MEASUREMENT (INDIA – WORLD GURU OF MATHEMATICS, PART – 11)

Posted on November 4, 2011

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MEASUREMENTS

The people of the Indus Civilization achieved great accuracy in measuring length, mass, and time. They were among the first to develop a system of uniform weights and measures. Their measurements are said to be extremely precise however, a comparison of available objects indicates large scale variation across the Indus territories. Their smallest division, which is marked on an ivory scale found in Lothal, was approximately 1.704 mm, the smallest division ever recorded on a scale of the Bronze Age. Harappan engineers followed the decimal division of measurement for all practical purposes, including the measurement of mass as revealed by their hexahedron weights.

These chert weights were in a perfect ratio of 4:2:1 with weights of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500 units, with each unit weighing approximately 28 grams, similar to the English Imperial ounce or Greek uncia, and smaller objects were weighed in similar ratios with the units of 0.871.  A particularly notable characteristic of Harappan weights and measures is their remarkable accuracy. A bronze rod marked in units of 0.367 inches points to the degree of precision demanded in those times. Such scales were particularly important in ensuring proper implementation of town planning rules that required roads of fixed widths to run at right angles to each other, for drains to be constructed of precise measurements, and for homes to be constructed according to specified guidelines. The existence of a gradated system of accurately marked weights points to the development of trade and commerce in Harappan society. However, as in other cultures, actual weights were not uniform throughout the area. The weights and measures later used in Kautilya`s Arthashastra (4th century BCE) are the same as those used in Lothal.

Unique Harappan inventions include an instrument which was used to measure whole sections of the horizon and the tidal lock. In addition, Harappans evolved some new techniques in metallurgy and produced copper, bronze, lead and tin. The engineering skill of the Harappans was remarkable, especially in building docks after a careful study of tides, waves and currents. The function of the so-called `dock` at Lothal, however, is disputed.

In 2001, archaeologists studying the remains of two men from Mehrgarh, Pakistan, made the discovery that the people of the Indus Valley Civilisation, from the early Harappan periods, had knowledge of proto-dentistry. Later, in April 2006, it was announced in the scientific journal Nature that the oldest (and first early Neolithic) evidence for the drilling of human teeth in vivo (i.e., in a living person) was found in Mehrgarh. Eleven drilled molar crowns from nine adults were discovered in a Neolithic graveyard in Mehrgarh that dates from 7,500-9,000 years ago. According to the authors, their discoveries point to a tradition of proto-dentistry in the early farming cultures of that region.

A touchstone bearing gold streaks was found in Banawali, which was probably used for testing the purity of gold (such a technique is still used in some parts of India).

Measurement Units in Ancient India

The highest prefix used for raising 10 to a power in today’s maths is ‘D’ for 10 to a power of 30 (from Greek Deca). While the largest numbers the ancient Greeks and the Romans used were 10 to the power of 6, whereas Hindus used numbers as big as 10 to the power of 53 with specific names as early as 5000 B.C. during the Vedic period.

1= Ekam =1, 10 was Dashakam, 100 was Shatam (10 to the power of 10), 1000 was Sahasram (10 power of 3), 10000 was Dashasahasram (10 power of 4), 100000 was Lakshaha (10 power of 5), 1000000 was Dashalakshaha (10 power of 6), 10000000 was Kotihi (10 power of 7)……Vibhutangamaa (10 power of 51), Tallaakshanam (10 power of 53).

ANCIENT NUMBERS:

Kharoshti Numerals

Kharoshti Numerals

The Bhrami Numerals

The Bhrami Numerals

The Gupta Numerals

The Gupta Numerals

The Nagari Numerals

The Nagari Numerals

Periodical Changes of The Bhrami Numerals

Periodical Changes of The Bhrami Numerals

MEASUREMENT OF TIME:

The ancient Hindus had given the world the idea of the smallest and largest measuring units of Time. Astonishingly, the ancient Hindus used the following units of time:

measurement

India gave the largest measurement of time as 8.64 billion years.

The Gregorian calendar on your desk simply adds on one day for every 4 years and is not in coherence with the movement of sun. But, Hindu calendar is in coherence as the short fall is corrected in the month itself by adding Adhikamasa as postulated by Maharshi VishwamitraRig Veda 1.164.1, 2, 14 and 15 describe sun’s motion, ritus and colours of spectrum. Kalyana varma, Varahamihira, Jaimini, Vidyanatha Deekshita, Kalidasa, Mantreshwara, Satyacharya, Venkatadri, Parashara, Ramadayalu and Garga have immensely contributed for the development of Hindu astrology.

The famous Hindu mathematician, Bhaskaracharya, in his treatise Surya Siddhanta, calculated the time taken for the earth to orbit the sun to nine decimal places (365.258756484 days).

Bhaskaracharya rightly calculated the time taken by the earth to orbit the sun hundreds of years before the astronomer Smart. His calculations was – Time taken by earth to orbit the sun: ( 5th century ) 365.258756484 days.

Today’s accepted measurement is 365.2564 days. Therefore, assuming that today’s figures are correct, it means that Bhaskaracharya was off by only 0.0002%.

SIMILAR MEASUREMENTS IN SOUTH INDIA

                   The Dravidians also had a large scale of measurement of time, length and weight from pre-historic period.

Tamil units of measurement

Measurements in ancient Tamil land were of seven kinds. They were number counts, balance weights, fluid volumes, grain volumes, length, time and the likeness.

 Units of time in ancient Tamil history

  • 1 kuzhi(kuRRuzhi)= 6.66 millisecond-the time taken by the Pleiades stars(aRumin) to glitter once.
  • 12(base 8 ) or 10 kuzhigaL= 1 miy= 66.6666 millisecond-the time taken by the young human eyes to flap once.
  • 2 kaNNimaigaL= 1 kainodi= 0.125 second
  • 2 kainodi= 1 maatthirai= 0.25 second
  • 6(base 8 ) or 6 miygaL= 1 siRRuzhi(nodi)= 0.40 second-the time taken for a bubble (created by blowing air through a bamboo tube into a vessel 1 saaN high, full of water) to travel a distance of one saaN .
  • 2 maatthiraigaL= 1 kuru= 0.50 second
  • 2(base 8 ) or 2 nodigaL= 1 vinaadi= 0.80 second-the time for the adult human heart to beat once
  • 212 nodigaL= 2 kuru= 1 uyir= 1 second
  • 5 nodigaL= 2 uyir= 1 saNigam= 1/2 aNu= 2 seconds
  • 12(base 8 ) or 10 nodigaL= 1 aNu= 4 seconds
  • 6(base 8 ) or 6 aNukkaL= 12 saNigam= 1 thuLi= 1 naazhigai-vinaadi= 24 seconds
  • 12(base 8 ) or 10 thuLigaL= 1 kaNam= 4 minutes
  • 6(base 8 ) or 6 kaNangaL= 1 naazhigai= 24 minutes
  • 12(base 8 ) or 10 naazhigaigaL= 4 saamam= 1 siRupozhuthu= 240 minutes= 4 hours
  • 6(base 8 ) or 6 siRu-pozhuthugaL= 1 naaL(1 day)= 24 hours
  • 7 naaTkaL= 1 kizhamai(1 week)
  • 15 naaTkaL= 1 azhuvam(1 fortnight )
  • 29.5 naaTkaL= 1 thingaL(1 lunar month)
  • 2 thingaL= 1 perum-pozhuthu(1 season)
  • 6 perum-pozhuthugaL= 1 AaNdu(1 year)
  • 64 aaNdugaL= 1 vattam(1 cycle)
  • 4096(=8^4) AaNdugaL= 1 Oozhi(1 epoch)

Area Measurement

  • 1 Marakkal vaedaipadu (seeds required for planting rice) = 8 cents
  • 12.5 Marakkal vaedaipadu = 100 cents (one acre)

Area calculation and Measurement Chart 

  • 1 hectare = 2 acre 47 cent
  • 1 hectare = 10,000 sq.m.
  • 1 acre = 0.405 hectare
  • 1 acre = 4046.82 sq.m.
  • 1 acre = 43,560 sq.ft.
  • 1 acre = 100 cent = 4840 sq.gejam
  • 1 cent = 435.6 sq.ft.
  • 1 cent = 40.5 sq.m
  • 1 ground = 222.96 sq.m. = 5.5 cent
  • 1 ground = 2400 sq.ft.
  • 1 kuli = 44 cent
  • 1 kaani = 132 cent = 3 kuli
  • 1 kaani = 1.32 acre
  • 1 kaani = 57,499 sq.ft.
  • 1 acre = 2.25 kuli
  • 1 dismil = 1.5 cent
  • 1 furlong = 660 feet = 220 kejam
  • 1 kilometre = 5 furlong
  • 1 link / chain = 0.66 foot = 7.92 inch
  • 1 kejam = 3 feet
  • 1 mile = 8 furlong
  • 1 ares = 1076 sq.ft. = 2.47 cent
  • 1 chain = 22 kejam
  • 1 furlong = 10 chain
  • 1 kejam = 0.9144 metre
  • 1 township = 36 sq.mile
  • 1 sq.mile = 640 acre

Units of ancient trade

Balance weights

GOLD WEIGHTS

  • 4 nel edai= 1 kunRimaNi
  • 2 kunRimaNi= 1 manjaadi
  • 1 manjaadi= 1 paNavedai
  • 5 paNavedai= 1 kazhanju
  • 8 paNavedai= 1 varaaganedai
  • 20 paNavedai= 4 kazhanju = 1 kaqhsu
  • 80 paNavedai= 16 kazhanju= 4 kaqhsu= 1 palam.
  • 1.5 Kazhanji = 8 gram or one pown
  • 32 kunRimaNi= 1 varaaganedai
  • 10 varaaganedai= 1 palam
  • 40 palam= 1 veesai
  • 1000 palam =1 kaa
  • 6 veesai= 1 thulaam
  • 8 veesai= 1 maNangu
  • 20 maNangu= 1 paaram.
  • 1 kuNam= smallest unit of volume
  • 9 kuNam= 1 mummi
  • 11 mummi= 1 aNu
  • 7 aNu=1 immi
  • 7 immi= 1 uminel
  • 1 sittigai= 7 uminel
  • 360 nel= 1 sevidu
  • 5 sevidu= 1 aazhaakku
  • 2 aazhaakku= 1 uzhakku
  • 2 uzhakku= 1 uri
  • 2 uri= 1 padi
  • 8 padi= 1 marakkaal(kuRuNi)
  • 2 marakkaal(kuRuNi)= 1 padhakku
  • 2 padhakku= 1 thooNi
  • 5 marakkaal= 1 paRai
  • 80 paRai= 1 karisai
  • 96 padi= 1 kalam
  • 120 padi= 1 pothi(mootai)
  • 21 marakkal = 1 Kottai

GOODS WEIGHTS

Grain volume

padi, = 1800 avarai pods = 12,800 miLagu seeds = 14,400 nel grains = 14,800 payaRu grains = 38,000 arisi grains = 115,200 sesame seeds

Fluid volume

  • 5 sevidu= 1 aazhaakku
  • 2 mahani = 1 aazhakku (arai kal padi)
  • 2 aazhaakku= 1 uzhakku (Kal padi)
  • 2 uzhakku= 1 uri (Arai padi)
  • 2 uri= 1 padi
  • 8 padi= 1 marakkaal
  • 2 marakkaal(kuRuNi)= 1 padhakku
  • 2 padhakku= 1 thooNi
  • 21 Marakkal = 1 Kottai
  • 10 koaN= 1 nuNNaNu
  • 10 nuNNaNU= 1 aNu(atom)
  • 8 aNu= 1 kathirtthugaL
  • 8 kathirtthugaL= 1 thusumbu
  • 8 thusumbu= 1 mayirnuni
  • 8 mayirnuni= 1 nuNmaNal
  • 8 nuNmaNal= 1 siRu-kadugu
  • 8 siRu-kadugu= 1 eL
  • 8 eL= 1 nel
  • 8 nel= 1 viral= 8^8 aNu(atom)= 1.9444 centimetre
  • 12 viral= 1 saaN= 100 immi= 23.3333 centimetre
  • 2 saaN= 1 muzham= 46.6666 centimetre
  • 2 muzham= 1 kajam
  • 4 muzham= 1 paagam
  • 625 paagam= 1 kaadham= 5000 saaN= 1166.66 metres= 1.167 kilometre

Length

Likeness (Saartthal)

Likeness has attributes of tone, sound, colour and shape for comparison of a given substance with a known standard.

Numbers

* 1 = ONDRU -one
* 10 = PATHU -ten
* 100 = NOORU-hundred
* 1,000 = AAYIRAM-thousand
* 10,000 = PATHAAYIRAM -ten thousand
* 100,000 = LATCHAM-hundred thousand
* 1,000,000 = PATHU LATCHAM - one million
* 10,000,000 = KODI-ten million
* 100,000,000 = ARPUTHAM-hundred million
* 1,000,000,000 = NIGARPUTHAM- one billion
* 10,000,000,000 = KUMBAM-ten billion
* 100,000,000,000 = KANAM-hundred billion
* 1,000,000,000,000 = KARPAM-one trillion
* 10,000,000,000,000 = NIKARPAM -ten trillion
* 100,000,000,000,000 = PATHUMAM -hundred trillion
* 1,000,000,000,000,000 = SANGGAM -quadrillion
* 10,000,000,000,000,000 = VELLAM -ten quadrillion
* 100,000,000,000,000,000 = ANNIYAM -hundred quadrillion
* 1,000,000,000,000,000,000 = ARTTAM -quintillion
* 10,000,000,000,000,000,000 = PARARTTAM -ten quintillion
* 100,000,000,000,000,000,000 = POORIYAM -hundred quintillion
* 1,000,000,000,000,000,000,000 = MUKKODI -sextillion
* 10,000,000,000,000,000,000,000 = MAHAYUGAM -ten sextillion

Fractions

  • 1= onRu
  • 3/4= mukkaal
  • 1/2= arai
  • 1/4= kaal
  • 1/5= naalumaa
  • 3/16= moonRu veesam
  • 3/20= moonRumaa
  • 1/8= araikkaal
  • 1/10= irumaa
  • 1/16= maakaaNi (veesam)
  • 1/20= orumaa
  • 3/64= mukkaal veesam
  • 3/80= mukkaaN
  • 1/32= araiveesam
  • 1/40 araimaa
  • 1/64= kaal veesam
  • 1/80= kaaNi
  • 3/320= araikkaaNi munthiri
  • 1/160= araikkaaNi
  • 1/320= munthiri
  • 1/102,400= keezh munthiri
  • 1/2,150,400= immi
  • 1/23,654,400= mummi
  • 1/165,580,800= aNu
  • 1/1,490,227,200= kuNam
  • 1/7,451,136,000= pantham
  • 1/44,706,816,000= paagam
  • 1/312,947,712,000= vintham
  • 1/5,320,111,104,000= naagavintham
  • 1/74,481,555,456,000= sinthai
  • 1/1,489,631,109,120,000= kathirmunai
  • 1/59,585,244,364,800,000= kuralvaLaippidi
  • 1/3,575,114,661,888,000,000= veLLam
  • 1/357,511,466,188,800,000,000= nuNNmaNl
  • 1/2,323,824,530,227,200,000,000= thaertthugaL

 

THE STORY OF ONE – DOCUMENTARY VIDEO – THE BBC CHANNEL

Posted in: Mathematics