The ancient Greek alphabetical numeric system:This chart illustrates both the ancient Greek acrophonic and alphabetical numeric systems. However, the acrophonic system, used primarily in Classical Athens ca. 500 – 400 BCE, came much later than the alphabetical system. So in effect we must resort to the only Greek numeric system we can use to represent numbers in Mycenaean Greek numbers, i.e. the alphabetical system. The alphabetical numbers are displayed in the second column after the modern numbers, 1 – 100,000 in the following chart. Here are some examples of alphabetic numbers representing Mycenaean numbers:
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Tag Archive: mathematics
The Antikythera mechanism is a 2,100-year-old computer: Wikipedia116 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.”
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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:
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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.
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:![]()
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)” :
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. Younger’s 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:
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:
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:
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.