The Minoan “Seki” (尺)

· Architecture, Linear A
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Updated on April 29, 2012

[This article presumes knowledge about both the Minoan civilization and the Linear A transcriptions.]

A hallmark of Minoan architecture is ashlar masonry, which refers to stone that has been cut and finished (dressed). Ashlar masonry is common throughout prehistoric Crete and Greece. The width of large ashlar, as used on Crete, is generally larger than the 14″ (35 cm) that is used in European masonry. Comparatively, the width of small ashlar is less than 12″ (30.48 cm) [“Ashlar”]. Costis Davaras states that the basis of Minoan measurement was the Minoan “foot”, which was 30.36 (.996 ft) [Davaras 19]. Compare the Japanese shaku (尺), which “is almost indistinguishable from the Minoan foot” [Knight and Butler] and may exhibit symbolic similarity.

The basis of the archaic, Japanese shaku is 30.30 cm (.994 ft) [“Shaku”]. However, the shaku, as the kane-jaku (曲尺), is still used in Japanese architecture. The kane-jaku is decimally based and may be divided into 10 sun, 100 bun, and 1,000 rin [“Measure”]. When multiplied, 10 kane-jaku equal 1 jo [“Shaku (unit)”]. Note that kane-jaku has been defined as metal jaku to distinguish it from the kujira-jaku that is used in tailoring [“Shaku (unit)”].

However, there are two definitions for kane. The first uses the kanji for gold (kin) and means metal. The second is an archaic term and uses the kanji for carpenter’s square. Alternate definitions in this latter sense are perpendicularity or straightness, on the one hand, and model or standard, on the other hand. Consequently, the kane-jaku may also be called the standard, or common, jaku, while metal jaku appears to be a reanalysis of the original term, since carpenter’s squares typically comprise metal.

shaku

The sinistroverse and the dextroverse LinA symbols are identical to the dextroverse Japanese symbol, which may be read as either seki or shaku. Neither of these Japanese readings provides a phonetic value for *301 as it appears in LinA texts. Nevertheless, it should be noted that seki and shaku mean stone. It should also be noted that an alternate word for stone is ishi and that the Japanese word for ashlar is kiriishi, from kiri “to cut” + ishi “stone”. Compare ki.ri.si (kirishi) (TY 4). Consequently, the kane-jaku may be defined as a square for cutting stone.

The kane-jaku may be distinguished from the korai-jaku [“Shaku (unit)”], or ancient jaku. The korai-jaku, while no longer used, measured 35.50 cm, which is slightly less than 14” (35.56 cm). It is no small coincidence that the kane-jaku and the korai-jaku respectively correspond to the measurements of small and large ashlar.

In a comparison between the Minoan foot and the Japanese kane-jaku, the difference, after 3,500 years, is .06 cm (.002 ft)! Nevertheless, this .06 cm difference proves significant when multiplied 1,000 times. Alexander Thom is credited with the discovery of the neolithic standard of measurement, which he called the “megalithic yard” and which measures 82.96656 cm (2.722 ft). Consequently, the megalithic yard, when multiplied by 366 [Knight and Butler], equals 1,000.18 Minoan feet, 1,002.17 kane-jaku, and 996.25 English feet, with fit accuracies of .9998 (Minoan), .9978 (Japanese), and 1.0038 (English). The order of these tolerances suggests that the English foot may have been an “inaccurate” derivation of the Minoan foot.

The shaku is said to have originated in China during the Shang Dynasty in the 13th century BCE [“Japanese”]. However, the shaku’s Chinese origin is problematic for at least three reasons.

Firstly, since the Shang Dynasty, the Mandarin chi, as the shaku is known, has steadily grown from 16.75 cm to the present length of 33.33 cm. Over the centuries, the length has changed approximately 11 times and has included at least two regressions (see tables) [“Chinese Units”]. The period during which the chi and the kane-jaku were approximately identical briefly occurred during the Ming Dynasty. Consequently, it is not feasible that the kane-jaku, which is nearly identical to the ancient Minoan foot, is inspired by the Mandarin chi, which was variously applied to astronomy, customs and trade, engineering, and surveying [“Shaku (unit)”].

Secondly, modern China recognizes three disparate modern units:

  • the Mandarin (Chinese) chi (尺), which measures 33.33 cm,
  • the Hong Kong (Cantonese) chek (呎), which measures 37.15 cm, and
  • the Taiwanese chi, which measures 30.30 cm [“Shaku”].

The megalithic yard, when multiplied by 366, equals 911.06 Chinese chi, 817.38 Cantonese chek, and 1002.17 Taiwanese chi. The fit accuracies for these values are 1.0976 (Chinese), 1.2234 (Cantonese), and .9978 (Taiwanese). Moreover, the Cantonese chek suggests a borrowed term, since, linguistically, it is closer to shaku than to chi.

Thirdly, while only the Taiwanese chi is identical to the Japanese shaku, China did not recognize Taiwan until the 17th century CE [“Taiwan”]. More than likely, the Minoan foot, via the Japanese shaku, influenced the Taiwanese chi, rather than vice versa.

Given the correspondences of the Japanese shaku to Minoan architecture, to the megalithic yard, and to LinA, it is highly unlikely that Japan borrowed from China, as is commonly believed. It is highly likely, however, that China adapted the Japanese system to a multitude of very different applications and that historians gave to China undeserved credit.

Addendum

Consistent with research findings and with the information provided by Roland A. Boucher (see comments), I am assigning the phonetic value, RI, to AB *188.  In ancient times, the ri was considered equal to the length of a village [“Li”]. Consequently, the modern Japanese kanji has a Chinese on reading of RI and a Japanese kun reading of sato. The latter reading is found in furosato, which means ancient village (see Naru Kanashi: The Paradise Across the Ocean).

Added on 24 Apr 2012.

MLA Citation:

  • Leonhardt, Gretchen E. The Minoan “Seki”. Naru Kanashi. 25 Dec 2011. Ret. on [date]. <geleonhardt.wordpress.com>.

REFERENCES:

  1. Ashlar. Golden Map. goldenmap.com. Ret. on 25 Sep 2011.
  2. Chinese Units of Measurement. Wikipedia.org. Ret. on 28 Dec 2011.
  3. Davaras, Costis. A Guide to Cretan Antiquities. Park Ridge, NJ: Noyes Press, 1976.
  4. Japanese Units of Measurement. Global Oneness. ExperienceFestival.com. Ret. on 25 Dec 2011.
  5. Knight, Christopher, and Butler, Alan. Megalithic pint, anyone? Red Ice Creations. 2008. Ret. on 25 Dec 2011. <redicecreations.com>.
  6. Linear A and Linear B. Aegean 600: Unicode Fonts for Ancient Scripts. (PDF) Edited by George Douros. 2011. Downloaded on 03 Aug 2011.
  7. Li (unit). Wikipedia.org. Ret. on 17 Mar 2012.
  8. Measure: Shaku / Sun / Bu / Rin. chibabudogu.com. Ret. on 25 Dec 2011.
  9. Shaku. Fact-Index.com. Ret. on 11 Nov 2011.
  10. Shaku (unit). Wikipedia.org. Ret. on 11 Nov 2011.
  11. Taiwan. Wikipedia.org. Ret. on 25 Dec 2011.

6 Comments

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  1. Donald Kingsbury, Mathematician, McGill University, retired

    My hobby is ancient metrology (the science of measurement), especially of length as it pertains to the question: “Could this length have been calibrated by an ancient pendulum?”

    The Japanese shaku (30.30cm) and the Minoan foot (30.48 cm) are easy to calibrate, although the result on Okinawa may differ from the result on Crete due to the slightly different gravitational acceleration, which varies a little by latitude and altitude.

    According to the computational-knowledge engine, WolframAlpha, the gravity at Knossos is 9.79753 meters per solar second, squared (m/s^2) at 57m altitude, and the gravity at Okinawa is 9.78849 m/s^2 at 86m altitude; I’ll use the latter calculation for my pendulum simulation. But first I must calibrate my pendulum.
    [Ed. note: When superscript is unavailable, ^ may be used for exponential notation.]

    The ancients, as far as I know, were limited in their use of solar time via the sundial, which is not a very accurate clock because (a) the solar second (sol-sec), unlike my manufactured second, varies over the course of a year, and (b) the large sun produces a fuzzy shadow, which makes difficult the computation of precise seconds. Sidereal time is a different matter because (a) the sidereal second (sid-sec) does not vary over the course of a year, and (b) since stars appear as points, the timing of a star as it crosses an angular slot of arc is very accurate.

    So, to calibrate a pendulum using sidereal time, I need a long base-line radius with an angular slot of night sky on the circumference of circular arc. I then count the swing cycles of my pendulum as a star crosses my slot. In one swing cycle, the pendulum begins at center (equilibrium), swings to its highest point, returns through equilibrium to the opposite point, and returns to equilibrium. The count gives me the period (P) of my pendulum, which, when squared, is proportional to its length (L). By varying the count, I can vary the length, which, later, can be accurately duplicated by using the same count.

    The shaku is determined by a nice count of 45000 (2^3 x 3^2 x 5^4) swings per sidereal day (86400 sid-sec).

    So, to simulate a pendulum on Okinawa, I must first convert gravity (g) from the given units of m/sol-sec^2 to sidereal gravity in units of m/sid-sec^2. The conversion factor is about (366.25/365.25)^2 or, more accurately, 1.005483315. Thus, I convert the gravity at Okinawa from 9.78849m/sol-sec^2 to 9.73511 m/sid-sec^2.

    Also, I am not going to spend a whole sidereal day counting (which is slave labor even for graduate students!), so I will divide the arc of the sky with an angular slot that uses a convenient integer such as 360 (360 arc sec = 1° of sky): 45000/360 = 125 swings as the star passes through 1° of sky. If I count more than 125 swings, my pendulum must be lengthened; if I count less than 125 swings, my pendulum must be shortened.

    At both Okinawa and Knossos, P = 86400/45000 = 1.92.

    At Okinawa:
    g = 9.78849m/sol-sec^2 or 9.73511m/sid-sec^2
    Therefore,
    L = P2 x (g / 4 x pi^2) = 1.922 x 9.73511 / (4 x 3.14159^2) = 0.9090412m. Dividing by three, I get the Okinawan shaku of 0.3030137m. A small swing angle will make it a hair’s breadth shorter.

    At Knossos,
    g = 9.79753m / sec^2 or 9.74410m / sid-sec^2.
    Therefore,
    L = P^2 x (g / 4 x pi^2) = 1.92^2 x 9.7441 / (4 x 3.14159^2) = 0.9098807m. Dividing by three, I get a Cretan foot of 0.303294m.

    Since the sidereal day is universal to all cultures, these two similar feet may be independent discoveries. However, cultural contact cannot be ruled out. The Minoans, were, after all, a really great sea people before that volcano did them in, and every culture includes crazy adventurers who sometimes accomplish amazing things. Genetic markers might just provide traces of such adventurers!

    Reply

  2. Roland A. Boucher: Independant Scholar, Engineering

    Editor’s Note: Mr. Boucher is a retired engineer who received his master’s degree from Yale in 1955.

    The one-second pendulum is based upon the one-second interval, or beat, between two passes through the vertical axis. A pendulum must complete this cycle ten times in ten seconds to be considered a one-second pendulum. The length of this pendulum–-which can be created with a metal washer, string or dental floss, and a pencil–-should measure approximately 39 inches, or 994 mm (0.994 meters), from the bottom edge of the pencil to the center of the washer. The beat can be shortened by knotting the string.

    The cable is derived by multiplying the length of the one-second pendulum by 360. The Sumerians wrote 360 as 1000. The French did not use a sexagesimal numbering system so wrote 1,000 as 10x10x10. In each case, the length of the cable was the standard, so that each foot equaled 1/1000 of the cable.

    Ancient scholars modified, by small increments, the length of the pendulum and the multiplication factor that was used to establish the cable. They used numbers that made sense to astronomers. There may be 360 degrees in a circle, but there are 366 sidereal days in a year. The Minoans used 365.25, which is recognized as the solar year.

    Consequently, all cable lengths were approximately 1/360 of a degree or 1/6 of a nautical mile, which is defined as the length of one minute of latitude at 50 degrees north. The WGS84 defines the nautical mile as 1853.82 meters. One sixth of this distance is 308.97 meters, or 1000 Greek feet.

    There was considerable variation among the ancient Phoenician, Minoan, Sumerian, and Greek cables, all of which were approximately 1/6 nautical mile. The length of the Phoenician cable equalled 300.00 meters (366 x 819.67 mm), and the length of six Phoenician cables equalled 0.97097 of one nautical mile. The length of the Minoan cable equalled 303.6 meters (366 x 829.51 mm), and the length of six Minoan cables equalled .98262 of one nautical mile. The length of the Minoan pendulum can be found in the megalithic yard, which has been determined to be between 829.0 and 830.2 mm. The length of the Greek cable equalled 308.97 meters (360 x 858.25 mm), and the length of six Greek cables equalled 1.0000 of one nautical mile. The length of the Sumerian cable equalled 357.84 meters (360 x 994 mm), and the length of six Sumerian cables equalled 1.15817 of one nautical mile.

    The British cable is a modern measurement that may have been influenced by the furlong (660 British feet) or by the Greek stadia (600 Greek feet). In any case, it is defined as 1/10 of a nautical mile. Since the ancient Sumerian, Minoan, Phoenician, and Greek cables were all approximately 1/6 nautical mile, they are not related to the British cable except in name.

    Reply

  3. Roland A. Boucher: Independant Scholar, Engineering

    Gretchen, using two references, here is what I have found so far:

    In Japanese units of measurement, the Table of Lengths shows that one shaku equals .3030 meters and that one ri equals 12,960 shaku or 3,926.88 (3,927) meters.

    One hundred shaku, or 30.30 meters, equal approximately one arc second. There are 360 x 3,600, or 1,296,000, arc seconds in 360 degrees. Therefore, one ri equals 129.6 arc seconds or 1/10,000 of the earth’s circumference.

    In Li (unit), the value of the li during the Western Zhou Dynasty (1045-771 BCE) equalled 358 meters. This value represents 360 units of a one-second pendulum that is exactly 994.44 mm. This latter measurement is nearly identical to the 994 mm found in ancient Sumerian records and can easily be replicated.

    In conclusion, the Japanese ri makes use of a measurement that is directly related to the Minoan cable and that represents a decimal division of the earth’s circumference, while the Chinese li replicates the Sumerian cable.

    Reply

    • Gretchen E. Leonhardt: Independant Scholar, Minoan/Japanese Studies

      This is great information. I’m just trying to wrap my mind around the historical implications.

      However, I have some questions:

      Does the one-second pendulum refer to a distance interval (i.e. arc second) or to a time interval? Also, I understand that the British Imperial cable equals 1/10 of a nautical mile. How does it compare to the Minoan and the Sumerian cables?

      Reply

  4. Gretchen E. Leonhardt: Independant Scholar, Minoan/Japanese Studies

    Roland, thank you for your comments and your endorsement. Your engineering background provides invaluable insight about ancient navigation. Perhaps you would be interested in reconciling the traditional Japanese ri–especially as it relates to the Chinese li–with these other navigational standards.

    You stated that

    “[m]aybe it’s not so surprising that sea-faring nations a half world apart used the same navigational standards so long ago.”

    My main premise is not that the Minoan and the Japanese civilizations are concurrent cultures but that the Japanese culture is an extension of the Minoan culture. While I’m still researching this premise, preliminary evidence suggests that the foundation of the advanced Japanese culture appeared sometime around 1200-1000 BCE, about 200 to 400 years after the “collapse” of the Minoan civilization. Japanese lore suggests, perhaps, two waves of this culture, whether by sea or by land. Evidence to support my premise is forthcoming on an indefinite timetable.

    Reply

  5. Roland A. Boucher: Independant Scholar, Engineering

    Re: the similarity between the Minoan foot and the the Japanese shaku, these ancient standards of measurement are, in all probability, closely related. At first glance, the standards seem to differ by 0.6 mm out of 303 mm, but, on further examination, they are much closer and, in fact, could be considered identical. There can be no question that both of these standards belong to the same attempt to replicate a length equal to 1/6 of today’s nautical mile, a standard of accuracy that was only surpassed by the Greek foot and the Greek and the Roman stadia.

    The ancient Sumerians, in the third millennium BCE, created a system of measurements that was based on an imaginary one-second pendulum, which was almost one meter long. Distances were measured in multiples of this standard. One of these distances was a little longer than 1/6 of a nautical mile, and is known as an arc minute, while the next distance was about 30 times the arc minute, or five nautical miles. The accuracy of the Sumerian standard was improved throughout the centuries.

    Consequently, the Minoan foot was precisely derived from the length of an imaginary pendulum that swings 366 times in the period that the earth rotates 1/366 of its circumference, as measured on a line of sight with Venus. The length of this imaginary pendulum is doubled and then multiplied by 366 to produce a length which is approximately 1/6 of an arc minute. The Minoan foot is 1/1000 of this distance.

    In a similar manner, using the same formula and taking into account the difference in gravity between two locations–the origination and the destination–as well as allowing for the properties of an actual pendulum, the error is well within the measuring ability of ancient civilizations.

    Today, the arc second and the arc minute are shown on every navigational chart used on both the sea and in the air. Maybe it’s not so surprising that sea-faring nations a half world apart used the same navigational standards so long ago.

    1 Comment RSS

    Roland A. Boucher: Independent Scholar, Engineering
    March 14, 2012
    This may not seem important to the layman but, to a navigator, it meant that 360 of these basic units was one degree and that 360 degrees was all of the way around the world on a meridian through Japan. Taking a trip on this meridian would take us southward through Australia and Antarctica, then northward though Brazil, the Atlantic Ocean, Canada, Iceland, and the north pole, and then southward through Siberia and back to Japan. The length of this journey taken over 3000 years ago would have been 99 percent of what we know the true distance to be. I would like to thank Gretchen Leonhardt, on her website, “Kanashi”, for bringing this ancient Japanese measurement to the attention of scholars throughout the world.

    Reply

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