"Zero" is in Veda itself...

When we count from number 1 onwards and beyond number 9... how can we proceed if we don't have a number 10. To have a the number 10 then we must have the number "0". Else how 10 can be written - First writing 1 and followed by a 0. We are not familiar with other method of writing in Decimal system (decimal system origination was Ancient India). If so, then how shall the Vedic rishis could have mentioned such large numbers such as ayuta (अयुत) for ‘ten thousand’, niyuta (नियुत) for ‘hundred thousand’, prayuta (प्रयुत) for ‘million’, arbuda (अर्बुद) for ‘ten million’, nyarbuda for ‘hundred million’ etc. (these are used in Yajur Veda).

Today all encyclopedias are wrongly attributing the invention of "0" to Babylonian mathematics in 7nd century BCE, and also giving a passing remark about Acharya Pingala in 3rd Century BCE as the one who used "0" in the Chandas shastram. Chandas shastram is a Vedanga - limb of Veda. Acharya Pingala's Chandas shastram like Paninian Grammar was written for both Vedic and Worldly branches of Samskritam. The original Chandas shastram is a part of Veda itself in the earlier Era. Thus it is evident that "0" was there from time of Veda - which is time immemorial. Reference of "0" in Pingala Chandas shastram - in Sutra 8.29 "rupe shunyam" and Sutra 8.30 "dvihi shunye" - both these sutras use connect the 'valueless' usage of "0".

In "Brhadaranyaka Upanishad 5.1" of the Shukla Yajur Veda 1.4.10 quotes "Kham Brahmn" based on "adhibhoudika" meaning of this passage "Zero is Brahman" (complete, infinite, etc...)

Again Yajurveda sukta 17.2 elaborates on the decimal place value system, without "0" how can decimal place value be represented ?. 

Sri. Aryabhata used the word "Kha" widely to denote emptiness ("Kham"). Sri.Suryadeva commenting on Aryabhata’s "Kha", says that , “khani sunya upa lakshitani”  In Brahmagupta’s work, the word "Kha" gets prominence. "Kha" and Shunya (void) is used synonymously. In Lilavati, when one come across the chapter on description of Shunya (zero), it’s a veritable carnival of kha. The verse reads as follows: 

"Yoge kham kshepsamam, vargado kham, khabhajito rashi Khahara syat, khaguna kham, khaguna nishchantayashcha sheshavidhau!!"

- verse 46, Lilavati

From the above it is evident that "0" as a place value system was there and also "0" as a number was also there since the Vedic times  - in other words means "anaadi" - beginingless or time immemorial.

So let's not keep repeating the mistake that Sri.Aryabhatta invented "0" etc. No doubt Sri. Aryabhatta was a great mathematician and scientist. But saying that  Sri. Aryabhatta invented "0" would be an insult our scientific advancements before him. To elaborate further, during Mahabharata war - Astras (missiles) were widely used. Launch of such aerial weaponary requires precise calculations involving topography, geometry, trignometry, etc.  Such calculations certainly require the use of "0". - Like today how a missile launch can't be done without precise calculations requiring the use of "0".

Furthermore, Maharishi Vyasa write slokas on celestial maps with references to three sequential solar eclipses and to planetary positions. Reference to the first solar eclipse comes in the Sabha Parva 79.29. Second solar eclipse just before Mahabharata war second in the Bhisma Parva 3.29, following a lunar eclipse occurring within the same fortnight. He warns that these successive eclipses are sign of bad times (we can now use these celestial positions to do the detailed astronomical map and also do the dating to precisely estimate Mahabharata war time), all such complex calculations require the useage of "0", thus "0" was in usage in Mahabharata time and even before.

The English word zero came via → French zéro which is from → Venetial zero, which came from (together with Ciper /Cypher) via → Italian zefiro which came from → Arabic صفر, ṣafira = “is empty", ṣifr = "zero", “nothing” This was translation of  →  the Samskritam word shoonya /shunya (शून्य), meaning "Valueless" or "empty".

The etymological chain confirms that only the word "Shunya" (which is used to denote "0" as a valueless number) had travelled and the same word is used for all other purposes of "0" even today. Such as "0" as a valueless number, or place value system, or fraction, etc. Though various mathematical calculations using "0" for other purposes travelled later, but the other Samskritam words didn't travel till 20th century. Later in early 20th century the words such as Void (from Sanskrit word व्योम Vyoma) were starting to be used in computer programming languages.

In Samskritam we have many words for "0" depending on its value. They are below:

पूज्य, /सत् (poojya /sat) = Holy (complete) - from the word Wholly

शून्य, रिक्त, रन्द्र (shunya, rikta, randra) = Valueless

आभु, अव्यक्त (Aabhu, avyakta) = Inexpressible (value can't be determined)

पूर्ण, अनन्त (purna, ananta) = Complete, full, endless (infinite value)

ख, दिब, व्योम, (kha /kham, diba, vyoma) = Infinity

बिन्दु (bindu) = Point /Dot (used in fractions)

अव्यय, (avyaya) = NaN / Indeclinable

साङ्खेय, द्रबिणम् (saankheya, drabinam) = Ordinal (while counting "0" as a number)

Such wide veriety of names used for denoting "0" is found in many places  starting from Vedas, Kalpa sutras, Chandas shastra, and many other treatises. Many of the mathematicians of ancient Bharatam were Vaiyakaranaas - as the entire vyakarana sutras of Maharishi Panini by themselves are based on Bija Ganita (Algebra) principles. Maharishi Panini in Ashtadyayi refers an equivalent of "0" as "lopa" - in this kind of usage the value which was originally there has been removed after a particular phonetical change and loss of a phoneme.

The Ganita shaastra (mathematics) has developed into a separate branch of study very long back starting with the Shulba sutras of Sri.Bodhayanacharya and Jyotisha shastra times. "0" was in wide useage for a very long time even before the development of Ganita as a separate branch of study. Sri. Aryabhatta, Sri.Bhaskara, Sri.Bramhgupta, Sri. Neelakanta Somayaji, etc. these were Ganita Shastragnas after the Period of Sri. Gautama Buddha.

Even before and after the period of Sri. Gautama Buddha, Jain mathematicians were quite popular, and even before Jainism came, Vaiyakaranaas were great mathematicians as well as linguists as the entire Samskritam language is based on mathematics and thus it is most suitable for Computing.

In the ancient times the Ganita shaastra (mathematics) has its branches as -  Geometry (Gyamiti) is the study of shapes and their applications; Algebra (Bija Ganita) is the study of operations and their applications; Trigonometry (Trikonamiti) is study of Triangles and the relationships between their sides and the angles and Calculus (Chalana-kalana Ganita) the study of change.

The standard arithmetic algorithms actually originated in India, where they were known by various names such as patiganita (slate arithmetic). However, the word “algorithm” comes from “algorithmus”: the Latinised name of al Khwarizmi of the 9th century House of Wisdom in Baghdad. He wrote an expository book on Indian arithmetic called "Hisab al Hind". Gerbert d’Aurillac (later Pope Sylvester II), the leading European mathematician of the 10th century, imported these arithmetic techniques from the Umayyad Khilafat of Córdoba. He did so because the primitive Greek and Roman system of arithmetic (tied to the abacus), then prevailing in Europe, was no match for Indian arithmetic. However, accustomed to the abacus (on which he wrote a tome), Gerbert was perplexed by algorithms based on the place-value system, and foolishly got a special abacus (apices) constructed for these “Arabic numerals” in 976 CE.

Hence the name “Arabic numerals” — because a learned pope amusingly thought there was some magic in the shape of the numerals which made arithmetic efficient. Later, Florentine merchants realised that efficient Indian arithmetic algorithms conferred a competitive advantage in commerce. Fibonacci, who traded across Islamic Africa, translated al Khwarizmi’s work, as did many others, which is why they came to be known as algorithms. Eventually, after 600 years, Indian algorithms displaced the European abacus and were introduced in the Jesuit syllabus as “practical mathematics” circa 1570 by Christoph Clavius. These algorithms are found in many early Indian texts, such as the Patiganita of Sridhara or the "Ganita Sara Sangraha" of Mahavira, or the Lilavati of Bhaskara II. 

Sri. Ananda Coomarswami had written an short piece on the concept in 1934, Kha and other words denoting Zero, in connection with the Indian Metaphysics of space. He has tried to trace the origin of the use of "kha" for space to Rigveda in the context of the “hole in the nave of a wheel through which the axle runs”. He states that "sunya" (void) as well as "purna" (full) have a common reference in the Vedas.  Since, the Vedic seers were enamored by the wheel (chakra - cycle), the names of various parts of wheel were  used to explain metaphysical concepts. Now, "kha" is the "Naabhi" of the wheel, the space within the hub. "Naabhi" is also the navel, navel of beings and things. Thus, "kha" is the central space of things and beings. In the Rigveda, "kha" or "Naabhi" of the world wheel is regarded as the receptacle and  fountain  of all order, formative ideas and goods” - Ananda K. Coomarswami, Kha and other words denoting Zero, in connection with the Indian Metaphysics of space (Bulletin of the School of Oriental Studies, VII (1934)

 

What is "Sabda" - Shikshaa and Vyakarana in Samskrit - Science of Sound

शब्दानुशासनम् व्याकरणम् । The science of sound is Vyakaranam.

संप्रत्ययः शब्दः । ध्वानिः शब्दः  - इति महाभाष्ये - both knowledge (meaning) and the original "sound" is associated with "Sabda" in Samskrit. The sound is given more importance in Samskrit lanaguage than the word (पदम्) as the natural sound in itself has inheritted meaning with it. The "word" being its derivative added with a suffix, conveys the derived /modified meaning of the original sound. Thus the language is also its derivative. However vyakarana is made to convey the meaning grammar - it is more than just grammar,  as vyaakarana deals with all the derivations of the primordial sounds such as - words, word-sense,  phrases, sentenses, figures of speech, etc. (यद्यपि पदशास्त्रम् इति विश्रुतं तथापि शब्दसाधुत्वासादुत्वविषयैव अस्य वेदाङ्गस्य महत्वम् इति). The shaastra that deals with 'sound' in its basic form is called as Shikshaa (शिक्षा) which is primarily a Vedanga (a part of Veda like Vyaakarana)

Shikshaa (शिक्षाशास्त्रम्) shaastra is the foundation for studying the 2 branches of Samskrit language (भाषा नाम संस्कृतं - वैदिकं लौकिकञ्च) Vaidika (Vedic Samskrit) and Laukika (Classical Samskrit) - Laukika is the part of language that is in use for all purposes other than Vedic - including Science, Literature, Medicine, and all other worldly things.

Shikshaa (शिक्षा) shaastra in its full form is a complex and intricate science based on human vocal system. Which in its full capacity in use in Vedic part of Samskrit (वैदिकसंस्कृतं). The same shaastra is also used in a limited manner in the all purpose non-Vedic part of Samskrit (लौकिकसंस्कृतं).

Even though Sandhi (सन्धिः) is studied along with Grammar, Sandhi deals only with the pronunciation of syllable (Varna वर्णः) with respect to the factors such as - Place (स्थानम्), Effort (प्रयत्नम्), Duration (मात्रा), Pitch (स्वरः), etc. (स्थानादयः). All these deals with Syllabicity (syllables) and phonological aspects (which are part of Shikshaa) than words and meanings. Thus Sandhi is primarily a subject of Shikshaa than grammatical processes - even though Sandhi rules are given in grammar texts (व्याकरणम्), however the place, etc. (स्थानादयः) are elaborated in 'Varnochaarana shikshaa' and 'Paniniya Shiksha' of Maharishi Panini. The rules for changing of syllables based on enjoining of syllables, though found in Grammar texts but are in essence part of the Shikshaa /Phonology.

Thus the linguistics treatise Ashtaadyayi not only deals with Grammar (which is primarily Syntax & Semantics - विभक्तिः कारकम् च) it also deals with the rules of Phonetics - Shikshaa and in general all aspects of "Sound" (शब्दः) which forms the basis for language - including morphology, etc.

Not just Sandhi, the fundamental formations in Sanskrit Roots + Suffixes (प्रकृतिः + प्रत्ययः) and the word generation (व्युत्पत्तिः) processes essentially are based on phonetics (शिक्षा) like Vriddhi, Guna, Samprasaaranam etc. (वृद्धिः गुण सम्प्रसारणम् इत्यादिप्रक्रियाः) - Process of expansions of syllables which purely natural sound modifications while joining syllables. These are evident across word formations - in both Noun forms and Verb forms from singular to plural forms and also declensions. The Vriddhi, Guna, etc.  part in primary and secondary Noun derivatives from Noun roots, Nouns and Verb roots, etc.  (वृद्धिगुणादयः - कृत्तद्धितेषु) are again strictly follow the rules of phonetics. In addition the the phonetic features such as Natvam, Shatvam (णत्वम् षत्वम् उभयमपि) are also part of shikshaa. Also the letter 'h' (ह्) becoming the forth letter of the group consonents (वर्गीयचतुर्तम् अक्षरम्) are again shikshaa. Similarly all most all the Dhaatus (निज​-धातुः) - Verbal roots are also single syllable phonetic (sound) forms - also the suffixes (प्रत्ययः). The prefixes (उपसर्गः) are again mostly dual syllable sound forms.


There are many shikshaa shaastras (शिक्षाशास्त्राणि) more than 40 so far we have got for Four Vedas (चतुर्वेदाः) and their shaakhaas. Of these Paniniya shikshaa for Laukika (non-vedic) branch of Samskrit is famous. Thus Maharishi Panini integrated all these branches of 'the science of language" in his monumental work Ashtaadyayi.  It appears that the entire work of Maharishi Panini is to make rules for pronouncing the "Word" correctly as the "Word" in itself has the inseperable meaning attached with it - thus the perfect pronunciation of just one "Word" takes you to heaven as per Maharishi Patanjali.

The word "vyaakaranam - vi+aa+kr+lyut (suffix)" (व्याकरणम् = वि+आ+कृ+ल्युट्) itself means a "Special form" (of language) - with stress on the verb (creation of the form), the other 2 similar words (1)"aakaarah - aa+kr+ghan (suffix)" (आ+कृ+घञ्) and (2)"aakritih - aa+kr+ktin (suffix)" (आ+कृ+क्तिन्) both represent form and shape respectively in common usage. The extra 'vi' (वि उपसर्गः) prefix gives the meaning of Special. Thus the word vyaakaranam itself means the entire science of the creation of the language. Which includes abiding by the natural phonetic capabilities of human vocal faculties and also reflecting the natural and eternal "sound-meaning" combination (शब्दार्थयोः निसर्गनित्यसम्बन्धत्वम्).

The entire Shikshaa shaastram is based on Human vocal anatomy and its primary purpose in laukika part of language - is to make pronunciation easy and natural (similar to Veda) in addition to shortening, softening, replacing, adding, etc. of syllables based on natural movement of tongue and natural functioning of vocal chord. This has also helped in making the entire language musical - which in-turn helped in easy communication and retention of huge volumes of treatises over 1000s of years, generations after generations based on the most natural and easy to remember phonological sounds.

The natural inter-wining of phonology and language - music and literature, - a true Wonder!. Hope we understand, hold it dear (in our tongues) and preserve it by passing to the next generation without any deterioration...

This shikshaa shaastra is primarily a Vedanga - which means a part of Veda... and also used in Yoga, Tantra and Shastras. The natural relationship between Language and Phonology proves that  Samskrit is a well constructed (not by human) language and is indeed the greatest gift to mankind, from who? - who else...! 
------------

Personally this has lead me to the conclusion that originally all 6 Vedangaas (Shikshaa, Chandas, Nirukta, Vyaakaranam, Jyotisha and Kalpa) must have been a single shaastra (may be called as Vyaakaranam - based on the Yogaartha of the word) and must have been an integral part of Veda in the earlier Era (Dwapara Yuga) where Veda was just one !

Basic details of Shikshaa you can fine here https://vedavichara.com/the-vedas/vedangas-the-limbs-of-vedas.html
and
http://en.wikipedia.org/wiki/Shiksha


To continue...

Why Sanskrit? in Computational Linguistics - Part 1

This is a concise introduction to "How Sanskrit is the most suitable language for Computing?" and now "In what way Sanskrit is suitable for Computational Linguistics?"

When I first heard a few years back that Sanskrit is the most ideally suited language for Computing - I was curious to know How ? - I couldn't get any straight forward answer.  Later I found out on my own, with a bit of research in the Web and discussions with Linguistic scholars.

Two linguists namely Dr. Leonard Bloomfield and Dr. Zellig Harris who were living in early 20th Century were responsible for coming out with the theories of Structural Linguistics - main reason for the development of Computer programing languages. Widely used in the first and second generation of Programming languages

These two linguists - Leonard Bloomfield and Zellig Harris, I found that both of them went Germany during late 19th century /early 20th century and studied intensely both Vedic Grammar (Pratisakyam) and Paninian system - for 7 years !. in their post Doctoral research /studies. They both studied in details the works of Dr. Otto von Böhtlingk - a German Indologist and Sanskrit Scholar - specializing in Vyakarana

"From Wikipedia - page http://en.wikipedia.org/wiki/Otto_von_B%C3%B6htlingkBöhtlingk was one of the most distinguished scholars of the nineteenth century, and his works are of pre-eminent value in the field of Indian and comparative philology. His first great work was an edition of the Sanskrit grammar of Panini, Aṣṭādhyāyī, with a German commentary, under the title Acht Bücher grammatischer Regeln (Bonn, 1839–1840)."

"From Wikipedia - page http://en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form
The idea of describing the structure of language with rewriting rules can be traced back to at least the work of Pāṇini (before the 4th century BC), who used it in his description of Sanskrit word structure. American linguists such as Leonard Bloomfield and Zellig Harris took this idea a step further by attempting to formalize language and its study in terms of formal definitions and procedures (around 1920–60)"

IAL (Intelligent Application Language) the first Computer Programming Language - from IAL born ALGOL-58 the first-generation popular programming language - John Backus a programmer in IBM labs developed the first notation  based on Sanskrit Grammar methods. Later when Peter Naur further developed the original ALGOL (58) into ALGOL-60 and created the Backus-Norm Form (BNF Notation) - it become a huge success and brought in major developments to the computer field.

From Wikipedia page - http://en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form
"Further development of ALGOL led to ALGOL 60; in its report (1963), Peter Naur named Backus's notation Backus Normal Form, and simplified it to minimize the character set used. However, Donald Knuth argued that BNF should rather be read as Backus–Naur Form, as it is "not a normal form in any sense" unlike, for instance, Chomsky Normal Form. The name Pāṇini Backus form has also been suggested in view of the facts that the expansion Backus Normal Form may not be accurate, and that Pāṇini had independently discovered a similar notation centuries earlier"

Later date programming languages and linguistics got further development when Naom Chomsky introduced Generative Grammar. (Naom Chomsky is the student of Dr. Zellig Harris - Linguist and Sanskrit Vyakarana scholar) - Sanskrit language's speciality itself is its Generative Grammar & Morphology.

Thus it is very clear that Maharishi Panini not only helped to protect the Sanskrit grammar by writing his linguistic canon "Ashtadyayi". He also helped create Computer Programming languages. Panini - the first Computer Scientist.

Part 2 - How the rules of Ashtadyayi helped the Programming languages or how many of Panini's ideas are used "as it is" in programming languages.

Panini - Sanskrit Linguist (Grammarian) could have lived 4000 years back

There were great Vaiyaakaranaas (not just grammarians but Linguists) before and after Sage Panini. Sage Panini himself refers about 16 Vaiyaakaranaas (linguists) in his book Ashtadyayi (some are also referred by Sage Yaska the etymologist who lived before Sage Panini). Sage Panini borrowed some of their rules to build Ashtadyayi - The greatest linguistic canon in existence.  There were sure other Vaiyaakaranaas whose works are lost and also Sage Panini hadn't referred /used in Ashtadyayi. Names of these linguists who were referred by Sage Panini (partial) are:

Apishaali, Audumbaraayana, Chakravarma, Gaargya, Galava, Kaasakritsna, Kasyapa, Paushkarasaadi, Shaakalya, Shaakataayana, Shaunaka, Sphotaayana, Vaarshayani, Vaarthaaksha, Vaajapyaayana, Vyaadi, and the Etymologist Yaska

Can we say that all those 16 Vaiyaakaranaas (linguists) who Sage Panini referred were neighbors of Sage Panini and were living in the same time? - It would be silly to say like that - but some western scholars and so called "Indian rationalists" say that or mean that in an indirect way.

First, western Indologists have fixed the time of Sage Panini to 2500 years back or around 500 BC. (The rationale behind fixing this timeframe is not properly established). This date fixing was done during 19th Century during British rule with very limited data and very little understanding of Sanskrit. Because Buddha conveyed his message in Paali the colloquial dialect of Eastern India spoken that time – Paali was chosen, so that the message not only reaches the educated elite (Sanskrit scholars) but also the uneducated masses - thus it is very evident that the widespread scholarly language used at that time was Sanskrit. If so, then it must be much older than Buddha and a scholarly language must have a tight grammar – thus the Grammar of Sanskrit must be much older. In my view Sage Patanjali and his linguistic cannon Mahabhashyam must have existed before Buddha’s /Mahavira’s time – this is evident from the fact that Jaina texts of Mahavira and Parswanatha discussions didn’t have any non-Paniniya usage (apaniniya prayoga) where as the Ramayana and Mahabharata and many puranas have many non-Paniniya usage.

Secondly some Indologists keep writing that Sage Panini invented Sanskrit language, etc. without any basis or research. Ashtadyayi, the linguistic canon written by Sage Panini was descriptive and not Prescriptive in those days. - only after the days of Buddha when scholars embraced Buddhism and started writing in Paali it has become Prescriptive - so it is unwise to say Sage Panini Structured the language etc. - the structure (grammar) was existing before - Sage Panini structured the Grammar Rules in an easy-to-read manner in a small book having 4000 formulas (3959 to be precise). In those days Ashtadyayi was much easier in comparison with other grammar texts or Pratishakyam (vedic grammar) texts. 

Thirdly some argue that Sanskrit wasn’t a spoken language Sage Patanjali’s Mahabhashyam explains how the usage of Sanskrit was in various regions.  He highlights the differences of same verb /noun usage with different meanings in different parts of Ancient India.

Those 16 Vaiyaakaranaas (linguists) who Sage Panini referred must have lived at least 100s of years before Sage Panini if not more. Because since we are reading the texts of Sage Panini now - after 2500 years (this timeframe is again as per western Indologists). So it could be possible that Sage Panini was reading the texts of earlier Vaiyaakaranaas (linguists) who lived 1000 years before Sage Panini. More over the works of earlier linguists were spread in many volumes and also they were having regional grammatical flavors and possibly some outdated usages of Sanskrit. Finally to provide an easy way of understanding the structure of the language, and instead of having to refer many works, Sage Panini wrote a treatise in which all the rules of the language were codified in a simple manner - thus born Ashtadyayi.

Most importantly those 16 Vaiyaakaranaas  (linguists) and their schools referred by Sage Panini were different from the "Nava-Vyakarana" (9 grammatical traditions) - referred in Valmiki Ramayana (Sri. Hanumaan is a Navavyakaranavettaa - a scholar of all the nine grammar schools). (The 9 grammar schools are Aindra, Kaumaara, Shaakta, Saaraswata, Chandra, Soorya, Braahma, etc.). Some of the Indian scholars themselves confuse between the 9 Vyakarana schools (which are Devataa or God’s schools) and the pre-Paninian 16 Vyakarana schools, which are the grammar traditions of various regions /various times of Ancient Bharata (India) and not that of Devataa – both these 2 groups are different.

After Sage Panini, Sage Katyayana in 300 BC (this timeframe is again as per western Indological theories) added 23,000 new words - in linguistics parlance these many words take over 100s of years to get added to the language - provided the language has in-built word generation capabilities - Morphological capabilities. Sage Katyayana also added few missing rules to Ashtadyayi as the language and its usage has transformed from the time of Sage Panini - this itself proves that there is a long gap between these 2 linguists.

Later in 200 BC (this timeframe is again as per western Indologists) Sage Patanjali in his explanation treatise of Ashtadyayi called Mahabhashyam added another 28,000 new words due to the usage patterns and transformation of the language - this proves that a]. Sanskrit was widely used, b]. there existed a long gap between the times of Sage Panini and Sage Patanjali. These facts are known to Sanskrit scholars of Vyakarana - it is a pity that still many choose to tread the lines of western indological theories either because of no point in fighting with people who do surface level research and fix timeframe for Sanskrit or out of indifference. Which ever way this is injustice to the language and to our forefathers. I'm not writing this so that we all can feel proud that the language is much older, than what it was thought of, but to do justice to this great language. No point in simply talking about Sanskrit without putting it to use. We have responsibility to learn Sanskrit deeply and unlock the secrets hidden in millions of Sanskrit scientific treatises - still many of then are in Palm-leaf /wooden Manuscript forms.

Great Vaiyaakaranaas (linguists) like Bartrhari, Battoji Dikshita, Narayana Battathiri, Kaunta Bhatta, Nagesa Bhatta are Post Panini/Katyayana /Patanjali – just to quote few names. Each one of these and many other great Linguists have contributed many things to the Sanskrit linguistic science. Eg:. Semantics, Psycholinguistics, Neuro-Linguistics, etc. were dealt in detail in 5th Century AD itself by Sage Bartrhari in his work Vakyapadiyam.

Since Vyakarana (grammar) is a Vedanga (part of Veda) like Veda and the Sanskrit language, Vyakarana is also Anaadi (time immemorial). So when we talk /quote about Sanskrit Language we need to keep all these in Mind. Some myopic views do exist that Sanskrit was born in 1500 BC and not before, etc.  We as learned should know how to brush aside the untruth.

Thus with all these we can assume that Sage Panini could have lived before 4000 years back, not later – After the period of rebuilding of the Vedic civilizations during the start of Kali yuga and after the deluge due to which the Dwaraka City /state submerged in the ocean – 5114 years back. These dates are debated in Indian Science Congress and some are proven (accepted by majority of scientists) based on planetary positions and astronomical calendar systems. – some info http://en.wikipedia.org/wiki/Kurukshetra_War and http://articles.timesofindia.indiatimes.com/2007-03-10/special-report/27883505_1_mahabharata-ramayana-epics ; on Dwaraka http://www.youtube.com/watch?v=zeDMSXOhDbY

- CGK