Showing posts with label PANINI. Show all posts
Showing posts with label PANINI. Show all posts

Friday, April 24, 2015

Science of Om, frequency corresponds with earth


Ancient Sanskrit Diagram of Energy Centres or Chakras and Nadis
chakrasIf you want to find the secrets of the universe, think in terms of energy, frequency and vibration” – Nikola Tesla
Many illiterate people think Om is religios and sign of Hindu religion. On the contrary, it is the most universal syllable that neither refers to any particular religion nor God. In fact it is  cosmic sound which initiated the creation of universe (big bang theory). But that alone would not have been sufficient to turn it into a regular practice in Indian culture.
To know that you have to know scientific and practical explanation (based on the physics of sound, vibrations & resonance)-

Each syllable resonates with certain organ or part of the body.

For example, by chanting “aaaaaaa”, one can feel the sensation and hence resonance of nervous system in the stomach and chest region. Chanting “ooooo” creates sensations in throat & chest region and resonates with them. Similarly, chanting/humming “mmmm” resonates with the nasal cavity as well as skull/brain region. Earth produces a sound of 7.83 hctz, not audible by human ears, called earth hum and that corresponds to om's frequency. Time frequency analysis was published in a journal

The Hermetic philosophy of macrocosm and microcosm (as above-so below) is said to hold the key to all mysteries. The Cosmos is mirrored in man the small universe. The easiest way to visualize this is to compare the atom, that smallest of building bricks, with our universe, the electron orbits the nucleus in the same way as the planets orbit our sun.
OM or Schumann frequency.

Ohm- 7.83 Hz
Gam - 14 Hz
Hleem - 20 Hz
Hreem - 26 Hz
Kleem - 33 Hz
Krowm - 39 Hz
Sreem - 45 Hz

An atom and the Solar System


108 number and its significance .Om produces sri yantra




Here is a short clip in which a Doctor explains the same:
 

What happens when we concatenate (join together) the above syllables into one mantra? We get the AUM mantra which when chanted sequentially activates the stomach, spinal cord, throat, nasal and brain regions. The energy moves from the abdomen all the way up to the brain, thereby channelizing energy and activating the spinal cord & brain.
Following is an excerpt from a research paper which shows the waveform of A-U-M mantra made up of 3 syllables. Following research and linked abstract and full article are self evident-
AUM_waveforms
Research paper:http://nopr.niscair.res.in/bitstream/123456789/9347/1/IJTK%203(2)%20154-161.pdf
time_frequency_analysis
Research paper:
http://paper.ijcsns.org/07_book/200808/20080825.pdf
spectrogram_analysis
Research paper:
http://paper.ijcsns.org/07_book/200901/20090151.pdf
resonance_imaging_png


The Sri-Yantra-Mandala is the image of the OM mantra, the primordial Hindu sound of creation. When OM is intoned into a tonoscope, it first produces a circle. As the tone is completed, the circle is filled sequentially with concentric squares, triangles and finally, as the "mmm" dies away, the Sri Yantra [i].

[i] How do Yantras work? ?At the basis of yantra operation is something called "shape energy" or "form energy". The idea is that every shape emits a very specific frequency and energy pattern. Examples of old believes in shape energy are the yantras and mandalas of eastern philosophies, the star of David, the five pointed star (pentagon), the Christian cross, the pyramids and so on. Certain 'powers' are ascribed to the various shapes.
When one focuses on a yantra, his mind is atomatically "tuned in" by resonance into the specific form energy of that yantra. The process of resonance is then maintained and amplified. The yantra acts only as a "tune in" mechanism or a doorway. The subtle energy does not come from the yantra itself, but from the macrocosm.
Basically yantras are secret keys for establishing resonance with the benefic energies of the macrocosm. Very often the yantras can put us in contact with extremely elevated energies and entities, being of invaluable help on the spiritual path. Available at

Om sounded in a tonoscope [© Madhu Khanna] - top row
3D Sri Yantra (middle row)
Sri yantra mandala (bottom row)
It is stunning how similar cymatic sound pattern is to the yantra, the Star of David at the centre is surrounded by lotus petals, spookily similar to the geometry of the yantra.

Chakra Centres 

Cymatic Light Picture                             Traditional Yantra
With kind permission from Photo/copyright:
Alexander Lauterwasser, homepage: www.wasserklangbilder.de
In Sanskrit, 'YANTRA' means machine or absorber of cosmic energy, Yantra resonate with our solar system, a tuning fork connecting to universal consciousness. Vedic scholars understood the symbiotic relationship of wave energy; that sound vibrations ARE geometry [i]. The entrainment phenomenon, where weak pulsations are engulfed by stronger ones, would create the frequency of OM within the mantra-chanting devotee. The Hindus knew the transubstantiating [1] ability of sound [ii] and geometry.
The efficacy of mantra and drugs for the attainment of perfection has been mentioned by Patanjali in his Yogasutra (iv. I). Antiquity of Tantricism By Chintaharan Chakravarti, in The Indian Historical Quarterly Vol. VI, No.1 March, 1930 pp. 114-126. Available at http://ccbs.ntu.edu.tw/FULLTEXT/JR-ENG/chak.htm  Iyengar, B.K.S. (2002) Light on the Yoga Sutras of Patanjali Thorsons; New Ed edition (21 Oct 2002) 288 pages.
---
 [ii] The identity of the ancient plant known as Soma is one of the greatest unsolved mysteries in the field of religious history. Common in the religious lore of both ancient India and Persia, the sacred Soma plant was considered a God, the ancient worshipper who imbibed it gained the powerful attributes of this God. The origins of Soma go back to the common Aryan ancestors of both the Vedic Hindu religion of India and the Persian religion of Mazdaism. This common ancestry can be seen in surviving religious texts such as the Hindu Rig Veda and the Persian Avesta. A major connection is their use of a sacred plant, known in India as Soma, and in Persia as Haoma. From ancient descriptions, Soma/Haoma must have been a very special plant. The qualities of this sacred herb are given in poetic detail, and the love and admiration these ancient authors had for the plant can still be felt thousands of years after the texts were composed. Available at http://www.cannabisculture.com/articles/3155.html    


According to Vedas, sound called "NAD" is starting point of existence of what modern scientist call Big-Bing theory. Sanskrit with 54 alphabets is a divine language unlike other languages of the world. 

The human ear can hear only 20 Hz to 20000 Hz. The rest is inaudible. This is why NO cosmic sound can be heard by the human ear. 

These cosmic sounds were heard by 12 strand DNA maharishis in their spiritual trances which broadened their sense spectrums.  However our brain can register the vibrations.


When Shiva started beating Damaru ,Sri Yantra and thus Om came in to existence.

Dmitri Ivanovich Mendeleev , the great Russian chemist and inventor formulated the Periodic Law, and the periodic table of elements. 
He was denied a Nobel prize for telling that his table is based on the divine Sanskrit alphabets. Mendeleev, studied Sanskrit at a university in St Petersburg, used Sanskrit prefixes eka, dvi, and tri to name those yet-to-be-discovered elements. 

Mendeleev had expressed his appreciation and debt to the great Sanskrit grammarian Panini of ancient India, who had created sophisticated theories of language based on their discovery of the two-dimensional patterns in basic sounds.
When Panin was in meditation, Lord Shiva appeared before him and played his damaru in a specific manner 14 times.
Panini understood all that Shiva wanted to tell him and  captured the sounds and translated them into syllables. From these sounds emerged the 14 syllables which provided Panini with the basis for formulating the rules of Sanskrit grammar. 
These 14 verses are known as "Maheshwara Sutras" or "Maheshwara Sutrani" (in Sanskrit)
These verses are just a collection of sounds and if you say them aloud, in one breath, they really sound like drum beats. 

14 Maheshvara sutras

nR^ttAvasAne naTarAjarAjaH nanAda DakkAm navapanchavAram 
uddhartu kAmassanakAdi siddhAn etadvimarSe SivasUtrajAlam

At the end of the cosmic dance Lord Shiva the Lord of dance, sounded his damaru fourteen times.
For the sake of the upliftment of sages like sanaka. 

According to legend, these sutras were written by Panini upon mystically hearing the beats of Siva-Nataraja’s damaru (hourglass-shaped drum).  It has been said that the mantra is God in the form of sound.  Therefore, words are an extension of that power. The tantra stresses the importance of sound as a divine substance and vehicle for salvation.  And hence, entire cosmos is in the form of
 these sutras.The 14 sutras are (in ITRANS format):

aiuN
R^iL^ik
eo~N
aiauch
hayavaraT
laN
~nama~NaNanam
jhabha~n
ghaDhadhaSh
jabagaDadash
khaphaChaThathachaTatav
kapay
shaShasar
hal

Among those present at Nataraja’s dance was Panini. For him these 14 sounds meant the fourteen cardinal sutras of Grammer and on them he based his “Ashtadhyayi”. Given are the 16 vowels and 33 consonants that are evolved from these 14 Shiva Sutras.

16 vowels (a – ch)

a, Aa, i, Ii, u, Uu, ri, rii, lri, lrii, e, ai, o au, am, ah

33 consonants (ha l)

ka, kha, ga, gha, gna
ca, cha, ja, jha, jna
ta, ttha, da ddha, nna
ta, tha, da, dha, na
pa, pha, ba, bha, ma
ya, ra, la, va
sa, sha, sa
ha



om_genes
News report:
http://commonhealth.wbur.org/2013/05/genes-altered-after-relaxation-practice

 Some more youtube video are linked here-

 







Pythagoras, whose life in the seventh century BC marks the inception of Hermetic philosophy and numerological mysticism among the Greeks. He travelled the world while still in his thirties and forties, studying with every priesthood and esoteric college he could reach and procuring the texts of those he couldn't physically visit. When he finally settled down to start his own school, he credited the Hebrew Kabbalists and Hindu Brahmans for enlightening him about their number mysteries in which his own teachings about the whole numbers and Sacred Geometry were grounded.
Available at
http://www.tarot.com/about-tarot/library/essays/history


If you visualise quantum reality as a cloud of undulating glitter, each particle is a holographic film transparency, which contains all of the information needed to visualise the material world from that particular angle. This vision in combination with an understanding of how our senses [i] synthesise reality by only processing 20 conscious moments [ii] per second out of a possible 20,000, you can begin to understand how reality may not be how it so virulently appears. Hindu [iii] and Buddhist [iv] texts sit easily in the baffling arena of quantum thought. The illusiveness of material reality is the focus of the Upanishads[v]c.3, 000BCE.
[i] Not all the body parts receive the same attention of the brain. The relative importance is often represented by mapping over the length of the sensory or motor cortex. These cortical maps (Figure 22b) are not drawn to scale; instead they are variously distorted to reflect the amount the neural processing power devoted to different regions. This accounts for the grotesque appearance of the human body in the homunculus, which is a translation of the body's sensory map into the human form.
---
 [ii]That reality is an illusion constructed by our limited and inaccurate senses is a theme beautifully considered by Marshall McLuhan in the Gutenberg Conspiracy. Penny Lee explains in a passage entitled 'The biological segmentation of reality', Penny Lee in "The Whorf Theory Complex" quotes Bertalanffy: 'from that great cake of reality, every living organism cuts a slice, which it can perceive and to which it can react owing to its psycho-physical organization, that is, the structure of its receptor and effector organs', and further: 'any organism so to speak, cuts out from the multiplicity of surrounding objects [and actions!] a small number of characteristics to which it reacts and whose ensemble forms its "ambient". All the rest is non-existent for that particular organism. Every animal is surrounded, as by a soap bubble, by its specific ambient, replenished by those characteristics, which are amenable to it. If, reconstructing an animal's ambient, we enter the soap bubble, the world is profoundly changed. Many characteristics disappear, others arise and a completely new world is found.' [iii] Einstein Meets the Vedas: Parallel Sayings in Science and Spirituality Comparing wisdom from scientists and great religious leaders. Edited by Thomas McFarlane
Top of Form
A mathematical truth is timeless, it does not come into being when we discover it. Yet its discovery is a very real event.
Erwin Schrödinger
Realization is nothing to be gained afresh; it is already there. All that is necessary is to get rid of the thought `I have not realized'. 
Sri Ramana Maharshi
If we ask, for instance, whether the position of the electron remains the same, we must say "no"; if we ask whether the position of the electron changes with time, we must say "no"; if we ask whether the electron is at rest, we must say "no"; if we ask whether it is in motion, we must say "no." 
J. Robert Oppenheimer
He is far and he is near, He moves and he moves not. 
The Bhagavad Gita

It is a primitive form of thought that
things either exist or do not exist. 
Sir Arthur Eddington
To say "it is" is to grasp for permanence. To say "it is not" is to adopt the view of nihilism. Therefore a wise person does not say "exists" or "does not exist." 
Siddha Nagarjuna
The smallest units of matter are in fact not physical objects in the ordinary sense of the word; they are forms.  
Werner Heisenberg
All things-from Brahma the creator down to a single blade of grass-are the apparently diverse names and forms of the one Atman.  
Shankara
There is no essential distinction between mass and energy. Energy has mass and mass represents energy. Instead of two conservation laws we have only one, that of mass-energy. 
Albert Einstein
...Only an arbitrary distinction in thought divides form of substance from form of energy. Matter expresses itself eventually as a formulation of some unknown Force. 
Sri Aurobindo
People like us, who believe in physics, know that the distinction between past, present and future is only a stubborn, persistent illusion.
 Albert Einstein
The past, the future...are nothing but names, forms of thought, words of common usage, merely superficial realities. 
T. R. V. Murti  
The common words "space" and "time" refer to a structure of space and time that is actually an idealization and oversimplification. 
Werner Heisenberg
There is nothing like an absolute time which remains as a reality apart from successive events. Time and space are derived notions, modes of reference. 
K. Venkata Ramanan
What we perceive through the senses as empty space...is the ground for the existence of everything, including ourselves. The things that appear to our senses are derivative forms and their true meaning can be seen only when we consider the plenum, in which they are generated and sustained, and into which they must ultimately vanish.  
David Bohm
Wherefrom do all these worlds come? They come from space. All beings arise from space, and into space they return: space is indeed their beginning, and space is their final end. 
The Upanishads
Causality may be considered as a mode of perception by which we reduce our sense impressions to order. Niels Bohr
Time, space, and causation are like the glass through which the Absolute is seen.... In the Absolute there is neither time, space, nor causation.
 Vivekananda
A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. 
Albert Einstein
As in science, so in metaphysical thought, that general and ultimate solution is likely to be the best which includes and accounts for all so that each truth of experience takes its place in the whole. 
Sri Aurobindo


Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world.
-Einstein
All such notions as causation, succession, atoms, primary elements...are all figments of the imagination and manifestations of the mind. 
-Buddha
Time and again the passion for understanding has led to the illusion that man is able to comprehend the objective world rationally by pure thought without any empirical foundations—in short, by metaphysics. 
-Einstein
By becoming attached to names and forms, not realising that they have no more basis than the activities of the mind itself, error rises…and the way to emancipation is blocked.
-Buddha
In our thinking...we attribute to this concept of the bodily object a significance, which is to high degree independent of the sense impression which originally gives rise to it. This is what we mean when we attribute to the bodily object "a real existence." ...By means of such concepts and mental relations between them, we are able to orient ourselves in the labyrinth of sense impressions. These notions and relations...appear to us as stronger and more unalterable than the individual sense experience itself, the character of which as anything other than the result of an illusion or hallucination is never completely guaranteed.  
-Einstein
I teach that the multitudinousness of objects have no reality in themselves but are only seen of the mind and, therefore, are of the nature of maya and a dream. ...It is true that in one sense they are seen and discriminated by the senses as individualized objects; but in another sense, because of the absence of any characteristic marks of self-nature, they are not seen but are only imagined. In one sense they are graspable, but in another sense, they are not graspable.  
-Buddha
According to general relativity, the concept of space detached from any physical content does not exist. 
 –Einstein
If there is only empty space, with no suns nor planets in it, then space loses its substantiality. 
 -Buddha
Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world.  

-Einstein
All such notions as causation, succession, atoms, primary elements...are all figments of the imagination and manifestations of the mind. 
 -Buddha
 [v] Einstein Meets the Vedas: Parallel Sayings in Science and Spirituality Comparing wisdom from scientists and great religious leaders. Edited by Thomas McFarlane
 Available at http://www.integralscience.org/einsteinbuddha/ 

A mathematical truth is timeless, it does not come into being when we discover it. Yet its discovery is a very real event. 
Erwin Schrödinger
Realization is nothing to be gained afresh; it is already there. All that is necessary is to get rid of the thought `I have not realized'. 
Sri Ramana Maharshi
Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world.  
Einstein
All such notions as causation, succession, atoms, primary elements...are all figments of the imagination and manifestations of the mind.   
 Buddha






News Report:http://www.dailymail.co.uk/health/article-1258234/Chants-fine-thing-It-sound-daft-doctors-believe-meditation-really-lower-blood-pressure.html
Modified from guruprasad.net

Sunday, March 29, 2015

Pingala, Inventor of Binary Numbers in 2nd Century BCE


Pingala MathematicianPingala (Devanagari: पिङ्गल) is the author of Chandaḥśāstra (Chandaḥsūtra), the earliest known Sanskrit treatise on prosody.
Very less historical knowledge is available about Pingala, though his works are retained till date.
He is identified either as the younger brother of Pāṇini (4th century BCE), or of Patañjali, the author of the Mahabhashya (2nd century BCE).
His work, Chandaḥśāstra means science of meters, is a treatise on music and can be dated back to 2nd century BCE.
Main commentaries on ‘Chandaḥśāstra‘ are ‘Vrittaratnakara‘ by Kedara in 8th century AD, ‘Tatparyatika‘ by Trivikrama in 12th century AD and ‘Mritasanjivani‘ by Halayudha in 13th century AD. The complete significance of Pingala’s work can be understood by the explanations found in these three commentaries.
Pingala (in Chandaḥśāstra 8.23) has assigned the following combinations of zero and one to represent various numbers, much in the same way as the present day computer programming procedures.
0 0 0 0 numerical value = 1
1 0 0 0 numerical value = 2
0 1 0 0 numerical value = 3
1 1 0 0 numerical value = 4
0 0 1 0 numerical value = 5
1 0 1 0 numerical value = 6
0 1 1 0 numerical value = 7
1 1 1 0 numerical value = 8
0 0 0 1 numerical value = 9
1 0 0 1 numerical value = 10
0 1 0 1 numerical value = 11
1 1 0 1 numerical value = 12
0 0 1 1 numerical value = 13
1 0 1 1 numerical value = 14
0 1 1 1 numerical value = 15
1 1 1 1 numerical value = 16
Other numbers have also been assigned zero and one combinations likewise.
Pingala’s system of binary numbers starts with number one (and not zero). The numerical value is obtained by adding one to the sum of place values. In this system, the place value increases to the right, as against the modern notation in which it increases towards the left.
The procedure of Pingala system is as follows:
  • Divide the number by 2. If divisible write 1, otherwise write 0.
  • If first division yields 1 as remainder, add 1 and divide again by 2. If fully divisible, write 1, otherwise write 0 to the right of first 1.
  • If first division yields 0 as remainder that is, it is fully divisible, add 1 to the remaining number and divide by 2. If divisible, write 1, otherwise write 0 to the right of first 0.
  • This procedure is continued until 0 as final remainder is obtained.
Example to understand Pingala System of Binary Numbers :
Find Binary equivalent of 122 in Pingala System :
        Divide 122 by 2. Divisible, so write 1 and remainder is 61.
1
          Divide 61 by 2. Not Divisible and remainder is 30. So write 0 right to 1.
    10
            Add 1 to 61 and divide by 2 = 31.
            Divide 31 by 2. Not Divisible and remainder is 16. So write 0 to the right.
      100
              Divide 16 by 2. Divisible and remainder is 8. So write 1 to right.
        1001
                Divide 8 by 2. Divisible and remainder is 4. So write 1 to right.
          10011
                  Divide 4 by 2. Divisible and remainder is 2. So write 1 to right.
            100111
                    Divide 2 by 2. Divisible. So place 1 to right.
              1001111
              Now we have 122 equivalent to 1001111.
              Verify this by place value system : 1×1 + 0x2 + 0x4 + 1×8 + 1×16 + 1×32 + 1×64 = 64+32+16+8+1 = 121
              By adding 1(which we added while dividing 61) to 121 = 122, which is our desired number.
              In Pingala system, 122 can be written as 1001111.
              Though this system is not exact equivalent of today’s binary system used, it is very much similar with its place value system having 20, 20, 21, 22, 22, 23, 24, 25, 26 etc used to multiple binary numbers sequence and obtain equivalent decimal number.
              Reference : Chandaḥśāstra (8.24-25) describes above method of obtaining binary equivalent of any decimal number in detail.
              These were used 1600 years before westeners invented binary system.
              We now use zero and one (0 and 1) in representing binary numbers, but it is not known if the concept of zero was known to Pingala— as a number without value and as a positional location.
              Pingala’s work also contains the Fibonacci number, called mātrāmeru, and now known as the Gopala–Hemachandra number. Pingala also knew the special case of the binomial theorem for the index 2, i.e. for (a + b) 2, as did his Greek contemporary Euclid.
              Halayudha (10th century AD) who wrote a commentary on Pingala’s work understood and used zero in the modern sense but by then it was commonplace in India and had also begun to make its way to West Asia as well to countries like Indonesia, Cambodia and others in East and Southeast Asia. It took several centuries more before being accepted in Europe. It was Leonardo of Pisa, better known as Fibonacci who seems to have introduced it in Europe in the 13th century. (He learnt it from the Arabs but noted that it came from India. His successors were not so careful, and for centuries they were known as Arabic numerals.)
              Halayudha was himself a mathematician no mean order. His discussion of combinatorics of poetic meters led him to a general version of the binomial theorem centuries before Newton. (This was the integer version only and not the full general version with arbitrary index given by Newton.) This too traveled east and west with the Persian mathematician and poet using the results in the 13th century.
              Halāyudha’s commentary includes a presentation of the Pascal’s triangle for binomial coefficients (called meruprastāra).
              Chandaḥśāstra presents the first known description of a binary numeral system in connection with the systematic enumeration of meters with fixed patterns of short and long syllables (Short = 0, Long = 1).
              Use of zero is sometimes mistakenly ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, while Pingala used short and long syllables.
              As Pingala’s system ranks binary patterns starting at one (four short syllables—binary “0000”—is the first pattern), the nth pattern corresponds to the binary representation of n-1, written backwards. Positional use of zero dates from later centuries and would have been known to Halāyudha but not to Pingala.
              CITATION-BOOKSFACT.COM

              Friday, May 23, 2014

              PANINI

              Panini


              Born: about 520 BC in Shalatula (near Attock), now PakistanDied: about 460 BC in India

              Show birthplace location
                   
               

               



              Panini was born in Shalatula, a town near to Attock on the Indus river in present day Pakistan. The dates given for Panini are pure guesses. Experts give dates in the 4th, 5th, 6th and 7th century BC and there is also no agreement among historians about the extent of the work which he undertook. What is in little doubt is that, given the period in which he worked, he is one of the most innovative people in the whole development of knowledge. We will say a little more below about how historians have gone about trying to pinpoint the date when Panini lived.
              Panini was a Sanskrit grammarian who gave a comprehensive and scientific theory of phonetics, phonology, and morphology. Sanskrit was the classical literary language of the Indian Hindus and Panini is considered the founder of the language and literature. It is interesting to note that the word "Sanskrit" means "complete" or "perfect" and it was thought of as the divine language, or language of the gods.
              A treatise called Astadhyayi (or Astaka ) is Panini's major work. It consists of eight chapters, each subdivided into quarter chapters. In this work Panini distinguishes between the language of sacred texts and the usual language of communication. Panini gives formal production rules and definitions to describe Sanskrit grammar. Starting with about 1700 basic elements like nouns, verbs, vowels, consonants he put them into classes. The construction of sentences, compound nouns etc. is explained as ordered rules operating on underlying structures in a manner similar to modern theory. In many ways Panini's constructions are similar to the way that a mathematical function is defined today. Joseph writes in [2]:-
              [Sanskrit's] potential for scientific use was greatly enhanced as a result of the thorough systemisation of its grammar by Panini. ... On the basis of just under 4000 sutras [rules expressed as aphorisms], he built virtually the whole structure of the Sanskrit language, whose general 'shape' hardly changed for the next two thousand years. ... An indirect consequence of Panini's efforts to increase the linguistic facility of Sanskrit soon became apparent in the character of scientific and mathematical literature. This may be brought out by comparing the grammar of Sanskrit with the geometry of Euclid - a particularly apposite comparison since, whereas mathematics grew out of philosophy in ancient Greece, it was ... partly an outcome of linguistic developments in India.

              Joseph goes on to make a convincing argument for the algebraic nature of Indian mathematics arising as a consequence of the structure of the Sanskrit language. In particular he suggests that algebraic reasoning, the Indian way of representing numbers by words, and ultimately the development of modern number systems in India, are linked through the structure of language.
              Panini should be thought of as the forerunner of the modern formal language theory used to specify computer languages. The Backus Normal Form was discovered independently by John Backus in 1959, but Panini's notation is equivalent in its power to that of Backus and has many similar properties. It is remarkable to think that concepts which are fundamental to today's theoretical computer science should have their origin with an Indian genius around 2500 years ago.
              At the beginning of this article we mentioned that certain concepts had been attributed to Panini by certain historians which others dispute. One such theory was put forward by B Indraji in 1876. He claimed that the Brahmi numerals developed out of using letters or syllables as numerals. Then he put the finishing touches to the theory by suggesting that Panini in the eighth century BC (earlier than most historians place Panini) was the first to come up with the idea of using letters of the alphabet to represent numbers.
              There are a number of pieces of evidence to support Indraji's theory that the Brahmi numerals developed from letters or syllables. However it is not totally convincing since, to quote one example, the symbols for 1, 2 and 3 clearly do not come from letters but from one, two and three lines respectively. Even if one accepts the link between the numerals and the letters, making Panini the originator of this idea would seem to have no more behind it than knowing that Panini was one of the most innovative geniuses that world has known so it is not unreasonable to believe that he might have made this step too.
              There are other works which are closely associated with the Astadhyayi which some historians attribute to Panini, others attribute to authors before Panini, others attribute to authors after Panini. This is an area where there are many theories but few, if any, hard facts.
              We also promised to return to a discussion of Panini's dates. There has been no lack of work on this topic so the fact that there are theories which span several hundreds of years is not the result of lack of effort, rather an indication of the difficulty of the topic. The usual way to date such texts would be to examine which authors are referred to and which authors refer to the work. One can use this technique and see who Panini mentions.
              There are ten scholars mentioned by Panini and we must assume from the context that these ten have all contributed to the study of Sanskrit grammar. This in itself, of course, indicates that Panini was not a solitary genius but, like Newton, had "stood on the shoulders of giants". Panini must have lived later than these ten but this is absolutely no help in providing dates since we have absolutely no knowledge of when any of these ten lived.
              What other internal evidence is there to use? Well of course Panini uses many phrases to illustrate his grammar any these have been examined meticulously to see if anything is contained there to indicate a date. To give an example of what we mean: if we were to pick up a text which contained as an example "I take the train to work every day" we would know that it had to have been written after railways became common. Let us illustrate with two actual examples from the Astadhyayi which have been the subject of much study. The first is an attempt to see whether there is evidence of Greek influence. Would it be possible to find evidence which would mean that the text had to have been written after the conquests of Alexander the Great? There is a little evidence of Greek influence, but there was Greek influence on this north east part of the Indian subcontinent before the time of Alexander. Nothing conclusive has been identified.
              Another angle is to examine a reference Panini makes to nuns. Some argue that these must be Buddhist nuns and therefore the work must have been written after Buddha. A nice argument but there is a counter argument which says that there were Jaina nuns before the time of Buddha and Panini's reference could equally well be to them. Again the evidence is inconclusive.
              There are references by others to Panini. However it would appear that the Panini to whom most refer is a poet and although some argue that these are the same person, most historians agree that the linguist and the poet are two different people. Again this is inconclusive evidence.
              Let us end with an evaluation of Panini's contribution by Cardona in [1]:-
              Panini's grammar has been evaluated from various points of view. After all these different evaluations, I think that the grammar merits asserting ... that it is one of the greatest monuments of human intelligence.

              Tuesday, January 28, 2014

              PANINI- GREAT INDIANS/BHARTIYA


              Panini was born in Shalatula, a town near to Attock on the Indus river in present day Pakistan. The dates given for Panini are pure guesses. Experts give dates in the 4th, 5th, 6th and 7th century BC and there is... also no agreement among historians about the extent of the work which he undertook. What is in little doubt is that, given the period in which he worked, he is one of the most innovative people in the whole development of knowledge. We will say a little more below about how historians have gone about trying to pinpoint the date when Panini lived.

              Panini was a Sanskrit grammarian who gave a comprehensive and scientific theory of phonetics, phonology, and morphology. Sanskrit was the classical literary language of the Indian Hindus and Panini is considered the founder of the language and literature. It is interesting to note that the word "Sanskrit" means "complete" or "perfect" and it was thought of as the divine language, or language of the gods.

              A treatise called Astadhyayi (or Astaka ) is Panini's major work. It consists of eight chapters, each subdivided into quarter chapters. In this work Panini distinguishes between the language of sacred texts and the usual language of communication. Panini gives formal production rules and definitions to describe Sanskrit grammar. Starting with about 1700 basic elements like nouns, verbs, vowels, consonants he put them into classes. The construction of sentences, compound nouns etc. is explained as ordered rules operating on underlying structures in a manner similar to modern theory. In many ways Panini's constructions are similar to the way that a mathematical function is defined today. Joseph writes in [2]:-

              [Sanskrit's] potential for scientific use was greatly enhanced as a result of the thorough systemisation of its grammar by Panini. ... On the basis of just under 4000 sutras [rules expressed as aphorisms], he built virtually the whole structure of the Sanskrit language, whose general 'shape' hardly changed for the next two thousand years. ... An indirect consequence of Panini's efforts to increase the linguistic facility of Sanskrit soon became apparent in the character of scientific and mathematical literature. This may be brought out by comparing the grammar of Sanskrit with the geometry of Euclid - a particularly apposite comparison since, whereas mathematics grew out of philosophy in ancient Greece, it was ... partly an outcome of linguistic developments in India.

              Joseph goes on to make a convincing argument for the algebraic nature of Indian mathematics arising as a consequence of the structure of the Sanskrit language. In particular he suggests that algebraic reasoning, the Indian way of representing numbers by words, and ultimately the development of modern number systems in India, are linked through the structure of language.

              Panini should be thought of as the forerunner of the modern formal language theory used to specify computer languages. The Backus Normal Form was discovered independently by John Backus in 1959, but Panini's notation is equivalent in its power to that of Backus and has many similar properties. It is remarkable to think that concepts which are fundamental to today's theoretical computer science should have their origin with an Indian genius around 2500 years ago.

              At the beginning of this article we mentioned that certain concepts had been attributed to Panini by certain historians which others dispute. One such theory was put forward by B Indraji in 1876. He claimed that the Brahmi numerals developed out of using letters or syllables as numerals. Then he put the finishing touches to the theory by suggesting that Panini in the eighth century BC (earlier than most historians place Panini) was the first to come up with the idea of using letters of the alphabet to represent numbers.

              There are a number of pieces of evidence to support Indraji's theory that the Brahmi numerals developed from letters or syllables. However it is not totally convincing since, to quote one example, the symbols for 1, 2 and 3 clearly do not come from letters but from one, two and three lines respectively. Even if one accepts the link between the numerals and the letters, making Panini the originator of this idea would seem to have no more behind it than knowing that Panini was one of the most innovative geniuses that world has known so it is not unreasonable to believe that he might have made this step too.

              There are other works which are closely associated with the Astadhyayi which some historians attribute to Panini, others attribute to authors before Panini, others attribute to authors after Panini. This is an area where there are many theories but few, if any, hard facts.

              We also promised to return to a discussion of Panini's dates. There has been no lack of work on this topic so the fact that there are theories which span several hundreds of years is not the result of lack of effort, rather an indication of the difficulty of the topic. The usual way to date such texts would be to examine which authors are referred to and which authors refer to the work. One can use this technique and see who Panini mentions.

              There are ten scholars mentioned by Panini and we must assume from the context that these ten have all contributed to the study of Sanskrit grammar. This in itself, of course, indicates that Panini was not a solitary genius but, like Newton, had "stood on the shoulders of giants". Panini must have lived later than these ten but this is absolutely no help in providing dates since we have absolutely no knowledge of when any of these ten lived.

              What other internal evidence is there to use? Well of course Panini uses many phrases to illustrate his grammar any these have been examined meticulously to see if anything is contained there to indicate a date. To give an example of what we mean: if we were to pick up a text which contained as an example "I take the train to work every day" we would know that it had to have been written after railways became common. Let us illustrate with two actual examples from the Astadhyayi which have been the subject of much study. The first is an attempt to see whether there is evidence of Greek influence. Would it be possible to find evidence which would mean that the text had to have been written after the conquests of Alexander the Great? There is a little evidence of Greek influence, but there was Greek influence on this north east part of the Indian subcontinent before the time of Alexander. Nothing conclusive has been identified.

              Another angle is to examine a reference Panini makes to nuns. Some argue that these must be Buddhist nuns and therefore the work must have been written after Buddha. A nice argument but there is a counter argument which says that there were Jaina nuns before the time of Buddha and Panini's reference could equally well be to them. Again the evidence is inconclusive.

              There are references by others to Panini. However it would appear that the Panini to whom most refer is a poet and although some argue that these are the same person, most historians agree that the linguist and the poet are two different people. Again this is inconclusive evidence.

              Let us end with an evaluation of Panini's contribution by Cardona in [1]:-

              Panini's grammar has been evaluated from various points of view. After all these different evaluations, I think that the grammar merits asserting ... that it is one of the greatest monuments of human intelligence.