The application of geometric co-ordinate analysis (GCA) to parsing scribal hands: Part A: Cuneiform
Introduction:
I propose to demonstrate how geometric co-ordinate analysis of cuneiform, the Edwin-Smith hieroglyphic papyrus (ca. 1600 BCE), Minoan Linear A, Mycenaean Linear B and Arcado-Cypriot Linear C can confirm, isolate and identify with great precision the X Y co-ordinates of single characters or syllabograms in their respective standard fonts, and in the multiform cursive “deviations” from their fixed font forms, or to put it in different terms, to parse the running co-ordinates of each character, syllabogram or ideogram of any scribal hand in each of these scripts. This procedure effectively encapsulates the “style” of any scribe’s hand, just as we would nowadays characterize any individual’s handwriting style. This hypothesis constitutes a breakthrough in the application of graphology a.k.a epigraphy based entirely on the scientific procedure of geometric co-ordinate analysis (GCA) of scribal hands, irrespective of the script under analysis.
Cuneiform:
Any attempt to isolate, identify and characterize by manual visual means alone the scribal hand peculiar to any single scribe incising a tablet or series of tablets common to his own hand, in other words, in his own peculiar style, has historically been fraught with difficulties. I intend to bring the analysis of scribal hands in cuneiform into much sharper focus by defining them as constructs determined solely by their relative positioning on the X Y axis plane in two-dimensional Cartesian geometry. This purely scientific approach reduces the analysis of individual scribal hands in cuneiform to a single constant, which is the point of origin (0,0) in the X Y axis plane, from which the actual positions of each and every co-ordinate on the positive planes (X horizontally right, Y vertically up) and negative planes (X horizontally left, Y vertically down) are extrapolated for any character in this script, as illustrated by the following general chart of geometric co-ordinates (Click to ENLARGE):
Although I haven’t the faintest grasp of ancient cuneiform, it just so happens that this lapsus scientiae has no effect or consequence whatsoever on the purely scientific procedure I propose for the precise identification of unique individual scribal hands in cuneiform, let alone in any other script, syllabary or alphabet ancient or modern (including but not limited to, the Hebrew, Greek, Latin, Semitic & Cyrillic alphabets), irrespective of language, and even whether or not anyone utilizing said procedure understands the language or can even read the script, syllabary or alphabet under the microscope.
This purely scientific procedure can be strictly applied, not only to the scatter-plot positioning of the various strokes comprising any letter in the cuneiform font, but also to the “deviations” of any individual scribe’s hand or indeed to a cross-comparative GCA analysis of various scribal hands. These purely mathematical deviations are strictly defined as variables of the actual position of each of the various strokes of any individual’s scribal hand, which constitutes and defines his own peculiar “style”, where style is simply a construct of GCA analysis, and nothing more. This procedure reveals with great accuracy any subtle or significant differences among scribal hands. These differences or defining characteristics of any number of scribal hands may be applied either to:
(a) the unique styles of any number of different scribes incising a trove of tablets all originating from the same archaeological site, hence, co-spatial and co-temporal, or
(b) of different scribes incising tablets at different historical periods, revealing the subtle or significant phases in the evolution of the cuneiform script itself in its own historical timeline, as illustrated by these six cuneiform tablets, each one of which is characteristic of its own historical frame, from 3,100 BCE – 2,250 BCE (Click to ENLARGE),
and in addition
(c) Geometric co-ordinate analysis is also ideally suited to identifying the precise style of a single scribe, with no cross-correlation with or reference to any other (non-)contemporaneous scribe. In other words, in this last case, we find ourselves zeroing in on the unique style of a single scribe. This technique cannot fail to scientifically identify with great precision the actual scribal hand of any scribe in particular, even in the complete absence of any other contemporaneous cuneiform tablet or stele with which to compare it, and regardless of the size of the cuneiform characters (i.e. their “font” size, so to speak), since the full set of cuneiform characters can run from relatively small characters incised on tablets to enormous ones on steles. It is of particular importance at this point to stress that the “font” or cursive scribal hand size have no effect whatsoever on the defining set of GCA co-ordinates of any character, syllabogram or ideogram in any script whatsoever. It simply is not a factor.
To summarize, my hypothesis runs as follows: the technique of geometric co-ordinate analysis (GCA) of scribal hands, in and of itself, all other considerations aside, whether cross-comparative and contemporaneous, or cross-comparative in the historical timeline within which it is set ( 3,100 BCE – 2,250 BCE) or lastly in the application of said procedure to the unambiguous identification of a single scribal hand is a strictly scientific procedure capable of great mathematical accuracy, as illustrated by the following table of geometric co-ordinate analysis applied to cuneiform alone (Click to ENLARGE):
The most striking feature of cuneiform is that it is, with few minor exceptions (these being circular), almost entirely linear even in its subsets, the parallel and the triangular, hence, susceptible to geometric co-ordinate analysis at its most fundamental and most efficient level.
It is only when a script, syllabary or alphabet in the two-dimensional plane introduces considerably more complex geometric variables such as the point (as the constant 0,0 = the point of origin on an X Y axis or alternatively a variable point elsewhere on the X Y axis), the circle and the oblong that the process becomes significantly more complex. The most common two-dimensional non-linear constructs which apply to scripts beyond the simple linear (such as found in cuneiform) are illustrated in this chart of alternate geometric forms (Click to ENLARGE):
These shapes exclude all subsets of the linear (such as the triangle, parallel, pentagon, hexagon, octagon, ancient swastika etc.) and circular (circular sector, semi-circle, arbelos, superellipse, taijitu = symbol of the Tao, etc.), which are demonstrably variations of the linear and the circular.
These we must leave to the geometric co-ordinate analysis of Minoan Linear A, Mycenaean Linear B and Arcado-Cypriot Linear C, all of which share these additional more complex geometric constructs in common. When we are forced 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 manually parse scribal hands or handwriting by visual means or analysis at all. Prior to the advent of the Internet and modern supercomputers, geometric co-ordinate analysis of any phenomenon, let alone scribal hands, or so-to-speak 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 applied at that time. But nowadays, this procedure 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 an innumerable number of unique scribal hand(s) or of handwriting styles can be isolated and identified beyond a reasonable doubt, and in the blink of an eye. Much more on this in Part B, The application of geometric co-ordinate analysis to Minoan Linear A, Mycenaean Linear B and Arcado-Cypriot Linear C. However strange as it may seem prima facie, I leave to the very last the application of this 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.
© by Richard Vallance Janke 2015 (All Rights Reserved = Tous droits réservés)
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Peter J. Keyse provides a thorough analysis of Linear B tablet KN Dd 1171 in this fascinating article, which is well worth reading for anyone who is familiar with the Linear B syllabary, and certainly for anyone who is studying Linear B in depth. His article is not without errors. For instance, he deciphers PoRo as the name of someone in what he calls the PoMe “worker class” = a shepherd,
but his interpretation of of PORO is clearly incorrect, as this word has 3 distinct meanings, one of which is the Linear B word for “a foal”, as demonstrated by Chris Tselentis in his Linear B Lexicon, here:
(The other 2 meanings of POME offered by Tselentis do not fit the context) while POME is quite obviously Mycenaean Greek for “shepherd”:
Keyse also notes that Michael Ventris identified 3 major styles for incisions - those at Knossos, Pylos and Mycenae. In his own words: The vertical lines are quite faint scratches and not easily seen. The cuts in the clay are ‘under-cut’ i.e. pushed in at an angle . This preoccupation with Linear B scribal hands recurs in a great many articles on Linear B. Keyse also covers the what he ascertains to be the phonetic sounds of the numerics on this tablet. He also emphasizes the nature and particulars characteristics of the scribal hand on this tablet. But it his conclusion which is most fascinating. He says, In conclusion: What would Dd1171 sound like if read aloud? Po-Ro. 20 OVISm, 72 OVISf. Pa-I-To. Pa 8 OVISm. While it reasonable to say that Linear B was no more the spoken language of its day than ‘double-entry bookkeeping’ speak is for accounting clerks today it is also true to say that accountants do on occasions talk in journals and double-entry (and not only when at dinner parties and down the pub) and they certainly call over inventories to each other. It is clear that Linear B had a sound but perhaps it is unlikely that we can fairly reproduce it today. Considering the importance of numbers within the Linear B archive I find it surprising that no phonic system has been devised to represent them or if devised is not clearly documented in the literature. COMMENT by Richard Vallance Janke on the sound, i.e. the general pronunciation of Linear B. In actuality, we probably do have some idea of how Mycenaean Greek was pronounced. Its closest cousin was Arcado-Cypriot, represented both by its own syllabary, Linear C, and by its own archaic alphabet. The Mycenaean and Arcado-Cypriot dialects were much closer phonetically than even Ionic and Attic Greek. Phonological details of the archaic Arcado-Cypriot dialect appear in C.D. Buck, The Greek Dialects, © 1955, 1998. ISBN 1-85399-566-8, on pg. 144. He provides even more information on Arcado-Cypriot on pp. 7-8, and classifies it as an East Greek dialect, pg. 9. This is highly significant, because if Arcado-Cypriot is East Greek, ergo Mycenaean Greek also is. This places both of the archaic East-Greek dialects, Mycenaean and Arcado-Cypriot, firmly in the camp of all East Greek dialects, including Arcadian, Aeolic, Lesbian, Cyprian, Pamphylian, Thessalian, Boeotian, and the much later Ionic and Attic dialects. So it is probably fair to say that we may have at least an idea, even if somewhat inaccurate, of how Mycenaean Greek was pronounced. And this has huge implications for the further study of Mycenaean Greek phonology.
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