शुक्रवार, 27 अप्रैल 2018

वृत्ति -- पाणिनीके संदर्भसे -- अल्गोरिथम के लिये

Kiran Varanasi varanasi_kiran@yahoo.com 

Dear list members

Sorry for reviving this old post. I found the discussion on the Sanskrit equivalent for "algorithm" very interesting.

Prof. Kannan and Prof.Ramasubramanian suggested "Śaraṇī" सरणि (arrangement) which probably has previously been used by the Sanskrit mathematicians. Some others also  suggested "Kuṭṭaka" कुट्टक (iterative refinement) which was used by Āryabhaṭa.

But these suggestions ignore the historical trajectory of development of ideas in Europe. When Europe discovered the "Sind Hind" of Al-Khwarizmi, which is nothing but a translation and commentary of Brahmagupta's works, it experienced a major transformation in how a rigorous mathematical procedure should be formulated. Instead of relying on "proof" by geometry as the ultimate arbiter, we have a series of precise instructions for "constructively" accomplishing a task. This is a computational method of thinking, instead of a geometric method of thinking. This important turn in scientific thinking is described in the works of Prof. Roddam Narasimha and Prof. C.K. Raju. In western academia, India has not been credited for this important scientific revolution. So why not call "Āryabhaṭam" instead of "Algorithm" ? We can refer to the far earlier original Indian procedures instead of the secondary ideas of the later scholar Al-Khwarizmi. As a computer scientist, I have seen no single textbook, museum or university discuss Āryabhaṭa. People can visit the computer history museum in Mountainview, CA to see how marginally these Indian ideas are presented. Unless Indian computer scientists demand it, this place in history will not be ceded to India.

However, the computational method in India is even earlier to Āryabhaṭa. We can definitely state that Pāṇini's methods for word derivation are precise algorithms. Not only that, Pāṇini's Ashṭādhyāyi anticipated many future developments in computer programming: Lambda calculus, encapsulation in object oriented programming, and even some ideas which may not yet have been implemented in computer programming ! In short, Pāṇini's methods have far more rigor and computational creativity than what reached Europe via Al-Khwarizmi. In India, Vyākaraṇa (grammar) was clearly the queen of the sciences. The scientific texts in every single disciplone were shaped by the computational methods of Pāṇini and other grammarians.

The word that Pāṇini used to describe a precise computational instruction is "Vṛtti" वृत्ति. I suggest this nice paper by Paul Kiparsky for understanding how these computational instructions are given.(https://web.stanford.edu/class/linguist289/encyclopaedia001.pdf ) The objective of Pāṇini's Ashṭādhyāyi is greater than giving a series of instructions (algorithm) for one specific task. It is to produce a complete "generative model" for all the variations in language. In other words, he gives a set of algorithms for all possible tasks. This is known as a generative grammar, and it is only until Noam Chomsky's work that this is understood to be a precise equivalent to a Turing Machine. So in India, we started our computational thinking with a full Turing Machine, and not a half-baked idea like an "algorithm". 

The operational rules of "vṛtti" are of the form: A -> B (C_D). A is transformed into B, when it is enclosed between C and D. One such rule can encode a full algorithm. This is because the variables A, C and D can all be recursively defined using rules of the exact same form. It is an automaton or a state-transducing machine. As such, in my opinion, the word "vṛtti" वृत्ति has the full descriptive power of an algorithm. It is a short word and can be used to derive longer Sanskrit words to describe algorithms of different types and for different domains. Sanskrit is a very fecund language and many new words can be created for algorithm (e.g, Kalana-vidhi is perfectly fine), but we often forget (a) brevity and (b) importance of projecting the historical trajectory of ideas.

The understanding of "vṛtti" as a procedure for transformation is deployed in many other contexts. Patanjali uses this famously to describe the transformations of mental states : "Yōgas chitta vṛtti nirōdhaḥ". By using the word "vṛtti" he ties this understanding of human cognition to the computational methods of Pāṇini. Symbolism in Itihāsas like the ten heads of Rāvaṇa (more accurately, "daśa Kanṭha" or ten necks) is discussed by later philosophers as "daśēndriya vṛtti" (the transformations of mind owing to being bound by the sense-objects of the ten senses: 5 Jñānēndriya+5 Karmēndriya). Thus, we have a history of Indian scientists in psychology referring to the computational method of "vṛtti". It is only recently that such computational thinking has penetrated the cognitive sciences in "modern science". In India, we had it from the very beginning, owing to the importance of Vyākaraṇa and its computational methods.

The word "vṛtti" inherently refers to the cyclical understanding of time (vṛtta = circle). A transformative rule to a cyclical motion is obained to setting up of secondary cycles e.g, through a gear mechanism. This is precisely how the mind is transformed by getting entangled in secondary motions owing to the sense objects. This understanding of Yōga is very ancient, even earlier to Pāṇini, going back to the Vēdas. Another word Pāṇini used is Pratyāhāra, as an equivalent for compacting of information, to refer to a larger group of variables on which the same computational transformation (vṛtti) can be applied. In Yōga, pratyāhāra refers to withdrawing the mind away from the sensory objects i.e, moving towards the "Bindu" which is at the centre of the circle (vṛtta). These are very precise notions for encoding human-computer interaction, on which aspects of a computational system the user has to pay attention to.

It will be unfortunate if we don't refer to this native tradition of computational thinking in India, when we coin new Sanskrit words for computer science.

- Kiran Varanasi

शनिवार, 7 अप्रैल 2018

Zend Avesta -- chhand upastha

There Never Was A Language Called Avestan

The average reader can be excused for wondering what on earth Avestan might be and why anyone should be interested. Avestan is a language that ancient Zoroastrians (Parsis) are said to have spoken. If this is enough information for the reader – the rest of this article may not interest you. But it should be of interest to the general question of ancient Indian history and the history of Indian languages.
To simplify the story let me relate what philologists (scholars of the history of languages) of the 19th and 20thcenturies said about Avestan. They theorized that there was some mother language in Russia (or Europe) that was carried by migrating (or invading) people towards India. On the way – some people broke off from this group and became Zoroastrians, going towards Iran, inventing and speaking “Avestan” and the rest went to India and started speaking Sanskrit and composed the Vedas. Because the “Avestan” speaking people, the Zoroastrians, were in Iran – it was called an “Iranian language”. According to this theory, Sanskrit of India and Avestan of Iran were “sister languages” – having both sprung from an imaginary mother language.
So how was the name “Avestan” given to this language? There are no ancient Zoroastrian texts that refer to their language as “Avestan” In fact no one knew of any original Zoroastrian language of any name, be it Avestan or any other name. But here is how the name was given. In the late 1700s a man called Anquetil du Perron came to India and lived for a few months with Parsi priests in Surat, who taught him what they knew of Zoroastrian chants (gathas) and rituals. Perron also collected some Zoroastrian texts and returned to Europe where he wrote a book in French called “Zend Avesta – Ouvrage du Zoroaster” meaning “Zend Avesta – the work of Zoroaster”. Perron’s work was initially dismissed but 60 years later it was validated and corrected by a man called Eugene Burnouf. To make the corrections Burnouf used a 13th century Sanskrit book by an Indian called Neryosangh Dhaval. That book was a Sanskrit translation of a Pahlavi language version of Zoroastrian holy texts. So whatever is written about the  3000 plus year old “Zend Avesta” is derived from verbal accounts of 17th century Parsi scholars, contemporary texts and a 13th century book that was written in Pahlavi language and translated to Sanskrit. A 3000 year gap between the original language and the translation does not inspire confidence about the linguistic theories regarding the identity of the original Zoroastrian language.
The meaning of “Zend Avesta” itself has been the subject of confusion – with scholars and linguists thinking that it means Zoroastrian holy text, or alternatively, commentary in the Zoroastrian language.  “Avestan” was simply named as a language that existed 3000 years in the past spoken by Zoroastrians in Iran.  However the minor issue of a 3000 year gap did not discourage linguists from making up their own language and a story to go with it.  And linguists proceeded to “reconstruct” the ancient language from fragments of texts that were written 3000 years later. And since the main source of reconstruction was from a 1300 AD Sanskrit text they ended up with a language that sounded somewhat like Sanskrit but had some differences such as the sound “sa” being replaced by the sound “ha” and some other changes. Linguists called this language Avestan; claimed that it was spoken 3000 years ago by Zoroastrians and made up a story of how a mother language came from somewhere and split into Avestan that went to Iran and Sanskrit that developed in India
Here the reader would be justified in asking that if Avestan did not exist as a language, and was simply cooked up by linguists by a process of guesswork which they called “reconstruction”, what language did Zoroastrians speak?  Is there an alternate story and is there any proof for an alternate story?  Yes there is.
First, what does “Zend Avesta” mean? Modern scholars now claim that the word “Avesta” represents the texts and that “Zend” are commentaries on the texts. It is notable that Zend is also pronounced as Zand. In fact in French, the language of Perron’s translation, Zend would be pronounced as Zand. The greatest 20th century scholar who has translated the Zend Avesta is Jatinder Mohan Chatterji who points out that in Sanskrit “zand” has a cognate word “chhand”.  Zand Avesta corresponds to chhand upastha which simply means Vedic hymns.  Chatterji quotes Panini as evidence of authenticity of this meaning. The great grammarian Panini knew of the existence of these Zoroastrian texts. The connection between the Zend Avesta and the Vedas are profound and seminal.
The links between the Vedas, particularly the Atharva Veda and the Zend Avesta are critical to the question of what language the early Zoroastrians may have spoken and whether it was a “sister language” of Sanskrit that developed independently while a group of Euroasians migrated separately to Iran and India as postulated by theories proposed by linguists.
Jatinder Mohan Chatterji notes that the Gopatha Brahmana (a commentary on the Atharva Veda) speaks of five Vedas. The Mahabharata too mentions five Vedas. But all standard references to the Vedas speak of only four Vedas. So what is the missing “fifth veda”? Chatterji points out that the last and most recent Veda, the Atharva Veda was known as the “Bhrigu-Angirasa Veda” where Bhrigu and Angirasa are the names of ancient rishis (priestly scholars) associated with that Veda. However the modern Atharva Veda is associated only with the rishi Angirasa. It transpires that the Zend Avesta is the fifth Veda – the Bhrigu Veda or Bhargava Atharva Veda. This explains the great commonality in the two texts, with chanting in a characteristic meter as well as oral transmission over centuries.
These are not radical new revisionist constructs, but facts that have been published in multiple works by a series of scholars in the west.  But they are fatal to the theories of language spread favoured by linguists and hence lie buried in large and unopened volumes. Fortunately, in the age of the Internet, these volumes can be accessed and searched.
In his book, “The Zend-Avesta” first published in 1880 James Darmetester says: ”the Vedas come from the same source as the Avesta”.  Darmetester further records that other scholars too had noticed this. He writes “Roth showed after Burnouf how the epical history of Iran was derived from the same source as the myths of Vedic India, and pointed out the primitive identity of Ahura Mazda, the supreme god of Iran, with Varuna, the supreme god of the Vedic age.”  What Darmetester is trying to say is that the Vedas and the Zend Avesta arose from the same source. The statement is interesting because European scholars have always considered the Zend Avesta as the history of Iran as opposed to the Vedas representing an Indian past.
Dr. Martin Haug, in his book on the Zoroastrian religion notes that the Zend Avesta has references to the Atharva Veda, showing that the Atharva Veda already existed at the time of composition of the Zend Avesta.
In her book, “A History of Zoroastrianism (Volume 1)”, Mary Boyce includes a chapter on the “pagan gods” that existed before Zoroaster. Boyce describes in great detail how every one of these gods is also mentioned in in the Vedas. In other words, all pre-Zoroastrian gods that are mentioned in Zoroastrian texts and absorbed into the Zoroastrian tradition are also mentioned in the Vedas. There can be no better evidence of the origin of the Zoroastrian pantheon from an earlier Vedic one. Boyce and other scholars choose to term the earlier common pantheon as “Indo-Iranian” gods that were known before Zoroastrian and Vedic gods. There is no factual basis for this terminology, although it is semantically accurate. A fact that is consistently ignored by linguists is that at the time of the Vedas and Zoroaster – there was no separate country called “Iran”. Western India formed a continuum from Punjab, to Balochistan, Afghanistan and Iran. Common geographical references exist within the Vedas and the Zend Avesta.
The same gods find earlier mention in the Indian Vedas and later mention in the supposedly Iranian Zoroastrianism. These so-called Indo-Iranian gods are unknown outside Zoroastrianism and the Vedas. The evidence that Boyce presents points to the Vedic gods having existed earlier and Zoroastrian gods were selected as a later development from the Vedic pantheon. The name “Indo-Iranian gods” might as well be replaced by the perfectly accurate name “Vedic deities”.
The facts clearly point to the following conclusions:
  1. The Vedas and the Zend Avesta have a common source
  2. The Vedas date from an era earlier than the Zend Avesta
  3. The last Veda (the Atharva Veda) and the Zend Avesta have a contemporaneous origin

Now we come back to the theory made up by linguists that the Vedas and the Zend Avesta represent separate religions that split off from a common source, with the Vedic people going toward India, and the Zoroastrians going towards Iran, and each developing a similar but distinct language.
Here is the problem. The three earlier Vedas, Rig, Yajur and Sama Veda were composed and existed before the Atharva Veda. All these works are in Sanskrit. There is evidence found by comparing the Atharva Veda with the Zend Avesta that the early Atharva Veda preceded the Zend Avesta. At some time in the remote past the Atharva Veda consisted of works of two “fire priests” – or Atharvans, named Bhrigu (Bhargava) and Angirasa. At that remote time the Atharva Veda was also known as the “Bhrigu-Angirasa samhita”. But the modern Atharva Veda as known to Hindus is associated only with Angirasa.  The Zend Avesta is associated with the rishi “Bhrigu” (or Bhargava).  The Atharva Veda and the Zend Avesta are both orally transmitted hymns chanted to a characteristic “meter” – a rhythmic pulse within the beat of the chant. The main part of the Zend Avesta are called “gathas” which is a word recognizable by almost any Indian as relating to music or chanting.
In detail, the Zend Avesta appears to consider all the gods mentioned in the Atharva Veda as evil, or as enemies. This appears to have been a philosophical split within an existing Vedic group.
The “sound changes” indicating differences in pronunciation between the Zoroastrian holy texts and the Vedas – such as Vedic “soma” being Zoroastrian “haoma” cannot irrefutably indicate a separate people and separate geography. In fact the main Atharvan priest of the Zend Avesta – Bhrigu has an ancient town bearing his name in the Indian state of Gujarat – namely Bharuch. The historic name of Bharuch was “Bhrigu-kaksha”. Even today – “Bharucha” is a well-known name among Parsis. That apart there are certain areas of modern day Gujarat where the people speak Gujarati with the exact same “sound changes” of “sa” to “ha” – which linguists claimed is a special change that occurred among Zoroastrians in Iran. Obviously that sound change is no Iranian specialty.
From these facts it is impossible to claim that the language of the Zend Avesta developed separately in Iran in parallel to a separate development of Sanskrit in India. The holy texts have a common origin, with the Vedas being earlier. It is most likely that the early Zoroastrians spoke Sanskrit or a dialect of Sanskrit rather than the “reconstructed” and patently artificial imagined language that linguists created and called “Avestan”. The Zoroastrian language probably split off from Sanskrit as the Zoroastrians migrated further towards Iran, and is more likely to be a daughter language of Sanskrit than a sister language. The idea of Avestan as a “sister language” of Sanskrit is needed only to support a particular theory of migration of languages that is favoured by linguists but is increasingly being shown to be false by archaeological and genetic evidence. But even without these modern developments it is clear that the linguistic story is contrived and untenable. There was never a language called Avestan.