Samskritam Notes: Navigating Non-linear Thought with Sentence Structure

The boy goes to school from his mother’s home with a friend at 8 am to study.

In Ted Chiang’s short story, Story of Your Life, a few alien ships appear and orbit around the Earth. The aliens (called heptapods, because they have seven lidless eyes that ring all the way around the top of their bodies) send communication devices called looking glasses to communicate with the humans. Louise Banks, a linguist, is called by the military to assist in decoding the alien language. She soon finds that the alien sentence possesses several distinctive qualities that set it apart from English:

Instead of displaying multiple characters or “words,” the heptapods display a single pattern containing variations, such as extra strokes or flourishes. How the strokes in a given symbol are arranged visually provides the context for understanding how all the parts of the symbol fit together and, thus, its meaning.
The order of the “words” doesn’t matter. A heptapod sentence is presented as one symbol, and how each constituent stroke in any given symbol is oriented provides the context for understanding the nuance of each expression.
This way of expressing all ideas simultaneously, rather than linearly, as in human languages, results from the radial symmetry of the heptapods’ physiology. Since their bodies have no front or back, their language doesn’t either.
The writing is semasiographic and independent of speech, like the no-walk or right-turn sign.

While English forces a linear way of thinking, one of the interesting features of Samskritam is that, in a sentence, the order of the words doesn’t matter. You can switch them around, and the meaning remains the same.

For example, a sentence like “Rama is going to the forest” in Samskritam is written as रामः वानमं गाच्छति

It can also be written as

गाच्छति रामः वानमं
गाच्छति वानमं रामः
वानमं गाच्छति रामः

You can’t do this in English. You can’t do “Forest going to be Rama the.” It is possible in Samskritam because the word form changes by incorporating the preposition into it. This process is called vibhakti, and there are 7 types of them. (Technically, 8, but I will exclude Sambodhana from this). You might have mugged it as रामः रामौ रामाः …, but lets see what it means.

Here is a bit of a complex sentence: The boy goes to school from his mother’s home with a friend at 8 am to study.

There are 17 words in this sentence.

The first question to ask is: What is the verb? What indicates action?. That would be “goes.” In Samskritam, that is गाच्छति.

The next question is: who goes? The answer is “The boy”. In Samskritam, it becomes बालकः Since it is the subject, it is in the first vibhakti form बालकः instead of something else. As we look at other vibhaktis, this will become clear what other forms बालकः can take.

Thus, we have a simple sentence: बालकः गाच्छति. (The boy goes).

With the subject and verb sorted out, let’s find out the object. In this case, it is the school or विद्यालय:. Since it is the object, it cannot be in the first vibhakti form विद्यालय:. It will change to the second vibhakti विद्यालयं.

Now our sentence becomes बालकः विद्यालयं गच्छति

Next question: with whom? Answer: with a friend.

A friend in Samskritam is मित्रं . If it is “with a friend,” it becomes the third vibhakti. Thus मित्रं, which is the first vibhakti form of a friend, becomes मित्रेण.

Now our sentence is: बालकः मित्रेण विद्यालयं गच्छति

Next question: for what? Answer: for studying, which becomes पठनाय which is the fourth vibhakti.

Next question: from where? The answer is home or गृहं. But “from” indicates the fifth vibhakti, and hence it becomes गृहात्.

Next question: whose house? Answer: mother’s. Mother is माता. But since this indicates a belonging, it becomes the sixth vibhakti, and the form changes to मातुः

Next question: At what time? Answer: 8 am which is अष्ट वादनम् . Since this represents “at” a time, it becomes the seventh vibhakti or अष्ट वादने

Putting it all together, the sentence becomes बालकः विद्यालयं गच्छति मातुः गृहात् मित्रेण पठनाय अष्टवादने

Thus, 17 words in an English sentence become 8 words in Samskritam. This is because all the prepositions are now part of the word.

We achieve a few things due to this.

The first is compactness. By cleverly combining word endings and cases, Samskritam packs a lot of information into fewer words. In an oral tradition, this makes it easy to memorize texts.

Second, this makes switching the word order and preserving the same meaning easy. Hence our sentence can also be written as बालकः मातुः गृहात् मित्रेण अष्टवादने पठनाय विद्यालयं गच्छति. In English, the sentence follows a linear order. Scramble the words, and the meaning is lost. In Samskritam, poets and writers can play with word order for emphasis, rhythm, or specific effects. It unlocks a non-linear way of thinking and expression, allowing the Samskritam’s beauty to shine.

Finally, with each word complete by itself, we get a good idea of its relationship with other words. For example, when we see the word मित्रेण, it gives out a clue that it is the third vibhakti form of मित्रं and that it has a “with” relationship. Each vibhakti case acts like a flag attached to a word, indicating its role and relationship with other words in the sentence. So, regardless of the order, every word, with its own special ending, gives us hints about what it’s doing in the sentence, making it easier to understand quickly.

In the short story, the heptapods reveal that they know an entire sentence before it is written down. Instead of writing each element following the other, they write all of them simultaneously. As Louise learns this language, she realizes that it allows for more flexibility of thought. The English language is constraining for a species with simultaneous mode of consciousness like the heptapods. It explains why their language evolved that way.

Towards the end, it affects her way of thinking. She learns how to write without planning every stroke ahead of time. She sees ideas form in her mind’s eye as semagrams rather than words. Finally, her perception of time is no longer linear; she experiences future events alongside the present and understands her life as a whole rather than a sequence of moments.

References:

Based on Lecture 03: Sentence construction and its underlying logic by Prof. Anuradha Choudry, IIT Kharagpur.
Stories of Your Life and Others by Ted Chiang. This short story was made into the movie Arrival.

Samskritam Notes: Sounds and Vibrations

The above picture shows the organization of Samskritam varṇamālā in Devanagari script. First, there are the swaras at the top, followed by the vyañjanas. This sequence is the same in all Indian languages.

But why so? Why not in some other sequence? Why is क the first vyañjana or अ the first swara? In this article, we will look at the reason for such an organization of the aksharas. We will also see how the effects of the points of articulation were understood by Samskritam grammarians. Finally, we will also see what makes Om such a unique sound and how this ties to mantra sadhana.

Points of Articulation

This organization of aksharas is based on understanding how sounds are produced in the human mouth. In Samskritam, five areas of the mouth are important for producing various aksharas. Among these five areas, there is a progression from the back of the mouth to the front, forming the basis of the organization. The sound originates based on the contact between the tongue and these areas. Once you learn this, you will observe how the tongue shifts as you say different aksharas.

Let’s go over each area and see what sounds originate there. The following picture shows our vocal system with the vital sound sources marked.

The first position is the kaṇṭah or throat. When your tongue makes contact at the back of the throat to produce those aksharas those sounds are called the kaṇṭhya. To experience this, say क and feel where your tongue hits the mouth.

The aksharas that come from there are the following.

swaras	vyañjana	antastha	ushmana	ayogavāha
अ	कु		ह	visargah

Here अ means both अ and आ. In fact it represents 18 variations of अ (See: Classification of Letters)

Now what the heck is कु? This is a short form for क ख ग घ ङ. Instead of repeating those five vyañjana, Panini calls it कु.

To understand this short form, you have to get into the mindset of Panini. He was obsessed with brevity. If you can compress 8 bytes into 1, he would do it. In an oral tradition, there is limited memory, and you need to find ways to abbreviate. This kind of brevity helps develop a sutra to make it easy to remember. In this case, you can remember the sutra अ-कु-ह-विसर्जनियानां कण्ठः Look at the first three characters of the sutra – अ कु and ह. Then it adds the visarga and says all of these come from the kaṇṭah.

As you move up from kantah, you reach the talu at the back of the mouth. This is the place where your tongue touches your back teeth. To feel this, try saying इ very slowly and see how your tongue stretches at the back and pushes against the back teeth. talu is the pressure between the tongue and the upper back teeth.

The following sounds come from the tālu and are called the tālavya.

swaras	vyañjana	antastha	ushmana
इ	चु	य	श

Try saying च. Do you feel the contact of the tongue at the front of the mouth or the back? It feels like the front. If you are not feeling that pressure, you are not pronouncing it correctly. Next time pay attention. If you are going to events like Gita Chanting Competition, this will help.

The next spot in the mouth is the murdha. This is the roof of your mouth. These sounds originate when your tongue touches the top of the mouth. Try saying ट, and you can feel it. These are the mūrdhanya sounds.

swaras	vyañjana	antastha	ushmana
ऋ	टु	र	ष

The next place in your mouth is where the tongue hits the teeth. They are called the dantya

swaras	vyañjana	antastha	ushmana
ऌ	तु	ल	स

Now you can see the pattern here.

Finally, when the contact happens at the lips, it is called the oṣṭhya.

swaras	vyañjana	antastha	ushmana
उ	पु

What’s left now? ए ऐ ओ औ and व. These come from a combination of two places in the mouth.

ए and ऐ come from both kantah and talu. Hence it is called kantatalu. The best way to experience this is to say अ (kantah) and इ (talu) really fast. Then, you will end up saying ऐ. Now, if you start saying अ and slowly transition to इ, somewhere in the middle, it will transition to ए. That’s why it is known as kantatalu. ए and ऐ have some proportion of अ and इ and is actually a combination letter.

ओ and औ are produced by a combination of kantah and oshtah. Hence it is called kanṭhoṣṭhya. The same process applies here as well. Say अ (kantah) and उ (oshtah) really fast. You will say औ. If you start at अ and slowly transition to उ, you will say ओ. Remember how we saw that ए and ऐ have some proportion of अ and इ. Similarly, ओ and औ have some proportion of अ and उ.

Finally, what’s left is व. That’s a combination of dantah and oshtah. So it is a dantoṣṭhya.

Going back to our original layout of letters, we now see the format based on the points of articulation.

Nāsikā

There are one more places where sounds come from. The nose. There are five nasal sounds in the varṇamālā, the last five letters in the pillar. ङ ञ ण न म They are also called nāsikā.

But didn’t we say that these letters originate in various other places? So these letters need the original place in the vocal and the nose.

Anuswara & Visarga

What about the anuswara and visarga. The anuswara is just a nasal sound and takes on a variation of the vyañjana that follows it. Let’s look at the word संपदः. The anuswara is above स. Look at the vyañjana that follows स. That is प. Now in the varṇamālā, find the location of प. Move your finger all the way to the right, and you hit म.

The sound of anuswara becomes the sound of the vyañjana in the fifth column. Hence the word gets pronounced as sam-pada.

visarga is just the release of the breath. So, for example, if you have the word हरिः, then the ending इ remains as-is, and you release your breath.

Sounds and Vibrations

In Samskritam pronunciation, there is a conscious use of the breath. For example, say क followed by ख and watch the breath pattern. (If you did not feel any difference, you might not be saying ख with intensity). This is like a natural pranayama. Look at the breath pattern when you do the visargah. It is like a sigh, a natural de-stressor. If you take a swara like अ, there are 18 ways to say it with varying breath patterns. (See: Classification of Letters) Due to these varying breath patterns, there is a physiological impact on you. Like when you chant a mantra.

Thus these sounds don’t exist in isolation; they create an experience. Specifically, specific sequences have an impact on the mind and the body. For example, there is a systematic way in which the tongue touches the vocal system. This, in turn, causes the nerve endings to be simulated and hence the corresponding brain regions. The science of mantra believes that if you can use the right words to train your mind, sharpen its focus, and to channelize the divinity in the universe, you can rise above every negative tendency that holds you back and go past the shackles of your limited conscious mind.

Look at the mantra Om. It is made up of three sounds अ उ and म. अ starts at the throat and is the first swara the human vocal system can produce. उ comes from the lips and is the last swara the vocal system can make. Going from अ to उ covers the entire range of the vocal system. The final म is the settling down or containment of the sound produced.

Chanting Om is a mantra sadhana. Aurobindo says, “The function of a mantra is to create vibrations in the inner consciousness that will prepare it for the realization of what the mantra symbolizes and is supposed indeed to carry within itself.”

The basic principle of mantra sadhana is to practice the utterance of a sound with such intensity, fervor, and determination, that your whole being starts reverberating with that sound. You become that sound, and that sound transports you to another dimension of consciousness. Mantra is a systematized sound technology. The Samskritam sounds have been organized to affect the person chanting them. This comes from a deep understanding that everything in the universe is a vibration. The rishis knew that certain benefits could be achieved by creating those vibratory patterns through our vocal system.

References

Lecture by Varun Khanna at Chinmaya International Foundation.
The Sounds of Sanskrit: Its Alphabet by Prof. Anuradha Chowdry at IIT Kharagpur
The Ancient Science of Mantras: Wisdom of the Sages by Om Swami.

Postscript

The technical term for replacing क ख ग घ ङ as कु is udit

Bharat – A Civilization State

Bharat during Mahabharata times https://www.loc.gov/resource/g7651e.ct000605/

Recently the Member of Parliament from Wayanad, Kerala, stated that India is just a union of states. The mischievous subtext is that India is not a single nation but a collection of various nations like Europe. It also implies that the country is an artificial construct with nothing unifying the various states and territories.

This is not a new allegation. The MP from Wayanad had some illustrious predecessors. John Stratchley (some British dude) said, “The first and most essential thing to learn about India — that there is not and never was an India .” Winston Churchill (the British dude responsible for the Bengal genocide) said, “India is a geographical term. It is no more a nation than the equator.”

India was a nation in ways these people could never fathom. The concept of Bharat has been alive for many millennia and has culturally united this land. Ancient Hindus understood this. They made pilgrimages to various holy places around Bharat. Students understood this. They traveled around to get the best education. Saints understood this. Adi Shankara established various mutts are four corners of Bharat. Besides them, our grammarians understood this and united the country with Samskritam.

In this article, we will look at evidence of these. I will be relying on the narratives of some historians you would have never heard of, like Har Bilas Sarda, Radha Kumud Mookerji, and R. C. Majumdar. I picked the summary of their arguments from J Sai Deepak’s excellent book India, that is Bharat: Coloniality, Civilisation, Constitution. I will also rely on what my Samskritam teachers taught me about Paninian grammar.

Bharat as a civilization state

A few years back, I went from Kerala to participate in the Kumbh Mela. I was among the millions of Indians walking along the banks of Ganga and Yamuna for the holy bath. Our boat to the Triveni Sangam had people from Rajasthan and Bengal. Though we were from three corners of the country, we all had the same reverence for Ganga and Yamuna and faith that the Saraswati met the other rivers at the Sangam.

There are two aspects here. The first is that people across the land venerated the geography of Bharat. Rivers, mountains, hills — all have a sacred story and are remembered in hymns and prayers. The nation itself is revered as a mother. This is quite different from how the West views nature.

The second: people traveled across the land for pilgrimages. Visit to a holy place was a religious duty. Even before modern transportation systems arrived, people traveled long distances for this purpose. The lack of physical comforts did not stop anyone. During these long trips, pilgrims took breaks, creating a network of numerous sacred spots. These pilgrims did not think of the country as different nations but as a unified cultural entity extending from the Himalayas to the oceans. This combination of nature and faith generated patriotism and cultural unity, of which the Kumbh Mela is a perfect example.

These pilgrimage spots were centers of higher learning as well. Think of Benares, Nalanda, Mathura, Takshashila, Ujjain, Prayag, Kanchi, Madhura, and Nawadwaip. Students from all over Bharat went to study at these places. With pilgrimage spots and learning centers unifying this land, it is no wonder that Chaitanya and Adi Shankara traveled from one end of Bharat to another. If there was no cultural unity, establishing four mutts at the four corners of Bharat would not make sense.

These indicate that the people of Bharat had an expanded geographical consciousness irrespective of the political boundary of the kingdom they lived in. There was a civilizational oneness despite the diversity, and this unity existed before the invaders and colonizers showed up. This unity exists even now. Thus Adi Shankara was not limited in his Malayali identity but had geographical consciousness to treat Bharat as one cultural unit.

Unification through Samskritam grammar

There is the story of a child who went to the gurukul and found the going quite hard. He wanted to quit. So the father told him, “Even if you don’t study a lot, please study vyākaraṇam. Else, instead of saying swajana (my people), you might say shva-jana (dog) or instead of saying sakalam (everything), you might say shakalam (part)”. Pronunciation and intonation are important; else, the meaning will be unintended and sometimes the exact opposite.

Among the six Vedangas, vyākaraṇa or grammar, is considered the most important by Patanjali, the author of Mahabhashyam. Among the grammarians, Panini is the most famous for many reasons:

1. He organized Samskritam using brilliant techniques with four thousand sutras. Just look at the concept of pratyahara, an elegant and impressive in-memory language compression technique.

2. He incorporated the works of other Shakalya, Sphotaka, Senaka, and other grammarians into his work.

3. He did not just mention how words are formed but also their meaning and relation.

Due to Panini, vyakarana-darshana became an important field of study.

But beyond these, there are two crucial points where Panini shined.

Panini’s grammar has sutras for both Vedic Samskritam and non-Vedic Samskritam. For example, the plural form of देवः is देवाः in Samskritam, while it’s देवासः in Vedic Samskritam. Panini’s grammar has a sutra to address this. In Samskritam, there is a word called jahāra, whereas, in the Vedic texts, it’s used as jabhāra. If no grammar specified the rules, someone reading this could assume it as a typo and rewrite the word. Due to this guardrail, the Vedas remain like a tape recording from millennia back. This is why we say vyākaraṇam protects the Vedas.

Why does this matter? If not for this protection, a naughty Samskritam professor at Harvard could declare that the rishis made a typo in the Vedas. He could declare that the Harvard version of Vedas will fix this, and anyone who does not follow that is anti-minority and a Hindu nationalist. I am not kidding about this. Here is a case where the Vedas were misinterpreted to support the Aryan Invasion Theory. The preservation of personal names in Rig Veda has helped us understand how the various tribes migrated, giving a radically different view of the ancient world. Now, Panini could have left the Vedic Samskritam alone. That was language from a distant past. Instead, he saw a cultural continuity from the past use of language to his present.

Panini was aware of Samskritam used in different parts of India and their variations. So, he integrated all the variations into this grammar. If he just cared about his political boundary, he could have ignored the regional usage at a distant place. But he did not. He had the geographical consciousness to see that all these lands were part of one unified cultural unit. The political boundaries have changed in various ways since the time of Panini. However, the land of Bharata still has the same name and culture since those times.

Finally

The British treated Bharat as a collection of countries in a Eurocentric way. But that view does not work for India because we did not operate on European concepts of nation and state. India bounded by the majestic mountains and vast oceans was designated by one name – Bharat. The geography was marked out by nature itself. If you think of the concept of nation as a monochromatic picture, India is a civilization drawn with a dazzling array of colors. In this civilization state, there was cultural unity within a federation of creeds. Each of them had the freedom to preserve their special features and enrich the central culture.

By parroting old British propaganda, the Member of Parliament from Wayanad is just following the path of his great-grand father who wrote The Discovery of India which discovered India, but not Bharat.

The Katapayadi Number System

By Image: http://collections.lacma.org/sites/default/files/remote_images/piction/ma-31973398-O3.jpg Gallery: http://collections.lacma.org/node/171573 archive copy, Public Domain, Link

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.

Sanskrit Notes: Why Siddhanta Kaumudi?

(This article requires basic understanding of Samskritam grammar)

When it comes to Samskritam grammar, the definitive books are Panini’s Ashtadhyayi and Dhatupaatah. Then why do we have so many other books like vartikas, bhashyas and kaumudis. What gap do they address? Specifically, what does a book like Siddhanta Kaumudi adress? To understand that we need to start with the basics and go down in a systematic way.

Let’s start with a simple sentence

गृहतः कार्यालयं गच्छति

When you see this sentence and have no clue about Sanskrit, you will know that, this sentence is made up of three words.

It can split once again by separating the प्रकृति: and प्रत्यय as follows. In each section, the first word is the प्रकृति: and the second, the प्रत्यय

Can this be split even further, like how we can split NaCl into Sodium and Chlorine and then into atoms and other sub-atomic particles? How far can we split the words in Samskritam and what is the end beyond which we cannot split further? In Samskritam, that root is called a धातु. There are approximately around 2000 धातु and 480 प्रत्यय. All the known words are formed by a combination of these.

Samskritam grammar is essentially a reverse engineering of the rules of the spoken language. The language came first and then the grammar. If you are a grammarian, and want to construct the rules of the language, there are two ways of doing it.

List the rule for each word. This obviously does not scale. The real world example would like calling the name of each student in the school and asking them to come into the class.
Come up with generalized rules which apply to a broad category. Come up with exceptions to those rules. The general rule could be, everyone enter the class and the exception could be – except Rahul. This makes the encoding of the rules simpler and easier to remember.

List the rule for each word. This obviously does not scale. The real world example would like calling the name of each student in the school and asking them to come into the class.
Come up with generalized rules which apply to a broad category. Come up with exceptions to those rules. The general rule could be, everyone enter the class and the exception could be – except Rahul. This makes the encoding of the rules simpler and easier to remember.

Panini demonstrated that with just less than 4000 sutras, he could come up with all the rules for all the words in Samskritam. This was possible only because the approach he took was the second one.

Panini’s two books cover this

Dhatupatah – covers all the dhatu and their meaning
Ashtadhyayi – covers all the प्रत्यय, (Chapters 3, 4, and 5)

The Ashtadhyayi consists of 8 chapters and they cover the following topics

1, 2 – संज्ञा, परिभाषा, समासः, कारकं
3,4,5 – प्रत्ययाः
6, 7, 8 – संधिः, प्रत्ययानां योजनम्

Among the Sanskrit grammarians, the most famous are Panini, Katyayana and Patanjali. Katyayana wrote vartikas (explanatory texts) and Patanjali wrote mahabhashyam (great commentary). The books they wrote are succinct and does not contain examples of the rules. This makes it hard for a student who try to study the grammar.

Then came a second set of books called व्रित्तिग्रन्धा: These books have more details about the sutra, like how to split it, the meaning of these words, examples, clarification of doubts, etc. Among these the famous are काशिकवृत्तिः and प्रथमावृत्तिः These texts follow the same order as the sutras in Ashtadhyayi.

This becomes a problem if you are interested in one topic like समासः. The sutras for these are not together and hence a student following the original texts or the व्रित्तिग्रन्धा: will have to collate the related sutras and figure it out.

To address this issues, there came a type of text called the प्रक्रियाग्रन्धा: These are organized according to topics with everything related to संधिः in one place and everything related to समासः in one place. Famous in this category are रूपावतारः, प्रक्रियाकौमुदि. But these books had some issues and caused confusion. Then Bhattoji Dikshit wrote सिद्धान्तकौमुदि fixing all the issues among the previous books. He explained all the sutras, in the style of प्रक्रियाग्रन्धा:and corrected the issues with the previous books.

(Based on the lecture by Tilak Rao. If you are interested in learning Siddhanta Kaumudi, here is the playlist)

Sanskrit Notes: Order of Words

One of the interesting features of Sanskrit is that, in a sentence, the order of the words don’t matter. You can switch them around and the meaning remains the same.
Take for example a sentence like, Rama is going to the forest. You can’t say, “Rama going forest.” You need the “is” and “to the” to make sense of the sentence. The “is going” indicates that it is one person who is doing the action. Now, “to the forest” indicates that the forest is the object of the action.
In simple Sanskrit, you would write it like this
रामः वानमं गाच्छति
It reads, “Ramah vanam gachati”, When you say “Ramah”, it indicates one Rama. A forest is “vana”, but in the sentence, we wrote it as “vanam”. That indicates, it is the object of Rama’s destination. The “ti” at the end of “gacchati” indicates that it is one Rama who is going (not two)”. If there were many Ramas, it would have become “gacchanti”. Thus the “is going” and “to the” are built into the words themselves.
This makes it interesting. Now you can write

गाच्छति रामः वानमं
गाच्छति वानमं रामः
वानमं गाच्छति रामः

All these sentences mean the same even though the order of words are switched around. Since each word has the part which maintains its relationship to the verb, the order does not matter. Due to this, in poetry, you can switch words around to fit the meter. In Hindu tradition, almost everything is written in poetry form and this made it easier for an oral society to remember anything forever.
Here is a complicated sentence
भारत ! यदा यदा धर्मस्य ग्लानिः अधर्मस्य अब्युधानं च भवति तदा अहम् आत्मानं सृजामि
Take those words and resequence them and apply the sandhi rules, and you get the following verse from chapter 4 of Gita

यदा यदा हि धर्मस्य ग्लानिर्भवति भारत ।

अभ्युत्थानमधर्मस्य तदात्मानं सृजाम्यहम् ॥४-७॥

Here is an exercise. Try the “Rama is going to the forest” in your mother tongue and see how it behaves. Does it work the same in Dravidian languages and Indo-European languages? In Malayalam, it behaves exactly the same as in Sanskrit. In Hindi, it does not.
PS:

Based on the lectures of Varun Khanna at Chinmaya International Foundation
Gitapravesha by Samskrita Bharati

Three Stage Evolution of Mahabharata – jayam, bharatam, mahabharatam

There are clues in Mahabharata which tells us about how the itihaas grew to become the longest poem with over a lakh verses. Mahabharata is divided into 18 parvas with Harivamsha as the 19th. The core of it — around 24, 000 — verses are about the war between the Pandavas and Kauravas. Besides this, there are tales of gods, kings, sages, discourses on philosophy, religion, law and various asramas of life. We know that Vyasa was the composer who taught it to Vaisampayana who then narrated it to Janamejaya at his sarpa yagna. Ugrasravas, the suta, then narrated it to others at Namisharanyam. Recently I read a book — A short history of Sanskrit Literature — which elaborates on a theory on how Mahabaharatam came to be.
Here are three verses from Mahabharata which refers to three different lengths

This verse refers to the first stage that has over 8000 verses

Mahabharata – Reference to ashtau shloka sahasrani or 8000 shlokas
This is the reference to the 24,000 verses

Mahabharata – chatur vimshati sahasrim – or 24,000 verses
This is the reference to the third stage that has over a lakh verses.

Mahabharata – shata sahasram or 100, 000 shlokas

It is not just that the number of verses increased; the name of the itihaas changed as well. The very first line in adi parvam refers to it as jayam.

नारायणं नमस्कृत्य नरं चैव नरॊत्तमम
देवीं सरस्वतीं चैव ततॊ जयम उदीरयेत

Then it became bharatam and finally mahabharatam. Was it because it passed through three people — Vyasa, Vaisampayana, and Ugrasravas?

A short history of Sanskrit Literature, by TK Ramachandra Aiyar

The author of the book, T. K. Ramachandra Aiyar, thinks that the core of Mahabharata is the rivalry of Kurus and Panchalas. Their enemosity is historic. They quaralled for a long time and finally there was a union. The Yajurveda — which was composed in a nearby region — mentions this. The Kathaka Samhita, though speaks of a dispute between Vaka Dalbhya from Panchala and a Dritharashtra who is the son of a Vichitravirya, a Kuru. Over time, the kingdoms split again and engaged in constant rivalry. By the time of Mahabharata, the Kuru and Panchala kingdom were separate.
Prior to the war, there was a turn of events which caused the annexation of Northern Panchala by the Kurus. This is the incident, where Drona defeats Drupada using Arjuna. This event upset the balance of poweer between the two kingdoms. The Kurus were defeated in the war and the Panchalas won along with the Pandavas. (Here is an interesting explanation about the Mahabharata war, not as a rivalry between Kauravas and Pandavas, but as a war between Kurus and Panchalas).
With this background, here is the theory on what might have happened. The defeat of the Kurus would have resulted in various songs glorifying the victory of the Pandavas and their allies. Sutas would have sung this in various assemblies. This would have been Jayam. By the second stage, when it reaches 24,000 verses, the life of Pandavas was elaborated. Krishna was represented as an incarnation of Vishnu and Shiva and Vishnu become more prominent than Brahma. The epic became popular all over bharatavarsha and other additions like the stories of gods and sages were added and it became a treatise on dharmashastra. This was the third stage.
The book became an authority on dharma dealing with religion, law and morality. It was accorded the status of the 5th veda. There are land grants dating between 462 CE and 532 CE, which talks about the one-lakh verse Mahabharatam compiled by Vyasa. There are numerous literary evidence from Sanskrit authors on the stature of Mahabharata. From Ujjayini to Khamboja, the ithihaas was read in temples. It became a national epic.

Sanskrit Notes: Tenses

Learning Sanskrit by Avanish Tiwary (Flickr) — Learning Sanskrit by
Avanish Tiwary (Flickr)

Like any language, Sanskrit has the three tenses: the present, past and future. They are called वर्तमानकालः, भूतकालः and भविष्यत्कालः respectively. For the present tense, there is just one way of saying it. In Sanskrit grammar, it is called लट् लकार.
When we look at the past and the future it gets interesting. There is more than one way of representing the future or there are two लकार.

लृट्- Commonly used for future tense
लुट् – is used to represent अनद्यतन events which means any event that did not happen today. Used to refer to events happening tomorrow and after. Thus technically you cannot say,रामः शवः वनं गमिष्यति. The correct version is रामः शवः वनं गन्ता

When it comes to the past, there are three ways

1. लङ्घ् – अनद्यतन भूतकालम means, the event did not happen today.
2. लुङ्ग् – Used commonly
3. लिट् – It happened, but I did not see it with my own eyes