PART B: The application of geometric co-ordinate analysis (GCA) to parsing scribal hands in Minoan Linear A and Mycenaean Linear B
Introduction:
I propose to demonstrate how geometric co-ordinate analysis of Minoan Linear A and Mycenaean Linear B can confirm, isolate and identify with precision the X Y co-ordinates of single syllabograms, homophones and ideograms in their respective standard fonts, and in the multiform cursive “deviations” from the invariable on the X Y axis, the point of origin (0,0) on the X Y plane, and how it can additionally parse the running co-ordinates of each character, syllabogram or ideogram of any of the cursive scribal hands in each of these scripts. This procedure effectively epitomizes the “style” of any scribe’s hand, just as we would nowadays characterize any individual’s handwriting style. This hypothesis is at the cutting edge in the application of graphology a.k.a epigraphy exclusively based on the scientific procedure of artificial intelligence geometric co-ordinate analysis (AIGCA) of scribal hands, irrespective of the script under analysis.
If supercomputer or ultra high speed Internet generated artificial intelligence geometric co-ordinate analysis of Sumerian and Akkadian cuneiform is a relatively straightforward matter, as I have summarized it in my first article [1], that of Minoan Linear A and Mycenaean Linear B, both of which share more complex additional geometric constructs in common, appears to be somewhat more of a challenge, at least at first glance. When we come to apply this technique to more complex geometric forms, the procedure appears to be significantly more difficult to apply. Or does it? The answer to that question lies embedded in the question itself. The question is neither closed nor open, but simply rhetorical. It contains its own answer.
It is in fact the hi-tech approach which decisively and instantaneously resolves any and all difficulties in every last case of geometric co-ordinate analysis of any script, syllabary or indeed any alphabet, ancient or modern. It is neatly summed up by the phrase, “computer-based analysis”, which effectively and entirely dispenses with the necessity of having to parse scribal hands or handwriting by manual visual means or analysis at all. Prior to the advent of the Internet, modern supercomputers and artificial intelligence(AI), geometric co-ordinate analysis of any phenomenon, let alone scribal hands, or handwriting post AD (anno domini), would have been a tedious mathematical process hugely consuming of time and human resources, which is why it was never attempted then.
The groundbreaking historical epigraphic studies of Emmett L. Bennet Jr. and Prof. John Chadwick (1966):
All this is not to say that some truly remarkable analyses of scribal hands in Mycenaean Linear B were not realized in the twentieth century. Although such studies have been few and far between, one in particular stands out as pioneering. I refer of course to Emmett L. Bennet Jr.’s remarkable paper, “Miscellaneous Observations on the Forms and Identities of Linear B Ideograms” (1966) [2], in which he single-handedly undertook a convincing epigraphic analysis of Mycenaean Linear B through manual visual observation alone, without the benefit of supercomputers or the ultra-high speed internet which we have at our fingertips in the twenty-first century. His study centred on the ideograms for wine (*131), (olive) oil (*130), *100 (man), *101 (man) & *102 (woman) rather than on any of the Linear B syllabograms as such. The second, by John Chadwick in the same volume, focused on the ideogram for (olive) oil. As contributors to the same Colloquium, they essentially shared the same objectives in their epigraphic analyses. Observations which apply to Bennett’s study of scribal hands are by and large reflected by Chadwick’s. Just as we find in modern handwriting analysis, both Bennett and Chadwick concentrated squarely on the primary characteristics of the scribal hands of a considerable number of scribes. Both researchers were able to identify, isolate and classify the defining characteristics of the various scribal hands and the attributes common to each and every scribe, accomplishing this remarkable feat without the benefit of super high speed computer programming.
Although Prof. Bennett Jr. did not systematically enumerate his observations on the defining characteristics of particular scribal hands in Mycenaean Linear B, we shall do so now, in order to cast further light on his epigraphic observations of Linear B ideograms, and to situate these in the context of the twenty-first century hi tech process of geometric co-ordinate analysis to scribal hands in Mycenaean Linear B.
I have endeavoured to extrapolate the rather numerous variables Bennett assigned determining the defining characteristics of various scribal hands in Linear B. They run as follows (though they do not transpire in this order in his paper):
(a) The number of strokes (vertical, horizontal and diagonal – right or left – vary significantly from one scribal hand to the next. This particular trait overrides most others, and must be kept uppermost in mind. Bennett characterizes this phenomenon as “opposition between varieties”. For more on the concept of ‘oppositions’, see my observations on the signal theoretical contribution by Prof. L. R. Palmer below.
(b) According to Bennet, while some scribes prefer to print their ideograms, others use a cursive hand. But the very notion of “printing” as a phenomenon per se cannot possibly be ascribed to the Linear B tablets. Bennet’s so-called analysis of scribal “printing” styles I do not consider as printing at all, but rather as the less common scribal practice of precise incision, as opposed to the more free-form cursive style adopted by most Linear B scribes. Incision of characters, i.e. Linear B, syllabograms, logograms and ideograms, predates the invention of printing in the Western world by at least two millennia, and as such cannot be attributed to printing as we understand the term. Bennett was observing the more strictly geometric scribal hands among those scribes who were more meticulous than others in adhering more or less strictly to the dictates of linear, circular and other normalized attributes of geometry, as outlined in the economy of geometric characteristics of Linear B in Figure 1: Click to ENLARGE
But even the more punctilious scribes were ineluctably bound to deviate from what we have established as the formal modern Linear B font, the standard upon which geometric co-ordinate analysis depends, and from which all scribal hands in both Minoan Linear A and Mycenaean Linear B, the so-called “printed” or cursive, must necessarily derive or deviate.
(c) as a corollary of Bennet’s observation (b), some cursive hands are sans serif, others serif.
(d) similarly, the length of any one or any combination of strokes, sans serif or serif, can clearly differentiate one scribal hand from another.
(e) as a corollary of (c), some serif hands are left-oriented, while the majority are right-oriented, as illustrated here in Figure 2: Click to ENLARGE
(f) As a function of (d) above, the “slant of the strokes” Bennett refers to is the determinant factor in the comparison between one scribal hand and any number of others, and as such constitutes one of the primary variables in his manual visual analytic approach to scribal hands.
(g) In some instances, some strokes are entirely absent, whether or not accidentally or (un)intentionally.
(h) Sometimes, elements of each ideogram under discussion (wine, olive oil and man, woman or human) touch, just barely touch, retouch, cross, just cross, recross or fully (re)cross one another. According to Bennet, these sub-variables can often securely identify the exact scribal hand attributed to them.
(i) Some strokes internal to each of the aforementioned ideograms appear to be partially unconnected to others, in the guise of a deviance from the “norm” as defined by Bennett in particular, although I myself am unable to ascertain which style of ideogram is the “norm”, whatever it may be, as opposed to those styles which diverge from it, i.e. which I characterize as mathematically deviant from the point of origin (0,0) on the X Y co-ordinate axis on the two-dimensional Cartesian plane. Without the benefit of AIGCA, Bennett could not possibly have made this distinction. Whereas any partially objective determination of what constitutes the “norm” in any manual scientific study not finessed by high speed computers was pretty much bound to be arbitrary, the point of origin (0,0) on the X Y axis of the Cartesian two-dimensional plane functions as a sound scientific invariable from which we define the geometrically pixelized points of departure by means of ultra high speed computer computational analysis (AIGCA).
(j) The number of strokes assigned to any ideogram in Linear B can play a determinant role. One variation in particular of the ideogram for wine contains only half the number of diagonal strokes as the others. This Bennett takes to be the deviant ideogram for must, rather than wine itself, and he has reasonably good grounds to make this assertion. Likewise, any noticeable variation in the number of strokes in other ideograms (such as those for olive oil and humans) may also be indicators of specific deviant meanings possibly assigned to each of them, whatever these might be. But we shall never know. With reference to the many variants for “man” or human (*101), I refer you to Bennett’s highly detailed chart on page 22 [3]. It must be conceded that AI geometric co-ordinate analysis is incapable of making a distinction between the implicit meanings of variants of the same ideogram, where the number of strokes comprising said ideogram vary, as in the case of the ideogram for wine. But this caveat only applies if Bennet’s assumption that the ideogram for wine with fewer strokes than the standard actually means (wine) must. Otherwise, the distinction is irrelevant to the parsing by means of AIGCA of this ideogram in particular or of any other ideogram in Linear B for which the number of strokes vary, unless corroborating evidence can be found to establish variant meanings for each and every ideogram on a case by case basis. Such a determination can only be made by human analysis.
(k) As Bennett has it, the spatial disposition of the ideograms, in other words, how much space each ideogram takes up on the various tablets, some of them consuming more space than others, is a determinant factor. He makes a point of stressing that some ideograms are incised within a very “cramped and confined space”. The practice of cramming as much text as possible into an allotted minimum of remaining space on tablets was commonplace. Pylos tablet TA 641-1952 (Ventris) is an excellent example of this ploy so many scribes resorted to when they discovered that they had used up practically all of the space remaining on any particular tablet, such as we see here on Pylos tablet 641-1952 (Figure 3): Click to ENLARGE
Yet cross comparative geometric analysis of the relative size of the “font” or cursive scribal hand of this tablet and all others in any ancient script, hieroglyphic, syllabary, alphabetical or otherwise, distinctly reveals that neither the “font” nor cursive scribal hand size have any effect whatsoever on the defining set of AIGCA co-ordinates — however minuscule (as in Linear B) or enormous (as in cuneiform) — of any character, syllabogram or ideogram in any script whatsoever. It simply is not a factor.
(l) Some ideograms appear to Bennett “almost rudimentary” because of the damaged state of certain tablets. It is of course not possible to determine which of these two factors, cramped space or damage, impinge on the rudimentary outlines of some of the same ideograms, be these for wine (must), (olive) oil or humans, although it is quite possible that both factors, at least according to Bennet, play a determinant rôle in this regard. But in fact they cannot and do not, for the following reasons:
1. So-called “rudimentary” incisions may simply be the result of end-of-workday exhaustion or carelessness or alternatively of remaining cramped space;
2. As such, they necessarily detract from an accurate determination of which scribe’s hand scribbled one or more rudimentary incisions on different tablets, even by means of AIGCA;
3. On the other hand, the intact incisions of the same scribe (if they are present) may obviate the necessity of having to depend on rudimentary scratchings. But the operative word here is if they are present. Not only that, even in the presence of intact incisions by said scribe, it all depends on the total number of discrete incisions made, i.e. on the number of different syllabograms, logograms, ideograms, word dividers (the vertical line in Linear B), numerics and other doodles. We shall more closely address this phenomenon below.
(m) Finally, some scribes resort to more elaborate cursive penning of syllabograms, logograms, ideograms, the Linear B word dividers, numerics and other marks, although it is open to serious question whether or not the same scribe sometimes indulges in such embellishments, and sometimes does not. This throws another wrench into the accurate identification of unique scribal hands, even with AIGCA.
The aforementioned variables as noted though not explicitly enumerated by Bennett summarize how he and Chadwick alike envisioned the prime characteristics or attributes, if you like, the variables, of various scribal hands. Each and every one of these attributes constitutes of course a variable or a variant of an arbitrary norm, whatever it is supposed to be. The primary problem is that, if we are to lend credence to the numerous distinctions Bennet ascribes to scribal hands, there are simply far too many of these variables. When one is left with no alternative than to parse scribal hands by manual visual means, as were Bennet and Chadwick, there is just no way to dispense with a plethora of variations or with the arbitrary nature of them. And so the whole procedure (manual visual inspection) is largely invalidated from a strictly scientific point of view.
In light of my observations above, as a prelude to our thesis, the application of artificial geometric co-ordinate analysis (AIGCA) to scribal hands in Minoan Linear A and Mycenaean Linear B, I wish to draw your undivided attention to the solid theoretical foundation laid for research into Linear B graphology or epigraphy by Prof. L.R. Palmer, one of the truly exceptional pioneers in Linear B linguistic research, who set the tone in the field to this very day, by bringing into sharp focus the single theoretical premise — and he was astute enough to isolate one and one only — upon which any and all research into all aspects of Mycenaean Linear B must be firmly based.
I find myself compelled to quote a considerable portion of Palmer’s singularly sound foundational scientific hypothesis underpinning the ongoing study of Linear which he laid in The Interpretation of Mycenaean Greek Texts [4]. (All italics below mine). Palmer contends that....
The importance of the observation of a series of ‘oppositions’ at a given place in the formulaic structure may be further illustrated... passim... A study of handwriting confirms this conclusion. The analysis removes the basis for a contention that the tablets of these sets were written at different times and list given herdsmen at different stations. It invalidates the conclusion that the texts reflect a system of transhumance (see p. 169 ff.).
We may insist further on the principle of economy of theses in interpretation... passim... See pp. 114 ff. for the application of this principle, with a reduction in the number of occupational categories.
New texts offer an opportunity for the most rigorous application of the principle of economy. Here the categories set up for the interpretation of existing materials will stand in the relation of ‘predictions’ to the new texts, and the new material provides a welcome opportunity for testing not only the decipherment but also interpretational methods. The first step will be to interpret the new data within the categorical framework already set up. Verificatory procedures will then be devised to test the results which emerge. If they prove satisfactory, no furthers categories will be added.
The number of hypotheses set up to explain a given set of facts is an objective measure of the ‘arbitrary’, and explanations can be graded on a numerical scale. A completely ‘arbitrary’ explanation is one which requires x hypotheses for y facts. It follows that the most ‘economical’ explanation is the least ‘arbitrary’.
I could not have put it better myself. The more economical the explanation, in other words, the underlying hypothesis, the less arbitrary it must necessarily be. In light of the fact that AIGCA reduces the hypothetical construct for the identification of scribal style to a single invariable, the point of origin (0,0) on the two-dimensional Cartesian X Y plane, we can reasonably assert that this scientific procedure practically eliminates such arbitrariness. We are reminded of Albert Einstein’s supremely elegant equation E = Mc2 in the general theory of relatively, which reduces all variables to a single constant.
Yet, what truly astounds is the fact that Palmer was able to reach such conclusions in an age prior to the advent of supercomputers and the ultra high speed Internet, an age when the only means of verifying any such hypothesis was the manual visual. In light of Palmer’s incisive observations and the pinpoint precision with which he draws his conclusion, it should become apparent to any researcher in graphology or epigraphy delving into scribal hands in our day and age that all of Bennet’s factors are variables of geometric patterns, all of which in turn are mathematical deviations from the point of origin (0,0) on the two-dimensional X Y Cartesian axis. As such Bennet’s factors or variables, established as they were by the now utterly outdated process of manual visual parsing of the differing styles of scribal hands, may be reduced to one variable and one only through the much more finely tuned fully automated computer-generated procedure of geometric co-ordinate analysis. When we apply the technique of AI geometric co-ordinate analysis to the identification, isolation and classification of scribal hands in Linear B, we discover, perhaps not to our surprise, that all of Bennet’s factors (a to m) can be reduced to geometric departures from a single constant, namely, the point of origin (0,0) on the X Y axis of a two-dimensional Cartesian plane, which alone delineates the “style” of any single scribe, irrespective of the script under analysis, where style is defined as a function of said analysis, and nothing more.
It just so happens that another researcher has chosen to take a similar, yet unusually revealing, approach to manual visual analysis of scribal hands in 2015. I refer to Mrs. Rita Robert’s eminently insightful overview of scribal hands at Pylos, a review of which I shall undertake in light of geometric co-ordinate analysis in my next article.
Geometric co-ordinate analysis via supercomputer or the ultra high speed Internet:
Nowadays, geometric co-ordinate analysis can be finessed by any supercomputer plotting CGA co-ordinates down to the very last pixel at lightning speed. The end result is that any of a number of unique scribal hands or of handwriting styles using ink, ancient on papyrus or modern on paper, can be identified, isolated and classified in the blink of an eye, usually beyond a reasonable doubt. However strange as it may seem prima facie, I leave to the very last the application of this practically unimpeachable procedure to the analysis and the precise isolation of the unique style of the single scribal hand responsible for the Edwin Smith papyrus, as that case in particular yields the most astonishing outcome of all.
Geometric co-ordinate analysis: Comparison between Minoan Linear A and Mycenaean Linear B:
Researchers and linguists who delve into the syllabaries of Minoan Linear A and Mycenaean Linear B are cognizant of the fact that the syllabograms in each of these syllabaries considerably overlap, the majority of them (almost) identical in both, as attested by Figures 4 & 5: Click to ENLARGE
By means of supercomputers and/or through the medium of the ultra-high speed Internet, geometric co-ordinate analysis (AIGCA) of all syllabograms (nearly) identical in both of syllabaries can be simultaneously applied with proximate equal validity to both.
Minoan Linear A and Mycenaean Linear B share a geometric economy which ensures that they both are readily susceptible to AI geometric co-ordinate analysis, as previously illustrated in Figure 1, especially in the application of said procedure to the standardized font of Linear B, as seen here in Figure 6: Click to ENLARGE
And what applies to the modern standard Linear B font inevitably applies to the strictly mathematical deviations of the cursive hands of any number of scribes composing tablets in either syllabary (Linear A or Linear B). Even more convincingly, AIGCA via supercomputer or the ultra high speed Internet is ideally suited to effecting a comparative analysis and of parsing scribal hands in both syllabaries, with the potential of demonstrating a gradual drift from the cursive styles of scribes composing tablets in the earlier syllabary, Minoan Linear A to the potentially more evolved cursive hands of scribes writing in the latter-day Mycenaean Linear B. AICGA could be ideally poised to reveal a rougher or more maladroit style in Minoan Linear A common to the earlier scribes, thus potentially revealing a tendency towards more streamlined cursive hands in Mycenaean Linear B, if it ever should prove to be the case. AIGCA could also prove the contrary. Either way, the procedure yields persuasive results.
This hypothetical must of course be put squarely to the test, even according to the dictates of L.R. Palmer, let alone my own, and confirmed by recursive AICGA of numerous (re-)iterations of scribal hands in each of these syllabaries. Unfortunately, the corpus of Linear A tablets is much smaller than that of the Mycenaean, such that cross-comparative AIGCA between the two syllabaries will more than likely prove inconclusive at best. This however does not mean that cross-comparative GCA should not be adventured for these two significantly similar scripts.
Geometric co-ordinate analysis of Mycenaean Linear B:
A propos of Mycenaean Linear B, geometric co-ordinate analysis is eminently suited to accurately parsing its much wider range of scribal hands. An analysis of the syllabogram for the vowel O reveals significant variations of scribal hands in Mycenaean Linear B, as illustrated in Figure 2 above, repeated here for convenience:
Yet the most conspicuous problem with computerized geometric co-ordinate analysis (AIGCA) of a single syllabogram, such as the vowel O, is that even this procedure is bound to fall far short of confirming the subtle or marked differences in the individual styles of the scores and scores of scribal hands at Knossos alone, where some 3,000 largely intact tablets have been unearthed and the various styles of numerous other scribes at Pylos, Mycenae, Thebes and other sites where hundreds more tablets in Linear B have been discovered.
So what is the solution? It all comes down to the application of ultra-high speed GCA to every last one of the syllabograms on each and every one of some 5,500+ tablets in Linear B, as illustrated in the table of several Linear B syllabograms in Figures 7 and 8, through which we instantly ascertain those points where mathematical deviations on all of the more complex geometric forms put together utilized by any Linear B scribe in particular leap to the fore. Here, the prime characteristics of any number of mathematical deviations of scribal hands for all geometric forms, from the simple linear and (semi-)circular, to the more complex such as the oblong, wave form, teardrop and tomahawk, serve as much more precise markers or indicators highly susceptible of revealing the subtle or significant differences among any number of scribal hands. Click to ENLARGE Figures 7 & 8:
By zeroing in on Knossos tablet KN 935 G d 02 (Figure 9) we ascertain that the impact of the complexities of alternate geometric forms on AIGCA is all the more patently obvious: Click to ENLARGE
When applied to the parsing of every last syllabogram, homophone, logogram, ideogram, numeric, Linear B word divider and any other marking of any kind on any series of Linear B tablets, ultra high speed geometric co-ordinate analysis can swiftly extrapolate a single scribe’s style from tablet KN 935 G d 02 in Figure 9, revealing with relative ease which (largely) intact tablets from Knossos share the same scribal hand with this one in particular, which serves as our template sample. We can be sure that there are several tablets for which the scribal hand is in common with KN 935 G d 02. What’s more, extrapolating from this tablet as template all other tablets which share the same scribal hand attests to the fact that AIGCA can perform the precise same operation on any other tablet whatsoever serving in its turn as the template for another scribal hand, and so on and so on.
Take any other (largely) intact tablet of the same provenance (Knossos), for which the scribal hand has previously been determined by AIGCA to be different from that of KN 935 G d 02, and use that tablet as your new template for the same cross-comparative AICGA procedure. And voilà, you discover that the procedure has extrapolated yet another set of tablets for which there is another scribal hand, in other words, a different scribal style, in the sense that we have already defined style. But can what works like a charm for tablets from Knossos be applied with relative success to Linear B tablets of another provenance, notably Pylos? The difficulty here lies in the size of the corpus of Linear B tablets of a specific provenance. While AIGCA is bound to yield its most impressive results with the enormous trove of some 3,000 + (largely) intact Linear B tablets from Knossos, the procedure is susceptible of greater statistical error when applied to a smaller corpus of tablets, such as from Pylos. It all comes down to the principle of inverse ratios. And where the number of extant tablets from other sources is very small, as is the case with Mycenae and Thebes, the whole procedure of AIGCA is seriously open to doubt.
Still, AIGCA is eminently suited to clustering in one geometric set all tablets sharing the same scribal hand, irrespective of the number of tablets and of the subset of all scribal hands parsed through this purely scientific procedure.
Conclusion:
We can therefore safely conclude that ultra high speed artificial intelligence geometric co-ordinate analysis (AIGCA), through the medium of the supercomputer or on the ultra high speed Internet, is well suited to identifying, isolating and classifying the various styles of scribal hands in both Minoan Linear A and Mycenaean Linear B.
In Part C, we shall move on to the parsing of scribal hands in Arcado-Cypriot Linear C, of the early hieratic handwriting of the scribe responsible for the Edwin Smith Papyrus (1600 BCE) and ultimately of the vast number of handwriting styles and fonts of today.
References and Notes:
[1] The application of geometric co-ordinate analysis (GCA) to parsing scribal hands: Part A: Cuneiform
https://www.academia.edu/17257438/The_application_of_geometric_co-ordinate_analysis_GCA_to_parsing_scribal_hands_Part_A_Cuneiform
[2] “Miscellaneous Observations on the Forms and Identities of Linear B Ideograms” pp. 11-25 in, Proceedings of the Cambridge Colloquium on Mycenaean Studies. Cambridge: Cambridge University Press, © 1966. Palmer, L.R. & Chadwick, John, eds. First paperback edition 2011. ISBN 978-1-107-40246-1 (pbk.)
[3] Op. Cit., pg. 22
[4] pp. 33-34 in Introduction. Palmer, L.R. The Interpretation of Mycenaean Texts. Oxford: Oxford at the Clarendon Press, © 1963. Special edition for Sandpiper Book Ltd., 1998. ix, 488 pp. ISBN 0-19-813144-5
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All of the aforementioned examples make it quite clear that ideograms, whether they be as ancient as those in Linear A and Linear B (i.e. about 3,400 years old) or modern ... or for that matter, neolithic or even earlier, all bear a striking resemblance to one another. Take for instance the Linear A ideogram for “scales” and compare it with just one modern one (among so many others), and we see immediately that they are extremely similar. Now take the Linear B ideograms for “man” and “woman” and compare these with the washroom symbols for the same and once again the similarity is almost too good to be true. Then there is the Linear B ideogram for a four-spoke wheel compared with a modern one for an eight-spoke wheel. The number of spokes is not relevant to this discussion, only the fact that the ancient Linear B ideogram for “wheel” is practically identical to the modern one. The implications for the decipherment of ideograms in any language, ancient or modern (let alone Linear A and Linear B) versus those in any modern language are staggering. We can be sure that the ancient ideograms varied little from one language to another, let alone between Minoan and Mycenaean. In fact, the syllabogram TE, which sometimes represents wheat, in Linear A and Linear B is almost identical to the same ideograms in cuneiform! It is patently obvious that since the distinction between the ancient ideograms and their modern equivalents enumerated above is so thin, all of these ideograms (or logograms or icons) are not only time independent (atemporal) and spatially independent (aspatial), they are also language independent. This is a stunning phenomenon. The implications for the further decipherment of Linear A are simply overwhelming. And this is why in the movie, Arrival, the heptapods assert, “There is no time.”
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