Subject: [HM] Zero to infinity in ancient Indian texts
From: Dinesh Maheshwari (dsm@cypress.com)
Date: Thu Jan 27 2000 - 22:07:33 EST
Zero to infinity in ancient Indian texts
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There are numerous reference to the number system in the Vedic literature
and some instances are listed below. The instances are from Atharvaveda
and Yajurveda.
By the way, Atharvaveda is dated around 3100BC based on astronomical
observations recorded within it. Yajurveda is older than Atharvaveda and
more recent than RigVeda (around 4300BC-4000BC).
Please refer to the article by Koenraad Elst, Leuven (Belgium) on
"Astronomical data and the Aryan question" dealing with the dating of
the ancient Indian texts.
The article is available on-line at
http://members.xoom.com/_XMCM/KoenraadElst/articles/astronomy.html
http://members.xoom.com/_XMCM/KoenraadElst/articles/astronomy2.html
http://members.xoom.com/_XMCM/KoenraadElst/articles/astronomy3.html
The 10 base system
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The concept of a number system with basis 10 was prevalent during
Vedic times itself. Consider the following hymn from Atharvaveda.
Translation of the hymn: Atharvaveda 5.15
(1) O companion and embodiment of universal law, grant me sweetness.
May revilers be one and ten.
(2) O companion and embodiment of universal law, grant me sweetness.
May revilers be two and twenty.
(3) O companion and embodiment of universal law, grant me sweetness.
May revilers be three and thirty.
(4) O companion and embodiment of universal law, grant me sweetness.
May revilers be four and forty.
(5) O companion and embodiment of universal law, grant me sweetness.
May revilers be five and fifty.
(6) O companion and embodiment of universal law, grant me sweetness.
May revilers be six and sixty.
(7) O companion and embodiment of universal law, grant me sweetness.
May revilers be seven and seventy.
(8) O companion and embodiment of universal law, grant me sweetness.
May revilers be eight and eighty.
(9) O companion and embodiment of universal law, grant me sweetness.
May revilers be nine and ninety.
(10) O companion and embodiment of universal law, grant me sweetness.
May revilers be ten and hundred.
(11) O companion and embodiment of universal law, grant me sweetness.
May revilers be hundred and thousand.
Original Sanskrit for the hymn: Atharvaveda 5.15
(1) eka cha me dasha cha me apavaktara osadhe. Ritajata ritavari
madhu me madhula karah.
(2) dve cha me vinshatishcha me apavaktara osadhe. Ritajata ritavari
madhu me madhula karah.
(3) tistramcha me trinshachcha me apavaktara osadhe. Ritajata ritavari
madhu me madhula karah.
(4) Chatasrashcha me chatvarinshachcha me apavaktara osadhe. Ritajata
ritavari madhu me madhula karah.
(5) pancha cha me panchashachcha me apavaktara osadhe. Ritajata
ritavari madhu me madhula karah.
(6) sat cha me sastishcha me apavaktara osadhe. Ritajata ritavari
madhu me madhula karah.
(7) sapta cha me saptatishcha me apavaktara osadhe. Ritajata ritavari
madhu me madhula karah.
(8) asta cha me ashitishcha me apavaktara osadhe. Ritajata ritavari
madhu me madhula karah.
(9) nava cha me navatishcha me apavaktara osadhe. Ritajata ritavari
madhu me madhula karah.
(10) dasha cha me shatam cha me apavaktara osadhe. Ritajata ritavari
madhu me madhula karah.
(11) shatam cha me sahasram chapavaktara osadhe. Ritajata ritavari
madhu me madhula karah.
A mantra from Yajurveda describes numbers increasing by a factor of
ten up to a trillion.
"Ima me agna istaka dhenavah santveka cha dasha cha dasha cha
shatam cha shatam cha sahasram cha sahasram chayutam chayutam
cha niyutam cha niyutam cha prayutam charbudam cha nyarbudam cha
samudrashcha madhyam chantashcha parardhashchaita me agna ishtaka
dhenavah santvamutramusminlloke." Yajurveda 17.2
Translation:
"O Agni! May these bricks be cows for me. One and ten, and ten and
hundred, and hundred and thousand, and thousand and ten thousand, and
ten thousand and hundred thousand, and hundred thousand and million,
and ten million, and hundred million, and billion, and ten billion,
and hundred billion, and trillion, O Agni, may these bricks be cows
for me in this world and in the other world." Yajurveda 17.2
However, the largest number used in ancient India in the context
of astronomy was 10 to the power 53
Infinity
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The Vedic people didn't stop there, but took the concept of large
numbers to all the way to infinity. Infinity was termed as Purna.
Purna is derived from root "Pri" meaning to fill. Purna literally
means full or complete and mathematically means infinity.
"Purnamadah Purnamidam Purnatpurnamudachyate.
Purnasya Purnamadaya Purnamevavashisyate." Yajurveda, Shanti
Mantra , Chapter 40,
meaning,
"That is Purna, this is Purna, Purna comes out of Purna.
If Purna is subtracted from Purna, still Purna is left." Yajurveda,
Peace Mantra, Chapter 40
This line then yields that the result of subtracting infinity from
infinity is still infinity.
Zero
----
The concept of zero came from the concept of void in Indian philosophy.
It was indicated as a dot ("Bindu" ) and was termed "Pujyam"(the term
"Pujyam" also means holy). The other terms used to describe zero were
"bindu" and "shunyam"( a more recent term meaning blank) and the concept
of void was termed "Shubra". The Arabs derived the word "Siphra" from
"Shubra" . And the english term "cipher" seems to come from "Siphra" to
connote zero or any Arabic numeral.
Best regards,
Dinesh
--
Dinesh Maheshwari
Advanced Design Methods
Cypress Semiconductor
San Jose, CA, USA
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