CONTINUUM IN TOWN-PLANNING

AND METROLOGY

FROM INDUS CIVILIZATION

TO CLASSICAL INDIA

by Michel Danino

(micheldanino@gmail.com)

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