The Antikythera mechanism is a 2,100-year-old computer: 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.” 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:
Researcher Cites Ancient Minoan-era Computer:
This Minoan object preceded the heralded Antikythera Mechanism. If we take the definition of a computer as being a device that can compute, even at the most basic level, then this computer meets the bottom line of the definition.
A stone-made matrix has carved symbols on the surface of this computer related with the Sun and the Moon, serving as a cast to build a mechanism that functioned as an analog computer to calculate solar and lunar eclipses. The mechanism was also used as sundial and as an instrument calculating the geographical latitude. In this sense, it predates the astrolabe, an instrument of some antiquity (i.e. since Minoan times).
Researcher Cites Ancient Minoan-era Computer:
Researcher Minas Tsikritsis who hails from Crete — where the Bronze Age Minoan civilization flourished from approximately 2700 BC to 1500 century BC — maintains that the Minoan Age object discovered in 1898 in Paleokastro site, in the Sitia district of western Crete, preceded the heralded “Antikythera Mechanism” by 1,400 years, and was the first analog and “portable computer” in history.
“While searching in the Archaeological Museum of Iraklion for Minoan Age findings with astronomical images on them we came across a stone-made matrix unearthed in the region of Paleokastro, Sitia. In the past, archaeologists had expressed the view that the carved symbols on its surface are related with the Sun and the Moon,” Tsikritsis said.
The Cretan researcher and university professor told ANA-MPA that after the relief image of a spoked disc on the right side of the matrix was analysed it was established that it served as a cast to build a mechanism that functioned as an analog computer to calculate solar and lunar eclipses. The mechanism was also used as sundial and as an instrument calculating the geographical latitude.
Source: Athens News Agency [April 06, 2011]
For the definition of the astrolabe, see
Persian models dating as far back as the eleventh century have been found, and Chaucer wrote a Treatise on it in the late 1300s. But different models of astrolabes date as far back as somewhere around 400 BCE, when Theodora of Alexandra wrote a detailed treatise on the astrolabe. Historically, many different versions of the astrolabe have arisen since then. For a full account of astrolabes, consult Wikipedia: Astrolabe. But the whole point is that the Minoan computer predates even the earliest of these (vide supra), by at least 1,000 years!
By the Elizabethan era it consisted of a large brass ring fitted with an alidade or sighting rule:
Notice the astonishing resemblance between the Minoan computer and the astrolabe from 1608 above.
For the amazing Antikythera Mechanism, see the next post.
Earth-shattering linguistic data from the Movie, Arrival (2016) Not too long ago, I had the distinct pleasure of watching what is undoubtedly the most intellectually challenging movie of my lifetime. The movie is unique. Nothing even remotely like it has ever before been screened. It chronicles the Arrival of 12 apparent UFOs, but they are actually much more than just that. They are, as I just said, a unique phenomenon. Or more to the point, they were, are always will be just that. What on earth can this mean? The ships, if that is what we want to call them, appear out of thin air, like clouds unfolding into substantial material objects ... or so it would appear. They are approximately the shape of a saucer (as in cup and saucer) but with a top on it. They hang vertically in the atmosphere. But there is no motion in them or around them. They leave no footprint. The air is undisturbed around them. There is no radioactivity. There is no activity. There are 12 ships altogether dispersed around the globe, but in no logical pattern. A famous female linguist, Dr. Louise Banks (played by Amy Adams), is enlisted by the U.S. military to endeavour to unravel the bizarre signals emanating from within. Every 18 hours on the mark the ship opens up at the bottom (or is it on its right side, given that it is perpendicular?) and allows people inside. Artificial gravity and breathable air are created for the humans. A team of about 6 enter the ship and are transported up an immense long black hallway to a dark chamber with a dazzlingly bright screen. There, out of the mist, appear 2 heptapods, octopus-like creatures, but with 7 and not eight tentacles. They stand upright on their 7 tentacles and they walk on them. At first, the humans cannot communicate with them at all. But the ink-like substance the heptapods squirt onto the thick window between them and the humans always resolves itself into circles with distinct patterns, as we see in this composite: Eventually, the humans figure out what the language means, if you can call it that, because the meanings of the circles do not relate in any way to the actions of the heptapods. Our heroine finally discovers what their mission is, to save humankind along with themselves. They tell us... There is no time. And we are to take this literally. I extracted all of the linguistic data I could (which was almost all of it) from the film, and it runs as follows, with phrases and passages I consider of great import italicized. 1. Language is the foundation of which the glue holds civilization together. It is the first weapon that draws people into conflict – vs. - The cornerstone of civilization is not language. It is science. 2. Kangaroo... means “I don't understand.” (Watch the movie to figure this one out!) 3. Apart from being able to see them and hear them, the heptapods leave absolutely no footprint. 4. There is no correlation between what the heptapods say and what they write. 5. Unlike all written languages, the writing is semiseriographic. It conveys meaning. It doesn't represent sound. Perhaps they view our form of writing as a wasted opportunity. 6. How heptapods write: ... because unlike speech, a logogram is free of time. Like their ship, their written language has forward or backward direction. Linguists call this non-linear orthography, which raises the question, is this how they think? Imagine you wanted to write a sentence using 2 hands, starting from either side. You would have to know each word you wanted to use as well as much space it would occupy. A heptapod can write a complex sentence in 2 seconds effortlessly. 7. There is no time. 8. You approach language like a mathematician. 9. When you immerse yourself in a foreign language, you can actually rewire your brain. It is the language you speak that determines how you think. 10. He (the Chinese general) is saying that they are offering us advanced technology. God, are they using a game to converse with... (us). You see the problem. If all I ever gave you was a hammer, everything is a nail. That doesn't say, “Offer weapon”, (It says, “offer tool”). We don't know whether they understand the difference. It (their language) is a weapon and a tool. A culture is messy sometimes. It can be both (Cf. Sanskrit). 11. They (masses 10Ks of circles) cannot be random. 12. We (ourselves and the heptapods) make a tool and we both get something out of it. It's a compromise. Both sides are happy... like a win-win. (zero-sum game). 13. It (their language) seems to be talking about time... everywhere... there are too many gaps; nothing's complete. Then it dawned on me. Stop focusing on the 1s and focus on the 0s. How much of this is data, and how much is negative space?... massive data... 0.08333 recurring. 0.91666667 = 1 of 12. What they're saying here is that this is (a huge paradigm). 10Ks = 1 of 12. Part of a layer adds up to a whole. It (their languages) says that each of the pieces fit together. Many become THERE IS NO TIME. It is a zero-sum-game. Everyone wins. NOTE: there are 12 ships, and the heptapods have 7 tentacles. 7X12 = 84. 8 +4 =12. 14. When our heroine is taken up into the ship in the capsule, these are the messages she reads: 1. Abbott (1 of the 2 heptapods) is death process. 2. Louise has a weapon. 3. Use weapon. 4. We need humanity help. Q. from our heroine, How can you know the future? 5. Louise sees future. 6. Weapon opens time. 15. (her daughter asks in her dream). Why is my name Hannah? Your name is very special. It is a palindrome. It reads the same forward and backward. (Cf. Silver Pin, Ayios Nikolaos Museum and Linear A tablet pendant, Troullous). 16. Our heroine says, * I can read it. I know what it is. It is not a weapon. It is a gift. The weapon (= gift) IS their language. They gave it all to us. * If you learn it, when your REALLY learn it, you begin to perceive the way that they do. SO you can see what’'s to come (in time). It is the same for them. It is non-linear. WAKE UP, MOMMY! Then the heptapods disappear, dissolving into mere clouds, the same way they appeared out of nowhere in clouds, only in the opposite fashion. There is no time. They do not exist in time. The implications of this movie for the further decipherment of Linear A and Linear B (or for any unknown language) are profound, as I shall explain in greater detail in upcoming posts.
“Can quantum computers assist in the decipherment of Minoan Linear A?” Keynote article on academia.edu (Click on the graphical link below to download this ground-breaking article on the application of potentially superintelligent quantum quantum computers to the decipherment, even partial, of the ancient Minoan Linear A syllabary): This is a major new article on the application of quantum computers to the AI (artificial intelligence) involvement in the decipherment of the unknown ancient Minoan Linear A syllabary (ca. 2800 – 1500 BCE). This article advances the hypothesis that quantum computers such as the world’s very first fully functional quantum computer, D-Wave, of Vancouver, B.C., Canada, may very well be positioned to assist human beings in the decipherment, even partial, of the Minoan Linear A syllabary. This article goes to great lengths in explaining how quantum computers can expedite the decipherment of Minoan Linear A. It addresses the critical questions raised by Nick Bostrom, in his ground-breaking study, Superintelligence: Paths, Dangers, Strategies (Oxford University Press, 2014), in which he advances the following hypothesis: Nick Bostrom makes it clear that artificial superintelligence (AS) does not necessarily have to conform to or mimic human intelligence. For instance, he says: 1. We have already cautioned against anthropomorphizing the capabilities of a superintelligent AI. The warning should be extend to pertain to its motivations as well. (pg 105) and again, 2. This possibility is most salient with respect to AI, which might be structured very differently than human intelligence. (pg. 172) ... passim ... It is conceivable that optimal efficiency would be attained by grouping aggregates that roughly match the cognitive architecture of a human mind. It might be the case, for example, that a mathematics module must be tailored to a language module, in order for the three to work together... passim ... There might be niches for complexes that are either less complex (such as individual modules), more complex (such as vast clusters of modules), or of similar complexity to human minds but with radically different architectures. ... among others respecting the probable advent of superintelligence within the next 20-40 years (2040-2060). This is a revolutionary article you will definitely not want to miss reading, if you are in any substantial way fascinated by the application of supercomputers and preeminently, quantum computers, which excel at lightning speed pattern recognition, which they can do so across templates of patterns in the same domain, to the decipherment of Minoan Linear A, an advanced technological endeavour which satisfies these scientific criteria. In the case of pattern recognition across multiple languages, ancient and modern, in other words in cross-comparative multi-language analysis, the astonishing capacity of quantum computers to perform this operation in mere seconds is an exceptional windfall we simply cannot afford not to take full advantage of. Surely quantum computers’ mind-boggling lightning speed capacity to perform such cross-comparative multi-linguistic analysis is a boon beyond our wildest expectations.
Can quantum computers assist us in the potentially swift decipherment of ancient languages, including Minoan Linear A? No-one knows as yet, but the potential practical application of the decryption or decipherment of ancient languages, including Minoan Linear A, may at last be in reach. Quantum computers can assist us with such decipherments much much swifter than standard digital supercomputers. Here are just a few examples of the potential application of quantum computers to the decipherment of apparently related words in Minoan Linear A: dide didi dija dije dusi dusima ida idamete japa japadi japaku jari jaria jarinu kireta2 (kiretai) * kiretana * kuro * kuru kuruku maru (cf. Mycenaean mari/mare = “wool” ... may actually be proto-Greek maruku = made of wool? namikua namikudua paja pajai (probably a diminutive, as I have already tentatively deciphered a few Minoan Linear A words terminating in “ai”, all of which are diminutives. qapaja qapajanai raki rakii rakisi sati sato sii siisi taki taku takui etc. All of these examples, with the exception of * kireta2 (kiretai), kiretana & kuro *, each of which I have (tentatively) deciphered, are drawn from Prof. John G. Younger’s Linear A Reverse Lexicon: It is to be noted that I myself have been unable to decipher manually on my own any of the related terms above, with the exception of the 3 words I have just mentioned. The decipherment of kuro = “total” is 100 % accurate. I would like to add in passing that I have managed to (at least tentatively) decipher 107 Minoan Linear A words, about 21 % of the entire known lexicon. But everyone anywhere in the world will have to wait until 2018 to see the results of my thorough-going and strictly scientific research until the publication of my article on the partial decipherment of Minoan Linear A in Vol. 12 (2016) of Archaeology and Science (Belgrade), actually to be released in early 2018. But if you would like to get at least a very limited idea of what my eventual decipherment is all about, you can in the meantime consult this preview on my academia.edu account here:
The staggering implications of the power of our unconscious mindset coupled with quantum computint in the endeavour to make great technological strides in linguistics! PART A:
Or look at it this way! Quantum computers can tunnel through any complex quantum landscape, visiting all points simultaneously! This feat leaves conventional digital computers in the dust! To illustrate again:
The partial decipherment of Minoan Linear A: what I started, quantum computing could polish off! PART B
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 , 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) , 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 . 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 . (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:  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  “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.)  Op. Cit., pg. 22  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
Uploaded to academia.edu, my research on: Alan Turing & Michael Ventris: a Cursory Comparison of their Handwriting Although I originally posted this brief research paper here on our blog about two months ago, I have just uploaded a revised, and slightly more complete version of it here: which anyone of you visiting our blog may download at leisure, provided that you first sign up with academia.edu, which is a free research clearinghouse, replete with thousands of superb research articles in all areas of the humanities and arts, science and technology and, of course, linguistics, ancient and modern. The advantages of signing up with academia.edu are many. Here are just a few: 1. While it is easy enough to read any original post on our blog, it is very difficult to upload it, especially since almost all of our posts contain images, which do not readily lend themselves to uploading into a word processor such as Word or Open Office. 2. On the other hand, since almost all research articles, papers, studies, journal articles and conference papers are in PDF format, they can be uploaded from academia.edu with ease. You will of course need to install the latest version of the Adobe Acrobat Reader in order to download any research paper or article, regardless of author(s) or source(s). You can download it from here: 3. academia.edu is the perfect venue for you to set up your own personal page where you may upload as many of your research papers as you like. 4. academia.edu is also one of the best research resource hubs on the entire Internet where you can find not just scores, but even hundreds of papers or documents of (in)direct interest to you as a researcher in your own right in your own field of expertise. 5. Of course, you will want to convey this great news to any and all of your colleagues and fellow researchers, whether or not they share your own interests. My own academia.edu home page is: I would be most grateful if you were to follow me and if you would like me to follow you back, please let me know. Richard
Comparison of the Merits/Demerits of the Linear B, Greek & Latin Numeric Systems: Linear B: As can be readily discerned from the Mycenaean Linear B Numeric System, it was quite nicely suited for accounting purposes, which was the whole idea in the first place. We can see at once that it was a simple matter to count as far as 99,999. Click to ENLARGE: In the ancient world, such a number would have been considered enormous. When you are counting sheep, you surely don't need to run into the millions (neither, I wager, would the sheep, or it would have been an all-out stampede off a cliff!) It worked well for addition (a requisite accounting function), but not for subtraction, multiplication, division or any other mathematical formulae. Why not subtraction, you ask? Subtraction is used in modern credit/deficit accounting, but the Minoans and Mycenaeans took no account (pardon the pun) of deficit spending, as the notion was utterly unknown to them. Since Mycenaean accounting ran for the current fiscal year only, or as they called it, “weto” or “the running year”, and all tablets were erased once the “fiscal” year was over, then re-used all over for reasons of practicality and economy, this was just one more reason why credit/deficit accounting held no practical interest to them. Other than that, the Linear B numeric accounting system served its purpose very well indeed, being perhaps one of the most transparent and quite possibly the simplest, ancient numerical systems. Of course, the Linear B numerical accounting system never survived antiquity, since its entire syllabary was literally buried and forgotten with the wholesale destruction of Mycenaean civilization around 1200 BCE (out of sight, out of mind) for some 3,100 years before Sir Arthur Evans excavated Knossos starting in early 1900, and successfully deciphered Linear B numerics shortly thereafter. This “inconvenient truth” does not mean, however, that it was all that deficient, especially for purposes of accounting, for which it was specifically designed in the first place. Greek: On the other hand, the Greek numeric system was purely alphabetic, as illustrated above. It was of course possible to count into the tens of thousands, using additional alphabetic symbols, as in the Mycenaean Linear B system, except that the Greeks were not anywhere near as obsessive over the picayune details of accounting, counting every single commodity, every bloody animal and every last person employed in any industry whatsoever. The Minoan-Mycenaean economy was hierarchical, excruciatingly centralized and obsessive down to the very last minutiae. Not surprisingly, they shared this zealous, blinkered approach to accounting with their contemporaries, the Egyptians, with whom the Minoan-Mycenaean trade routes and economy were inextricably bound on a vast scale... much more on this later in 2014 and 2015, when we come to translating a large number of Linear B transactional economic and trade records. However, we must never forget that the Greek alphabetic system of numeric notation was the only one to survive antiquity, married as it is to the universal Arabic numeric system in use today, in the fields of geometry, theoretical and applied algebra, advanced calculus and physics applications. Click to ENLARGE: It would have been impossible for us to have made such enormous technological strides ever since the Renaissance, were it not for the felicitous marriage of alphabetic Greek and Arabic numerics (0-10), which are universally applied to all fields, both theoretical and practical, of mathematics, physics and technology today. Never forget that the Arabians took the concept of nul or zero (0) to the limit, and that theirs is the decimal system applied the world over right on through to computer science and the Internet. Latin (Click to ENLARGE): When we come to the Roman/Latin numeric system, we are at once faced with a byzantine complexity, which takes the alphabetic Greek numeric system to its most extreme. Even the ancient Greeks and Romans were well aware of the convolutions of the Latin numeric system, which made the Greek pale in comparison. And Roman numerics are notoriously clumsy for denoting very large figures into the hundreds of thousands. Beside the Roman system, the Linear B approach to numerics looks positively like child's play. Thus, while major elements of the alphabetic Greek numeric system are still in wide use today, the Roman system has practically fallen into obscurity, its applications being almost entirely esoteric, such as on clock faces or in dating books etc. And even here, while it was still common bibliographic practice to denote the year of publication in Roman numerals right on through most of the twentieth century, this practice has pretty much fallen into disuse, since scarcely anyone can be bothered to read Roman numerals anymore. How much easier it is to give the copyright year as @ 1998 than MCMXCVIII. Even I, who read Latin fluently, find the Arabic numeric notation simpler by far than the Latin. As for hard-nosed devotees of Latin notation, I fear that they are in a tiny minority, and that within a few decades, any practical application of Latin numeric notation will have faded to a historical memory. Richard