A REMARKABLE TABLE OF LENGTH .
The Royal Cubit of Egypt is the distance from the Elbow to the end of the fingers, date back to the 5000 years. All great civilizations had their own scheme of measure. In 1101 AD English Yard was the distance from Nose of Henry I to end of his extended finger. French in 1796 defined the Metre which was one ten millionth of the distance from North pole to the equator. These were not satisfactory for scientific measure of length.
In 1960 the metre was defined to be 1,650,763.73 Wave lengths of a radiation of the Krypton gas. This too was unsatisfactory, then the metre was defined as the distance traveled by light in 11299,792,458th of a second in vacuum. I don’t know if they have improved on this if they are to land a space craft on Mars.
The Table of length Abidhamnappadipika Palm Leaf Munuscript
A remarkable table of length of the Sinhalese defined in an Medieval Ola-leaf Sinhalese manuscript attributed to the period of King Parakramabahu I in middle 12 Cent AD compiled by a author named Maha Moggallana. This manuscript was in verse, and discussed at length by Prof.Rhys David in his book Coins and Measure of Ceylon and edited in 1870s and now available for sale at Lake House Bookshop. The scheme of measurement is shown below with its equivalents in metric units. I am assuming that an Angula is 1 Inch or 0.0245 Metres. The Angular has been divided in 7 x 7 x 7 x 32 x 32 x 32 x 32 to arrive at the lowest unit called Paramanu.
The 21 Cent accepted small unit for measurement of small objects was [1 x 10-10 is an Anstron Unit], the Sinhalese in the 12 cent divided the centre portion of the figure into 36 x 36 x 36 x 36 x 7 x 7 x 7 , as shown below.
Assuming that the finger-Measure length 1 inch , the length of a Basic unit of measurement of the Sinhalese works out to 0.0245 divided by 576,108,288 which is 0.000000000044 metres or 0.44 x 10-10 metres. In scientific terms 0.44 Angstrom units. It is amazing that this value agrees with the latest scientific beliefs the Atomic or molecular radii is between 0.1 – 1 Angstrom unit. It is truly remarkable that the Sinhalese did use the atomic radii as the basic unit to calibrate their scheme of measures of length. Their choice could not have being ad-hock as they have achieved astonishing accuracy with in the varying orbit of an atom.
The smaller unit is not mentioned in any context, perhaps they were used to explain the reality of all living and non-living things in Buddhist discussion during the ancient period. The ancient Aruveda and the non traditional system of medicine that was practiced in the many ancient hospital , the ruins of which is found in most monasteries in ancient cities, used principle akin to the applications of nano-technology. For example the application of gold particles at nano-particle level to cure cancer.
Nanotechnology in Ancient India (!)
Did you know that the Ancient Indian Acharyas applied Nanotechnology too!
Nanoparticles are produced industrially now in big amounts for various purposes including medicine. But the ancient technology which provided an economical way of creating nanosized particles used for curing various ailments are really commendable.
It was Neil Bohr who postulated a model of an hydrogen Atom with a atomic radii of 0.53 Angstrom units or 5.3 x 10-10 metres . But it is impossible to deter mine actual representation of an Atom, as the orbit is unstable and varies. The ancient Greeks Lucretius and Democratic [466-370 BC] and Aristotle[380-321 BC], defined the atomic concept where they explained the manner in which all things that happen on earth with out assistance of a God.
The Buddha [563-483 BC], perhaps a little earlier defined that all matter made up of irreducible particles. He based his teachings on ANNICHA – the principle of impermanence of all living and non-living things. The Buddha when he was constantly interrogated on this subject of the condition of mans selflessness answered.
“ If we ask whether the position of the electron remains the same, we must say no; if we ask whether the electrons position changes with time we must say no ; if we ask whether it is in motion we must say no”.
“““““““““““““““““““““““““““““““““““`J Robert. Oppenheimer.
The religious texts of the Vedic Period provide evidence for the use of large numbers. By the time of the Yajurvedasaṃhitā (1200–900 BCE), numbers as high as 1012 were being included in the texts. For example, the mantra (sacrificial formula) at the end of the annahoma (“food-oblation rite”) performed during the aśvamedha, and uttered just before-, during-, and just after sunrise, invokes powers of ten from a hundred to a trillion:
“Hail to Sata (“hundred,” 102), hail to sahasra (“thousand,” 103), hail to ayuta (“ten thousand,” 104), hail to niyuta (“hundred thousand,” 105), hail to prayuta (“million,” 106), hail to arbuda (“ten million,” 107), hail to nyarbuda (“hundred million,” 108), hail to samudra (“billion,” 109, literally “ocean”), hail to madhya (“ten billion,” 1010, literally “middle”), hail to anta (“hundred billion,” 1011,lit., “end”), hail to parārdha (“one trillion,” 1012 lit., “beyond parts”), hail to the dawn (uśas), hail to the twilight (vyuṣṭi), hail to the one which is going to rise (udeṣyat), hail to the one which is rising (udyat), hail to the one which has just risen (udita), hail to the heaven (svarga), hail to the world (loka), hail to all.”.
THE LARGE NUMBERS OF THE SINHALESE.[ 4 CENT AD TEXT – DIPAVANSA].
The large numbers of years between the king king Mahasammata from whome the first Sinhalese king descended, is described by perhaps a mathematical expression now known as Exponential of Ten in the ancient text the Dipavansa- chapter III verse ten-. Perhaps the author of this text over 1600 year ago and the readers would have been able to comprehend the meaning, when the author states that all these numbers are Numerable and calculable by means of calculation but the stage of numbers beyond this is called ASAMKHEYYA[ non calculable or infinite? . This perhaps gives an idea of the mathematical thinking of that time in Sri Lanka.
LARGE NUMBERS.[ GO TO WIKIPEDIA ANCIENT MATHMATICS LARGE NUMBERS]
Larger number in Buddhism works up to Bukeshuo bukeshuo zhuan (不可說不可說轉) or 1037218383881977644441306597687849648128, which appeared as Bodhisattva‘s maths in the Avataṃsaka Sūtra., though chapter 30 (the Asamkyeyas) in Thomas Cleary’s translation of it we find the definition of the number “untold” as exactly 1010*2122, expanded in the 2nd verses to 1045*2121 and continuing a similar expansion indeterminately.
Units Of Time.
The Sri Lankans had a 60 base system for time. he had 60 year periods, 60 hour per day etc. They had to use smaller unit for astrology. Some in region of 10 minus 7 units is recorded from texts in India.
THE MEASUREMENT OF TIME. ACCORDING LN
WHY SMALL AND LARGE NUMBERS?.
You will wonder how the people of the ancient period ever made use of these small and large numbers. It is said that between 3 Cent BC and 12 Cent AD there were many schools of Buddhist philosophy. Even with in the Mahavihare, Abeyagiri and Jetawana schools, there many difference in opinion argued in many subjects. Some of these subjects mentioned by Proffessor Y Karunadasa are
1.Nature of the phenomenal existence as a dynamic process.
2The reduction of mind and matter into mental and material phenomena.
3Time and space as as a conceptual constructs.
4Incessant change as instantaneous being.
Perhaps practical problems of the existence of smallest particle to the Aparamita Lokadhatu[ Boudless Universe] a word used in many inscriptions of the 3 Cent BC need to hammered out by the generations of followers of the Buddha the Sanga. It is no wonder that Rev Mahinda tested out with logical thinking Venn’s Theory type of question put to the King Devanampiyatissa[ King Uttiya elder Brother] to test his IQ . He passed the test and Rev Mahinda immediately knew the people of the country had enough intellect to understand the doctrine.
Boundless Universe is mentioned in the Inscription[ No 338 IC Vol I] of Queen of King Uttiya[3 Cent BC] at Preriya-Puliyakulama.
Few example of Measurements from the 5 Cent AD Ola-leaf Muniscript the Mahawansa.
2. The Mahawansa in Chapter XXIX verse 53 to 56 describes the marking out and laying the foundation of the Maha seya. It starts with the fragrant flowers that was passed hand to hand around three times. Similar to the flowers and dane[ Food offering] items going from hand to hand prior to the offering in temples of the present day. A technicalities about the size or circumference been too big to be completed in the life time of Dutugemunu, and on a the advise of a Thero Sidatta who has great powers [ perhaps to estimate the labour and material requirement] a smaller dimension is agreed upon. The measuring out is described as done by a Minister [ named in Tika as Samangalika] who is commanded to place a pure tuning staff for tracing the circular boundary made of silver and secured by a rope to a post of gold. He ordered him to walk around with the walking staff in hand on the ground already prepared and mark out the circular out line. Giegers translation describes him as Minister of noble birth, well attired in festival array. But considering the degree of accuracy and skill required for this enormous task perhaps he was what is known a Bematiste or a trained surveyor of sorts who is able to walk with equal measured steps[ and count them. Perhaps the skilled nobles attire and dress `or the lower cloths he wore was designed to restrict him to walk in a uniform measured steps [perhaps cubits] and count them.
Few Records of Calculations in ancient text of the Sinhalese from 2 Cent BC.
1.Chapter XXIX Verse 2.The foundation at Mahaseya is 7 cubits [17.5 feet? ] deep. ChapterXV verse 109, the Tee is 120 cubits high. Here W. Gieger quotes the Abhidhannapadipika- A Ratna or Hatta is equal to= 2 vidatthi[ = 8 1/2 inches]. According to Smither’s in Architectural Remains, Anuradhapura Page 27 Plate XXIV. The Ruvanveliseya was exactly 180 feet without the Tee
2.ChapterXXVII Para14-Nuggets of Gold of different sizes; the greatest measured a Span , the least was of a Finger measure [ Angula] at Acaravittigama in NE direction of Anuradapura a distance of 3 Yoganas in a field of 16 Karisa of land measure.
3.Vinya Rule- Dvanugulakappa Finger measures was used to when Buddhist monks rule of partaking of the mid day meal, after the Suns shadow should not have passed the meridian by more than two finger measures. Chapter IV -Verse 9.
4.Measure of length – Mahavansa -Lankatilake Vihare Pollonnaruva. Accurately establishing the length of Sinhala Yatthi or Rod and the Hattha or Cubit. From outer wall to the northern boundary pillar is 322 feet 8 inches, as per the Mahavansa this divided b 45 is 7 feet 2 inches to the Rod or Yatthi. Divide this by 5 and we get 1 foot 5 ½ inhes to a cubit. This is close to the length of a Sinhalese forearm to from the Elbow to the tip of the little finger. Archeological Survey of Ceylon – AM Hocart. 1926.Perhaps we should recalculate the Length of a Paramanu using this value.