CONTINUUM IN TOWN-PLANNING
AND METROLOGY
FROM INDUS CIVILIZATION
TO CLASSICAL INDIA
by Michel Danino
Paper presented at a seminar on“How deep are the roots of Indian civilization? An archaeological and historical perspective”
organized by the Draupadi Trust in New Delhi on 25–27 November 2010
Proportions of
Mohenjo-daro‟s
acropolis
Proportions at
Kalibangan
(Rajasthan)
Dockyard: 217 m x 36 m;
ratio = 6:1
Proportions at Lothal: 280 x 225 m; ratio = 1.244 or 5:4
Superimposition of
Dholavira‟s plan on
a satellite
photograph
Dholavira: main dimensions
(margin of error: 0.5% or less)
First GPS readings made on 16 March 2009
GPS readings (in red)
770 616
341.6
The deviation is a mere 0.1% for the
first two dimensions and 0.3% for the
third, well within the published error
margin.
Chief ratios
at Dholavira
Search for Dholavira’s master unit
— two assumptions:
• A specific unit of length was used (not just steps).
• Most of the major dimensions should be integral
multiples of that unit (= n times U).
Problem:
• What is the largest unit of length in terms of
which most of Dholavira‟s dimensions can be
expressed as integers?
Basic Data
• Lt / Wt = Lci / Wci = Lco / Wco = D / A = C / B = 5/4
• Lm / Wm = 7/6
• Lt / Lm = Lm / Lco = 9/4
• Lci / Lco = 3/4
• Lg / Wg = 6
• Lg / Lm = 5/6
• A / C = 3/2
• P = Q
Calculations
General proportions Middle town Castle
A / Lt = 12/23 P / Lt = Q / Lt = 68/483 Lci / Lm = 1/3
C / Lt = 8/23 Lm1 / Lm2 = 75/86 Lci / Lt = 4/27
D / Lt = A / Wt = 15/23 Lg / Lt = 10/27 Lco / Lt = 16/81
A / B = D / C = 15/8 K = Lco / 8 = Lci / 6
• Let the unknown unit be “D”. The smallest dimension is K.
• Let K = nU, where n is an integer. Therefore:
• Lci = 6K = 6 nU, Wci = 4/5 Lci = 24/5 nU.
• Lco = 8K = 8 nU
• Wco = 4/5Lco = 32/5 nU.
• Lm = 3Lci = 18 nU.
• Lg = 5/6 Lm = 15 nU
• Wg = 1/6 Lg = 5/2 nU.
• Lt = 9/4 Lm = 81/2 nU
• Wt = 4/5 Lt = 162/5 nU
• Choose n as the least common multiple of the above
fractions‟ denominators: n = 2 x 5 = 10.
• Therefore K = 10U. Other dimensions follow.
Lt = 771.1 m = 405 D,
therefore D = 1.904 m
Comparison between theoretical and actual dimensions
Stone columns in
Dholavira‟s Castle
Study of Dholavira‟s reservoirs
Reservoir Length Width Ratio Length (D) Width (D)
Eastern 73.5 (top) 29.3 (top) 5 : 2 (0.3%) 39 (?) —
SR1* 30.35 13.9 9 : 4 (3%) 16 (0.2%) —
SR2* 9.6 4.5 2 : 1 (?) 5 (1%) —
SR3-1 33.4 9.45 (max) 7 : 2 (1%) 17.5 (0.4%) 5 (0.5%)
SR3-2 15.5 5.65 11 : 4 (0.2%) — 3 (0.9%)
SR-4* 11.4 (max) 7.53 (av.) 3 : 2 (0.9%) 6 (0%) 4 (0.9%)
SR-5* 16.35 11.1 3 : 2 (1.8%) — —
Almost all reservoirs were designed according to precise proportions.
Almost every reservoir has at least one dimension expressible as an
integral multiple of D.
* Poorly defined, irregular or incomplete reservoirs.
Eastern reservoir
Southern reservoirs SR3-1 & SR3-2
Other Harappan sites
Ratio 5:4 – Harappa’s ―granary‖
Dimensions : 50 x 40 m (ratio 5:4 or 1.25)
Ratio 5:4
Mohenjo-daro’s
―fire temple‖(in the HR area
of the lower town)
Dimensions:
62 x 50 feet
ratio = 1.24 (0.8%)
Mohenjo-daro‟s
acropolis:
ratios and
multiples of
Dholavira‟s unit
Harappan ratios:
a non-random
distribution
Many dimensions of
important
structures turn out
to be integral
multiples of D.
Note that the
probability of this
being a coincidence
decreases as the
ratio increases.
Historical sites & structures:
a few case studies
Sirkap (Taxila): blocks of 38.4 = 19.2 x 2 m
Drupal Kila (Kampilya)
Sirkap: blocks of 38.4 = 19.2 x 2 m
Mohenjo-daro: cluster blocks of 19.2 m
Thimi (a town east of Kathmandu): blocks defined by east-west
streets: average width of 38.42 m
Thimi: pattern of divisions on a long nearby strip of fields:
average 38.48 m
Proposed a danda (a term synonymous with dhanus in the
Arthashastra) of 1.92 m equal to 108 angulas (1.78 cm), and a
rajju of 10 dandas or 19.2 m
Mohan Pant & Shuji Funo (2005):
• Lothal‟s measuring scale (27 graduation lines spanning
46 mm): 1 unit = 1.77 mm.
• V. Mainkar in 1984: 10 Lothal units come close to the
Arthashāstra‟s angula (1.778 cm in his estimate).
• D = 108 x 1.77 cm (0.4%)
Search for the smallest unit of length
Kalibangan‟s terracotta „scale‟: grooves 1.75 cm apart
(analyzed by Prof. R. Balasubramaniam)
Averaging the Lothal and Kalibangan scales gives 1.76 cm.
Is this a unit related to D? D = 1.76 x 108 = 190.1 cm. A
Harappan „angula‟?
“108 angulas make a dhanus, a measure
[used] for roads and city-walls....”
(Arthashāstra 2.20.19,
Kangle 1986: 139).
Arthashāstra:
units of length for
fortifications
Dholavira‟s ratios
and units reflected
in the Delhi Iron
Pillar (by Prof. R.
Balasubramaniam)
Correlations with Vedic concepts
• Addition of a fraction to the unit:
• 1 + ¼ (= 5/4)
• 1 + 1 + ¼ (= 9/4) etc.
• Recursion: repetition of a motif (5/4, 9/4), as
in classical architecture.
Varāhamihira (in ch. 53 of Brihat Samhita):
“The length of a king‟s palace is greater than the
breadth by a quarter [1 + 1/4 = 5/4].... The length of
the house of a commander-in-chief exceeds the
width by a sixth [1 + 1/6 = 7/6].”
Dholavira‟s citadel and middle town leave the
maximum vacant space in the north-eastern sector of
the town.
Continuity with Vāstu-Vidya
Origin of ancient units: the human body
• digit (angula)
• palm, generally 4 angulas
• span (vitasti), generally 12 angulas
• cubit (hasta), generally 24 angulas
• height of a man (nara, purusha), generally 96 angulas
Varāhamihira’s Brihat Samhita (68.105)
Height of a man With 1.9 cm With 1.76 cm
tall = 108 angulas 205 cm 190 cm
medium = 96 angulas 182 cm 169 cm
short = 84 angulas 160 cm 148 cm
• Pratap C Dutta: From a study of 260 skeletons, Harappan
males "had an average stature of 1691.87 mm" (169.2 cm). ("Bronze Age Harappans", in The People of South Asia, ed. John R. Lukacs, 1984, p. 64)
• If we divide by 96 angulas, we get 1.762 cm — almost exactly
the value of the suggested Harappan angula.
Shringaverapura: physical data (from Prof. B.B. Lal)
96A 12A 24 A
Averages: 166.3 7.37 21.3 45.24
Resulting angula: 1.73 1.84 1.77 1.88
• The Harappan system of units of length seems to be the
origin of the Arthashāstra system (as regards
fortifications).
• Harappan ratios are visible at many historical sites,
structures, monuments.
• Varahamihira’s mention of Dholavira’s two master ratios
seems too much of a coincidence.
• Concepts of auspicious ratios, fractions, addition to unity,
recursion are common to Harappan and Vedic traditions.
• This continuity is one more piece of evidence bridging
the Indus-Sarasvati and the Ganges civilizations.
Conclusion: a case for continuity in India’s architectural traditions