On Unit of Length Measurement in the Indus-Saraswati Civilization, and Speed of Light in the Vedic Literature
Dr M R Goyal <mrgoyal@gmail.com> August 12, 2011
Abstract
An exact value of the unit of length measurement, used in IndusSaraswati Civilization, has been determined from the precise scale discovered by Ernest Mackay in the 1930-31 season excavation at Mohenjodaro, and further correlated with the present day units of measurement. It has then been calculated and shown that the speed of light as given in the Vedic literature, when referenced with this erstwhile unit of length measurement (used in Indus-Saraswati Civilization), works out to be precisely equal to the speed of light as per modern measurements. The present article is a step-wise process followed to unveil this equality.
The Precise Scale
In his 1930-31 season at Mohenjo-daro, Ernest Mackay discovered a broken piece of shell bearing 8 divisions of precisely 6.7056mm each, with a dot and circle ve graduations apart, which suggests a decimal system. However, attempts by Mackay, to relate such a unit to the dimensions in Mohenjo-daro, were not very successful(ref Michel Danino [1]) and thus were abandoned.
Units of Length in Chanakya's Arthashas-
tra
(Chanakya was the political mentor of the legendary Indian monarch Chandragupta Maurya of 4th century BC. He was a man learned in many disciplines and wrote the famous treatise on economics called the Arthashastra
meaning the book of money). types of
In Arthashastra, Chanakya mentions two
Dhanusha s as units for measuring lengths and distances. One is the ordinary Dhanusha, consisting of 96 Angula s, and the other Dhanusha is mentioned as Garhpatya Dhanusha and consists of 108 Angulas. Chanakya also mentions many other units including a Dhanurgraha, which consists of 1 4 Angula s and a Yojana , as consisting of 8000 Dhanusha s.
3
or 4
Decoding the Mohenjo-daro Scale
Angula s,
the precise length of an
If we keep 10 divisions of the Mohenjo-daro scale to be equal to a
Angula
Dhanurgraha
works out to be 16.764mm.
A Dhanusha of 96 Angulas = 96 16.764mm = 1.609344m
And
(1)
A Dhanusha of 108 Angulas = 108 16.764mm = 1.810512m. 1 Y ojana = 8000 Dhanushas(of 108 Angulas each)
Thus
(2)
(3)
1 Y ojana = 8000 1.810512m = 14.484096km
Further
(4)
14.484096km = 9 miles, (exactly!).
Also
(5)
1000 Dhanushas of 96 Angulas each = 1 mile
Interestingly, when we look into the history of
(6)
mile, we nd that the word mile is derived from mille, which means a thousand. This points to universal
adaptation of ancient units of length.
Corroboration from Other Sources
Indus Inch
1 In
was 1.32 Inches which is exactly equal to 2 Angulas of
The Indus Inch : The Indus civilisation unit of length, widely known as
16.764mm each.
Sanskrit-English dictionary, by Moniere William, a Yojana has been de ned as a measure of distance = 4 Kosas or about 9 miles. Apart from the Moniere William dictionary, several other books/sources also give the Yojana as equal to about 9 miles.
2
Mohenjo-daro's Great Bath : The height of the corbelled drain forming
the outlet of Mohenjo-daro's Great Bath[2, pp. 133-142] is about 1.8m, which is equal to a Dhanusha of 108 Angulas of 16.764mm each.
Standard Street-Widths :
Kalibangam, a city in the Indus-Saraswati
Civilization (in Rajasthan) had street widths[3] of 1.8m, 3.6m, 5.4m and 7.2m i.e. built to the standard dimensions being equal to 1 Dhanusha, 2 Dhanushas, 3 Dhanushas and 4 Dhanushas respectively. Such widths are found at other sites also. Bigger streets of Banawali[3] another town in Indus-Saraswati Civilization (in Haryana) measure 5.4m i.e they were built with the unit of 3 Dhanushas.
Ta j Mahal :
A Persian manuscript Shah Jahan Nama contains a very
particular description of three principal buildings of Agra the Taj Mahal, Moti Masjid and Jamah Masjid. In the Shah Jahan Nama, the dimensions of these three buildings are given in were got measured by col. in
Gaz.
These dimensions
J.A. Hodgson in December, 1825, in feet
and inches. The various (28) dimensions, in feet and inches, as well as
Gaz,
are given by Hodgson in his article[4], in Table A. He has also
given Table B (25 dimensions) excluding 3 dimensions which he thought were not very dependable. The weighted mean length of a
Gaz
works
out to 31.70 inches, (80.52cm) from Table A and 31.66 inches=80.42cm from Table B. The average of the two values in 31.68 inches=80.47cm. It is pertinent to mention here that Barraud[5, pp. 108-109, 258-259] in The Complete Taj Mahal and the River front Columns of Agra, has taken a 2 a
Gaz
as equal to 80.5cm which is very nearly equal to 80.47cm
as worked out above. Taking a Dhanusha of 96 Angulas to be equal to
Gaz, the length of an Angula works out to 16.764mm . It shows that Gaz of 48 Indus-Saraswati Angulas was being used, even in the days
of Shah Jahan's rule i.e 17th Century A.D.
The Gudea's Rule : The
Gudea's rule (2175 B.C.) preserved in the Louvre shows intervals in Sumerian Shusi of 0.66 inches, which is exactly equal
to the Indus-Saraswati Angula of 16.764mm.
Mayan Units of Measurement : Drewitt[6] and Drucker[7] made a study
of the ancient city of Teotihuacan, belonging to to the Indian Guz of 48 Angulas=80.47cm.
Mayan
Civilization , in
Mexico, and hypothesised a unit of 80.5cm, which is very nearly equal
Temple Wall-Engravings : Nearer home, two engravings on a wall of the
temple at Tiruputtkali (12th Century A.D.) near Kanchipuram, show
two scales[8] one measuring 7.24 metres in length, with markings dividing the scale into 4 equal parts, and the second one measuring 5.69 metres in length and markings dividing the scale into 4 equal parts. It may be observed that each division of the rst scale is precisely equal to a Dhanusha of 108 Angulas of 16.764mm each. second scale is precisely equal to Interestingly, the
times Dhanusha i.e. equal to the
circumference of a circle with one Dhanusha as its Diameter. It is interesting to note here that Mackay reports[9] at Mohenjo-daro, a lane and a doorway having both a width of 1.42m, which is precisely equal to one division of the second scale at the Tiruputtkali Temple, indicating that both the scales were prevalent in Indus-Saraswati Civilization as well as in South India. It proves beyond doubt that the Units of measurement as derived from the precise scale found at Mohenjo-daro were prevalent not only in the IndusSaraswati Civilization, but also in South India and in the ancient
Egyptian
and
Mayan
Sumerian,
Civilizations.
Speed of light in Vedic Literature
In the commentary on Rig-Veda, Mandal 1, Sukta 50, Mantra 4, which is in praise of the Sun god, Sayanacharya (14th Century AD) writes: ...
Meaning. . . It is remembered that . . . Salutations to Thee (the Sun) who approacheth (at a speed of )
2202 yojanas
This
in a
nimishardha
(half
nimisha ). shloka.
Clearly it is the Speed of light(or sunrays) that is mentioned in the
shloka
is attributed[10, pp.
67] to the son of Kanva Maharshi (4000
B.C.). Bhatt Bhaskara (10th Century A.D.) also mentions[11] this shlok, in his commentary on Taittiriya Brahmana. To put it in mathematical terms, as stated by the above shlok, the speed of light would be:
Speed Of Light = 2202 Y ojanas/N imishardha
the previous step(Equation 4), but we still do not know, what the
(7)
We have already calculated the value of Yojana in modern unit of km in
Nimishardha
translates into. Let us dig into another Vedic text In the Vishnu Puran (Book 1, Chapter 3,
the Vishnu Puran
to nd
how the erstwhile units of time can be related to the modern units of time.
Shloka
8,9), it is stated that:
15 30 30 30 Thus
Nimisha s Kashta s Kala s Mahurta s
= 1 = 1 = 1 = 1
Kashtha Kala Mahurta day & night
one day & night = 405, 000 N imishas = 810, 000 N imishardhas.
(Literal meaning of In that a
(8)
Nimishardha being half a Nimisha ). Surya Sidhant (Chapter 1, Shloka 12), it is stated Mahurta
=2
that 60
Nadis
con-
stitute one Sidereal Day and Night (
). It is also well known It is clear from this that in Astronom-
Ghati s or 2 Nadi s.
ical calculations, the sidereal day was taken as the unit of time. A sidereal day is the time taken by the stellar constellations to complete one revolution around the Earth. A sidereal day is equal to 23 hours, 56 minutes and 4.1 seconds, or equivalently 86,164.1 sec (ref Wikipedia Article [12]). Thus. . .
N imishardha = 86164.1/810000 sec = 0.1063754sec
be:
(9)
The speed of light as given in the Vedic Literature therefor comes out to
2202 14.484096 km = 2.998 105 km/sec 0.1063754 sec
(10)
which is precisely equal to the speed of light as per modern measurements.
Conclusions
The calculations and references in the article endeavor to establish the vast reach of the Indus Valley scholars, not only academically, but also geographically. Thousands of years before the modern scientists rediscovered the speed of light; our ancestors knew of the exact same value and referred to it as an exalted property of the Sun-God to salute Him. It is also heartening to know that the modern-age concept of globalization and sharing of ideas between cultures was also an established way of life in their era, as proven by the shared units of measurement found across far- ung cultures. When and how these ancient civilizations lost their in uence is still a mystery, but for now we can celebrate the knowledge that:
1. The Speed of Light as given in the Vedic literature, is precisely equal to the Speed of Light as per modern measurements. 2. The basic unit of length measurement in the Indus-Saraswati Civilization was an
Angul
of 16.764mm. This unit was used not only in the
Indus-Saraswati Civilization, but also in South India, and other ancient world Civilizations including tions.
Sumerian, Egyptian
and
Mayan
Civiliza-
References
[1] Danino, Michel Books, 2010. [2] Jansen, Michael
The Lost River On the Trail of Saraswati, Mohenjo-daro: architecture et urbanisme,
Penguin
Les cits ou-
blies de lndus: Archologie du Pakistan, 1988. [3] Lal, B.B.
The Earliest Civilization of South Asia, Aryan Books InternaMemoir on the Length of the Illahi, Guz,
Journal of
tional, New Delhi, 1997 [4] Hodgson, Col. J.A.
the Royal Asiatic Society of Great Britain and Ireland., 1840. [5] Barraud, R.A.
The Complete Taj Mahal and the Riverfront Gardens of Agra (ed. Koch E.) Thames and Hudson. London, 2006. Measurement Units and Building Areas at Teotihuacan,
1987
[6] Drewitt,
[7] Drucker, R. David.
Precolumbian Mesoamerican Measurement Systems: Unit Standards for Length, 1977
[8] James Heitzman and S. Rajagopal,
Urban Geography and Land Measurement in the Twelfth Century : The Case of Kanchipuram, The Indian
Economic and Social History Review. SAGE, 2004
[9] Mackay, E.J.H.,
Further Excavations at Mohenjo-daro,
Govt. of India.
vol. I. republished Munshiram Manoharlal, 1998. [10]
Pride of India,
Published by Sanskrit Bharati, 2006. 2001.
[11] Subhash Kak, [12]
The Speed of Light and Puranic Cosmology, Article on Sidereal
Wikipedia
Time,
http://en.wikipedia.org/wiki/Sidereal_time
