Age Engravings from South Africa. Science 295:5558 (15 February), pp. 1278-1280.

_________, Curtis W. Marean, Philip Chase, Iain Davidson, Clive Gamble, Trenton W. Holliday, Richard G. Klein, Sally McBrearty, and João Zilhão. 2003. The Origin of Modern Human Behavior: Critique of the Models and their Test Implications. Current Anthropology 44:5 (December), pp. 627-651.

Holden, Constance. 2004. Oldest Beads Suggest Early Symbolic Behavior. Science 304:5669 (16 April), p. 369.

Lewin, Roger. 1989. Ice Age Idea Toppled. Science 243:4897 (17 March), p. 1435.

Marshack, Alexander. 1964. Lunar Notations on Upper Paleolithic Remains. Science 146:3645 (6 November), pp. 743-745.

_________. 1972. The Roots of Civilization: The Cognitive Beginnings of Man's First Art, Symbol, and Notation. New York: McGraw-Hill Book Company.

_________. 1989. Ice Age Art Analysis. Science 244:4908 (26 April), p. 1029.

_________. 1995. Methodology and the Search for Notation among Engraved Pebbles of the European Late Paleolithic. Review of Francesco d’Errico, L’Art Gravé Azilien de la Technique à la Signification. Antiquity 69:266 (December), pp. 1049-1051.

_________. 1997. On ‘Close Reading’ and Decoration Versus Notation. Current Anthropology 38:1 (February), pp. 81-83.

_________. 1998. Notched Bone. http://202.38.126.651mirror/archives.math.utk.edu/hypermaillhistorialnov9810225.html, updated 23 November 1998, accessed 15 May 2007.

_________ and Francesco d’Errico. 1989. On Wishful Thinking and Lunar ‘Calendars.’ Current Anthropology 30:4 (August-October), pp. 491-500.

McCowan, Brenda, Sean F. Hanser, and Laurance R. Doyle. 1999. Quantitative Tools for Comparing Animal Communication Systems: Information Theory Applied to Bottlenose Dolphin Whistle Repertoires. Animal Behaviour 57:2, pp. 409-419.

Nadis, Steve. 2003. Look Who’s Talking. New Scientist 179:2403 (12 July), pp. 36-39.

Sharpe, Kevin and Mary Lacombe. 2002. Translating Paleolithic Line Markings. http://www.ksharpe.com/word/AR07.htm, updated 7 December 2002, accessed 22 April 2007.

_________ and Mary Lacombe. 2003. Line Markings as Systems of Notation? In Robert G. Bednarik, ed., Rock Art and Epistemology: Courting Sophistication. International Federation of Rock Art Organizations, Vol. 3 (Turnhout, Belgium: Brepols Publishers).

_________ and Leslie Van Gelder. 2006a. The Study of Finger Flutings. Cambridge Archaeological Journal 16:3 (October), pp. 281-295.

_________ and Leslie Van Gelder. 2006b. Evidence for Cave Marking by Paleolithic Children. Antiquity 80:310 (December), pp. 937-947.

_________ and Leslie Van Gelder. 2006c. Finger Flutings in Chamber A1 of Rouffignac Cave, France. Rock Art Research 23:2 (November), pp. 179-198.

_________ and Leslie Van Gelder. In Press a. Fluted Animals in the Zone of Crevices, Gargas Cave, France. To appear in the Proceedings of the Eleventh Congress of the International Federation of Rock Art Organizations, Lisbon, Portugal, 4-9 September 2006.

_________ and Leslie Van Gelder. In Press b. Four Forms of Finger Flutings as Seen in Rouffignac Cave, France. To appear in a festschrift for Alexander Marshack.

Stitt, J. Michael. 2007. Protowriting. http://www.unlv.edu/Faculty/jmstitt/Eng480/Writing/ProtoWriting.html, accessed 22 April.

Vanhaeren, Marian, Francesco d’Errico, Chris Stringer, Sarah L. James, Jonathan A. Todd, and Henk K. Mienis. 2006. Middle Paleolithic Shell Beads in Israel and Algeria. Science 312:5781 (23 June), pp. 1785-1788.

Zipf, George Kingsley. 1949. Human Behavior and the Principle of Least Effort. Cambridge, MA: Addison-Wesley Press.