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From:
alt.fan.jai-maharaj@googlegroups.com
Dr. Jai Maharaj posted:
In article <KQNZD.14663$wz4.9279@fx10.iad>,
FBInCIAnNSATerroristSlayer <FBInCIAnNSATe...@yahoo.com> posted:
ANCIENT INDIAN MATHEMATICIANS WERE WAY AHEAD OF THE REST OF
THE WORLD
http://www.pragyata.com/mag/numerical-imagination-of-ancient-india-518
Numerical Imagination of Ancient India
The conception of astronomical numbers by mathematicians in
India made them stand well above the rest.
by Abhijit Adhikari
Introduction
The mathematical achievements of ancient India have largely
remained hidden, but thanks to the internet age are coming
to the surface in recent times. Many books have been
written about the advanced mathematics, including
trigonometry and calculus discovered in India which reached
Europe in the Middle Ages through the Arabs. Here, I want
to go into an even more basic mathematical idea which turns
out to be one of the biggest leaps of imagination also.
This is the ancient Indian numeric system.
Other Civilizations
The most basic indicator of the mathematical abilities and
imagination of any civilization is the numeric system used
by them and the largest number which they have arrived at.
The following are some of the numbers used by ancient
civilizations.
The largest number having any representation in ancient
China was 10,000. That's it.
Chinese wrote Ten Thousand as:
Similarly, the largest named number for the ancient Greeks
was a Myriad, which was 10,000. To be fair, Archimedes did
write a paper calculating the number of sand grains in the
universe and therefore did imagine numbers as large as
1063, but that knowledge remained unused and quickly
forgotten.
Even the Romans, Persians and Egyptians never went beyond
One Million. Roman one million:
Egyptians wrote one million this way:
Of course, Arabs received all knowledge from India, so they
should not even be counted. Compared to the above numbers
from other civilizations, ancient India went far ahead.
Some of the largest numbers are referred to and defined in
the Valmiki Ramayan. Valmiki defines these numbers while
describing the size of Sri Ram's army in the Yuddha Kanda,
(6-28-33)
"Wise men call a Shata Shata Sahastra as a Koti. A Shata
Sahastra Koti is reckoned as a Shanku."
Shata is a hundred and Sahastra is a thousand. So a Koti is
10,000,000 (10 Million) and Hundred Thousand Koti is a
Trillion. These days, what we call as "one lakh crore" for
lack of proper terminology, actually had a name in ancient
times -- a "Shanku"!
So One Shanku (1012) is basically One Trillion.
Valmiki goes further to define even larger numbers:
Using Shatam Sahastram (same as Laksha) as Hundred Thousand
for easy understanding:
Hundred Thousand Shanku = Maha Shanku = 1017
Hundred Thousand Maha Shanku = Vrinda = 1022
Hundred Thousand Vrinda = Maha Vrinda = 1027
Hundred Thousand Mahavrinda = Padma = 1032
Hundred Thousand Padma = Mahapadma = 1037
Hundred Thousand MahaPadma = Kharva = 1042
Hundred Thousand Kharva = Maha Kharva = 1047
Hundred Thousand MahaKharva = Samudra = 1052
Hundred Thousand Samudra = Augha = 1057
Hundred Thousand Aughas = Maha Augha = 1062
How big is Maha Augha?
Does anyone know what 1062 is called in the modern metric
system? Probably not, because no one uses numbers as large
as these, except scientists working at the astronomical
scale (counting stars and galaxies) or atomic scale while
measuring the number of atoms in the universe.
Yes, that's how big this number is.
So, considering that there are 1023 stars and estimated
1080 atoms in the known universe, that's the scale we are
talking about. This is far far ahead of any civilization in
all of earth's history, that came up with a numeric system.
Even Further
Later on, the Buddhist monks went even further. The
Lalitavistara Sutra (a Mahayana Buddhist work) recounts a
contest which included writing, arithmetic, wrestling and
archery. In it the Buddha was pitted against the great
mathematician Arjuna and showed off his numerical skills by
citing the names of the powers of ten, up to 1
'tallakshana', which equals 1053, but then going on to
explain that this is just one of a series of counting
systems that can be expanded geometrically. The last number
at which he arrived at after going through nine successive
counting systems was 10421, that is, a 1 followed by 421
zeros! But he did not stop there, he actually named all the
numbers up to that, with 10421 being called as
"dhvajagranishamani (??????????????)". That is astounding!
Very small numbers
I can bet many people have no idea that ancient Indians
were interested in very small numbers also, especially when
defining the concept of Time.
And so on. I am sure it must come as a surprise to many
people that in ancient India we had names for numbers that
went to negative powers of ten also!
Infinity
After naming bewilderingly large numbers, it would have
been surprising if ancient Indians did not come up with a
shloka or two to define Infinity.
Om poornam-adah poornam-idah poorna-aat poornam-udachyate,
Poorna-asya poornam-aadaaya poornam-evaa vashishyate
That is whole, This is whole, From the whole comes the
whole. Even if the whole is taken away from whole, still
the wholeness remains.
Yes. That is the exact definition of Infinity, that many of
us use in our daily prayers!
Where are we now?
So, forget about using any of these numbers in our daily
lives, the mind boggles just at the thought of the
mathematical imagination of our forefathers. Remember,
Ramayan and Lalita-Vistara were religious scriptures, so it
is an ode to the mathematical genius of ancient Indians,
that they found it very normal to define huge mathematical
numbers even in our religious texts.
Maybe, in those days being good in mathematics was just
commonplace.
Compared to this, how does it sound now, when we hear
people using simple terms like "lakh crore" and "crore
core" being used in modern India when our own ancestors
were way smarter than us in using larger numbers?
References / Footnotes
o http://www.valmikiramayan.net/utf8/yuddha/sarga28/yuddha_28_frame.htm
o https://en.wikipedia.org/wiki/Indian_numbering_system
o https://en.wikipedia.org/wiki/The_Sand_Reckoner
o https://en.wikipedia.org/wiki/History_of_large_numbers
o https://en.wikipedia.org/wiki/Hindu_units_of_time
o https://archive.org/details/TheFlowerOrnamentScriptureATranslationOfTheAvatamsakaSutraByThomasClearypdfdtyxxytd
o http://www.storyofmathematics.com/
o http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Chinese_numerals.html
o http://www.universetoday.com/36302/atoms-in-the-universe/
Dhanyavaad for posting the article
Jai Maharaj, Jyotishi Om Shanti
Sanatan Dharm - WISDOM OF BHARAT: Spirutuality and science
SCIENCE. HINDUS DID IT FIRST - Concepts of zero, infinity,
numerals, etc.
[Excerpts below from the National Geographic Magazine,
Hinduism Today magazine, Arnold Toynbee...]
'SCIENCE. WE DID IT FIRST'
Vedic-Hindu principles and spirituality transcend the
Judeo-Christian-Islamic definition of "religion", and
contain much more -- they include the arts, sciences and
technology:
o Excerpt 1 - Indians originated concepts of zero, infinity, numerals
o Excerpt 2 - 'Science. We did it first'
o Excerpt 3 - Tachyons lose mass, energy the faster they travel
o Excerpt 4 - Mundakopanishad, Atharv Ved: Tachyons faster than light
o Excerpt 5 - Astronomy in ancient Bharat
o Excerpt 6 - Knowledge of equinoxes, precession, astrology, palmistry
o Excerpt 7 - Achievements of Vedic-Hindu sage-scientists
Continues at:
https://groups.google.com/d/msg/soc.culture.indian/rrWxaiFaH0A/vYW4Na67AgAJ
Jai Maharaj, Jyotishi
Om Shanti
https://tinyurl.com/jaimaharaj
--- SoupGate-Win32 v1.05
* Origin: www.darkrealms.ca (1:229/2)