Tag Archive: mathematics



The Antikythera mechanism is a 2,100-year-old computer:

Wikipedia
Antikythera mechanism Wikipedia

116 years ago (1902), divers found a chunk of bronze off a Greek island. It has radically changed our understanding of human history.

One hundred sixteen years ago, an archaeologist was sifting through objects found in the wreck of a 2,000-year-old vessel off the Greek island Antikythera. Among the wreck’s treasures, fine vases and pots, jewellery and, fittingly enough, a bronze statue of an ancient philosopher, he found a peculiar contraption, consisting of a series of brass gears and dials mounted in a case the size of a mantel clock. Archaeologists dubbed the instrument the Antikythera mechanism. The genius — and mystery — of this piece of ancient Greek technology is that arguably it is the world’s first computer. If we gaze inside the machine, we find clear evidence of at least two dozen gears, laid neatly on top of one another, calibrated with the precision of a master-crafted Swiss watch. This was a level of technology that archaeologists would usually date to the sixteenth century AD. But a mystery remained: What was this contraption used for? 

To archaeologists, it was immediately apparent that the mechanism was some sort of clock, calendar or calculating device. But they had no idea what it was for. For decades, they debated. Was the Antikythera a toy model of the planets or was it a kind of early astrolabe, a device which calculates latitude?

IMAGE ancient

At long last, in 1959, Princeton science historian Derek J. de Solla Price provided the most convincing scientific analysis of this amazing device to date. After a meticulous study of the gears, he deduced that the mechanism was used to predict the position of the planets and stars in the sky depending on the calendar month. The single primary gear would move to represent the calendar year, and would, in turn, activate many separate smaller gears to represent the motions of the planets, sun and moon. So you could set the main gear to the calendar date and get close approximations for where those celestial objects in the sky on that date. And Price declared in the pages of Scientific American that it was a computer: “The mechanism is like a great astronomical clock ... or like a modern analogue computer which uses mechanical parts to save tedious calculation.”
 
Anticythera mechanism frontal

Antikythera mechanism original
It was a computer in the sense that you, as a user, could input a few simple variables and it would yield a flurry of complicated mathematical calculations. Today the programming of computers is written in digital code, a series of ones and zeros. This ancient analog clock had its code written into the mathematical ratios of its gears. All the user had to do was enter the main date on one gear, and through a series of subsequent gear revolutions, the mechanism could calculate variables such as the angle of the sun crossing the sky. As a point of referencdee, mechanical calculators using gear ratios to add and subtract, didn’t surface in Europe until the 1600s. 

Since Price’s assessment, modern X-ray and 3D mapping technology have allowed scientists to peer deeper into the remains of the mechanism to learn even more of its secrets. In the early 2000s, researchers discovered text in the guise of an instruction manual that had never been seen before, inscribed on parts of the mechanism. The text, written in tiny typeface but legible ancient Greek, helped them bring closure to complete the puzzle of what the machine did and how it was operated.
 
The mechanism had several dials and clock faces, each which served a different function for measuring movements of the sun, moon, stars, and planets, but they were all operated by just one main crank. Small stone or glass orbs moved across the machine’s face to show the motion of Mercury, Venus, Mars, Saturn, and Jupiter in the night sky and the position of the sun and moon relative to the 12 constellations of the zodiac. Another dial would forecast solar and lunar eclipses and even, amazingly enough, predictions about their colour. Today, researchers surmise that different coloured eclipses were considered omens of the future. After all, the ancient Greeks, like all ancients, were a little superstitious. 

The mechanism consisted of:
- a solar calendar, charting the 365 days of the year 
- a lunar calendar, counting a 19 year lunar cycle 
- a tiny pearl-size ball that rotated to illustrate the phase of the moon, and another dial that counted down the days to regularly scheduled sporting events around the Greek isles, like the Olympics.  The mechanics of this device are absurdly complicated. A 2006, in the journal Nature, a paper plotted out a highly complex schematic of the mechanics that connect all the gears. 

Researchers are still not sure who exactly used it. Did philosophers, scientists and even mariners build it to assist them in their calculations? Or was it a type of a teaching tool, to show students the math that held the cosmos together? Was it unique? Or are there more similar devices yet to be discovered? To date, none others have been found.

Its assembly remains another mystery. How the ancient Greeks accomplished this astonishing feat is unknown to this day. Whatever it was used for and however it was built, we know this: its discovery has forever changed our understanding of human history, and reminds us that flashes of genius are possible in every human era. Nothing like this instrument is preserved elsewhere. Nothing comparable to it is known from any ancient scientific text or literary allusion,” Price wrote in 1959. “It is a bit frightening, to know that just before the fall of their great civilization the ancient Greeks had come so close to our age, not only in their thought, but also in their scientific technology.”

There are amazing fully operational modern versions of the Antikythera Mechanism, such as these:

3d-reconstruction-ancient-antikythera-mechanism-770x437

another modern version of the Antikythera mechanism

Antikythera_model_front_panel_Mogi_Vicentini_2007


Linear B numerals 100, 1k and 10k are atemporal, like those in the movie. Arrival:

It is quite clear from the following illustration of the numbers 1-12 in the Heptapod circular language, which correspond to the number of ships landing on earth, that their numbers, occurring in a circle, are similar to the numerals for 100, 1k and 10k in Mycenaean Linear A. This correspondence reveals an intriguing characteristic of these Linear B numerals, namely, that they can serve as ideograms for extraterrestrial communication. In other words, just as the Heptapod numbers serve to communicate from the extraterrestrials, the Linear B numerals can serve to communicate with them or any other extraterrestrial civilization.

movie Arrival heptapod 12 and Linear B 100 1k 10k

 


Is the Minoan Linear A labrys inscribed with I-DA-MA-TE in Minoan or in proto-Greek? PART A: Is it in the Minoan language?

In my previous post on the Minoan Linear A labrys inscribed with I-DA-MA-TE, I postulated that the word Idamate was probably either the name of the king or of the high priestess (of the labyrinth?) to whom this labrys has been ritually dedicated. But in so doing I was taking the path of least resistance, by seeking out the two most simplistic decipherments which would be the least likely to prove troublesome or controversial. In retrospect, that was a cop-out.

No sooner had I posted my two alternate simplistic translations than I was informed by a close colleague of mine in the field of diachronic historical linguistics focusing on Minoan Linear A and Mycenaean Linear B that at least two other alternative decipherments came into play, these being:

1. that the term Idamate may be the Minoan equivalent of the Mycenaean Linear B Damate, which is apparently an early version of the ancient Greek, Demeter, who was the goddess of cereals and harvesting:

demeter-ceres-greco-roman-marble-statue-state-hermitage-museum-st-petersburg

linear-b-lexicon-damate-demeter

2. that the term Idamate may be Minoan for Mount Ida, in which case, the word Mate = “mount”, such that the phrase actually spells out  “Ida mount(ain)” :

mount-ida-psiloritis

Since both of these decipherments make eminent sense, either could, at least theoretically, be correct.
 
But there is a third alternative, and it is far more controversial and compelling than either of the first two. 

3. It is even possible that the four syllabograms I DA MA & TE are in fact supersyllabograms, which is to say that each syllabogram is the first syllabogram, i.e. the first syllable of a word, presumably a Minoan word. But if these 4 supersyllabograms represent four consecutive Minoan words, what on earth could these words possibly signify, in light of the fact that we know next to nothing about the Minoan language. It appears we are caught in an irresolvable Catch-22.

Yet my own recent research has allowed me to tease potential decipherments out of 107 or about 21 % of all intact words in Prof. John G. Youngers Linear A lexicon of 510 terms by my own arbitrary count. Scanning this scanty glossary yielded me numerous variations on 3 terms which might conceivably make sense in at least one suppositious context. These terms (all of which I have tentatively deciphered) are:

1. For I: itaja = unit of liquid volume for olive oil (exact value unknown)

2. FOR DA: either:
daropa = stirrup jar = Linear B karawere (high certainty)
or
datara = (sacred) grove of olive trees
or
data2 (datai) = olive, pl. date = Linear B erawo
or
datu = olive oil
or
daweda = medium size amphora with two handles

3. For TE:
tereza = large unit of dry or liquid measurement
or
tesi = small unit of measurement

But I cannot find any equivalent for MA other than maru, which seemingly means “wool”, even in Minoan Linear A, this being the apparent equivalent of Mycenaean Linear B mari or mare.  The trouble is that this term (if that is what the third supersyllabogram in idamate stands in for) does not contextually mesh at all with any of the alternatives for the other three words symbolized by their respective supersyllabograms.

But does that mean the phrase is not Minoan? Far from it. There are at least 2 cogent reasons for exercising extreme caution in jumping to the conclusion that the phrase cannot be in Minoan. These are:    
1. that the decipherments of all of the alternative terms I have posited for the supersyllabograms I DA & TE above are all tentative, even if they are more than likely to be close to the mark and some of them probably bang on (for instance, daropa), which I believe they are;
2. that all 3 of the supersyllabograms I DA & TE may instead stand for entirely different Minoan words, none of which I have managed to decipher. And God knows there are plenty of them!  Since I have managed to decipher only 107 of 510 extant intact Minoan Linear A words by my arbitrary count, that leaves 403 or 79 % undeciphered!  That is far too great a figure to be blithely brushed aside. 

The > impact of combinations of a > number of Minoan Linear A words on their putative decipherment:

combinations-with-repetition-and-their-impact-on-the-decipherment-of-minoan-linear-a-terms

To give you a rough idea of the number of undeciphered Minoan words beginning with I DA & TE I have not been able to account for, here we have a cross-section of just a few of those words from Prof. John G. Younger’s Linear A Reverse Lexicon:
which are beyond my ken:

linear-a-reverse-lexicon

For I:
iininuni
ijadi
imetu
irima
itaki

For DA:
dadana
daini
daki
daku
daqaqa

For MA:
madadu
majasa
manuqa
masuri

For TE:
tedatiqa
tedekima
tenamipi
teneruda

But the situation is far more complex than it appears at first sight. To give you just a notion of the enormous impact of exponential mathematical permutations and combinations on the potential for gross errors in any one of a substantial number of credible decipherments of any given number of Minoan Linear A terms as listed even in the small cross-section of the 100s of Minoan Words in Prof. John G. Younger’s Reverse Linear A Lexicon, all we have to do is relate the mathematical implications of the  chart on permutations to any effort whatsoever at the decipherment of even a relatively small no. of Minoan Linear A words:

CLICK on the chart of permutations to link to the URL where the discussion of both permutations and combinations occurs:

permutations-and-the-decipherment-of-minoan-linear-a

to realize how blatantly obvious it is that any number of interpretations of any one of the selective cross-section of terms which I have listed here can be deemed the so-called actual term corresponding to the supersyllabogram which supposedly represents it. But, and I must emphatically stress my point, this is just a small cross-section of all of the terms in the Linear B Reverse Lexicon beginning with each of  the supersyllabograms I DA MA & TE in turn.

It is grossly obvious that, if we allow for the enormous number of permutations and combinations to which the supersyllabograms I DA MA & TE must categorically be  subjected mathematically, it is quite out of the question to attempt any decipherment of these 4 supersyllabograms, I DA MA & TE, without taking context absolutely into consideration. And even in that eventuality, there is no guarantee whatsoever that any putative decipherment of each of these supersyllabograms (I DA MA & TE) in turn in the so-called Minoan language will actually hold water, since after all, a smaller, but still significant subset of an extremely large number of permutation and combinations must still remain incontestably in effect.

The mathematics of the aforementioned equations simply stack up to a very substantial degree against any truly convincing decipherment of any single Minoan Linear A term, except for one small consideration (or as it turns out, not so small at all). As it so happens, and as we have posited in our first two alternative decipherments above, i.e.
1. that Idamate is Minoan for Mycenaean Damate, the probable equivalent of classical Greek Demeter, or
2. that Idamate actually means “Mount Ida”,

these two possible decipherments which do make sense can be extrapolated from the supersyllabograms I DA MA & TE, at least if we take into account the Minoan Linear A terms beginning with I DA & TE (excluding TE), which I have managed, albeit tentatively, to decipher.

However, far too many putative decipherments of the great majority of words in the Minoan language itself are at present conceivable, at least to my mind. Yet, this scenario is quite likely to change in the near future, given that I have already managed to tentatively decipher 107 or 21 % of 510 extant Minoan Linear A words, by my arbitrary count.  It is entirely conceivable that under these circumstances I shall be able to decipher even more Minoan language words in the near future. In point of fact, if Idamate actually does mean either Idamate (i.e. Demeter) or Ida Mate (i.e. Mount Ida), then:
(a) with only 2 possible interpretations for IDAMATE now taken into account, the number of combinations and permutations is greatly reduced to an almost insignificant amount &
(b) the actual number of Minoan Linear A words I have deciphered to date rises from 107 to 108 (in a Boolean OR configuration, whereby we can add either  “Demeter” or “Mount Ida” to our Lexicon, but not both).  A baby step this may be, but a step forward regardless. 


Before we can decipher even a single Linear A tablet on olive oil, we must decipher as many as we can in Linear B, because... PART A: delivery of olive oil

Before we can plausibly (and frequently tentatively) decipher even a single Linear A tablet on olive oil, we must decipher as many as we can in Linear B, because there are so many facets to be taken fully into consideration in the olive oil sub-sector of the agricultural sector of the Minoan/Mycenaean economy related to the production of olive oil which on an adequate number of Linear B tablets (at least 10), mostly from Knossos, dealing with harvesting from olive oil trees and the production and delivery of olive oil that we must account for every single term related to olive oil on the Linear B tablets, and then compile a list of all of these terms in order to cross-correlate these with equivalent terms on the Linear A tablets, mostly from Haghia Triada.

Another vital factor which just occurred to me is that the Minoan economy appears to have been primarily centred in Haghia Triada, while the Mycenaean primarily in Knossos, with valuable contributions from Pylos as well. In other words, the economic centre or power house, if you will, of the Minoan economy appears to have been Haghia Triada and not Knossos. I am somewhat baffled by the fact that researchers to date have not taken this important factor adequately into account. It appears to reveal that Knossos had not yet risen to prominence in the Minoan economy in the Middle Minoan Period (ca. 2100-1600 BCE):

the three Periods of Minoan Civilization

The gravest challenge confronting us in the cross-correlation of the several economic terms related to olive oil production in the late Minoan III 3a period under Mycenaean suzerainty (ca. 1500-1450 BCE)  with potentially equivalent terms in Minoan Linear A arises from the mathematical theoretical constructs of combinations and permutations. Given, for instance, that there are potentially a dozen (12) terms related to olive oil production on an adequate number (10-12)  Linear B tablets to afford effectual cross-correlation, how on earth are we to know which terms in Mycenaean Linear B correspond to apparently similar terms in Minoan Linear A? In other words, if we for instance extrapolate a total of 12 terms from Mycenaean Linear B tablets, how are we to line or match up the Mycenaean Linear B terms in a “Column A” construct with those in Minoan Linear B in “Column B”? There is no practical way that we can safely assert that term A (let us say, for the sake of expediency, that this word is apudosi = “delivery”) in Mycenaean Greek corresponds to term A in Minoan Linear  A, rather than any of B-L, in any permutation and/or in any combination. This leads us straight into the trap of having to assign ALL of the signified (terms) in Mycenaean Linear A to all of the signified in Minoan Linear B. I shall only be able to definitively demonstrate this quandary after I have deciphered as many Linear B tablets on olive oil as I possibly can.

340 APUDOSI

349 APUDOSI


379 APUDOSI

For the time being, we have no choice but to set out on our search with these 3 tablets, all of which prepend the first term apudosi = “delivery” to the ideogram for olive oil. In closing, I wish to emphatically stress that this is precisely the signified I expected to turn up in the list of terms potentially related to olive oil production in Mycenaean Linear B. It is also the most important of all Mycenaean Linear B terms prepended to the ideogram for “olive oil on the Linear B tablets. When we come to making the fateful decision to assign the the correct Minoan Linear A term meaning just that, delivery” on the Linear A tablets dealing with olive oil, how are we to know which Linear A signified corresponds to Linear B apudosi = “delivery”? Still the situation is not as bad as you might think, at least for this term. Why so? Because if it appears (much) more often on the Linear B tablets (say, theoretically, 5 times versus less than 5 for all the other terms in Linear B related to olive oil), then the term appearing the most frequently on Minoan Linear A tablets related to olive oil is more likely than not to be the equivalent of apudosi, i.e. to mean  “delivery”.

The less frequent the occurrence of any particular term relative to olive oil on the Mycenaean Linear B tablets, the greater the room there is for error, to the point that where a term appears only once on all of the Linear B tablets we can manage to muster up for translation, it becomes next to impossible to properly align that term with any of the terms occurring only once on the Minoan Linear A tablets, especially where more than one signified occurs on the Mycenaean Linear B tablets. If for example, 3 terms occur only once on the Linear B tablets, which one(s) aligns with which one(s) on the Linear A? A messy scenario. But we must make the best of the situation, bite the bullet, and cross-correlate these 3 terms in all permutations and combinations (= 9!) from the Linear B to the Linear A tablets containing them. This I shall definitively illustrate in a Chart once I have translated all terms related to olive oil production in Mycenaean Linear A.


PDF uploaded to academia.edu application to Minoan Linear A & Mycenaean Linear B of AIGCA (artificial intelligence geometric co-ordinate analysis) 

AIGCA (artificial intelligence geometric co-ordinate analysis) by supercomputers or via the high speed Internet is eminently suited for the identification and parsing unique cursive scribal hands in Mycenaean Linear B without the need of such identification by manual visual means.

To read this ground-breaking scientific study of the application of AIGCA (artificial intelligence geometric co-ordinate analysis)to the parsing of unique cursive scribal hands, click on this banner: 

geometric co-ordinate analysis Linear A & Linear B academia
 

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

a figure 1 geometric economy of Linear B

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

b figure 2 o cursive

(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

c figure3 Pylos tablet TA 641-1952

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

d figure 4 CF Linear A Linear B symmetric

e figure 5 circular Linear A & Linear B
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

f figure 6 ccomplex co-ordinate analysis

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:

b figure 2 o cursive

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:

g figure7 cmplex
h figure8 cursive scribal hands me no ri we

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

i figure 9 KN 935 G d 02 TW

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



The Linear B “pakana” or – sword – series of tablets, their translations and the implications: PART A

It is common knowledge in the Linear B linguistic research community that there are a great many series of Linear B tablets which share marked formulaic textual characteristics. Among these we find the Linear B “pakana” or – sword – series of tablets and fragments, amounting to some 15, from KN 1540 O k 01 to KN 1556 O k 11. I have assigned my research colleague, Rita Roberts, who is at the mid-term mark of her first year of university studies into Mycenaean Linear B, the challenging task of translating all 14 or 15 of these tablets and fragments (most of them fragments), in an effort to extrapolate from her translations findings which can and do confirm and validate the hypothesis that the tablets and fragments in this series are almost all variations on a “standard”, hence formulaic, text. This is the first of several posts in which we shall be analyzing the results of Rita’s findings. Once we have posted all of our co-operative findings, Rita and I shall be co-authoring an article on the formulaic nature of the tablets and fragments in this series in particular on academia.edu, the results of which can be extrapolated to any number of series of tablets and fragments of Linear B tablets from Knossos (and some from Pylos as well), regardless of the sector of the Minoan-Mycenaean economy on which they focus, the most notable being the sheep husbandry sub-sector of the agricultural sector, for which there are almost 700 (!) extant tablets, or some 10 times more than in any other sector of the Minoan-Mycenaean economy, inclusive of this one, the military. 

In the meanwhile, we are focusing our attention on this series of tablets in particular.

Here are the first three translations in series Rita Roberts has submitted, with her explanatory notes following them, these followed in turn by interpretive notes of my own, where applicable. The first tablet, largely intact, offers us an all but complete snapshot, so to speak, of the actual formulaic text underpinning almost all of the tablets in this series. Click to ENLARGE:

Military Affairs 1541 0k 09 (xc) tEXT

Mrs. Robert’s translation of this tablet is, as usual, precise, technically sound and elegant.

I do, however, have a few additional comments to make on the translation of this tablet among others strikingly similar to it, here: Click to ENLARGE

Knossos tablet KN 1541 O k 09 versus KN 1542 to KN 1556
It all comes to one observation and one only. The texts of all of the tablets I have mentioned above, however fragmentary, are merely minor variations of one another, in other words, they are all formulaic. The text of any one of them is close to a mirror image of any of the others, usually with only one or two attributes and the number of tablets inventoried in each at variance. That is the single factor we need to focus on above all else, though not exclusively to the exclusion of others.

The next translation Rita Roberts makes is of Knossos fragment KN 1542 OK 18 (XC), which contains only the tail end of a Mycenaean Linear B word terminating in “woa”  and the ideogram for sword. Click to ENLARGE:

Knossos tablet KN1542 O k 18 (xc) Text

It is painfully obvious that the left-truncated word ending in “woa” is in fact and can only be, “araruwoa”, meaning “bound” (a sword bound with a hilt) and nothing else. This, the only practicable translation for this little fragment, which is only a snippet or tiny subset of the missing text the fragment represents, leads us directly to the highly plausible inference that the actual text of this fragment, were it intact as a tablet entire, would have almost certainly have read very much like this:

A skilled horn worker has bound the hilt with horn and fixed it to the sword’s blade with rivets.

Sound familiar? You may very well protest, “Aren’t you jumping to conclusions?” and you might have been right, were it not for the fact that, as we soon shall see in subsequent posts detailing the contents of several other tablets and fragments in the same series, snippets of the very same text, more or less intact, keep popping up. And among these, two tablets — the first of which we have already seen as the first figure in this post — spell out the text entire (less one or two words, if any). So it stands to reason that if, in so far as the missing text of this tiny fragment almost certainly is the same as that of the other tablets, with minor variations in wording and in the number of swords tallied, this little scrap of text is a mathematical subset of the text we have already encountered in the first of the tablets posted in this series (KN 1541 OK 09 (xc)), then other, more complete, snippets of the same text appearing on other tablets we are soon to investigate simply confirm and validate our assumption, corroborated by the cumulative evidence brought to bear by the partial or complete text of those other tablets in this series.

Finally, turning our attention to the third translation Rita Roberts has effected (Click to ENLARGE):

Military Affairs 1543 0k 17 Trans

we discover, scarcely to our surprise at this point, that the text of KN 1543 OK 17, though not as complete as that of the first tablet posted here (KN 1541 OK 09 (xc)), is practically a mirror image of the former. The formulaic nature of the text of almost all of the tablets in this series ( KN 1540 O k 01 to KN 1556 O k 11), with few exceptions, is as we say nowadays, “in your face”. This simple fact based on strict observation of the variations on the recurrent text to be found on almost all of these tablets firmly confirms the hypothesis that in fact formulaic phrasing is a prime characteristic of all of the tablets in this series, and for that matter, in any number of series of tablets in Linear B from Knossos, regardless of economic sector. It is the tablets in the sheep husbandry sector, of which there around 700 (far more than in any other sector), which confirm and concretize this conclusion over and over.

Rita has also translated Knossos tablet KN 1540 O k 01 (xc) here: 

Rita Roberts translaton of Knosssos tablet KN 1540 OK 01
which I have just reblogged below for your convenience.

It is highly advisable for you to read this post in toto, as it sheds significant light on the present discussion. It is in fact this very tablet upon which we are to draw our ultimate conclusions with reference to the translations of this entire series of tablets. In our final post in this serial discussion, we shall actually  cite the text of this previous post in its entirety, with additional glosses reflecting any further conclusions we may have drawn once all of the tablets in this series have been posted.

Richard



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: 

cuneiform font
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):

A xy analysis
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),

B Sumerian Akkadian Babylonian stamping
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):

C geometric co-ordinate analysis of early mesopotamian cuneifrom

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):

D alternate geometric forms
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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