The Katapayadi Number System

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What’s common between the first verse of Mahabharata and the last verse of Mēlputtūr Nārāyaṇa Bhaṭṭatiri’s Narayaneeyam written in 1586 CE.?

The first verse of adi parva reads

नारायणं नमस्कृत्य नरं चैव नरॊत्तमम देवीं सरस्वतीं चैव ततॊ जयम उदीरयेत

(” Om ! Having bowed to Narãyana and Nara, the most exalted male being, and also to the Goddess Saraswati, must the word Jaya be uttered)

Mēlputtūr Nārāyaṇa Bhaṭṭatiri’s Narayaneeyam ends with the words ayur- ̄arogya-saukhyam. This wishes long life, health, and happiness to the readers of his devotional poem.

The words jayam and ayur- ̄arogya-saukhyam have two properties.

Both have proper meanings in the context of the sentence used (as in, they are not gibberish words.) This matters as we go into the details.
The second property is not well known. Both those words encode a number that has a deeper meaning.

In this system of encoding, jaya represents 18 and ayur- ̄arogya-saukhyam 17,12,210. Counting those many days from Kali Yuga, gives the date as 8th December 1586, the completion date of Narayaneeyam.

This article looks at this style of representing numbers using meaningful words.

Katapayadi Number System

Process-wise, the encoding is simple. Each Samskritam consonant is given a number. Hence the algorithm is as simple as reading it from right to left.

ja	ya
8	1

encoding of jaya in katapayadi system

The letter ja is assigned the number 8 and ya, 1. Reading from right to left, it becomes 18.

Why did Vyasa pick on the number 18 and encode it as jaya? Why did he call Mahābhārata as jaya. Mahābhārata has 18 parvas. Gita has 18 chapters. The war was fought for 18 days. There were 18 akshauhini’s in the war. Thus jaya was not a random selection.

Here is the full table of the consonant to number assignment.

1	2	3	4	5	6	7	8	9	0
ka क ക	kha ख ഖ	ga ग ഗ	gha घ ഘ	nga ङ ങ	ca च ച	cha छ ഛ	ja ज ജ	jha झ ഝ	nya ञ ഞ
ṭa ट ട	ṭha ठ ഠ	ḍa ड ഡ	ḍha ढ ഢ	ṇa ण ണ	ta त ത	tha थ	da द ദ	dha ध ധ	na न ന
pa प പ	pha फ ഫ	ba ब ബ	bha भ ഭ	ma म മ
ya य യ	ra र ര	la ल ല	va व വ	śha श ശ sha ष ഷ	sa स സ	ha ह ഹ

katapayadi table

Look at the letters which represent the number 1. ka, ta, pa, ya gives it the name katapayadi (adi in Samskritam means beginning). Vowels meant 0, and vowels followed by a consonant had no value. In the case of compound letters, the value of the last letter was used.

In its land of origin, Kerala, it was known by a different name Paralpperu where paral means seashell and peru name” (astronomical calculations were done using seashells).

Here is another example. The year 2010 is expressed as natanara.

This is because

Letter	Value
na	0
ta	1
na	0
ra	2

If you read this backward, you get 2010. An important point is that the letters are not chosen randomly. They mean something. In this case, natanara means “a man (nara) who is an actor ( nata)”. Since there are many possible letters for each number, the mathematician can create a meaningful word from the numbers.

Similarly, ayur- ̄arogya-saukhyam represents 17,12,210 to represent the date of 8 December 1586. Why was the epoch chosen as the beginning of Kali Yuga? It was the popular way of dating events called the Kali-ahargana. Kali-yuga started at sunrise on Friday, 18 February 3102 BCE, and computing the number of days from then was common in planetary calculations.

The fact that Bhaṭṭatiri used this system is not surprising. He was a student of Achyuta Pisharati, a member of the Hindu school of Mathematics from Kerala. This is also an example where it was used in non-scientific work.

Thus the katapayadi system allows the author to represent large numbers using easy-to-remember words. It also has the flexibility to let the author pick an appropriate word for the context and one that fits the meter if it’s a poem.

During the time of Aryabhatta, there were at least three methods of writing numbers. Mathematicians like Varahamihira and Bhaskaracharya used a system called the bhoot samkhya. Aryabhatta, though, invented his own system, which was a new contribution.(The Aryabhata Number System)

Katapayadi number system was primarily used by Hindu mathematicians and astronomers in Kerala. The fact that numbers can be converted to meaningful words that can be strung together helped Malayali mathematicians perform complicated calculations from memory. They computed eclipses, memorized the calculations using words, and committed to memory. This way, there was no dependency on books or tables. This system of memorization was prevalent till around 100 years back.

The book Moonwalking with Einstein talks about various techniques used by the ancients to memorize data. One of the techniques was called memory palace. The katapayadi system looks simpler as the data to commit to memory is that table.

Origins and Spread

If you ask, who started this number system, there are many answers. It’s possible that Vararuchi wrote them in Candra-vakyas in the fourth century. Aryabahata I, who lived 100 years after, was aware of it. It was then popularized in 683 CE in Kerala by Haridatta. ́Sankaranarayana ( 825–900 CE) mentions this name in his commentary on the Laghubhaskarıya of Bhaskara I. Subhash Kak argues that the the system is much older

Though the system originated in Kerala, it spread around India. Though it was well known in the northern part of India, it was not widely used. It spread from Kerala to Tamil Nadu and Pondicherry. That came due to their contact with Nilakanta Somayaji, another mathematician from the Madhava school. In Karnataka, Jains used it in their writing. Orissa has manuscripts that show usage of this system. Aryabhata II used this in the 10th century with some modifications. Bhaskara II used both Bhootsamkya system and Katapayadi system in his works.

This system was not used just in astronomy and mathematics but also in classifying music. For example, the 72 ragas were classified by musicologist Muddu Venkata Makki using the first two letters to indicate the serial number of the Melakartharagam. Thus Kanakangı shows the serial number 1, Rupavatı 12, Sanmukhapriya 56, or Rasikapriya 72.

You are too late if you think this system would help write something like Da Vinci Code. The National-Treasure-in-India script was done a few hundred years back. Ramacandra Vajapeyin, who lived in Uttar Pradesh, used this technique to forecast a dispute or war victory. His brother wrote a text to draw magic squares for therapeutic purposes.

Forgotten Mathematicians

I learned about the Hindu school of Mathematics (as opposed to the Jain school) from Kerala by reading A Passage to Infinity by George Gheverghese Joseph. Though there were few mathematicians in Kerala in the 9th, 12th, and 13th centuries, what is today called the Kerala School started with Madhava, who came from near modern-day Irinjalakuda. His achievements were phenomenal; they included calculating the exact position of the moon and what is now known as the Gregory series for the arctangent, Leibniz series for the pi and Newton power series for sine and cosine with great accuracy.

Some of these techniques were forgotten, but thanks to a renewed interest in Samskritam, there is a revival of knowledge. This whole article was triggered when I read the first chapter of my Samskrita Bharati book on sandhis which mentioned the katapayadi system.

Postscript

If are you curious to know why Mahābhārata was called jaya, then read this article.

References:

Vijayalekshmy M. “‘KATAPAYADI’ SYSTEM — A CONTRIBUTION OF MEDIEVAL KERALA TO ASTRONOMY AND MATHEMATICS.” Proceedings of the Indian History Congress, vol. 69, 2008, pp. 442–46, http://www.jstor.org/stable/44147207. Accessed 7 May 2022.
Anusha, R., et al. “Coding the Encoded: Automatic Decryption of KaTapayAdi and AryabhaTa’s Systems of Numeration.” Current Science, vol. 112, no. 3, 2017, pp. 588–91, http://www.jstor.org/stable/24912445. Accessed 7 May 2022.
Kak, Subhash. “INDIAN BINARY NUMBERS AND THE KAṬAPAYĀDI NOTATION.” Annals of the Bhandarkar Oriental Research Institute, vol. 81, no. 1/4, 2000, pp. 269–72, http://www.jstor.org/stable/41694622. Accessed 7 May 2022.
Iyer, P. R. Chidambara. “REVELATIONS OF THE FIRST STANZA OF THE MAHĀBHĀRATA.” Annals of the Bhandarkar Oriental Research Institute, vol. 27, no. 1/2, 1946, pp. 83–101, http://www.jstor.org/stable/41784867. Accessed 7 May 2022.
A. V. Raman, “The Katapayadi formula and the modern hashing technique,” in IEEE Annals of the History of Computing, vol. 19, no. 4, pp. 49-52, Oct.-Dec. 1997, doi: 10.1109/85.627900.

Review: The Kashmir Files

In one of the shocking scenes in the movie Kashmir Files terrorists line up 23 Kashmiri Hindus and start shooting them one by one. The camera moves behind the lone terrorist holding the gun. We see the face of the victim, and in the next instant, a bullet enters his forehead, and the body falls into the pit. The terrorist moves to the next Hindu and shoots him. The camera does not skip a single victim. Finally, to make up for a count of 24, the terrorist pulls in a little boy and shoots him. There was pin-drop silence in the theater as the movie ended on this note, and we all walked out silently. I mentioned “one of the shocking scenes” because this is not the most gruesome scene. There is one which I could not watch.

While there are many movies on the Holocaust, there is almost none on the Hindu genocide in Kashmir. As I watched this movie, which brings out an ignored past, I felt angry, sad, and horrified. Anger at how various governments did nothing for the Kashmiri Hindus, sadness at how we let it be forgotten, and horror at the brutality that was done. The movie demonstrates the total failure of the system, which stood by, turned a blind eye, and was complicit in the atrocities. Kashmir Files packs a powerful punch, and it’s a punch to your gut.

There is a reason why the movie — without the usual Hindi movie elite and mandatory Punjabi songs– became a critical and commercial success. The film is brilliantly made, and it exposes the elites.

Except for a few movies like Uri, Sardar Udham, Shershaah, or Ghazi Attack, most Hindi films tell the same tired story repeated and rinsed. The fashionable ones just copy “woke” ideas from the West. Kashmir Files is a different breed. The story is told through the eyes of a young Kashmiri, who was ignorant of the events of 1990. Falling into the trap of a treacherous and scheming university professor he is motivated to fight for aazadi. Switching to the past, the film shows what happened in 1990. This was when Kashmiri Hindus were asked to either convert, leave or die. This was when politicians formed alliances with terrorists and a time when Pakistani currency was returned as change.

The movie manages the challenge of telling the forgotten story of Kashmiri Hindus through the intense performance of Anupam Kher. The full impact of the violence is etched in his face, and we all experience his traumatic memories. The scene where he sits in a refugee camp with a box of two biscuits to when he walks around calling for the abrogation of Article 370 touches your heart. His transition from fear to sadness to numbness is one of the heart-wrenching performances by an actor in recent memory.

This is an event that the Indian “Ministry of Truth” has tried to suppress for the past 32 years. As part of writing this article, I searched up on some papers written about this incident and this is a gem by Haley Duschinski

Kashmiri Hindus are a numerically small yet historically privileged cultural and religious community in the Muslim- majority region of Kashmir Valley in Jammu and Kashmir State in India. They all belong to the same caste of Sarasvat Brahmanas known as Pandits. In 1989-90, the majority of Kashmiri Hindus living in Kashmir Valley fled their homes at the onset of conflict in the region, resettling in towns and cities throughout India while awaiting an opportunity to return to their homeland.
Haley Duschinski

A genocide was packaged as a voluntary exodus and then repeated by politicians, media, and intellectuals. This narrative was then sold to the public by the Hindi movie industry. Just watch Mission Kashmir, Haider, etc. The Malayalam movie industry, which shed copious tears over Gujarat, was busy re-reading Karl Marx while this happened in India.

Another reason this movie struck a chord is because it exposed the Leftists and their strategy. The Breaking India forces are called out, and the links between “eminent intellectuals” and terrorists are revealed. One of the interesting characters is the university professor portrayed by Pallavi Joshi. If you have read Breaking India, you know the playbook. There is an ominous dialogue she says, “The government might be theirs, but the system is ours.”

The movie brilliantly shows how fake news is created, truth is hidden, and how history is converted from “ashuddho” to “shuddho .” After watching this movie, you will not read the news the same way. It also calls out the current intellectual favorites, the Sufis, and their role in converting the Pandits many hundred years back. The technique was repeated in Malabar in 1921.

One of the most uplifting scenes in the movie is where we get educated on Kashmiri history. It answers the question: why should we care about Kashmir? Kashmir was the land of Kashyapa, Abhinavagupta, Charaka, Vagbhata, Panini, Vishnu Sharma, and Bharat Muni. It was the center of educational and cultural excellence and spirituality. Heard of Kashmiri Shaivism? Kashmir was the place for ambitious explorers seeking to grasp the vast reality of the mind, arts and sciences. A person from Kashmir was treated with respect like how we respect graduates from the best universities in the world. Unfortunately, it was this world that was ended by the Islamic invasion. The keepers of that knowledge were forced to flee at gunpoint.

The movies that have come in the past have tried to portray the terrorists as victims. However, Kashmir Files takes an unapologetic stance and shows what happened in the few days in 1990. Such movies need to be made to not forget the lessons from its aftermath. It’s not that such atrocities won’t happen again, but it will keep us on the alert to ensure that they are bought to light more quickly than in 1990 when the whole country looked the other way.

Book Review: Calling Sehmat

Book: Calling Sehmat by Harinder S. Sikka

In 1971, as the tensions between India and Pakistan were rising, the college girl Sehmat Khan agrees to marry a Pakistani Army officer to spy for India. It was a career chosen out of necessity, but she ends up being so good at it that she saved INS Vikrant from destruction. This is not fiction, but the story of a real life patriotic Indian, whose life was so extraordinary, that you would think it’s all made up. As she goes through her journey from a simple college girl to a spy who lived with the sole purpose of safeguarding India, you will find yourself in awe. She was the most beautiful Indian spy who single-handedly ravaged Pakistan’s security system.

The best part of the book is that it gives a well rounded portrayal of Sehmat as she goes through various phases of her life. A quarter of the book is about her college life which shows initial glimpses of her determination and passion. She got selected for a dance competition in which she was to portray Meerabai. She had seen her mother pray to Meerabai and for being the character, she spent hours in the college library, reading all about her. She danced with such intensity and absorption that she did not notice that her legs were bleeding.

Her transformation from college girl to a spy was to honor the wishes of her dying father who had instilled patriotism in her. Her philosophy was “there is no greater reward than to live and die for your country”, a lesson she got from her father. He had told her that there is nothing more disgraceful than being disloyal to the motherland. As a businessman who traveled across the border, he was instrumental in setting up a spy network in Pakistan.

Then you see another Sehmat, who sacrifices her college lover and moves to Pakistan. Her down to earth demeanor and good intentions earn her the trust of her immediate family, her father-in-law and her husband. It was due to her cleverness that they got promoted in their jobs and had career advances. It was during one scan of her father-in-laws office that she found the files which suggested that Pakistani submarines were targeting INS Vikrant.

Living behind enemy lines is not easy. The intelligence gathering techniques of 1971 could not be done remotely; it required acts of courage. The intricacies of these techniques and dangers it entails are covered well. There were many times she could have been exposed and she triumphs over those circumstances with her quick thinking. She even miraculously escaped including a bomb attack. She was a person who planned two steps ahead all the time and that saved her.

Eventually when she settled back in India, the pictures on her house demonstrated her beliefs. Her house had pictures of Bhagat Singh, Sukhdev, Rajguru, Ram Prasad Bismil and Khudiram Bose. In her private space she worshipped Allah, Ganesha, Krishna, Jesus and Wahe Guru. She was fascinated by Meerabai’s hymns.

I finished the book only because it’s inspiring to read about such unknown heroes. The book explores her fortitude and unwavering loyalty to India during a time of war. The initial part of the book about Sehmat’s simple life, her marriage and her activities in Pakistan are paced very well. The writing itself is really plain and starts meandering towards the end. It could have used multiple rewrites with a good editor.. I am not even sure why one chapter of a failed Indian navy attack was described. That would have been better in an appendix or could be the matter for another book.

Despite all the courageous self-assurance displayed by Sehmat during her mission, her life ends in tragedy. Well almost. Memories of the ruthless things she had to do haunt her. Since her life in Pakistan was messy, chaotic and non-formulaic, she ends up suffering from depression. The book describes her encounter with a fakir who gave her spiritual lessons from various scriptures including the Upanishads to get her out of her gloom. In turn she was attacked by Muslim fundamentalists in her area and it required an intervention from RAW.

Her life was about love; to her country, to her parents and to her college mate. There is also a movie based on the book, but it leaves out multiple dimensions of Sehmat. As always, the book is better.

Refuting AIT using Personal Names from Rig Veda and Avesta

Scheme of Indo-European language dispersal from c. 4000 to 1000 BCE according to the widely held Kurgan hypothesis By Joshua Jonathan (via Wikipedia)

There are many similarities between Avesta, the sacred texts of Zoroastrianism, and Rig Veda. Words are similar, like haoma (soma), daha(dasa), hepta (sapta), hindu (sindhu), and Ahura (Asura). Despite that, some of the words have reversed interpretations. For example, in Old Iranian, Ahura Mazdāh is the chief of the pantheon, and the daēuuas are considered demons or fallen gods. In contrast, the Vedic tradition considers devas as gods and asuras the demons.

The commonality of words suggests that these two cultures had a common origin and such an explanation comes from the Aryan Invasion Theory (AIT). The above map shows the scheme of Indo-European language dispersal. After spending time in Central Asia, a group went West and another to the East. The Westerners became Zoroastrians, and those who reached India became the Vedic people. Before the split, they spent time together in Central Asia, where the common culture developed.

According to Indian Marxist historians, Indo-European speakers had Central Asia as their habitat, and gradually over many centuries, they branched out in search of fresh pastures. According to them, these central Asian migrants wrote the Avesta in Iran and Rig-Veda in India. They argue that people who migrated to India were dissidents of the Old Iranian; hence you find a significant reversal of meaning in concepts common to both Avesta and Rig-Veda.

Evidence from Personal Names

The Rig Veda and The Avesta: The Final Evidence

While this is the view AIT presents, what evidence do we get from the sacred texts themselves.? In this post, I will lean on the arguments laid out by Shrikant G. Talageri in his book Rig Veda and The Avesta: The final evidence. Spoiler alert: His text analysis does not support the AIT picture.

Shri. Talageri uses many data points to argue against AIT, but in this post, I want to summarize one of his arguments based on an analysis of personal names. Personal names identify society in time; just look at the change in names from your grandparent’s time to yours. Similarly, you see interesting patterns when you look at personal names used in Rig Veda and Avesta. It definitely shows a shared cultural environment.

If you were constructing a mental model in your mind based on the AIT dispersal, the above picture would make sense, right? This is because the personal names, developed in the common period, then carried over to both the sacred texts. Hence the commonality.

The examination of the books reveals something different. The commonality of Avesta is not with the entire Rig Vedic corpus; it’s only with certain books. Shri. Talageri looks at the personal names mentioned in all the books in Rig Veda and Avesta and concludes that the commonality is with the late books of the Rig Veda.

When we say the commonality of Avesta is with the late books of Rig Veda, it implies there is a temporal ordering of the 10 books. The Rig Veda Samhita consists of 10 mandalas, numbered 1 to 10. It does not mean that mandala 1 was the first and 10, the last. The chronological ordering of the books is as follows:

Early Books: 6, 3, 7
Middle Books: 4,2
Late Books: 5,1, 8-10

Coming back to Shri. Talageri’s argument, he noticed that in the Early Books, names with basic prefixes were common and these prefixes were simple. For example

Su (Good) – Das
Deva (divine) -sravas
Puru (many) – panthas
Viswa (every) – mitra

These names found in the Early Books of Rig Veda are also found in Avesta. This might indicate the common origin theory very well. But, these names are found in the Middle and Late books of Rig Veda.

As we move in time and come to the Middle Books, there are four Rig Vedic personalities like Turviti, Gotama, Trita, and Krsanu referred to in Avesta. When we come to the Late period, there is a flood of names common to Rig Veda and Avesta. These are complex names with both prefixes and suffixes. In the book, Talageri lists about 4 pages worth of common names. Compare that with just four names in the prior period. There are just five hymns in the Early and Middle books that have common names. When it comes to the late books, there are 326 hymns

If the common period occurred before the Aryans and Iranians parted ways, then the Early Books of Avesta and Rig Veda should have common elements. Also, as these cultures evolved over time, the common elements should diminish. But, the data shows that Avesta evolved during the period of the Late Books of Rig Veda. It shows that the common culture of Rig Veda and Avesta occurred during the period of the late books, and Rig Veda books of the Early and Middle periods predate the Avesta.

We need to update our mental model to the above diagram.

The Final Sequence

Now that we have all the pieces let’s understand what happened. Among the ancient tribes of India, the Puru/Paurava are identified with the Rig Vedic Aryans. Around 3000 BCE, they lived around and to the east of the river Saraswati (See In Pragati: Book Review – The Lost River by Michel Danino). The proto-Iranians are identified with the Anu/Anava tribe. They were originally the inhabitants of north India of the Kashmir region during the pre-Rig Vedic period. During the later part of the Early Rig Vedic period, the conflicts during Sudas’ time forced them to migrate Westward. During the middle and late periods of Rig Veda, the proto-Iranians were settled in most western parts of Punjab and Afghanistan. They had continuous interaction with the Vedic Aryans, and the Avesta was composed.

Rig Veda and Avesta: The final evidence is filled with evidence against the Aryan Invasion Theory with some original research. This argument based on personal names is just one chapter of this book. Other evidence against AIT comes from the geography of Rig Veda, the internal chronology of Rig Veda, and the absolute chronology of Rig Veda. By analyzing textual data, Shri. Talageri shows common culture across Rig Veda, Avesta, and the Mittanis.

Samskritam Notes: Classification of Letters

(This article requires you to have some basic knowledge of Samskritam and uses Devanagari script in between)

I don’t know if grammarians of any other language have analyzed the letters of a language like Samskritam grammarians. Samskritam letters have been classified in many ways — from where the sound originates in the mouth to the amount of breath involved to the effort involved in saying the letter. In this post, I want to go over classifications based on length, tone, and nasalization.

In Samskritam, like most languages, there are vowels and consonants. In most Indian languages, they are kind of similar. For example, here are the Malayalam vowels. If you read the transliteration below the letter, you will find that your mother tongue has identical letters.

When it comes to Samskritam, the vowels are represented in the Maheshwara Sutras by the pratyahara अच् (See The brilliance of Panini). If you expand, अच्, you get the following letters: अ इ उ ऋ लृ ए ऎ ओ औ. There are just 9 letters.

The first letter is pronounced as “a” in both Malayalam and Samskritam. While Malayalam has “a” and “aa,” Samskritam has only “a.” Does it mean that Samskritam does not have a long a.?

In Samskritam, if you pick one of the vowels, it does not represent that single character but much more. For example, take the letter “a.” It’s not just one letter. It encompasses many different letters.

There are three different classifications of vowels, and they are based on

length (it can be short, regular, or long)
tone (there are three different tones or pitches at which you pronounce the letter)
nasalization (a letter can be said in a usual way and also in a nasalized way)

Length

Each vowel can be pronounced as either hrasva (ह्रस्व), deergha (दीर्घ ) or plutha ( प्लुत). Let’s say someone is mentioning the person named Krishna. They could say Krishna with a short ending and not elongating the end. That would be ह्रस्व or short. If they are calling on Latha, the ending “a” is long or दीर्घ. Now let’s say Krishna is far away in the field, and Yashoda calls him “Krishnaaa” with an elongated “a” for three beats. That would be a प्लुत. When you write a प्लुत letter, you put the number 3 next to it, to indicate that it should be elongated for three beats. Technically, ह्रस्व is of one matra of time, दीर्घ is two and प्लुत three.

If you put it into a table, it will look like this.

ह्रस्वाः	दीर्घाः	प्लुताः
अ	आ	अ ३
इ	ई	इ ३
उ	ऊ	उ ३
ऋ	ॠ	ऋ ३
ऌ	–	ऌ ३
–	ए	ए ३
–	ऐ	ऐ ३
–	ओ	ओ ३
–	औ	औ ३

Samskritam Aksharaprakaranam

As you can see, not all letters have all the variations.

लृ does not have a दीर्घ.
ए does not have a ह्रस्व. It starts off as दीर्घ
ओ, ऐ and औ does not have have ह्रस्व either.

The take away from this section is that, when you refer to the vowel अ, it refers to the three variations of अ, which are the ह्रस्व दीर्घ and प्लुत variations.

That’s not it.

Tone

Take the letter अ. You can utter it in a higher pitch, normal pitch, or low pitch. These three pitches are called उदात्त, अनुदात्त. and स्वरित

उदात्त is a higher pitch
अनुदात्त is a lower pitch
स्वरित happens when the उदात्त and अनुदात्त are combined, and you get the middle sound.

This is hard to explain verbally. So here are two videos where Vedic scholars demonstrate this concept. I visualize this as a sine wave. The उदात्त is the crest, अनुदात्त is the trough and स्वरित is the base.

Nasalization

Finally, you can utter a letter with a nasal sound or in a non-nasalized form.

These are referred to as

अनुनासिक (nasalized)
अननुनसिक (non-nasalized)

If you look at the अ mentioned in the Maheshwara Sutras, you can see that it has all these forms. If you take अ, it can have 3 lengths (ह्रस्व, दीर्घ, प्लुत), 3 tones(उदात्त, अनुदात्त, स्वरित), and 2 (अनुनासिक, अननुनसिक). Thus अ can have 18 forms. That is true for अ इ उ and ऋ. The remaining letters do not have three lengths. Hence they will only have 12 forms. So when you chant the Maheshwara Sutras, you should know that they have all these forms.

Who has ever thought about letters this way? Classifying and categorizing them in so many different ways.

References

संधिःby महबलेश्वरभट्ट्:
Lecture by Sri Varun Khanna at Chinmaya International Foundation

Taking Credit for Buddha’s Work

Having attention is the brain’s superpower, writes Amishi Jha in her book Peak Mind. Every moment, our mind is bombarded by signals from our sensory inputs. To prevent our brains from being overloaded, the brain filters out the unnecessary noise and keeps our attention on what’s important. Imagine that you are in a coffee shop. People are walking in and out, baristas are taking orders and making coffee while music is playing in the background. In the midst of this, you can focus on the conversation you are having with your friend. If not for our attention superpower, we would be paralyzed by the sheer load of information we have to process and act on.

While it’s a superpower, it’s hard to hold on to your attention. Over the past few years, I’ve squandered countless hours and a fair amount of money on productivity techniques and lifehacks to boost my attention. I have read books like Digital Minimalism, Deep Work, Focus, Atomic Habits, and the Power of Habit. I have learned techniques of using a Pomodoro Timer or using Time Blocking. I have done various productivity courses each having its own philosophy. All these techniques are really good, but they all fail for a simple reason. Attention is fragile. A notification ping on the phone and you drop everything and are scrolling infinitely.

A quick fix, you might think, is to just keep the phone in another room. That way you have outsmarted all the software engineers and psychologists who designed those addictive apps. Now try to focus on a task for 30 minutes. You will fail because your mind will start wandering. It has found an interesting thing from the past or a future activity to plan.

If you cannot hold your attention, the only thing you will achieve is to generate revenue for social media sites. At the same time, if you can better your attention span, you can achieve wonders.

Here is a recent example of someone deep in action with amazing focus.

In Game 1 of the 2018 Eastern Conference NBA finals, the Cleveland Cavaliers lost to the Boston Celtics 108-83. After the game, Cavaliers’ star Lebron James was asked about a stretch where the Celtics scored seven straight points. “What happened?” James repeated back to the reporter. He paused, and it seemed like he might dismiss the question, but then, “the first possession, we ran them down all the way to 2 [seconds] on the shot clock. [The Celtics’] Marcus Morris missed a jump shot. He followed it up, they got a dunk. We came back down, we ran a set for Jordan Clarkson. He came off and missed it. They rebounded it. We came back on the defensive end, and we got a stop. They took it out on the sideline. Jason Tatum took it out, threw it to Marcus Smart in the short corner, he made a three. We come down, miss another shot. And then Tatum came down and went ninety-four feet, did a Eurostep and made a right-hand layup. [We called a] timeout.”

It’s not just basketball. It works for anything you want to master. The challenge is in finding a technique that can help improve your attention span.

This is the end of the road for psychologists like Amishi Jha. They are excellent at identifying the problem, running experiments, and documenting the details. They know about various techniques used by successful people. For example, athletes use visualization as mental practice; golfers will practice swings in the mind and these mental rehearsals activate the motor cortex of the brain the way physical movement does.

Psychologists also know why many of the lifehack techniques don’t work. Imagine that you figured that time blocking is a wonderful technique. When you decide to focus for 30 mins on the presentation you are working on, your mind wanders. At this point, you have set goals, done your visualization, and are staying positive. The reason attention still wanders is that you need attention to implement any of these techniques, which is the original problem anyway.

At this point, science has given up. They can’t find a solution to increase your attention. Instead, in a sleight of hand, they offer you a solution – Meditation or Mindfulness or ancient teaching without the attachment of religion. This solution is not something found through the scientific process. It’s just an appropriation of a technique from the ancients.

This is not like when Einstein predicted that gravity can bend light and later experimentalists confirmed it. In this case, Buddha and his predecessors, the rishis of India had already proved that all of this works. These rishis subjected themselves to various techniques and came up with not just one, but many ways to maintain attention. They are the original scientists.

Now the research is simplified. Just prove that works by submitting it to folks in the army, students, firefighters, and whatnot. After running a battery of tests, they find that – hey this stuff works. Papers are produced, books are written and an expensive consulting business is started.

I just picked on Peak Mind because it was the most recent book I read on this topic. There are many others in this genre. They all follow a simple pattern of here is a problem and the answer in Buddhism, but without Buddha and karma and reincarnation. In a recent podcast, many high achievers admitted to practicing various dharmic practices. Hence it is lucrative to remove “otherworldly mumbo-jumbo” from Buddhism and sell it as “mindfulness” to corporates, hospitals, and stressed out people.

Demolishing the Aryan Invasion Theory in 1912

The Aryan Invasion Theory and its first cousin twice removed, the Aryan Migration Theory, are dominant theories that explain the peopling of India. Many folks wishfully think this theory has been debunked. Still, sadly that’s what’s being taught in universities and repeated in books. The Indian National Congress has more MPs in the Lok Sabha than the people fighting against AIT.

While browsing some papers, I came across this paper by Srinivas Iyengar from Madras University, published in 1912, which attacks the Aryan Invasion Theory. Mr. Iyengar lived during a time when some of these theories were constructed and he decided to tackle them. This article will look at Mr. Iyengar’s arguments and how he calls out selection bias.

He says

Emotion plays a large part in the manufacture of history, and any theory that soothes the vanity of a people is straightway elevated to the rank of a fact ; so today a scientific examination of the bases of the theory of a superior Aryan race is resented more in India than anywhere else in the world

Comparative study of languages started with the observation that the languages of India and Europe were related. Hence, there had to be a parent language from which all the European and Indian languages descended. This imaginary language was called Proto-Indo-European (PIE). At some point, India was considered to be the PIE homeland, but later it was moved to various places in Europe. Either way, we are considered to be a slice of that pie.

Mr. Iyengar mentions two points made by the invasionistas and refutes them.

The first invasion point is based on a significant body part – the nose. Foundational research on this was done 20 years before Mr. Iyengar wrote this paper. According to the British dude (the name does not matter) who did this research, the Aryans had a long head, a straight, finely cut nose, a symmetrically narrow face, a well-developed forehead, and a high facial angle. The purest form of the nose was in Punjab, where the Aryans first showed up. As you went down South, the nasal purity went down. (Rajnikanth’s nose was inferior compared to Manmohan Singh’s). This happened because when Aryans arrived, the previous occupants with their inferior noses retreated to the South.

The British dude who did this nasal science defined 2378 castes as 43 races based on their nasal index. Also, Indo-European, Dravidian, Austro-Asiatic, Tibeto-Burman linguistic groups were identified as different races with Indo-European speakers or Aryans at the top of the tree. Based on this mythology, the skeletons found in Mohenjo-Daro were classified as various races, primarily non-Aryan.

Mr. Iyengar asks: Wasn’t there many more invasions? Didn’t the Mughals, Persians, Greeks, and Huns all show up in India at some point after the supposed AIT event? What nasal standards did they bring? When the British genius measured people’s noses in the 1890s, around 4000 years had elapsed since the imaginary invasion.

This outdated theory was still taught at UCLA as recently as 2010.

The next piece of evidence for the invasion came from the Rig Vedic mantras. The composers called themselves Aryans and referred to another tribe they fought as Dasayus or Dasa.

In the scriptures, the battles were local and not invasions. The Aryans do not speak of displacing local tribes who were their predecessors. The Aryans have no memory of a distant homeland (“I miss the rhubarb pie of the Baltic”), nor do they have any memory of their trip (“Remember when Barack took the wrong turn at Qaemshahr and fell into the Caspian Sea”)

They remember living a settled life in the Punjab valley in towns and villages, tending to their cattle. The Dasayus were another tribe living similarly. The problem was that they both had two distinct ways of life.

The Aryans were fire worshipers, and the Dasayus were not. The Dasayus did not worship Indra or offer oblations to Agni. The Aryans loved soma and raided Dasayu territory to get it to provide as oblations to their gods. They had high respect for soma and considered Dasayu oblations to their gods as worthless. When the Aryans offered their sacrifices, they chanted verses from their scriptures, which the Dasayus did not. All of these led to violent disagreements.

How did the Aryans get these traditions which are different from the Dasayus? Were they bought by the invading Aryans along with their language? Considering this, Mr. Iyengar writes that no Indo-Germanic history seems to have reached India. The Indo-Germanic god, Dyaus, is not acknowledged as a god in the Vedic pantheon. Mitra is familiar to Vedas and Avesta but is not an important god. Indra is a minor god in Avesta. The prominence of the Vedic gods is purely an Indian development. A striking fact is that so few Aryan gods came to India. Even if some tribe came from outside, it was thoroughly Indianized like Curry Pizza.

Finally, Mr. Iyengar writes that the so-called Aryan conquest definitely was not the substitution of the white man for the dark-skinned one.

When all is said, there may still remain in the minds of some the feeling of doubt how a cult or a speech can travel by itself. The fire cult and the speech of the Aryas must have come to India in the wake of a peaceful overflow of people from the uplands of Central Asia into the plains of India, or been the result of a peace-intercourse between the Indian people and foreigners. But theories cannot be built on metaphors, and there is absolutely no evidence at present to guide to a solution of the problem

Mr. Iyengar did not write about this, but here is some interesting trade information. Long distance trade between the Indus-Saraswati people and rest of the world is not intriguing at all as there has been plenty of evidence for commodities from India appearing in far away places, even further back in in time. In Dhuwelia, a seasonal hunting site in Eastern Jordan, archaeologists found cotton thread embedded in lime-plaster dating to the fourth millennium BCE. Cotton is not native to Arabia. That particular species could have come from only one place in the world: Baluchistan, where it has been cultivated since the fifth millennium.

Queen Puabi, who lived in Iraq during the Mature Harappan period (2600 – 1900 BCE) had Harappan carnelian beads in her tomb. Following her, Sargon of Akkad (2334 – 2279 BCE) boasted about ships from Meluhha, primarily identified with this Indus region), docked in the bay. This suggests that ships from the Indus region journeyed all the way to Iraq about 5000 years back. If Indus-Saraswati people journeyed around the world before the Aryan Invasion, in what language did they speak to Queen Puabi?

To suggest that people can move only in one direction is plainly ignoring the trading culture of the Indus people. The existences of an Indus trading colony in Mesopotamia and the ancient trading hubs is nothing to sniff at.

References:

Iyengar, P. T. Srinivas. “THE MYTH OF THE ARYAN INVASION OF INDIA.” Journal of the Royal Society of Arts, vol. 60, no. 3113, 1912, pp. 841–846. JSTOR, www.jstor.org/stable/41340228. Accessed 13 Sept. 2021.

Are all ancient memories true?

Recently, a stone circle created during the Neolithic period was discovered near Wales in England. It has a diameter of 110 meters just like the more famous stone circle. The Welshian stone circle is also aligned on the midsummer solstice sunrise, just like Stonehenge. This similarity between the two circles proved a century-old theory that the original circle was created in Wales, dismantled, and dragged over to Wiltshire, where it stands now.

This incident was mentioned in an Anglo-Saxon myth recorded about 900 years back. The myth spoke of the wizard Merlin leading men to Ireland to capture a magical stone circle called the Giants’ Dance and rebuilding it in England as a memorial to the dead. Since it’s not kosher to trust “myths”, it was not taken seriously. This discovery shows that the “myth” had a kernel of truth.

Myths endure because there is some truth to them. They boil down some human experience to its core, making it easy to repeat and transmit. There is the tendency to think of ancient texts as either history or fiction with nothing in between. Usually, these texts blend stories, history, magic, supernatural elements, theology, etc. If historians and archaeologists had an open mind to peel through the layers of exaggeration and investigate, they might make discoveries that otherwise would have taken a lot of time.

Another example would be the discovery of the river Sarasvati. Displaying great familiarity with the Indian North-West, the nadistuti sukta lists nineteen rivers from the Ganga to the Kurram sequentially from East to West. According to the Vedic tradition, Sarasvati flowed between the Yamuna and Sutlej, a location mentioned in other texts.

When British explorers visited the region between Yamuna and Sutlej, instead of “mother of waters”, they found seasonal streams like Ghaggar, Sarsuti, Markanda, and Chautang. Synthesizing tradition, the Vedic texts, and the accounts of surveyors, geologists, administrators, and army officers, scholars identified the Ghaggar, Sarsuti, Markanda, and other small tributaries as part of the Rig Vedic Sarasvati. Historians like M. L. Bhargava, B.C.Law, H.C. Raychaudhuri, A.D. Pusalker, and D.C. Sirkar, along with many Western scholars, concurred.

Then, all ancient memories are not the same. Some are manufactured to rationalize a power grab or establish an earlier date of arrival, or rationalize conquest. They exist to create a truth.

A famous one is the Western mythology of Francisco Pizarro as a larger-than-life hero. According to this narrative, he was responsible for single-handedly conquering Peru with a small army. Conveniently left out was the fact that Pizarro was helped by a large army of native American allies and the battle was not between the Spaniards and Incas but between two Inca groups.

Another one is the Pocahontas-James Smith mythology, immortalized by the Disney movie. According to the popular narrative, Smith was about to be executed. As they were about to strike, Pocahantas threw herself on James Smith, and he is spared. According to a discussion in BBC’s In Our Time, this incident never happened. Pocahontas, who lived nearby, visited the colony often. Her age was around 10, making it unlikely that she threw herself to save a 30-year-old Smith. In a narrative written by James Smith in 1608, this incident is never mentioned. In another version written in 1624, seven years after Pocahontas died, this incident appears. Not just that, in his voyages, there seems to be a pattern; James Smith is saved by maidens three other times as well.

A popular one in Kerala is about the conversion of King Cheraman Perumal. Once a king — a Perumal, no less — was walking on the balcony of his palace when he spotted the moon splitting into two and joining back again. From a few Arab visitors, the king learned that Prophet Muhammad was behind this miracle. The king abdicated the throne, divvied up the kingdom, and set sail to Mecca to meet this man. He met the Prophet, converted to Islam, and lived in Arabia for a while. To spread the religion in his homeland, the converted Perumal returned to Kerala but died somewhere along the way. What does not smell right is that the mosque he established dates before the first mosques in Iraq (639 CE), Syria (715 CE), Egypt (642 CE), and Tunisia (670 CE), thus making it the oldest mosque after the first mosques in Saudi Arabia. Imagine this – a newly forming religion setups a mosque where it’s born, and the next one is in Kerala. There is a lot of evidence to show that this narrative is false.

Another one is the myth of St. Thomas. The myth says that a disciple of Christ left Jerusalem and came all way to Kerala to establish churches. According to Pope Benedict, St. Thomas went only as far as Western India. According to Romila Thapar, there is no historical evidence to the claim that he was martyred in Mylapore. According to her, the first coming of Christians is associated with the migration of Persian Christians led by Thomas Cana around 345 CE.

How do you know which ones to trust? If you pay attention to who benefits, you can get a clue. Brutal conquests required a mythological origin to erase the reality of a violent origin. The Pocahontas myth — the affair between a Native American and a White settler — gave imperialism a human face. This military and economic success required a foundational narrative, powered by literary conceit to justify land grabbing and the subsequent loot.

Sometimes, the absence of facts causes myths to be created. It could be to insert themselves into ancient antiquity like Cheraman Perumal’s myth. Considering the trade relations between Kerala and the Western world, it’s quite possible that someone went to Arabia and got converted. Elevating it to an elite gives respectability.

Fortunately, each of these can be verified. The ancients were not writing objective history for 21st-century historians. If the texts present a consistent tale, which agrees with archaeology, geology, and local tradition, it cannot be brushed away. The truth of ancient history is indifferent to our wishes, our politics, our religion.

Book Review: Breath by James Nestor

A long time back, in the Indus-Sarasvati civilization, some people had mastered the secrets of breathing, says James Nestor in his book Breath. The evidence is the meditating man seal or what we call the Shiva seal. It is from here that the wisdom spread to the world. The Indus-Sarasvati people discovered that breathing with different patterns — really fast, very slow, or holding breath — can cure diseases without medicines, influence body weight, and affect overall health. By influencing the nervous system and controlling the immune response, these breathing patterns can help a person live longer and healthier.

While the Yoga Sutras are well known, there are other ancient texts as well.

Thirteen hundred years ago, an ancient Tantric text, the Shiva Swarodaya, described how one nostril will open to let breath in as the other will softly close throughout the day. Some days, the right nostril yawns awake to greet the sun; other days, the left awakens to the fullness of the moon. According to the text, these rhythms are the same throughout every month, and they’re shared by all humanity. It’s a method our bodies use to stay balanced and grounded to the rhythms of the cosmos, and each other

This knowledge then surfaced worldwide, like Japan, Africa, Hawaii, and Native America. They developed breathing techniques and benefitted from the calming effects.

Two things make the book interesting. The first is when the author acts as a human guinea pig, trying out various techniques with breathing experts worldwide. These are not yogic techniques, but activities like Holotropic breathing or the Wim Hoff method or taking a carbon dioxide shot.

The other is when he explains what happens inside our body when you do these practices. Breathing is more than just the physical act. Medically it’s known that breath affects every single internal organ affecting heart rate, digestion, and moods. Deep breathing influences the parasympathetic nerves, which signals the organs to rest.

Often you see remarks like what’s there to learn about breathing, after all, it’s just inhaling and exhaling. The modern age has caused us to pay little attention to breathing. This has resulted in diseases like asthma, anxiety, and attention deficit hyperactivity disorder. Another aspect is that as we age, the lung capacity decreases, leading to high blood pressure and immune disorders.

The book acknowledges India as the source of all this knowledge. All the techniques the author tried, he says, comes from ancient Indian texts. The ancients people who did these experiments with breathing and discovered the possible miracles knew that breathing was not just inhaling and exhaling. They knew how to manipulate body functions by controlling their breath. They obviously knew a lot more than what Western science knows, like how the prana can control the mind.

When Buddhist monks chant their most popular mantra, Om Mani Padme Hum, each spoken phrase lasts six seconds, with six seconds to inhale before the chant starts again. The traditional chant of Om, the “sacred sound of the universe” used in Jainism and other traditions, takes six seconds to sing, with a pause of about six seconds to inhale. The sa ta na ma chant, one of the best-known techniques in Kundalini yoga, also takes six seconds to vocalize, followed by six seconds to inhale. Then there were the ancient Hindu hand and tongue poses called mudras. A technique called khechari, intended to help boost physical and spiritual health and overcome disease, involves placing the tongue above the soft palate so that it’s pointed toward the nasal cavity. The deep, slow breaths taken during this khechari each take six seconds.

There are a couple of issues with the book. While the book mentions Indus-Sarasvati civilization by that name, it also mentions the Aryan Invasion Theory. It has a fascinating twist – the Aryans came from Iran and not Russia. Second, the author gives credit to Indians for discovering the secrets of breathing, but to talk to a yogi, he goes to Brazil. Why not go to the land where it started and where it’s a living, breathing tradition.

If you were one of those skeptical about yoga and pranayama, this book would change the way you think about breathing. By combing ancient wisdom with scientific evidence and first-hand experience, the book distills the knowledge in an easy-to-read narrative. In the end, it advocates breathing slow and less through the nose as it sends the maximum amount of oxygen to the maximum amount of tissues.

Swami Vivekananda wrote that the breath is the fly-wheel of the body. In a big machine, the fly-wheel is set in motion first. That motion is conveyed to finer machinery until the delicate and finest machinery is in motion. “The yogi’s life is not measured by the number of his days, but the number of his breaths,” wrote B. K. S. Iyengar. The fact that a sick child would live to the age of 95 is proof of the book’s secrets.

Book Review: The Devil and the Dark Water

Author: Stuart Turton
Title: The Devil and the Dark Water

The book, The Devil and the Dark Water, set in 1634, starts when a fleet of spice-laden ships sets sail from Batavia to Amsterdam. Long before the British started looting the world, the United East India Company was the world’s wealthiest trading company. Among their outposts, Batavia was the most profitable. Navigational techniques were iffy, and the 8-month voyage was at the mercy of pirates, storms, and disease.

The lead ship, Saardam, has a set of interesting characters. First, there is the Governor-General along with his wife, daughter, and mistress. Another passenger is Samuel Pipps— an investigator who has solved many cases— jailed in the ship for execution at Amsterdam.

Then there is Old Tom, a supernatural demon, who previously wreaked havoc in various provinces. It possessed various wealthy nobles causing them to commit large-scale violence. It announced itself, in the provinces and on the ship, with a mark that resembled an eye with a tail.

Soon after the ship sets sail, stranger things begin; people get murdered. The narrative is that Old Tom is back — evident from his symbol, which mysteriously appears in random places — taking revenge. Old Tom whispered to others to murder, and one of his accomplices, a leper, stalked the cargo hold freely.

Since Samuel Pipps is a prisoner, it falls on his bodyguard Arent Hayes to find the truth. Hayes is not as talented as Pipps in figuring out a story after it has happened from bits of paper left behind. As Hayes starts investigating, uncomfortable truths about the past of various people surface. This is a ship filled with sailors for whom profit comes before principle, pride, and people. It seems they are all connected and have incentives for murder.

Such books, which are historical murder mysteries, are hard to come by. The last ones I read were the Snake Stone and its sequels. In a world where historical fiction means writing yet another book about the Tudor world, this book is like smelling air freshener in a fish market. Another positive is that the book is about the Dutch East India trade, which I do not know much about. Finally, the book’s locale, a floating vessel of wood and nails, make it unique.

The book is well written, bringing out the ship’s ambiance enriched by bilgewater with dead rats. There is mutiny, storm, and shady sailors who can murder anyone for a coin.

“Everybody thinks sailing is about the wind and waves. It ain’t. Sailing’s about the crew, which means it’s about superstition and hate. The men you’re depending on to get you home are murderers, cutpurses, and malcontents, unfit for anything else. They’re only on this ship because they’d be hanged anywhere else. They’ve got short tempers and violent passions, and we’ve locked them all together in a space we’d feel bad keeping cattle in. Captain Crauwels sails this ship, and I keep the crew from mutiny. If either of us makes a mistake, we’re all dead.”

Hayes follows the dictum of Pipps.

“Whether this is a devil dressed as a man or a man dressed as a devil, our course of action remains the same. We must investigate each incident, then follow the clues back to the truth.”

The book is a tad too long. It gets slow towards the middle, and you have to force yourself to read through to find out how a mysterious light could show up in the sea or how a “demon” could roam around a ship.