Author: Amir D. Aczel
Publisher: Palgrave and Macmillan 2015
(These lectures are in Sinhala and you can listen to all five lectures from the following site.)
https://www.youtube.com/playlist?list=PLq9tDy1opPs-vNuD9cHyoQhh61RtF7Uq_
Before going further, some clarifications have to be made. When the author said finding the first zero in the world, he meant finding the zero that was used as a placeholder for the first time in our base-10 number system. In our number system we have ten numerals (or symbols) namely; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We can use these ten symbols over and over again for counting purposes. For example, look at the following thirty symbols that can be used to count up to twenty nine (or thirty).
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
We may be able to keep track of how many times we have used the ten symbols for small numbers. But the list can get too long and difficult to keep track of for large numbers. The ingenious method of the base 10-system is to use numerals as placeholders. With that we can make unique symbols for each number.
00, 01, 02, 03, 04, 05, 06, 07, 08, 09,
10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26, 27, 28, 29.
If you agree to a convention not to leave leading zeros, then you get the system that we use today.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26, 27, 28, 29.
When counting in this system, 29 means 20 + 9 (Skip count to 20 and then count nine more.). Similarly, 605 means 600+00+5 (Skip count to 600 and then count five more.)
The first zero in the history of the world was invented by Mayans in Mesoamerica about two thousand years ago. However, they did not use zero as a place holder in their number system as we do now.
Dr. Nalin de Silva mentioned a ‘’Chatuskoti’ in his talk. (Chatuskoti is a Sanskrit word and it represents something called ‘’tetralemma’’ by the ancient Greeks.) In this book the author listed Nāgarjuna’s version of Chathuskoti from Mūlamādhyamakakārikā.
Anything is either true,
Or not true,
Or both true and not true,
Or neither true nor not true.
F. E. J. Linton from Wesleyan University provides an ‘’everyday’’ example of the Chatuskoti.
If you have a student who is brilliant in mathematics but also has a knack for getting arrested in campus demonstrations, you might rightly say that he is both very bright and not very bright.
(This is an example of the third line of the Chatuskoti with ‘’true’’ replaced by ‘’very bright’’.)
You can find Linton’s mathematical analysis of the Chatuskoti in this article.
http://tlvp.net/~fej.math.wes/SIPR_AMS-IndiaDoc-MSIE.htm
(Grothendick, a member of Bourbaki, invented a new concept called topos. It turns out the mathematics of a topos allows for a mathematically consistent and correct basis that satisfies the Eastern kind of logic like Chathuskoti. You can see some use of topos in Lynton’s paper. )
According to David Eugene Smith (in his History of Mathematics) the earliest known numerals are found in inscriptions of Asoka. Cunningham recorded the following in his book "Mahābodhi or The Great Buddhist Temple Under the Bodhi Tree at Buddha-Gaya".
This cloistered walk which still exists close to the north side of the Temple is a simple brick wall, 53 feet long, 3 feet 6 inches broad, and a little more than 3 feet in height. On each side there is a row of 11 Persepolitan Pillar-bases, of the well-known pattern of a vase placed above three or four steps, and surmounted by a parabolic moulding with an octagonal top for the reception of an octagonal shaft. Back of these bases was marked with an octagonal letter of the Asoka alphabet, the 11 bases on the south side bearing the 11 vowels, a, â, i, î, u, û, e, ai, o, au, ah, and the northern bases, the first 11 consonants, k, kh, g, gh, ng, ch, ahh, j, jh, ny, t.
The oldest known zero (in our modern number system) was found by George Coedès when he translated an inscription on a stone slab found in Cambodia in 1891. Coedès labeled this slab K-127. He did not have to use linguistic analysis to date the slab because that information was listed on the slab itself. It read:
The çaka era has reached 605 on the fifth day of the waning moon …
The çaka was a dynasty whose first king began to rule in 78 CE. So, the çaka year 605 is 683 CE.
Coedès published this finding in an article that appeared in Bulletin of the School of Oriental Studies in 1931.
Apparently K-127 was misplaced and feared destroyed during the Khmer Rouge reign in the 90s. It was the author’s determination to find K-127 and he wrote this book to publish his travelogue of finding K-127.
You may wonder why I downgraded this book to a travelogue. Let me let an evaluatee at the Amazon site speaks for me.
I’m writing this as a mathematician interested in (the) history of math. I read a library copy, as I was hesitant to purchase it. I found myself quite bored by the author's "odyssey", as I just wanted the facts about 0, which could have been written in a 10 page or so monograph.
His knowledge of Eastern religions and Eastern history is very poor and I felt that he has probably been brainwashed with a lot of misinformation and disinformation. It was extremely boring to read and (intellectually) a low quality book.
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The following are few interesting information found in the book.
(1) There were 85 temple built during the Chandal dynasty (870 - 1200 CE) at Khajuraho, in India. Cunningham found a magic square at the entrance to one of the Jain temples at Khajuraho. (Archeological Survey of India 2 (1871): 434)
(2) Naga Ghat cave inscription from Puna dated to about 100 years after Asoka has numerals representing 10 and 7.
(3) Khandela copper inscription is now lost. It was found 50 miles north east of Jaipur. Was it a Buddhist temple?
(4) Buddha was a mathematician according to the book Lalitha Visitara.
(5) Prabang was the name of the Buddha image presented to a Laotian king by the people of Thambapanni (Sri Lanka) in the first century CE. This image is in the national museum at Luang Prabang in Laos.
(6) Wht means temple in Angkor Wat.
(7) Wat Xieng Thong in Laos was built in 1565 CE.
(8) Infinite quantities and “multiple multiplication” are mentioned in a Jain sutta called Anuyoga-vara sutta.
(9) A Chinese traveler Chou-Ta-Kuan who came to Angkor in 1296 CE identified the large statue at the temple as a Buddha statue.
(10) The great king Jayaraman 7 (born in 1125 and died in 1218 CE) was a Buddhist king.
(11) Wat Langka is an old Buddhist temple south of the water front area of the confluence of the Mekong and Tonle rivers in Cambodia.
(12) Oldest zero in India is found at the Chatur-bhuja temple which was built in 876 CE.
(13) G.R. Kaye maintained that zero is a western concept until Coedès published his findings.
