Zero as used in couting ten heads of Ravana and hundred brothers of Kaurava and sahasra as used in Vedas

[sunil bhattacharjya]

Dear friends,

It seems there was a humorous piece in a Kannada magazine, where a student asked a question to the teacher “Aryabhata, the founder of zero, lived in the Kaliyuga, how then the people counted the 10 heads of Raavana in tretaayuga, 100 Kaurava brothers in the Mahaabhaarata and dasha, shata and sahasra in vedas (sahasraaksha, sahasrapaat, dashaangulam etc.) ? The teacher fainted.

Quoting this piece someone as asked “Is there any reasonable answer for this?”

I could think of the following reply. There may be better or more appropriate reply and the schlars in the list may kindly help.

Varahamihira mentioned Aryabhatta and that could be the reason why many people believe that Aryabhatta was the original writer of the Suryasidhaanta and he was the first user of "Zero", but the Suryasiddhanta itself says that Mayasura composed it around the beginning of the Treta yuga. That means Mayasura lived before the times of Ramayana and he could have been the first to introduce the "Zero". I am open to correction in this matter.

As regards the ten heads of Ravana, it is said that Ravana offered his head to Lord Shiva ten times and that is why he is called Dashanan or Dashagiva. He ignored the 11th Rudra and Hanumana, the avatara of the 11th Rudra, helped Lord Rama to kill Ravana.

As regards the 100 Kaurava brothers, all of them might not have been uterine brothers, as only 11 of them were maharathis, including Yuyutsu, and Yuyutsu was not the son of Gandhari. Other than these 11, the rest could have been the adopted children, who looked after Dhritarashtra and blind-folded Gandhari, particularly when the 11 kauravas underwent martial and other training under Guru Drona. Gandhari opened her eyes only once to see Duryodhana on the last day of Mahabharata war, when Duryodhana sought the blessings of his mother.

Regards,
Sunil KB

[Shrivathsa B]

hariH OM,

   If we ascribe discovery of zero to brahmagupta, then one finds it difficult to reconcile the shlokas of vAlmiikirAmAyaNa (kiShki 38) where the powers of ten are given and (sundara, 1) where hanumAn grows in multiples of ten yojanas to avoid being eaten by surasaa). One of these is possible:
1. Brahmagupta was laying on record whatever was the traditional way of counting.
2. If 1 is not true, then (i) either the shlokas are prakShipta or (ii) vAlmiiki was posterior to brahmagupta. (Pollock will love the latter proposition).

स्वस्ति,
      भवानीभारती जयतेतमाम्,
                                   श्रीवत्सः ॥

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[K S Kannan]

Explicitly stated powers of ten are as old as the Veda-s!

[G S S Murthy]

Place value system and decimal system are different. When one says Aryabhata discovered zero, I believe, one means that symbol zero attains different values depending on its position in writing the number.

Regards,

Murthy

My web site : http://murthygss.tripod.com/index.htm
and also my Sanskrit blog :

http://simplesanskrit.blogspot.com/

http://gssmurthy.blogspot.com

[rniyengar]

Zero as a concept associated with counting/arithmetic is different from its use in place value system. When subtraction of numbers became prevalent (example: Lagadha's Vedanga Jyotisha) there should have been instances when the same number got subtracted by itself ! But we do not find instances of explicit statements about this till later period. The text Krishi-paraashara has the rule R=[(3N+2)/7] for rainfall prognosis. N is the year counted from the beginning of the Shaka Era (78 AD). The remainder of the above equation would be one of the seven integers (0,1,2,...6). But the text treats 0 to be as 7 itself which is not wrong but this is not the way we do now. 

RNI

[Subrahmanyam Korada]

नमो विद्वद्भ्यः

पूर्णमदः ... पूर्णात् पूर्णमादाय पूर्णमेवावशिष्यते (उपनि) - some scholars take पूर्णम् as zero.

Zero was there in other branches of Veda - one has to search . ज्योतिषम् is a वेदाङ्ग  compared with नेत्रम् of वेदपुरुष (शिक्षा) ।

धन्यो’स्मि

Dr.Korada Subrahmanyam
Professor of Sanskrit, CALTS,
University of Hyderabad,
Ph:09866110741(M),91-40-23010741(R),040-23133660(O)

Skype Id: Subrahmanyam Korada

Blog: Koradeeyam.blogspot.in 

[sunil bhattacharjya]

Namaste,

I learnt that etymologically "Shunya" comes from "sve",i.e., to spread., and so much so that it cannot be perceived, or can be considered as non-existent for taking into account. If this derivation is valid, an example can be cited that a spoonful of water can be perceived, but not when it evaporates and gets spread in the air. Lord Vishnu has been called Shunya in this sense, as he is spread everywhere.

Now the question is, when did this shunya came to be used to suffix a numeral, to indicate a value ten-fold the numeral? From the ensuing dliberations, so far, it appears that shunya in this application was known from the times of Mahabharata and Ramayana or even before that.

Regards,

Sunil KB

[sunil bhattacharjya]

Namaste,

I learnt that etymologically "Shunya" comes from "sve",i.e., to spread., and so much so that it cannot be perceived, or can be considered as non-existent for taking into account. If this derivation is valid, an example can be cited that a spoonful of water can be perceived, but not when it evaporates and gets spread in the air. Lord Vishnu has been called Shunya in this sense, as he is spread everywhere.

Now the question is, when did this shunya came to be used to suffix a numeral, to indicate a value ten-fold the numeral? From the ensuing dliberations, so far, it appears that shunya in this application was known from the times of Mahabharata and Ramayana or even before that.

Regards,

Sunil KB

[Amba Kulkarni]

Namaste,

I have seen the use of the word शून्य in छन्दशास्त्र of पिङ्गल.
In the shlookas from 8.28-8.31, he is describing how to obtain powers
of 2. (2^n in modern notation). The relevant shlokas, their
translation, with an illustration and its equivalent mathematical
expression is given below.
(For more details you may refer to my unpublished paper:
http://arxiv.org/abs/math/0703658v2)


dviḥ arddhe (8.28)
rūpe śūnyam (8.29)
dviḥ śūnye (8.30)
tāvadardhe tadguṇitam (8.31)

If the number is divisible by 2(arddhe), divide by 2 and write 2(dvi).
If not, subtract 1 (rūpe), and write 0 (śūnyam).
If the answer were 0(śūnya), multiply by
2(dvi), and if the answer were 2(arddhe),
multiply (tadguṇitam) by itself (tāvad).

So for example, consider 8.
8
4 2 (if even, divide by 2 and write 2)
2 2 (if even, divide by 2 and write 2)
1 2 (if even, divide by 2 and write 2)
0 0 (if odd, subtract 1 and write 0).

Now start with the 2nd column, from bottom to top.
0 1*2 = 2 (if 0, multiply by 2)
2 2^2 = 4 (if 2, multiply by itself)
2 4^2 = 16 (if 2, multiply by itself)
2 16^16 = 256 (if 2, multiply by itself).

This algorithm may be expressed in modern notation as

power2(n) = [power2(n/2)] ^ 2 if n is even,
= power2(n-1/2) * 2, if n is odd,
= 1, if n = 0.


-- Amba Kulkarni

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--

Fellow,
Indian Institute of Advanced Study,
Shimla

आ नो भद्रा: क्रतवो यन्तु विश्वत: ll
Let noble thoughts come to us from every side.
- Rig Veda, I-89-i.
Prof. (On leave)
Department of Sanskrit Studies
University of Hyderabad
Prof. C.R. Rao Road
Hyderabad-500 046

(91) 040 23133802(off)

http://sanskrit.uohyd.ac.in/scl <http://sanskrit.uohyd.ernet.in/scl>
http://sanskrit.uohyd.ac.in/faculty/amba
<http://sanskrit.uohyd.ernet.in/faculty/amba>

[Amba Kulkarni]

Let me add a few more lines for clarity.

Following concepts are important when we talk about Zero or शून्य

a) Use of the word शून्य and its denotation
b) Mathematical symbol to denote शून्य
c) Place value system

In the example I provided, it is not clear what is the denotation of
शून्य. It is used (along with 2) just to store the intermediate
result, and an appropriate action is performed in the second step.

-- Amba Kulkarni

[G S S Murthy]

Pingala's Chandasshastra is in the form of sutras. It is not clear how Dr.Amba Kulkarni refers to shlokas in Pingala.

Regards,

Murthy

http://gssmurthy.blogspot.com

[Amba Kulkarni]

I am sorry. I meant suutras and not shlokas. Thanks for correction.

-- Amba Kulkarni

[Dipak Bhattacharya]

23.7.16

Dear  Scholar,

<If we ascribe discovery of zero to brahmagupta, then one finds it difficult to reconcile the shlokas of vAlmiikirAmAyaNa (kiShki 38) where the powers of ten are given and (sundara, 1) where hanumAn grows in multiples of ten yojanas to avoid being eaten by surasaa). One of these is possible:>

In fact the place value of zero was either discovered by Aryabhata or was inherited by him. In Ga.nitapaada vs.2 he states sthaanaat sthaana.m da;sagu.na.m syaat. This is the fundamental principle of the arrangement of numbers to get the place-value of individual digits and the series they make.

I shall be glad if any friend corrected if there is any wrong observation made by me.

The above ten includes zero

Best

DB 

On Fri, Jul 22, 2016 at 4:56 PM, rniyengar <narayana...@gmail.com> wrote:

[Kalicharan Tuvij]

नमस्ते ।

Even Roman numerals are base-ten, but don't need a zero for representation. This means, zero is not related per se to numeral representation or to base-ten.

Zero is not absolutely necessary for the purpose of counting, to say it in other words. One may represent the number ten by "10", "१०", "X" or some other symbol.

The essence of zero lies in the existence (or the proof of it) of negative numbers. Zero helps create the "realm" of negatives. So, even if zero is not explicitly mentioned, the presence of negative numbers necessary imply the presence of zero.

धन and ऋण are the words used for positive and negative numbers. These are also used in the banking/ finance system. In fact, the two implementations are one and the same. Archaeologically, we have the Indu-Saraswati seals available with us in large numbers; obviously these are the ऋण representations of some widely practised business/ banking activity.

The very words धन and ऋण imply zero. Yet we also have direct understanding and mention of zero in the Veda. सीर and शुना are the deity equivalent of the idea. शून्य comes from शुना and शुन्ना, whereas "zero" comes from (in my opinion) from सीर.

सीर is a female deity and सीरा / सीता is Her manifestation during the times of Ramayana.

There are deeper principles involved, but I believe this is the approach that can yield the best results, including a better understanding of Sanskrit the language itself.


KT

[Dipak Bhattacharya]

<The essence of zero lies in the existence (or the proof of it) of negative numbers. Zero helps create the "realm" of negatives. So, even if zero is not explicitly mentioned, the presence of negative numbers necessary imply the presence of zero.>

Nothing of that can be conceived without place value. 27 means 20+7= 2x10+7 That means the zero of twenty represents ten. So20 represents 2x10.21=2x10+1. If any number is placed in the series which our children are taught the place value is learnt from the top line

Thus 100th 10th unit
            1    6    7

hundred units of one,six units of ten, seven units of one.

This is a crude presentation, but the units in the series are recognisable.

I hope some colleague will make a finer presentation.

We were taught the above in the reverse order that made things complicated to me. But that was right as the numbers are written in our script in the reverse order beginning from unit in the extreme right.

I stated just what was and perhaps, is still taught in the rural primary schools where ancient India still lives. There was no attempt to sermonize
I am all praise for the system of teaching
Best

DB

[Nagaraj Paturi]

For the information of those who may not be aware:

There is one https://www.zerorigindia.org/

Sharing the contents of their FAQ page, interesting observations. 

--

Nagaraj Paturi

 

Hyderabad, Telangana, INDIA.

 

Former Senior Professor of Cultural Studies

 

FLAME School of Communication and FLAME School of  Liberal Education,

 

(Pune, Maharashtra, INDIA )

 

 

 

[Nagaraj Paturi]

Following is from http://www.livescience.com/27853-who-invented-zero.html

India: Where zero became a number

Some scholars assert that the Babylonian concept wove its way down to India, but others give the Indians credit for developing zero independently.

The concept of zero first appeared in India around A.D. 458. Mathematical equations were spelled out or spoken in poetry or chants rather than symbols. Different words symbolized zero, or nothing, such as "void," "sky" or "space." In 628, a Hindu astronomer and mathematician named Brahmagupta developed a symbol for zero — a dot underneath numbers. He also developed mathematical operations using zero, wrote rules for reaching zero through addition and subtraction, and the results of using zero in equations. This was the first time in the world that zero was recognized as a number of its own, as both an idea and a symbol.

(Highlighting mine)

[Nagaraj Paturi]

Kim Plofker (2009), Mathematics in India, Princeton University Press, ISBN 978-0691120676, page 54–56.

 

"In the Chandah-sutra of Pingala, dating perhaps the third or second century BC, there are five questions concerning the possible meters for any value “n”. [...] The answer is (2)⁷ = 128, as expected, but instead of seven doublings, the process (explained by the sutra) required only three doublings and two squarings – a handy time saver where “n” is large. Pingala’s use of a zero symbol as a marker seems to be the first known explicit reference to zero.

[sadasivamurty rani]

In my attempt of participating in this progressive discussion I could see the following traces of an early use of base-ten counting system in ancient times.

1. In the Rgveda: 

सह्स्रशीर्षा: पुरुष: सहस्राक्षस्सहस्रपात्।

स भूमिं विश्वतो वृत्वाऽत्यतिष्ठद्दशाङ्गुलम्॥ (पुरुषसूक्तम्)

Here in this Rk of Purusha sukta the numbers दश and सहस्रम् are used.

2. In the Krishna Yajurveda Samhita:

एकस्मै स्वहा द्वाभ्यां स्वाहा त्रिभ्य: स्वाहा चतुर्भ्य: स्वाहा......दशभ्य: स्वाहा .....विंशत्यै स्वाहा .... चत्वारिंशते स्वाहा .... अशीत्यै स्वाहा...

शताय स्वाहा .. शताय स्वाहा सहस्राय स्वाहाऽयुताय स्वाहा नियुताय स्वाहा प्रयुताय स्वाहाऽर्बुदाय स्वाहा न्यर्बुदाय स्वाहा समुद्राय स्वाहा मध्याय स्वाहाऽन्तायस्वाहा परार्थाय स्वाहा...सर्वस्मै स्वाहा॥ इति कृष्णयजुस्संहितायां ७ काण्डे २ प्रश्ने २० अनुवाक:॥

3. In the Brahmanda Purana:

एकं दश शतं चैव सह्स्रमयुतं तथा।

लक्षं च नियुतं चैव कोटिरर्बुदमेव च॥

बृन्दं खर्वो निखर्वश्च शंखपद्मौ च सागर:।

अन्त्यं मध्यं परारर्थं च दशवृद्ध्या यथा क्रमम्॥ - ब्रह्माण्डापुराणवचनम् ।

4. विराजो दिश:। पिंगळनगछन्दश्शास्त्रे ३/५

पाद इत्यनुवर्तते। यत्र क्वचिद्वैराज: पाद: इत्युच्यतेऽत्र  दशाक्षरा प्रत्येतव्य:। (इति हलायुधवृत्ति:।) (Here the word दिश: was used by Pingalanaga to represent TEN. 

These illustrations help to draw an inference that base-ten counting method was in wide use even in Vedic Times. In Vedic times and even in classical Sanskrit literature through a smooth transition the number of meters (sama vritttas in all the 26 metrical classes together were.. 13,42,17,726. Though a ZERO or its equivalent was not used the decimal system was used. 

Now as a second step we have to search for the written evidence to represent Indian ZERO.

If I found any such I shall add in course of time.  

Warm regards,  

Prof. Rani Sadasiva Murty

---

From: Kalicharan Tuvij <kalich...@gmail.com>
To: भारतीयविद्वत्परिषत् <bvpar...@googlegroups.com>
Sent: Saturday, 23 July 2016 8:02 PM
Subject: Re: {भारतीयविद्वत्परिषत्} Zero as used in couting ten heads of Ravana and hundred brothers of Kaurava and sahasra as used in Vedas

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[Amba Kulkarni]

Thanks Prof. Paturi for this quotation and reference. I did not have the book with me right now, and hence I could not mention this.

On 23 July 2016 at 23:47, Nagaraj Paturi <nagara...@gmail.com> wrote:

Kim Plofker (2009), Mathematics in India, Princeton University Press, ISBN 978-0691120676, page 54–56.

 

"In the Chandah-sutra of Pingala, dating perhaps the third or second century BC, there are five questions concerning the possible meters for any value “n”. [...] The answer is (2)⁷ = 128, as expected, but instead of seven doublings, the process (explained by the sutra) required only three doublings and two squarings – a handy time saver where “n” is large. Pingala’s use of a zero symbol as a marker seems to be the first known explicit reference to zero.

 

This is what the formula I presented at the end shows. From algorithmic point of view this is a faster algorithm to find 2^n.

If I remember correctly, Prof. Knuth also has mentioned in his book on Algorithms about this algorithm. Again, since I do not have the book with me right now, I can not quote.

-- Amba Kulkarni

--

Fellow,
Indian Institute of Advanced Study,
Shimla

आ नो भद्रा: क्रतवो यन्तु विश्वत: ll
Let noble thoughts come to us from every side.
- Rig Veda, I-89-i.
Prof. (On leave)
Department of Sanskrit Studies
University of Hyderabad

Prof. C.R. Rao Road 

Hyderabad-500 046

(91) 040 23133802(off)

http://sanskrit.uohyd.ac.in/scl

http://sanskrit.uohyd.ac.in/faculty/amba

[Nagaraj Paturi]

Prof. Amba Kulkarni, I knew that you mentioned the same. But I wanted to bring a western name so that what familiarity breeds is avoided.

[Nagaraj Paturi]

My son studying algorithms, sent me the following links when I told him about the ongoing discussion:

http://www.smithsonianmag.com/smart-news/you-can-visit-the-worlds-oldest-zero-at-a-temple-in-india-2120286/?no-ist 

http://www.smithsonianmag.com/history/origin-number-zero-180953392/

[Nagaraj Paturi]

https://en.wikipedia.org/wiki/Lokavibhaga

[Nagaraj Paturi]

https://en.wikipedia.org/wiki/Zero:_The_Biography_of_a_Dangerous_Idea

[Nagaraj Paturi]

Sharing the English translation of a Czech work on History of Ancient Indian Mathematics.

[Madhav M Deshpande]

I don't have a mathematical question about Ravana's (11) heads.  But in some representations, like the painting I have attached, his eleventh head is shown as an ass-head.  Can someone explain why that may be the case?  Is there a story about this ass-head?

Madhav Deshpande

Ann Arbor, Michigan, USA

[G S S Murthy]

Both references make interesting reading.

Thanks and regards,

Murthy

[sunil bhattacharjya]

Namaste,

Ravana was a very learned and wise person. In his young age he was greedy for power and he took away by force the kingdom of Lanka as well as the Vimana from his brother Kuvera. He also misbehaved with  a young lady, who cursed him,  but later on  he seems to have mended his ways. He was a great devotee of Lord Shiva and by Mother Parvati's grace he hadthe  most beautiful wife (Mandodari) as beautiful as Mother Parvati, Then he committed the most foolish and unpardonable act of taking way Mother Sita, not for lust, but due to the pleading of his dear sister Surpanakha, who was interested in marrying Lord Rama. Mandodari advised him to return Sita but he did not listen to her. Then Mandodari wanted to fight Lord Ram herself, Ravana did not allow that also.  It could be that because of  adamance and  foolishness, he was artistically represented with a head of an ass.

Regards,

skb

 

[rniyengar]

I came across a review of the book "Science in Saffron" by Meera Nanda:  http://thewire.in/53574/jagat-guru-science-history-meera-nanda/

I have not read the book yet. The phrase "Jagat-Guru Complex" is quite funny. My impression is, this syndrome is limited to some fanatical and ignorant circles only.  

But for the current thread on Zero the following portion of the review (by S. Sharma) may be relevant.

"A commitment to comparative history and attention to counter cultures are the basic principles that guide the author in her next chapter. Using these principles, the author concludes that a new perspective emerges in examining the evolution of zero. She writes, “(i) When the Indian evidence is placed alongside the evidence from other civilisations of comparable development, it becomes clear that the Indian contributions were neither unique, nor without precedent and (ii) when the sources of evidence are widened beyond metaphysical speculations to include every day, practical counting and computing practices of ordinary people, a new window opens up which faces East of India, to China and South-East Asia.” This chapter is a valuable guide in understanding the relevance of difference between ‘zero’, ‘place value’ and ‘decimal counting’, and how it is quite common (though erroneous) to give all three an Indian birth certificate." 

RN Iyengar

[Nityanand Misra]

On Sunday, 24 July 2016 19:02:14 UTC+5:30, Madhav M Deshpande wrote:

I don't have a mathematical question about Ravana's (11) heads.  But in some representations, like the painting I have attached, his eleventh head is shown as an ass-head.  Can someone explain why that may be the case?  Is there a story about this ass-head?

Madhav Deshpande

Ann Arbor, Michigan, USA

On the donkey-head of Ravana, it is seen commonly found in North Indian scultptures and paintings. This feature has been traced to sculptures dated to ninth century by Jayantika Kala (Epic Scenes in Indian Plastic Art, 1988, ISBN 9788170172284, p. 39) and in paintings dated to the Gupta period by Raghavan (The Ramayana in Greater India, 1973) as cited in Henk Blezer (ed., Tibet, Past and Present: Religion and secular culture in Tibet, 2002, ISBN 9789004127760, p. 445) as well as Sivaramamurti (Birds and Animals in Indian Sculpture, 1974, pp. 26, 41). The last book mentions on page 445 that in the Tibetan version of Ramayana, one of the ten heads of Ravana is that of a horse, while the Khotanese version of the Ramayana mentions a donkey head.  

[Nagaraj Paturi]

I do not know whether the following are the words of Shailza Sharma, the reviewer or Meera Nanda the author. But they need to be underlined:

However, are we alone in this endeavour? We can look at the work of David Pingree in Hellenophilia Versus the History of Science (1992) to understand that this is not entirely an Indian phenomena. Pingree states, “A Hellenophile [love for Greece and Greek culture] suffers from a form of madness that blinds him or her to historical truth and creates in the imagination the idea that one of several false propositions is true. The first of these is that the Greeks invented science; the second is that they discovered a way to truth, the scientific method, that we are now successfully following; the third is that the only real sciences are those that began in Greece; and the fourth (and last?) is that the true definition of science is just that which scientists happen to be doing now, following a method or methods adumbrated by the Greeks, but never fully understood or utilised by them.”

This is an important message to those who among Indians are absolutely sure that there were no scientific ideas at all in ancient India or ancient Sanskrit literature and all science originated in the west only.

The review has the following paragraph relevant to the present discussion:

In his book Crest of the Peacock: Non-European Roots of Mathematics (1991), George G. Joseph highlights the technological achievements India, China and Africa long before incursions of Europe into these areas; and he emphasises that, “In the minds of some, scientific progress becomes a uniquely European phenomenon, which can be emulated by other nations only if they follow a specifically European path of scientific and social development”, and thus it was the intention of the author to show that “the standard treatment of the history of non-European mathematics exhibited a deep-rooted historiographical bias in the selection and interpretation of facts, and that mathematical activity outside Europe has as a consequence been ignored, devalued, or distorted.”

Are not these Euro-centric notions of the origins of scientific ideas are the ones that are deep seated in the modern more particularly post-independence main stream academic world ? Are these not the poorva paksha /trigger /source of most of the endeavours of digging out the scientific ideas in the ancient sources of cultures outside the Hellenistic world including India?

Serious academic historians of Indian scientific ideas never had or have the idea that India was only a giver of ideas never a taker. 

It is those who conceived or perceived the history of science to be a purely linear monolithic euro-centric evolution who need the following message from the review:

This actually should be a way to understand science more generally; there are parallel enquiries, and nobody ‘owns’ a scientific achievement.  

This apart, there are many less informed or ill informed ideas about Sulvasutras , Charka, S'us'ruta and other books in the piece that need a separate discussion.

 

 

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[Nagaraj Paturi]

Sharing snapshots

[Nagaraj Paturi]

The following are from Jayantika Kala's book  Epic Scenes in Indian Plastic Art, 1988, ISBN 9788170172284 cited by AadaraNIya Nityanandji

[Nagaraj Paturi]

Theatre pics

[Madhav Deshpande]

Amazing pictures of Ravana.  Thanks, Paturi-ji, for all this information and the pictures of Ravana.

Madhav Deshpande

Ann Arbor, Michigan, USA

[Haresh Gala]

Namaste,

In Ancient time , Different symbols were used for 10, 20, 30, 100  etc. Infact Base was 20 , so we find different names from 1 to twenty.

Here attached  Images for Numbers used. In Western Kshatrap &  Gupta Period dates were written like 121 as symbol 100, 20 , 1

189     will be 100, 80 , 9 etc

Theatre pics

Sharing snapshots

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[Vinay Nair]

When we talk about Zero, we need to be clear as to what kind of zero are we referring to. Is it a Zero that refers to Nothingness? Is it a Zero that is used as a marker between positive and negative numbers (e.g. here 0 degrees does mean 'no temperature' because Zero refers to nothing also)? Is it Zero as a symbol/digit? Or is it Zero used in a Place value system? All of these are different zeros that evolved in due course of time. 

Regarding the belief that Aryabhatta discovered Zero, it is probably due to the fact that people started believing it without checking the authenticity of the claim.

In Pingala's Chandas Shastra, we see the appearance of Zero as a marker and also the use of binary system. In fact, the history and development of Zero in different civilisations is very interesting. Sharing a PPT that I had made to do a session on History and Development of Zero for school children (due to which there are some cartoon images in it). 

​

​Regards,​

Vinay Nair about.me/vinay_nair

Website: www.sovm.org

www.raisingamathematician.com

Email: vi...@sovm.org

Blog: http://vinayrnair.wordpress.com/

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[sunil bhattacharjya]

Dear friends,

There were two Aryabhattas. Alberuni also mentioned about the  two Aryabhhattas.  Aryabhatta-I was born in the 5th century CE.  Varahamihira in the 1st century BCE mentioned about Aryabhatta, who was obviously the  Aryabhatta -I , who was born in earlier times  than the 1st century BCE and it could even be before the times of Panini and his brother Pingala. There is a claim that Aryabhatta=I was born in 1325 BCE.

Regards,

skb

.

[Sivasenani Nori]

Words are not sufficient to describe the greatness of Panini, but is there a connection between अदर्शनं लोपः and zero? If anything, the zero-affixes or null pratyayas are conceptually closer to the zero of mathematics.

Regards
N Siva Senani

[Vinay Nair]

Adarshanam lopah and he also mentions Rupe Shunyam.

Here's the link of the lecture (conducted at IIT Madras by Prof. M.D.Srinivas) from where I have taken the reference https://youtu.be/YV_tu2Ucby4

[Sivasenani Nori]

Sri Vinay Nair

Thank you for giving the link to this very nice lecture by Prof. M. D. Srinivas. To me it seemed to be entirely on ChandaSSAstra and did not touch Panini. Or, did I miss something?

Regards

N. Siva Senani

[Vinay Nair]

Dear Siva ji,

Here's a link about Prof. Srinivas' talk on Panini and Mathematics https://youtu.be/qZsdAXF9DTE

Actually it's a series of 40 lectures on History and Development of Mathematics in India.

Regards,

Vinay

[sunil bhattacharjya]

Dear Vinayji,

Hope Prof. M. D. Srinivasji will come out with a book covering the contents of the lecture series.

Regards,

[Sivasenani Nori]

Once again, thank you, Sri Nair.

Prof. Srinivas, at around the 30th minute in the video, briefly mentions "lopa" as a "linguistic zero" and indicates its value in that the string value changes depends on whether lopa is specified or not, even though in reality there is nothing. One would have thought of other Sutras where this concept is explicitly stated, but anyhow, I would definitely like to read more before on this topic.

A quick google search revealed that there is a monograph "Zero in Panini" by M. D. Pandit. (http://manoharbooks.com/BookDetails.asp?Id=45461&isbn=).  I tried to order it but strangely it was not loading to the cart. Anyhow, enough people seem to have written on the aspect for me to get a start. Also, whatever sample of Prof. Srinivas, I heard, he comes across as an expert on development of mathematics in India, so I am sure there is more to the concept.

Regards

Senani

[Vinay Nair]

It's my pleasure. You can find more videos of his on YouTube. You can search using his name 'M D Srinivas'

4 years ago, we had taken a camp based on the ideas used in this video lectures on topic of learning Permutations and Combinations through Chandass Shastra at a camp at Chinmaya International Foundation, Cochin for students as young as 13 years old and the participants loved it. From May 2nd to 7th, 2017, Chinmaya International Foundation is doing a similar residential camp on 'Maths and Music' at Chinmaya Vibhooti (near Pune) using the ideas in Chandass Shastra. Anyone interested can visit the events section od www.chinfo.org after a couple of weeks or contact me.

Regards,

Vinay