Linguistics, Psycholinguistics and Semantics

Language, in other words the storehouse of all human Knowledge is represented by words and meanings. Language by itself has an Ontological structure, Epistemological underpinnings and Grammar. Across languages, even though words /usages differ, the concept of meanings remain the same in respective communications. Yet the "Meanings" are understood by human beings based on Contextual, Relative, Tonal and Gestural basis. The dictionary meanings or 'as it is' meanings are taken rarely into consideration, thus human language is ambigious in one sense and flexible in other.

Computers on the other hand are hard-coded to go by the dictionary meanings. Thus teaching (programming) Computers to understand natural language (human language) has been the biggest challange haunting Scientists ever since the idea of Artificial Intelligence (AI) came into existance. In addition this has lead to the obvious question of "What is intelligence" from a Computation perspective. Defining intelligence precisely being impossible, this field of study has taken many shapes such as Computational Linguistics, Natural Language Processing and "
Machine Learning" etc. Artificial Intelligence instead of being used as a blanket term, is now being used increasingly as "Analytics" in many critical applications.

Sanskrit being the oldest is also the most Scientific and Structured language. Sanskrit has many hidden Algorithms built into it as part of its vast scientific treatises, for analysing "Meanings" or "Word sense" from many perspectives since time immemorial. "It is perhaps our job to discover and convert the scientific methods inherent in Sanskrit into usable Computational models and Tools for Natural Language Processing rather than reinventing the wheel" - as some Scientists put it. This blog's purpose is to expose some of the hidden intricate tools and methodolgies used in Sanskrit for centuries to derive precise meanings of human language, to a larger audiance particularly Computational Linguists for futher study, analysis and deployment in Natural Language Processing.

In addition, Sanskrit even though being flexible as a human language, is the least ambigious as the structure of the language is precisely difined from a semantical and syntactical point of view. From a Psycholinguistic perspective this blog could also give us a glimpse of the advanced linguistic capabilities of our forefathers as well their highly disciplined approach towards the structure and usage.

Thursday, April 18, 2013

"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)