Archive for the ‘Ancient India’ Category

Tamil – Class: 3 / Teaching Tamil Through English

November 9, 2017

Class – 3

In class-1 we learnt Tamil Alphabets with their pronunciations. We learnt about basic vowels(6), extended vowels(6), consonants(18), and symbols for modifying these consonants. In class-2, we learnt a few words with their meanings. We also learnt about so called ‘northern alphbets’ to help us write and pronounce correctly, words from other languages. In this class-3, let us learn about some special features of Tamil phonetics.

First, let us see a few words where the hard consonants appear in there different vocal forms.

காரம் – KaaRaM – Spicy; ராகம் – RaaGaM – Melody, மேகம் – MEHum/MEGaM – Cloud. (Ka being used in three different vocal forms: Ka, Ga, Ha)

தங்கம் – ThaNGaM – Gold (here a soft consonant is explicitly used to soften ‘Ka’ to ‘Ga’)

சக்கை – ChaKKai – Remains of a fruit after Juice is extracted. Ka is doubled for harder accent.

சித்தி – ChiTThi – Mother’s younger sister, மோசம் – MoSaM – bad, பச்சை – PaChChai – Green, மஞ்சள் – MaNJaL –Yellow (here Cha is used in different vocal forms. Soft consonant again used in the last word, Tha is doubled for harder accent in the first word)

‘Ta, Tha, Pa, Rra’  (ட, த, ப, ற​)   also have different vocal forms as below

ட :  டீ – Tea – Tea, பாடு – PADu – Sing, பாட்டு – PATTu – Song, நண்டு – NaNDu – Crab

த : தங்கை – ThaNGai – Younger Sister, பாதி – PAdhi – Half, கத்தி – Katthi – Knife, பந்து – PaNDhu – Ball :

ப :  படம் – PaDaM – Picture, சுபம் – SuBaM – All well, கப்பல் – KaPPaL – Ship,  கம்பி – KaMBi – Metal Rod

ற : பறி – PaRri – Grab, வெற்றி – VeTRri – Victory, பன்றி – PaNDRri – Pig

It may be puzzling for some, to know which vocals to use. However in most of the cases meaning do not change even if we use a different vocal form. The words will be understood properly in its context.

There are some letters which even some Tamils do not pronounce correctly. They are La, (r)La and Zha; (i.e) ல, ள and ழ. Let us learn a few words involving these letters:

La (ல) is pronounced with the tip of the tongue just behind the upper teeth. (r)La (ள) is done with the tip of the tongue slightly behind in upper cavity. Zha (ழ) is done with the tip of the tongue still behind, deep in the upper cavity. The following words show their use. Sound bytes are included to help you pronounce them properly.

வலி, வளி, வழி – VaLi, Va(r)Li, VaZhi – Ache/Pain, Air(Atmosphere), Path

தலை, தளை, தழை – ThaLai, Tha(r)Lai, ThaZhai – Head, impediment/Bond, vegetation

பல்லி, பள்ளி, பழி – PaLLi, Pa(r)LLi, PaZhi – Lizard, School, Blame/revenge

வலம், வளம், பழம் – VaLaM, Va(r)LaM, PaZhaM – Right side, prosperity, Fruit

Ancient Tamil Literature

Tamil is one of the classical Languages of the world, along with Sanskrit. Tamil literary history is very ancient and rich. There were distinctly three periods of development of Tamil literature usually called as Sangam periods. Sangam means Academy and there were three Sangams. The last Sangam was from 400BC to 400AD and called as Kadai Sangam (கடைச்சங்கம், or the Last Academy). The literature of this period, known as Sangam Literature, are the only ones available from these ancient periods. The works of earlier two Sangams are many centuries older and now only known as just names. The literary history of Tamil records them as ‘lost in tsunami’. Sangam literatures, and even some ancient Sanskrit works, record a massive tsunami much before 400BC which destroyed a very big landscape known as Kumari Kandam (Continent of Kumari), also known as Lemuria. All the works of earlier two academies were lost forever as per this historical account. However modern history could not find much evidence of this tsunami and the Lost Land. The (3rd) Sangam literature is grouped into three parts – பத்துப்பாட்டு (Ten Anthologies), எட்டுத்தொகை (Eight Collections) and பதினெண்கீழ்கணக்கு (Eighteen Poetic Works).

Tirukkural (திருக்குறள்), by a saint poet Tiruvalluvar is one of the works in the last group of eighteen and is widely translated in almost all major languages of the world. I am giving below the first couplet of this great work consisting 1330 couplets, divided into 133 chapters of ten each

அகர முதல எழுத்தெல்லாம் – ஆதி

பகவன் முதற்றே உலகு

Akara Mudala ezhutthellam – Aadhi

Bhagavan Mudatre’ Ulagu

Meaning:

‘A’ is the start of all alphabets (of all languages) – (Just as)

GOD is the Origin of the world (of this whole Universe)

You may like to listen the audio of this verse given below:

 

Here is a Tamil proverb which states the importance of ‘Letters and Numbers’.

எண்ணும் எழுத்தும் கண் எனத் தகும்.

Ennum Ezhutthum Kann ena Thahum.

Meaning:

Numbers and Letters are rendered as the eyes (for obtaining knowledge)

 

With this thought let us conclude our Tamil class – 3


 

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24 Hours-Day X 7 Days-Week

October 5, 2017

24 Hours-Day X 7 Days-Week

L V Nagarajan

Introduction:

In one of my earlier blogs (titled Tamil/Indian Solar Calendar) I have discussed the periods of a day, a month and a year along with evolution of different calendars based on the astral movements of Earth, Moon, Sun and the Stars. I have only briefly discussed about a more convenient period of a week of 7-days. But the evolution of a ‘24-hours Day’ and a ‘7-days Week’ is also quite intriguing and interesting. I should thank my cousins Giri and Vasu, for inspiring me into this research.

History:

European and other Western scientific historians always attribute all ancient scientific developments initially to Greece, then to Egypt and Alexandria and then to Babylon. Generally they do not go beyond Babylon, because they know it will lead them to Hindu/India. In the case of establishment and evolution of Time/Day system, the researchers went one step further down to south-east of Babylon, up to a region known as Chaldea. It is now the general acceptance, that 24-Hours-Day and 7-Days-Week was established and evolved in Chaldea, in 2nd Century BC, the area becoming a part of Babylon in later periods. It is evident, the researchers did not see beyond Chaldea towards further south east, i.e. India.

Chaldea:

Let see briefly the history of Chaldea. Chaldea (/kælˈdiːə/) or Chaldaea (ref -1) was a Semitic-speaking nation which existed between the late 10th or early 9th and mid-6th centuries BC, after which it and its people were absorbed and assimilated into Babylonia. It was located in the marshy land of the far south eastern corner of Mesopotamia. Ur Kaśdim (ref -1) commonly translated as Ur of the Chaldees, is a city mentioned in the Hebrew Bible as the birthplace of the Israelite and Ismaelite  patriarch  Abraham. Chaldea is pronounced locally as ‘Kauldee’, which some scholars of Indology (ref -2) say has evolved from ‘Kauldev’ which is a sect of Kashmiri Brahmins.  “Chaldean, more correctly Kaul-Deva (Holy Kauls), was not the name of a specific ethnicity but the title of an ancient Hindu Brahmanical priestly caste, which lived in what are now Afghanistan, Pakistan, and the Indian state of Kashmir”. Chaldea region consists of people who have migrated from east through the regions of Afghanistan. Abraham’s father Terah was living in a place called Ur (yes, a town, in many languages in India). He was apparently of Hindu origin and hence he named his son Brahm, the supreme soul. It later evolved as Abraham. (ref -3)

The Chaldean religion is the outcome of three great religions, the Indian, the Mazdean, and the Egyptian, and bears direct relationship to all of these. To place it still clearer, the Babylonian system recognized  the first ONE (Ad), who is never named but only acknowledged in thought, just as the Hindu Swayambhuva (Or Tamil’s Adi Bhagawan – LVN).The Babylonian civilization was neither born nor developed in that country. It was imported from India, and the importers were Brahmanical Hindus. Science has discovered enough to inform us that Sanskrit originals of Nepal, were translated by Buddhist missionaries into nearly every Asiatic tongue. Likewise Pali manuscripts were translated in Siamese, and carried to Burma and Siam; it is easy therefore to account for the same religious myths circulating in so many countries. (ref-4).

Abraham, son of Terah, lived in Chaldea during 1900BC. The period of Biblical Abraham is also around 1900 BC (ref – 5). Abraham is considered to be the father of Jewish race and religion. Later on other Abrahamic religions like Christianity and Islam also followed.

“Bus was Abraham Real? Good Question. (ref-6) Historians today are divided on whether the tales about Abraham are mythology. The problem is lack of archaeological records. – – – – In the secular view, however, Judaism has to begin somewhere. Someone had to believe god had spoken to him. Why not call that person, Abraham?” According to the above research, even the area known as Chaldea is far south-east of the city of Babylon. The town Abraham lived, Ur, is on southern part of this area. Later on the whole area came to be called as Babylon.

With such a history of Chaldea, it is rather obvious we have to look elsewhere for the origin of 24×7 day/week system.

24 Hours-Day:

Initially, ancient men divided the day only into day and night. The first ever division of a day into smaller units are seen in ancient Hindu scriptures of 4000 BC. Herein there are mentions of a day being divided into Ghatikas (Nazhikai in Tamil). Sunrise to sunset was divided into 30 ghatikas and similarly sunset to sunrise was also divided into 30 ghatikas. It did not take them long to find that these periods are neither same nor consistent. They then standardised the time measure of a ghatika by a standard pot with a hole at the bottom. The time taken for this pot full of water to empty through the hole was standardized as a Ghatika and a gong was sounded to indicate this passage of time. It was calibrated in such a way that 60 Ghatikas was the time between two successive sunrises. Obviously in those days, Sun rise was considered as the start of the day. When ancient Hindus observed other heavenly objects also through their naked eye, especially the brighter planets like Mercury, Venus, Jupiter, Mars and Saturn, they believed that along with Sun and Moon even these visible planets affect the life on earth and that belief lead to a new ‘science’, Jyothish, now known as astrology. Earliest Hindu scripture available on Jyothish is Brihat Parasara Hora Sastra (ref -7). It is a compilation of Indian astrology existing at the time. In this text, Sage Parasara first describes how to record one’s time of birth, or lagna. He describes several lagnas- House Lagna (or Bhava), Hora lagna, Ghatika Lagna. “After noting down the time of birth after sunrise in Ghatikas and fractions of a Ghatika (known as Vighatika or Vinadi), it is divided by 5 to get House Ghatika or (Bhava). Hora lagna is obtained by dividing the time of birth in ghatikas, further by 2. For ghatika lagna only Ghatikas and Vighatikas are considered”, (i.e.) Bhava = Ghatikas/5 and Hora = Bhava/2.  Since 60 ghatikas make a day, which clearly amounts to 24 horas. This may perhaps be the start of 24-Hour day. How this Hora became Hour is another story.

“Parasara was the father of Sage Vyasa of Mahabharata. According to Varahamihira, Yuthishtra, the Pandava King of Mahabharata lived 2526 years ahead of Saka Era, which means 2448 BC. This will place Parasara’s time to be at least 2600BC” (Ref-8).

‘Hora’ is a word used for time/hour in many languages, especially in the regions around Egypt. Most accepted theory is that the word ‘Hora’ is of Jewish origin, historically derived from early Chaldean civilisation.  As we had discussed earlier, Abraham’s father Terah named his son Brahm, the supreme soul. It later evolved as Abraham. So Abraham was a follower of the Vedic religion, which at that time was spread all over the world and was not confined to India alone, as it later came to be. Abraham, father of Jewish and Ismaelite religions, must have learnt about Ghatika, Hora and Yama (Jama) time periods from his father or from their traditional Hindu holy texts.

With all the above studies, it is safe to assume that Abraham, credited with the idea of 24-Hours-Day was actually aware of definition of Ghatika, Hora and Yama (Or Jama, 3-Hours)) as divisions of time periods in the ancient Hindu way of life in which he also once belonged to. Even today we call the modern clocks as Ghadi in Hindi and Ghatikaram in Tamil. Please refer to   http://sowingseedsofthought.blogspot.in/2011/06/was-indian-time-keeping-technique.html for an interesting account of how the time was kept throughout the day in ancient India. Abraham was not perhaps interested in Indian astrology and hence he was interested to take up only Hour (or Hora), Minutes and Seconds as units of time. Since India was already using Hora as a unit of time it was fairly easy and acceptable for modern India to adapt to the international time standard of HH:MM:SS, with 24-hour days. But for religious and cultural purposes even now we use Ghatikas and Vighatikas (or Nazhikai and Vinadi in Tamil). We also use Shuba Horas for finding auspicious periods. Other time periods used till today, are the Yama (or Jama for temple rituals) and Muhurtha for holy rites like marriages.

7 Days-Week

Now let us consider the time period of a WEEK. Many Egyptian, European and Abrahamic cultures had time periods of a week which were neither consistent nor regular. They started by coinciding them with the phases of the moon. The 28/29 day cycle of moon was divided into 4 parts to make a week, but needing constant adjustment with intermittent 8-day weeks. There were cultures which had even working weeks of 8/10 days. Here again the Chaldean Hindus came to the rescue.

At some point of time in ancient astral history of India, Hindus started attributing the influence of the 7 heavenly objects (Sun, Moon and the 5 visible planets) to every hour (or Hora) of the day, in addition to every day, to every luni/solar month and to every planetary year. They found the planet Saturn to be the slowest around the sun, and the Moon to be the fastest around the sun, relative to Earth. Saturn’s average orbital velocity was observed as 0.33 times the orbital velocity of earth. As seen from the earth Sun takes 365 days to go around the Earth whereas Moon, following a similar path in the ecliptic, just takes 29 days to go around the earth. Hence its speed is the fastest at 365/29=12.59 relative to Earth. The table below gives the speeds of other planets relative to Earth.

No.

Moon/ Planet

Orbital  Speed (kM/s)

Speed relative to Earth

1

Moon

365 days / 29 days

12.59

2

Mercury 47.87

47.87/29.78

1.61

3

Venus 35.02

35.02/29.78

1.18

4

Earth/Sun 29.78

29.78/29.78

1.00

5

Mars 24.08

24.08/29.78

0.81

6

Jupiter 13.07

13.07/29.78

0.44

7

Saturn 9.69

9.69/29.78

0.33

I have made two significant changes in the above table. Moon has been included as the fastest heavenly object. Earth will be replaced by Sun, as relative to Earth, Sun is rotating the earth. The ancient Hindus believed that slower planets had larger influence on the lives on Earth even on daily and hourly basis. As said earlier, at some point of time in ancient history, Hindus started to believe in a 7-hour cycle of influence by all the seven Grahas as above, starting with Saturn and then going through all the Grahas from Jupiter to Moon, each period of influence lasting for one hour, beginning from sunrise. The cycle looks as below:

The above cycle starts from Sunrise of Day-0 and continues. By Hindu astrology each day is defined by the first Hora of the day (i.e. the first hour after sun rise) and hence named the days after the graha which rules the first hour of the day after sunrise. The days were called ‘vaaraas’ in Sanskrit and hence we had Ravi Vara, Soma Vara, Mangal Vara, Buddh Vara, Guru Vara, Shukra Vara, and Sani Vara (which directly translate into Sun-Day, Mon-Day etc). The cycle naturally repeated on and on, and ancient Hindus landed on a 7-day weekly cycle more by default than by design. A ‘week’ was never used as an explicit time period in ancient cultural history of India.

Abraham of Chaldea might have struggled hard to make the other cultures of the world to accept the week days named after planets. Many western communities accepted the 7-day week some time during 4th Century AD, but used numbers 1 to 7 to represent week days. When they eventually did accept Sunday to Saturday nomenclature, for centuries, they could not figure out why the days/planets were ordered specifically this way.  Perhaps westerners were never interested to know or to acknowledge, the Indian contribution behind this. As recorded in (ref – 9): “No one is certain as to how the idea of planetary hours came into being.  The only thing that is certain is that it is responsible for the order of the days of the week and therefore predates the Bible and the Genesis story for the creation. While the planetary hour’s true origin is something of a mystery, ancient astrologers used them to find the most auspicious time to start something important.  It was also used in horary astrology to see what influences were predominant for a given question. At some point in the distant past, by what philosophical reasoning is unknown, a sunrise or sunset defined the first planetary hour in history.  It has run on uninterrupted in this manner (as far as I know) longer than recorded history.” That nails the truth.

Twist In the Tail (or Tale)

I had an intriguing question. When did this Planetary-Hora cycle started, (i.e.) which and when was actually the day-0, mentioned in the above table? The first identifiable year for which a date is cited complete with day of the week is 6th Feb 0060 AD, as per the then existing Julian calendar. Found it very funny to note that this occurs in ‘Pompeiian graffito’. Pompei is a city in ancient Roman Empire that was immersed in ash from a volcano, Mount Vesuvius, in 0076 AD. It was dug up again only in 18th Century. They found thousands of graffiti in the walls and floorings of the ancient houses, many of them erotic. (You may google on this if interested). This particular graffiti mentions as below – “eighth day before the ides (middle) of February, day of the Sun”. Hence we know now 6th Feb 0060 was a Sunday. Or is it? As per the present system it is a Wednesday. We conclude two things from this:

  1. Romans started following 7-day week with planetary names in 0060 AD or earlier
  2. Romans were following Sunset as the start of the day. Day-4 in the planetary table given above is Sunday as per Sunset Hora and Wednesday as per Sunrise Hora.

Julian calendar used all over from 45 BC up to 16th century AD, which erred by 11 minutes, 14 Seconds in a tropical year. England accepted the new revised Gregorian calendar only in 1751 AD, 150 years after it was proposed, and it had to advance their calendar by 14 days to correct the accumulated error. Since it was exactly two weeks, the days of the week did not get affected. Luckily somewhere between 60AD and 1751AD world adopted Midnight as the start of the day, (00.00.00 Hrs after 23.59.59 Hrs) and start of the working week as Monday.

Conclusion:

I enjoyed this journey back in ‘TIME’ literally. Still it is a mystery, when and where did this idea of Planetary Hours originate. I could not find any reference to its origin. But one culture which is still using these ‘Horas’, to find auspicious and inauspicious times for various spheres of activities, are the Tamils. Readers may comment on this aspect, if they find any information.

References:

  1. Wikipedia
  2. http://brahminkhalifa.blogspot.in/2011/11/who-is-abrahm-ibrahm-brahma-and.html
  3. https://ocoy.org/original-christianity/the-aquarian-gospel/from-india-to-chaldea/)
  4. http://www.wisdomworld.org/additional/ListOfCollatedArticles/TheChaldeanLegend.html by H. P. BLAVATSKY )
  5. Comparative Religion For Dummies by William P. Lazarus, Mark Sullivan
  6. http://www.hermetics.org/Abraham2.htmlWho Was Abraham?  by Gene D. Matlock, B.A., M.A. 
  7. Ways of the natives – Parasara’s Hora Sastra – pp25, and from: http://www.barbarapijan.com/bpa/Amsha/lagna_vishesika_hora_bhava_ghati.htm
  8. Sūryasiddhānta: An Astro-linguistic Study By Sudhi Kant Bharadwaj
  9. http://www.astrology-x-files.com/help-timaeus/planet-hour.html
  10. https://io9.gizmodo.com/5825459/the-roman-city-of-pompeii-pictures-of-a-lost-world-frozen-in-time

Deluge – A Sequel?

October 19, 2016

A New Chapter

I am again returning to the Novel ‘Deluge – Agasthya Secrets’ by Dr Ramesh Babu. It is about a year since the Novel has been published. It is an ancient mystery novel set in modern times, in the style of Dan Brown. I thoroughly enjoyed the novel and had recommended the same to many of my friends. I had also written a review of the same, available elsewhere in my blog site. I felt it required a final chapter to tie up a few loose ends and also to give scope for a sequel, if ever, in the future. Initially I thought this added chapter, when read alone, will spoil the suspense element of the original narration and hence, I did not publish the same in my blog site. Now I have made a few changes which will hold the eventual suspense, and at the same time will induce the readers to read the whole novel. To begin with, I am introducing the important characters of the novel before going for the finale proposed by me.

Swathi: A medical intern starting on a career in medical research in micro biology for finding new antibiotics and pro-biotics. She teams up with an American professor in finding herbal antibiotics and takes the help of Ashwin, for locating herbal plants near Rameswaram.

Ashwin: An IIT(M) graduate in Marine Engineering and on internship at Indian Maritime University at Chennai, interested in Marine biology and Archeology.

Ravi: Director of Indian Maritime University at Chennai, a Marine Archeologist, guiding Ashwin in his internship.

MARCOS: Short form for Marine Commandos, a special operation unit of Indian Navy.

Shivani: Joined the team of Ashwin/Swathi, as a member of MARCOS, a marine commando unit, to prevent a possible terrorist attack from the sea, off the coast of Rameswaram.

Lee: Brings along a mini nuclear submarine Triton-1000 from China to help the team (!?!), in under water exploration.

 

THE FINALE

27th March 2016, 6.00 AM

After seeing off Ashwin/Swathi/Shivani trio, leaving for high seas by speed boat, Ravi was lucky to find a modest inn near Uvari itself and had a nap over night. But he got up early at 5 AM, with the village getting busy so early in the next morning. He tried to call Ashwin/Swathi, but their phones were out of range. He packed up his things and left, to take a tour of the shore temple as he had planned earlier. As he approached the Temple he again tried Ashwin/Swathi, as he was getting worried about them. He was looking at the sea intermittently for any sign of them. When he was trying his phone again, he sensed some movement in the sea. When he looked up with hope, he could only see a floating object slowly swaying towards the shore. It was semi-circular in shape and as it came nearer he realized it as a lifebuoy. But why is it floating vertically, as though some thing heavy is hanging from it? He approached the object and pulled the same to the shore. It was a lifebuoy with the inscription, TRITON 1000. Is it not the family of mini submarines, used for under water explorations, he suspected. As he pulled it completely, he saw a heavy object entangled with lifebuoy through some wild sea weeds. It was looking like a wheel guard of a heavy vehicle made of blue PVC material. It had a slit opening in which a black object was remaining stuck. On closer look he recognized it as the stone tablet Ashwin was handling the previous day. Now he was sure something serious has happened to Ashwin trio in the high seas. He again tried to contact them without success. He noticed the tablet now to have the inscriptions erased on both sides.

Sadly Ravi walks towards the shore temple ruins, after safe guarding his finds from the sea in his car. He went inside the temple ruins, to where sanctum sanctorum should have been. There was no Sivalinga – perhaps, it has been moved to the new Swayambu Linga temple nearby. The entrance to the sanctum was somewhat intact. He could see the carvings of Sages Patanjali and Vyagrapadar on either side of the entrance. But he was pleasantly surprised to see carvings of sage Agasthya below Patanjali and of sage Tirumoolar below Vyagrapadar. This carving of Agasthya was exactly the same as what they saw in Tiruchuli, again with the typical signature of Agasthiyar at the bottom, in Harappan script. Oh! What is this big space beneath the Agasthyar’s carving? It looks as though a tile of granite has been removed from this space. However on the other side there was a granite peace in place below Tirumoolar, though slightly damaged. Just as he was wondering about this, Sun’s rays started falling on these carvings. And in the sunlight he could see faintly a similar map in the space below Agasthya, as he has seen earlier on the tablet which he just now retrieved from the sea (with all inscriptions erased on both sides). But the Brahmi scripts on the map were not same. It did not take long for him to realize the map with the scripts was a mirror image of the original. Does it mean that the tablet originally belonged to this temple?

Ravi came hurrying to his car where he has stored the tablet and the lifebuoy. As he was about to return to the ruins with the tablet, he received a call from Swathi and was relieved to know they are safe. He asked them to come over to Uvari for the surprising revelation. As they arrived there in about twenty minutes along with Marcos team, they explained about what happened to them at the Spot-X. When Ravi showed them the tablet and lifebuoy of TRITON 1000, they all guessed that Shivani and Lee might have been involved in the mysterious explosion that occurred below the sea. Could they have ejected themselves and escaped? Or?

Ravi, Ashwin and Swathi approached the stone tablet in the car with all reverence. When they lifted it out into the sun, they could again see the map in the sun light at a particular angle. Ravi immediately reversed the tablet – Yes, they could see the inscription on the reverse also in the early morning sun light. Apparently the ancient chemical used for inscription is able to show up under ultra violet rays of the early morning sun!  They carried the Tablet as though it is a divine idol and tried to place it in the space below the Agasthya carving in the shore temple. Like a strong magnet the frame attracted the tablet with perfect fitting. It may require some force to take the same thing out again. Ravi observed a smile in the face of sage Agasthya. Or was it his imagination? But what is it about a similar tablet below Thirumoolar? Ravi made a mental note to come back soon to the site with ultraviolet lamp and other accessories to do further research.

With the sun still falling on the temple they could still read the inscription shining in the ultraviolet rays.

ஊழி அடைத்த உலக நாதன்

ஆழி வேலெறிந்த அய்யன் தலம்

Uuzhi adaitha Ulaga naathan

Aazhi vel erintha ayyan thalam

Ravi understood. Yes,

“Know this place from where the Swami

  Threw his spear to seal Tsunami”


 

(PS): I shared this proposed final chapter with the author Mr. Ramesh Babu. He liked this so much, he is proposing to include this finale in the next edition of the book. In his own words, “One reader Mr. L. Nagarajan has suggested an entire new chapter to my novel. It fits in so well just after the climax and also follows my style of narration! Hats off!” (https://plus.google.com/101148246018050836170). You may get this book ‘Deluge (Agasthya Secrets)’, at the following sites:

https://notionpress.com/read/deluge

https://store.kobobooks.com/en-US/ebook/deluge-20

http://bookstore.bookcountry.com/Products/SKU-001042017/Deluge.aspx

https://www.amazon.com/Deluge-Agasthya-Secrets-Ramesh-Babu-ebook/dp/B014XUEVR0

 

Dan Brown’s Inferno, the hell

August 19, 2016

I just finished (Aug 2016) reading the novel Inferno by Dan Brown. When I finished reading The Amber Room by Steve Berry, I wrote a blog about similar mysteries that abound in ancient and medieval India. I invoked English language writers of Indian origin to write such mysteries a-la Dan-Brown-Style, but with Indian artifacts and mysteries. (Please refer to my blog.

https://lvnaga.wordpress.com/2014/01/28/ancient-mystery-thriller/). My thirst for the same was quenched somewhat by a novel ‘Deluge – Agasthya’s Secrets’, by Dr. Ramesh Babu of Chennai. (https://lvnaga.wordpress.com/2016/03/22/dr-ramesh-babu-indian-version-of-dan-brown/).

This new novel ‘Inferno’ by Dan Brown is based on a biological ‘terrorism’ of scientific age placed in the surroundings of medieval mysteries of Ottoman Empire covering present day Florence of Italy and Istanbul of Turkey.

This novel is heavily based on Italian poet Dante Alighieri’s master piece ‘The Devine Comedy’ consisting of three cantos – Inferno, Purgatory and Paradise, describing the path of the dead/soul towards hell, punishment and finally perhaps the heaven. There are many articles available in the net comparing this piece of literature with similar ideas represented in ancient Hindu scriptures by Saint Veda Vyasa in his Garuda Purana. Some of them even suggest that Dante was inspired by this description of Hell (and the travel of soul with its pseudo-body through the hell to the Paradise). I wonder if any other Indian  literature has given annotations of this work in Sanskrit or any other modern languages. I am vaguely familiar with a story in Mahabharat where King Yutishtra, with all his integrity and moral equipoise, is made to undergo a horrible view of the Hell, as a punishment for his abetment of a lie in killing Aswatthama in the war. Any extract of description such a view, is it available, I wonder.

(Those who have not read this novel ‘Inferno’ and are planning to read the same, may please avoid reading further, to retain the mystery and suspense of the Novel.)

In this novel there are some unexplained ambiguities as below

  • How can a single type of vector virus would do equal harm to the fertility of both men and women? Evidently, their reproductive systems are quite different.
  • Neither it is necessary to affect random one-third of both male and female population equally, to reduce the birth rate by a third.
  • Hence it is better to say that the vector-virus modifies the DNA of whole population but switches on at random only in one-third of male population. This will reduce the birth rate by one-third and gradually reduce the population by a third, as this DNA-Virus from even unaffected males gets inherited by the subsequent population. It will be again switched on at random in one third of males in every generation.
  • Though a lot of anxiety is expressed by all the characters in the novel about this biological ‘terror’, it appears to be a very humane way of controlling the population. It is same as vasectomy and tubectomy, which are of course, voluntary. This type of population control is normally adopted in animals and pests.
  • The characters in the novel, opposed to this type of ‘terrorism’ initially, come around and accept the same and think of making it reversible.

However the novel is quite interesting and highly readable. I understand it is also coming as a movie soon with Indian actor Irfan Khan in the role of Provost, the off-shore expediter and the secondary antagonist in the novel.

PS: I remember playing a board game in my village (India) on the nights of Gokul Ashtami and Shivratri known as Parama Pada Shobanam. It is a kind of a snake and ladder game where we start from hell and pass through several evil images and then on to happy images and finally to the heavenly images of Gods.(i.e. Inferno, Purgatory and Paradise).  On the way we encounter many snakes (named after villains of Hindu epics) and ladders of good conduct and behaviors. I wish somebody adds an image of this board to this blog. (LVN)

 

 

Dr. Ramesh Babu, Indian Version of DAN BROWN

March 22, 2016

Deluge

Agasthya Secrets

A novel by Dr. Ramesh Babu

A REVIEW by L V Nagarajan

An Indian version of Dan Brown has risen in the horizon. Many of us might have read Dan Brown’s Novels Da Vinci Code, Angels & Demons, Digital Fortress and the like. These novels are based on ancient mysteries being interpreted and used in the present days for good or bad deeds. These mysteries involve codes, puzzles and secrets that existed in the context of medieval European History. We always felt Indian history and culture, being much older, offers much more scope for such novels.

Please refer to my blog:

(https://lvnaga.wordpress.com/2014/01/28/ancient-mystery-thriller/) wherein I have given some ideas on such themes.

 

Dr. Ramesh Babu’s novel DELUGE is a very successful attempt to create a full length fiction of ancient mystery thriller set in modern India. He has made an excellent mix of several ancient intrigues like, Nadi jyothish, Siddha philosophy, mythology of Lord Siva as Tripurandaka, mystical land of Lemuria, ancient Tamil-Brahmi scripts etc. This novel is about events set to happen in the near future. The parallel story of devas and asuras of yore and merging it with the tsunami of Lemuria keep the reader quite engaged. The synthesis of Vedic Culture and Tamil Culture has been brought out very well in the narration. Extremist views in Politics and Religion has also been brought out convincingly. Narration is very absorbing and it is difficult to believe that it is author’s first full length novel.

I recommend this novel to all my friends for a good read.

Following are the details

Deluge

Agasthya Secrets

By Dr. Ramesh Babu, MS, MCh, FRCS Glas, FRCS Edin, FRCS Paed
Professor of Paediatric Urology,
SRMC, Chennai.

https://notionpress.com/read/deluge

Nagarajan

Rhythmatics

February 27, 2016

Rhythmatics

Fibonacci – Hemachandra Sequence

Some of my readers will m remember, one Krishnagiri Kittappa, the official percussionist of Oho Productions in the great Tamil romantic comedy of 1960s, Kathalikaa Neramillai (No time for romance). He was initially a self-taught mridangam (Drum) player. He wanted to learn to play Tabla also. He went to a Tabla player to learn the same. He was started on his first lesson, of course, in Teen Tal (or Triputa Tal in Carnatic music) of 8 beats.

Na Din Dinnah – Na Din Dinnah

Na Din Dinnah – Na Din Dinnah

Na Din Dinnah – Na Din Dinnah  . . . . . . .

This went on for quite some time. Our man got bored of playing the same rhythm. It is the same 1,1,2 – 1,1,2 all the time for the 8-beat cycle. Why not 1,2,1, – 1,1,2, he thought.

Din Dinnah Din – Na Dhin Dhinna

Din Dinnah Din – Na Dhin Dhinna

Then, why not 2,1,1-1,2,1

Dinnah Din Din – Din Dinnah Din

Good. Now he further thought about how many such combinations of 1 and 2 (Din and Dinnah), he can make in a cycle of 8 beats. Ancient Indians have already thought about this and so, I gave him the answer as 34 different combinations. He was surprised. So many? How did they calculate?

Ancient Indians always depended on recursive technique in solving such problems. They started from 1-beat, then to 2-beats, 3-beats etc.

No. of Beats (n) Syllables – 1 & 2 Combinations Total Combinations Kn
1 Din 1 1
2 Din, Din

Dinnah

 

2

 

2

3 Din Din Din

Dinnah Din

Din Dinnah

 

 

3

 

 

3

4 Dinnah (+ 2-beats)

Din  (+ 3-beats)

2

3

 

5

Now they generalized:
(n+1) Beats Dinnah +  (n-1) beats

Din + (n) beats

K(n-1)

K(n)

K(n+1) = K(n-1) + K(n)

Therefore,

K4 = K2 + K3 = 2 + 3 = 5

K5 = K3 + K4 = 3+ 5 = 8

K6 = K4 + K5 = 5 + 8 = 13

K7 = K5 + K6 = 8 + 13 = 21

K8 = K6 + K7 = 13 + 21 = 34
Hence we have 34 combinations of 1-2 in an 8-beat cycle.

Now look at the series K1, K2, ….. Kn:

1, 2, 3, 5, 8, 13, 21, 34, 55 ……

This is the famous Fibonacci series ‘invented’ by Fibonacci (alias Leonardo Pisano Bogollo) in 13th Century AD. Ancient Indians knew about this, at least, a thousand years before him. Fibonacci himself acknowledges this fact. Fibonacci also helped spread Hindu- Arabic Numerals (like our present numbers 0,1,2,3,4,5,6,7,8,9) through Europe in place of Roman Numerals (I, II, III, IV, V, etc). The olden day knowledge route was from India to Alexandria (Egypt) to Europe.

Susantha Goonatilake (Ref-2) writes that the development of the Fibonacci sequence ” is attributed in part to Pingala (200 BC), later being associated with Virahanka (c. 700 AD), Gopāla (c. 1135), and Hemachandra (c. 1150). Parmanand Singh cites Pingala’s cryptic formula misrau cha (“the two are made together”) and cites scholars who interpret it in the context as saying that the cases for ‘n’ beats (Kn+1) is obtained by adding [Short or 1] to Kn cases and [Long or 2] to the Kn−1 cases. He dates Pingala before 450 BC ”.

“However, the clearest exposition of the sequence arises in the work of Virahanka (c. 700 AD), whose own work is lost, but is available in a quotation by Gopala (c. 1135). The sequence is also discussed by Gopala (before 1135 AD) and by the Jain scholar Hemachandra (c. 1150) “. Fibonacci was born only in 1170 AD.

Prof. Manjul Bhargava (R Brandon Fradd Professor of Mathematics, Princeton University, USA) gave a Lec-Dem on Music & Mathematics at the Music Academy, Madras during their annual conference 2015, on 31st December 2015. Being a Tabla player himself, he dealt with the above aspect of rhythm variations in detail. His talk was the inspiration for me to write this blog.

References:

  1. https://www.mathsisfun.com/numbers/fibonacci-sequence.html
  2. https://en.wikipedia.org/wiki/Fibonacci_number
  3. Manjul Bhargava’s Lec-Dem at the Music Acedemy, Madras (2015)

L V Nagarajan

 

Melakartha Chart (Scales of Carnatic Music)

November 26, 2015

Melakartha Chart – (Scales of Carnatic Music)

L V Nagarajan

Prologue:

Some time back I was listening to a young upcoming Carnatic vocalist in Shanmukhananda Hall in Mumbai. After a few items, he started the alap of an unfamiliar raga. Some of the knowledgeable members of the audience were guessing what raga it could be. Somebody said it is like another rare raga but with prati-madyama. Another one said it is a janya of melakartha75(?!) or so. After a short alap he allowed the violinist to play the raga. Violinist started a little hesitantly. Vocalist leaned towards him and spoke a few words. Violinist nodded and continued more confidently. Then the vocalist proudly announced the rare raga as Gopriya, janya of Rishabapriya scale. Some in the audience were happy but I was not happy. If he had told us the Melakartha number I could have also understood the scale easily; but Rishabapriya? Luckily I happen to know something about Katapayadi Sankhya, a code into which these Melakartha names are encoded. Now let us see:

Ka (adi) nava – Ka, Kka, Ga Gga, Gna, Cha, Ccha Ja, Jja.

Ta (adi) nava – Ta, Tta, Da, dda, Nna, Tha, Ttha, Dha, Ddha.

Pa (adi) pancha – Pa, Ppa, Ba, Bba, Ma

Ya (adi) ashta – Ya, Ra, La, Va, Sya, Sha, Sa, Ha

Ri-Sha-bapriya is the Mela. Ri is second letter in Yaadiashta and Sha is 6th in the same series. Hence It is Mela number 62. (i.e) =10×6 +2, 11th cycle of the Melakartha scheme, 5th Cycle of Prathi-madhyama group and the second raga in the cycle. (i.e.) S R2 G3 M2 P D1 N2 S is the scale. QED.

How nice it could have been if the vocalist told us this number 62 as he did to the violinist.

 

Dialogue

1. He! I understand all systems of music have seven notes. But, tell me, what is this scale, Mela or Melakartha?

The concept of present day scales in Carnatic Music has been imported from the western music. In the West an octave of eight notes are defined starting from a note of a specific frequency to its resonant note of double the frequency. This octave (set of eight notes) was initially divided into 7 frequency intervals between the notes, denoted as C-D-E-F-G-A-B-C. The musical scale of these major notes is known as Major scale. The frequency ratios selected for these intervals is same as Sankarbharanam (scale) of Carnatic music. However, a set of semi tones (or half intervals) were introduced, 2 between C-D-E and 3 between F-G-A-B.  In a piano or harmonium the white keys represent the major notes and the black keys(^) represent semi-tones – (C^D^EF^G^A^BC). The semi tone between C and D is called D-Flat or C-Sharp according the musical context. Same way the other semitones are also treated. For our convenience, we will call them as

C, D1, D2, E1, E2, F1, F2, G, A1, A2, B1, B2, C.

Frequency ratios of these semi-tones follow the rule of consonance and assonance. Many scales were developed using the 7 selected notes from these 12 semitones. Some of our main ragas (scales) like Karaharapriya and Mayamalavagowla matched these semitones.  Somewhere in the 17th century this concept of scale was adopted by theoreticians of carnatic music. They were also influenced by the keyed instruments of western music like piano and harmonium. Hence attempts were made to fit our ancient musical system into the keys of the above instruments. At this point scales were introduced in carnatic music, to group all the notes used in a raga. These attempts lead to the development of our own basic scales, Mela Karthas. Melas or new melodies were born out of these scales and hence the name Melakartha or melody-maker. (However, subsequently, sacrificing some amount of consonance and assonance between notes, Western music adopted 12 equal intervals for these 12 semitones. This system was called ‘equi-tempered’ as opposed to the earlier system called ‘just-tempered’ or ‘just intonations’ which takes care of consonance ratios. Western musical instruments are tuned accordingly.)

2. But how do these 12 semitones make 72 Melakarthas, I often hear about?

At this point it may be better to discuss about what constitutes a present day scale. A full scale constitutes seven notes or saptha swaras (sa, ri, ga, ma, pa, da, ni) in an octave. For convenience let us call these notes in short as S R G M P D N. These are selected from 12 basic nodes, which we may call as Sruthis’s, though they are called semitones in western music. The rules for selecting a basic-scale (a set of seven swaras from these 12 sruthis) can be summarized as below:

Swaras S       R       G      M P       D      N S
Semitones C D1 D2 E1 E2 F1 F2 G A1 A2 B1 B2 C
Sruthis 1 2 3 4 5 6 7 8 9 10 11 12 1
(12) Swara-sthanas S R1 R2 G1 G2 M1 M2 P D1 D2 N1 N2 S
(4) Vivadi-Swaras Gr Rg Nd Dn  
(16) Swara-sthanas S R1 R2 R3 M1 M2 P D1 D2 D3 S
G1 G2 G3 N1 N2 N3  

It may be noted above that notes nos. 3 and 4 are used as both Ri and Ga. Similarly notes 10 and 11 are used as both Da and Ni (though such usages are known as Vivadi Prayoga). In carnatic music system, these 16 swara-sthanas are called respectively: Shadjam, Suddha-Chatusruthi-Shatsruthi Rishabams, Suddha-Sadarana-Antara Gandharams, Suddha-Prati Madhyamams, Panchamam, Suddha-Chatusruthi-Shatsruthi Dhaivatams and Suddha-Kaisika-Kakali Nishadams. Here itself we can make out the attempt of reducing the number of sruthis from the original twenty-two to twelve. (Even in Western Music double-sharp and double-flat notes are used in a scale)

Any basic scale has two parts: Poorvanga, the notes upto and including M, (SRGM) and Uttaranga, the notes including P and above (PDNS). For each M (sudda-M1 and prati-M2), there are six types poorvangas based on six different combinations of notes R and G; namely R1-G1, R1-G2, R1-G3, R2-G2, R2-G3 and R3-G3. Similarly there are six types of uttarangas based on six different combinations of notes D and N. Hence we have 72 Melakartas – [(6+6) x 6].

3. Really ingenious! But what is this Katapayadi mumbo-jumbo being mentioned?

The above 72 melakarthas require some identification as most of them are not naturally available scales. They divided these in to twelve groups, each group having a specific R-G-M1 and R-G-M2 combinations with increasing order of R and G. Within each of this group, six scales with increasing order of D and N were included. Thus 36 scales or melakarthas using M1 were numbered 1 to 36. The others with M2 were numbered 37 to 72. Please refer to the chart at the end of this write-up. Each of this 12 groups known as chakras were named as Indu, Netra, ……, Rudra and Aditya. (Indu – one Moon, Netra – 2 eyes, ….., 11 Rudras and 12 Adityas). In the chart below each row represents two chakras. Since many of these scales were not in existence, these, as melakarthas, required some names also. The earlier day musicologists used a code to name these scales in such a way that one can find the number of a melakartha from the name itself. The code is known as Katapayadi Sankhya and is used in many applications of ancient Hindu science and mythology.

The numbers 1 to 9 are coded by using following letters: (Ka Ta Pa Ya)

Ka (adi) nava – 1 to 9 –  Ka, Kka, Ga Gga, Gna, Cha, Ccha Ja, Jja.

Ta (adi) nava – 1 to 9 – Ta, Tta, Da, dda, Nna, Tha, Ttha, Dha, Ddha.

Pa (adi) pancha – 1 to 5 – Pa, Ppa, Ba, Bba, Ma

Ya (adi) ashta – 1 to 8 – Ya, Ra, La, Va, Sya, Sha, Sa, Ha

Other letters are rendered as zero. In the scale Kamavardini, Ka decodes into number 1, and Ma decodes into number 5. Hence the number of the scale decodes into 5 tens plus one, 51. The same way other scales were also given such names. However, some scales are already established as popular and well known ragas from ancient times. Hence these names were modified, such as, DdheeraSankarabharanam (29), HanumaTodi (8), MechaKalyani (65), to fall into the Katapayadi scheme.

4. Looks neat! Why then people prefer melakartha numbers instead of names?

DdheeraSankarabharanam and Sulini are two different scales, the first one being a well known raga. Can you spot how these scales compare? Yes, only when one compares the numbers 29 and 35. we can now say immediately: Sulini uses R3 instead of R2 in Sankarabharanam. And Kosalam (71) is immediately identified as M2 of Sulini, (or R3, M2 of Sankarabharanam). With names these relationships are not immediately evident. Hence, the preference for numbers. Of course there are many who have completely memorized the Melakartha table

5. Is there a way to name these scales in a way to reflect these inter relationships?

To my knowledge, nobody has tried so far. However, I propose, in the following paragraphs, a way of encoding such relationships in the name itself.

Earlier the scale was split into two parts Poorvanga (SRGM) and Uttaranga (PDNS). Let us now split the scale into three parts: SRG, M, PDN. If we consider the variations in these parts, we get SRG(6) x M(2) x PDN(6) = 72 Scales. Let us now name these parts along with their variations:

S R1 G1 – athi M1- Daya P D1 N1- Vathi
S R1 G2 – Sakala P D1 N2 – Nidhi
S R1 G3 – Sarva P D1 N3 – Kari
S R2 G2 – Parama M2 – Kripa P D2 N2 – Varshini
S R2 G3 – Poorna P D2 N3 – Varithi
S R3 G3 – Poojya

P D3 N3 – Sagari

With these code names, Sankarabharanam (29) will be called as Poorna Daya Varithi. And Kalyani (65) will be known as Poorna Kripa Varithi. It is clear from the name that Kalyani scale is same as Sankarabharanam, but with M2. Poojya Daya Varithti is Sankarabharanam with R3, i.e. Shulini (35). Here I take the liberty of using the Melakarta Chart as developed by Dr. Mukund (http://www.carnaticcorner.com/articles/mukund_chart.htm). This chart is prepared on the same principle as mentioned above. I have superimposed the above code names on this chart, as shown below. We may use this chart to get used to the proposed new names. The melakarthas using Athi, Poojya, Vathi and Sagari codes are the 40 Nos. of Vivadi melas – the outer most squares of the chart.

Mukund-Chart

6. Umm…! I really need time to study and understand this.

Please take your time and do write your comments.

Epilogue:

  1. The material discussed in this blog has been extracted from my more detailed write-up on Melakartha scheme done in 2006. However I did not have a blog-spot then, to publicize it. I sent it to a few musicians and musicologists but there was not any response. I was enthused to write this note again, when I recently came across Mukund’s Chart. (http://www.carnaticcorner.com/articles/mukund_chart.htm).
  2. The rasikas of Chennai Music Festival (2015) may use this chart while attending the concerts.
  3. The above suggested codes/names can definitely be improved by musicologists like Dr. Mukund. It is only an idea to be adopted, or improved (or rejected, if found not suitable).
  4. While there are numerous advantages of this Melakartha scheme, there are a few disadvantages also. Though Melakartha formulation helps us to classify, formulate and document our music, it has limitations in formulating such nutpa-sruthis as Madhyama of Varali or Rishaba of Saveri. Possibly this was the reason why Harmonium (or Piano) was not preferred as a part of carnatic music ensemble. More so due to the equi-tempered tuning of Harmonium, where the 12 notes of the octave are tuned with equal frequency intervals. Here-in, even Sa-Pa consonance is sacrificed. We should not allow the Melakartha scheme to restrict our music to just 12 flat notes and 72 basic scales. We may discuss more about this later.  The author of this note is only a normal listener and follower of Indian music and whatever knowledge (or lack of it) displayed here are purely incidental. Let our Music and its traditions live forever.

Phonetics of Devanagari and Tamil scripts

October 14, 2015

Phonetics of Devanagari and Tamil scripts

These two scripts are phonetically related in a very odd way. Many of the north Indian languages closely follow the Devanagari script as used by Sanskrit presently. Other south Indian languages (I am consciously avoiding the term Dravidian languages) follow their own independently evolved scripts. I found some interesting contrast between the scripts of Sanskrit and Tamil which I want to share with my readers. These are all my own original ideas and purposely I have not read or referred any previous work or study on this aspect (which I will eventually do after I publish this write-up).

Like the scripts of all languages, these two scripts also have vowels and consonants. The Devanagari script has thirteen vowels as below. (I am giving only the phonetic value of these vowels);

Vowels : a, Aa, i, Ee, u, Uu, ru, eay, ai, oh, ou, amm, aha.

Actual Devanagari script is not of our interest as of now. Let us now look at the vowels in Tamil language:

Vowels : a, Aa, i, Ee, u, Uu, eay, Eaay, ai, oh, Oh, ou.

As we compare these phonetics we see, they are essentially similar, but with significant differences. When ‘a’, ‘i’ and ‘u’ have their extended phonetic as ‘Aa’, ‘Ee’ and ‘Uu’, the same extension is not given to ‘eay’ and ‘oh’ in Devanagari script. But Tamil script has extended phonetics for them also. Tamil seems to need them too. Look at the Tamil words –

mattu, mAattu, mittu, meettu, muttu, mUuttu, mettu, meayttu, mottu, mOhttu

– meaning respectively,

less, hang, earth/land, pluck a string of a musical instrument, butt or bang with your head, enflame (or bone joint), musical tune, raised level, flower bud and bulging. (Phew, look at the strength of Tamil vocabulary).

If we assume that Tamil phonetics were derived from Devanagari script, then Tamils have surely added two more vowels to meet their phonetic requirements. Let us wait till we see the consonants.

The primary consonants in Devanagari are:

Ka, kha, ga, gha, nga

Cha, chha, ja, jha, ngya

Ta, tha, da, dha, Nna

Tha, Thha, dha, dhha, na

Pa, pha, ba, bha, ma

The corresponding consonants in Tamil are:

(Ka, nga) – (Cha, ngya) – (Ta, Nna) – (Tha, na) – (Pa, ma)

Tamils added (perhaps after a later thought) one more set of similar consonant in

Rra – na, (literally at the end of the list of alphabets).

While an emphasized Rra (or tra) is required to handle a few important Tamil words, I always found a second ‘na’ superfluous, although the two ‘na’s are surely used in different contexts in the written language.

As can be seen above, Devanagari script appears to be an expanded version of Tamil phonetics. If it is still believed that Tamil phonetics were derived from Devanagari, what could have been the reason for dropping the different variations of Ka, Cha etc? When writing purely Tamil words, Tamils don’t feel the need for these emphasized consonants, as they are intended to be pronounced with such variations as per the context. Tamil also uses double letters for emphasized consonants such as KKa for Kha. However, when writing words of other languages in Tamil script, one feels handicapped by this deficiency in the script. Some authors use subscripts like 1, 2, 3 and 4 in the script for marking these variations. As you can see in the next section, in later days, a few Devanagari phonetics were also adopted in to Tamil script, even though purists do not use them.

Now let us write down the secondary consonants of Devanagari script, as below:

Secondary consonants: ya, ra, la, va, sha, sya, sa, ha

Tamil has similar consonants as below:

Secondary consonants: ya, ra, la, va, zha, Lla

Earlier Tamils did not adopt the latter half of the above set of Devanagari phonetics in to their script. As need arose to read and write words of foreign roots, they adopted the others also in to a set of special (Northern!) scripts – ‘sha, ksha, sa, ha and Sri’. Here again the purists do not use them. The consonants zha, Lla, Rra, na are special phonetics of Tamil, (especially the zha), and significantly they at the end of the list of Tamil alphabets.

From the above account it appears that the phonetic scripts of Devanagari and Tamil could have had their roots in a more ancient common script. Critical comments on the above are most welcome.

Meru Prastarah (or Pascal’s Triangle ?!?)

October 21, 2014

Meru Prastarah (or Pascal’s Triangle ?!?)

Let me start with an ancient (1000 CE) Sanskrit text as below:

Anena ekadvyaadilaghukriyasiddhyartham, yaavadabhimatam prathama prastaravat meruprastaram darsayati, uparistadekam chaturasrakoshtam likhitva, tasya adhastat ubhayatordhaniskrantam koshtadwayam likhet, tasyapiadhastatrayam tasyapiadhastatccaturtyamevam yaavadabhimatam sthanamiti meruprastarah tasya prathame koshte ekasamkhyam vyasthapyalakshanamidam pravarttayet, tatra dvikoshtaayaampanktau ubhayo koshtayorekaikamankam dadyaat, tatastritiyaayaam panktau, paryantakoshtayorekaikamankam dadyaat, madhyamakoshtethuparikoshtadvayaankamekikrtya purnam nivesayediti purnasabdarthah, chaturtyampanktavapi, paryantakoshtayorekaikamankam sthapayet, madhyamakoshtayothuparakoshtadvayaankamekikrtya purnam trisamkhya rupam sthapayeth,  uttaraataraapyevameva nyaasah, tatra dwikoshtaayaam pankatauekaakshrasya prastaarah,……. tritiyayaam pankatau, dviakshrasya prastaarah, chaturtyaam pankatau, triakshrasya prastaarah, ….

The above is not in praise of any god of Jain, Budha or Hindu religion. It is not a religious text at all. It is a text describing a method for constructing a mathematical table. Ancient Indian Mathematician Pingala (200 BC) in his Chandahsutra had given the rules for formation of different chandahs (≈ musical meters) for Sanskrit prosody. Another ancient Indian mathematician Halayudha (1000 CE) has given the explanation and commentary on this work by Pingala. Given above is a selected portion of his commentary. For some reasons unknown to me, ancient Sanskrit texts always use composite words very frequently. These words need to be broken into individual words properly to obtain the intended meaning of these words. Here is an attempt to translate the above text into English with proper separation of words.

Anena ekadvyaadi laghu kriya siddhyartham, yaavadabhi matam

(To get every combination of one, two, etc. syllables as required)

Prathama prastaravat meru prastaram darsayati.

(from first row onwards , the meru tabulation will be shown below)

Uparihi tad ekam Chaturasrakoshtam likhitva,

(At the top itself one square cell is drawn)

Tasya adhah tat ubhayato ardhani skrantam

(Below this row let us have a pair, half over lapping)

Koshtadwayam likhet.

(Two cells are drawn)

Tasyapi adhah tat trayam

(Again the row below will have three)

Tasyapi adhah tat chaturtyam,

(Again its next line will have four)

Evam yaavadabhi matam sthanam

(same way, up to the  required stage, cells are constructed)

iti meru prastarah.

(This is called Meru Prastara or Meru-Tabulation)

Tasya prathame koshte eka samkhyam

(Its first stage-cell will hold the number 1)

Vyvasthapya lakshanamidam pravarttayet

(From here on, the following is the way it grows)

Tatra dvikoshtaayaam panktau

(in its twin-cell row)

ubhayo Koshtayoh eka ekam ankam dadyaat

(the pair of cells holds numbers 1,1)

Tatah tritiyaayaam panktau, paryanta Koshtayoh Eka ekam ankam dadyaat

(then in the 3rd row, the extreme cells will hold numbers 1,1)

Madyama koshteth, upari koshtadvayah ankam eki krtya purnam nivesayeth

(middle cell takes the added value of the two cells above)

Iti purnasabdarthah

 (Thus completes the table for 2nd power)

Chaturtyam panktau api, paryanta Koshtayoh eka ekam ankam sthapayet

(then in the 4th row also, the extreme cells will hold numbers 1,1)

Madyama koshtayoth, upara koshtadvayah ankam eki krtya purnam

(middle cells take the added values of the two cells above each)

Trisamkhya rupam sthapayeth

(this completes the 3rd power)

Uttara utaaro api evameva nyaasah,

(next and next stages also follow the same rule)

tatra dwikoshtaayaam pankatau, eka akshrasya prastaarah

(Here the twin-cell row gives one syllable table)

tritiyaam pankatau, dvi akshrasya prastaarah

(the 3rd row gives two syllables table)

chaturtyaam pankatau, tri akshrasya prastaarah

(Thus 4th row gives three syllables table)

And so on.

Meru

If we follow the above step by step construction given so clearly by Halayudha (1000 CE), we get the above pyramid or Meru in Sanskrit, (stands for a mountain with a peak). What do we have here? It is the same as Pascal’s Triangle, “discovered” by Blaise Pascal (1623-1662 CE).

This table gives in every nth line the coefficients (a+b)**(n-1). i.e. the second line gives coefficients of (a+b) as 1,1; the second line gives 1,2,1, as coefficients of (a+b)2.; the third line gives 1,3,3,1 as coefficients of (a+b)3 and so on.

However Halayudha gives credit for this table to Pingala (200 BC). He claims to have derived this table from Pingala’s cryptic clue which he translates to a set of rules, as below (with a and b as the two syllables to be combined, in any n-syllable chandah):

  1. First write down all (‘n’ number of)  b’s as the first combination
  2. In the next line, replace the first ‘b’ with an ‘a
  3. At the same line, replace all letters to the left of this new ‘a’ with ‘b
  4. For the next and the subsequent lines repeat the steps 2 & 3.
  5. Continue as above till we arrive at a line with all a’s,

This can be clearly seen as a binomial expansion (a+b)n staring with bn and ending in an. Halayudha later puts these results on a table known as Meru Prasthara. He later gives a step-by-step method as above, for constructing this table without specifically going through the above rules. This Meru Prastarah traveled to China and the Chinese mathematician Yang Hui reported it in the thirteenth century, although his work was unknown in Europe until relatively recent times. The Meru Prastarah traveled to Europe a little later through Arabia, Egypt and Greece and gets “discovered” by Pascal in 17th century CE, 600 years after Halayudha. We are blaming all the time ‘the lack of scientific temper’ among Indians.

Ref:

  1. Binomial Theorem in Ancient India – By Amulya Kumar Bag, History of Science, Ancient Period Unit II, No.1, Park Street, Calcutta-16 (1966)
  2. Journey Through Genius – The Great Theorems Of Mathematics – by William Dunham – Wiley Science Editions, John Wiley & Sons Inc.(1990)
  3. Probability in Ancient India, by C K Raju., ckraju.net, 2011.

Connected Topics:

Meru Prastarah

Baudhayana’s Circles

Square Root of Two

Sine of an Angle

LVN/ Oct, 2014

Soul tied to physical body

May 28, 2014

Soul tied to physical body

L V Nagarajan

1.0 Soul, in a spiritual context

Last spring, I attended a spiritual workshop conducted in our neighborhood. In one of the sessions the Guru involved me in a demo conversation to bring out the concept of Soul or Atma.

He asked me : “Who are you?”

I replied, “I am Nagarajan”

“No that is your name. I know it. But who are You?”

After some thought I replied: “I am an Electrical Engineer.”

“No that is your profession. But who are YOU?”

After some more thought I pointed to my body somewhere near the heart and said – “This is Me.”

“No that is your body. But who are Y-O-U? Can you tell me who are you without referring to your extensions like name, profession, your body and such things. They are all temporary and subject to change.”

“How? Body can change ….?”

Guru did not reply. He went on to describe Soul or Atma in a spiritual context and how it will finally merge with the superior SOUL or PARAMATMA. But I was intrigued by the unanswered question – like name and profession, can you change your body also?

2.0 Soul, in Yogic context

I was surprised to find the answer to this question recently through the columns of Times of India. Writing in ‘The Speaking Trees’ of 30th April 2014, Sadhguru Jaggi Vasudev says: “Breath is not just the exchange of oxygen and carbon dioxide. For different levels of thought and emotion that you go through, your breath takes on different types of patterns. When you are angry, peaceful, happy or sad, your breath goes through subtle changes. Whichever way you breathe, that is the way you think. Whichever way you think, that is the way you breathe. Breath can be used as a tool to do many things with body and mind. Pranayama is the science whereby consciously breathing in a particular way, the very way you think, feel, you understand and experience life can be changed”. He further adds: “Breath is like the hand of the Divine. You don’t feel it. It is not the sensations caused by the air. This breath that you do not experience is referred to as Koorma Nadi. It is a string which ties you with this body, an unbroken string. If i take away your breath, you and your body will fall apart because the being and the body are bound by the Koorma Nadi. This is a big deception. There are two, but they are pretending to be one. There are two people here, the body and being, two diametrically opposite ones, but they pretend that they are one. If you travel through breath, deep into yourself, to the deepest core of breath, it will take you to that point where you are actually tied to the body. Once you know where and how you are tied, you can untie it at will. Consciously, you can shed the body as effortlessly as you would shed your clothes. When you know where your clothes are tied, it is easy to drop them. When you don’t know where it is tied, whichever way you pull, it does not come off. You have to tear them apart. Similarly, if you do not know where your body is tied to you, if you want to drop it, you have to damage or break it in some way. But if you know where it is tied, you can very clearly hold it at a distance. When you want to drop it, you can just drop it consciously. Life becomes very different. When somebody willfully sheds the body completely, we say this is mahasamadhi. This is mukti or ultimate liberation. It is a great sense of equanimity where there is no difference between what is inside the body and what is outside the body. The game is up. This is something every yogi longs for. Consciously or not, every human being is working towards this.”

Yes, here we have the answer. You are different from your body. I find this as a Yogic or elemental way looking at your soul. A yogic practice to realize oneself separated from one’s own body. This is perhaps the way Sri Ramana Maharshi found the answer for his monumental question WHO AM I? Subsequently he even achieves out-of-body experience and preaches these concepts to thousands of his followers and devotees. All this said and done, this is still not a complete answer to my question – ‘Like name and profession, can you change your body also?’

3.0 Soul, in a scientific context

Idly I turned my eyes away from ‘The Speaking Trees’ to the next page of the same issue of Times of India. To my surprise I found the missing part of the answer in another news item on science pages. It talks of ‘A device to let you ‘virtually’ swap your body with another’. Here goes the report: 

 “A group of artists based in Barcelona has created an unusual virtual reality device that can allow you to experience what it might be like to step into the skin of another person. The device, called ‘The Machine to be Another’ lets people experience life in another person’s body. Participants in a body swapping experiment at the ‘Be Another’ lab, don an ‘Oculus Rift’ virtual reality headset with a camera rigged to the top of it. The video from each camera is piped to the other person, so what you see is the exact view of your partner. If she moves her arm, you see it. If you move your arm, she sees it. To get used to seeing another person’s body without actually having control of it, participants start by moving their arms and legs very slowly, so that the other can follow along. Eventually, this slow movement becomes comfortable, and participants start to feel as though they are living in another person’s body, BBC News reported.”

Is the above an attempt to look at your soul from scientific aspect? Now we can look up to Jagat Guru Adi Sankara. He had achieved this feat of entering another body but without the aid of such devices as above. Even some lesser mortals have achieved this feat and this is known as one of ashta-ma-siddis, the eight great feats. In Tamil it is known as Koodu-vittu-koodu-paaydal, or ‘from one shell to another’.

We may meditate on this.

Ref:

  1. THE SPEAKING TREE, Life Breath & The Ultimate Expansion, by Sadhguru Jaggi Vasudev, Time of India 30th April 2014, page 20.
  2. A device to let you virtually swap bodies with another, BBC News report,  Time of India 30th April 2014, page 21

LVN/28 May 2014