The Ashtadhyayi Framework

In Software Programming, namespace is a very important concept. It is a context for identifying something uniquely. I strongly believe if a proper namespace or naming convention is not conceived, the ideas conveyed within the namespace will also be poor. Some examples are: domain names, namespaces in xml/xsd, package names in java which are mandatorily related to a folder hierarchy. In .Net also there are namespaces, though its not correlated to folder hierarchy, which I believe allows for ample confusion. The more the conventions, the lesser the code complexity.


Over the years I have reviewed how programmers have used package naming conventions in the Java world. In general there are two flavors of naming conventions: type-based and feature-based. Some used both conventions at the same time, I'm ignoring them as mutants.


Some examples of type-based conventions are com.acme.data, com.acme.controllers, com.acme.service, com.acme.exception. Here all the classes are grouped under "types" of the classes. While its easy to create and maintain such a structure, its really hard for a new-comer (or even for a revisit) to understand the functionality, unless all the classes are fully scanned and understood.


Imagine a "Purchase Order" functionality, which has the following classes:


com.acme.data.OrderInfo, com.acme.data.PaymentInfo;
com.acme.controllers.OrderForm, com.acme.controllers.PaymentForm;
com.acme.service.OrderService, com.acme.service.PaymentService;
com.acme.exception.OrderException, com.acme.exception.CreditCardException, com.acme.exception.StockUnavailableException


To understand the Purchase Order functionality, one should scan the whole hierarchy and associate the objects mentally. In a complex project, this would take several days to understand the code when there are several controllers, services etc especially if the classes themselves are named poorly or ambiguously.


The feature-based approach will define namespaces like: com.acme.order, come.acme.payment. So the classes will be


com.acme.order.OrderInfo, com.acme.order.OrderForm, com.acme.order.OrderException, com.acme.order.StockUnavailableException;
com.acme.payment.PaymentInfo, com.acme.payment.PaymentForm, com.acme.payment.CreditCardException.


Such grouping immediately draws focus on understanding the functionality. It is also easy to reverse-engineer the code into subject areas. One is not better than other as both techniques have merits. Every programmer would have written some kind of framework code. In a typical non-business framework code type-named conventions make more sense. For eg, the Spring-framework is arranged based on type-based packages. If I need to extend from a controller, it makes most sense for me to search for a "controller" package. In an application, feature-based package makes a lot of sense.


Now, what does pANini have to do with all this? Its illustrative to infer that there exists a very similar structure parallel in the sanskrita grammar literature. pANini's ashtadhyAyI is known for its outstanding brevity. However one cannot understand its application without pretty much scanning the whole work. Take for example the formation of word "rAma:"


arthavat adhAtu apratyaya: prAtipadikam (1.2.45)
svaujasamautchhastaabhyaamngebhyaambhyasngasibhyaambhisngasosaamngyossup (4.1.2)
upadeshe ajanunaasika it (1.3.2)
tasya lopa: (1.3.9)
sa sajusho ru: (8.2.66)
kharaavasaanayo: visarjanIya: (8.3.15)


Just to form the word rAma: ("application") one has to understand 1, 4, 8 chapters, pAda-s and several sutra-s and anuvritti-s within. Why? Because pANini has grouped his sutras based on "types". Package is called "adhikAra" in sanskrita. Each adhikAra is a namespace: pratyaya, samasa, samhitaayam, paribhasha etc. The order of these sutras are extremely important. Just like the folder hierarchy: com.acme.order is not the same as com.order.acme. Changing of the order sutras will invalidate the structure and the meaning too. There are no examples within Ashtadhyayi, just like you wont find an example within a framework itself.


The sanskrita vyAkarana literature that followed (a big list including Katyayana's vartika, Patanjali's Mahabhashya, Kasika vritti, Siddhanta Kaumudi, Laghu Siddhanta Kaumudi, Paribhasha indusekhara and so on) attempted to re-arrange sutras according to functionality  or "prakriya". They also supplied numerous examples ("test cases") and counter-examples ("negative test cases"). There are fantastic precise examples and counter-examples in Siddhanta Kaumudi by bhattoji dIkshita.


As a good programmer, lets end with good comments. If pANini had to write a javadoc header for his grammar, this is pretty much how it would have looked:


/**
* The Ashtadhyayi Framework
* vyAkaraNa.sUtrapATha.ashtAdhyAyI.framework
* @author pANini
* @since 1500 BC
* @version १.०.०
* @see SAkalya, SAkatAyana, SphotAyana, yAska etc. frameworks
* @see Siva-sutra, dhAtupATha, gaNapATha, uNAdi, Chandas
*
* This framework provides a complete set of base sutras, definitions, interpretations, sandhis, rules and exceptions for generating an infinite number of sentences in natural language using a finite set of rules.
*
*

* WARNING: Do not modify the order of the sutra-s without understanding the complete framework.
*

*
* Code Metrics:
* Number of lines of code: 3986
* PMD index: 0
* Cyclomatic complexity: 1000
*
*/

The c(o)urse of events

The Puranas are a great source of stories, generally counted as 18. Unfortunately these are wrongly refered as "Mythological stories". The context of "mythology" is more of Greek and Roman origin. The puranas were named "mythology" based on comparison of other cultures. Even Amar Chitra Katha, a pioneer in Indian story comics, categories these stories under "Epic and Mythology", which is according to me a misnomer. People who narrated the puranic stories to others are called paurAnikas and commanded great respect. If Puranas are mythology, can we call the paurANika's as mythologists? Several Puranas seem to be based on actual historical events, of course with a great flight of imagination, that took place in and out of the land of Bharata. I make a conscious effort to never call these 'mythology', instead call them as puranic.

In the fables like panchatantras, jataka and hitopadesha the story moves towards establishing or concluding a certain moral. While in purAnas, moral is not central, though the overall moral-base is "good triumphs over evil". The purAnic stories may not have any logical beginning, proceeding or an ending. Events happen due to fate, somebody's wish or just because it is so. There is a lot interplay, connections, tangential references between stories, yet there are plenty of contradictions too.

But There is one fundamental theme that occurs throughout the puranas and itihasas. Before we getting into that, lets try to answer a few questions:
Why did

• Vishnu take 10 avatars?
• Krishna die ?
• vAli die at the hands of Rama ?
• Dushyanta forget Shakuntala ?
• Hanuman hesitate to cross the ocean?

The answer is a simple "Because of a curse". Every little incident that happens in a Purana has a story behind it and it usually begins or ends in a curse. Curse makes fiction or adaptation very easy, I wonder why the modern writers do not use it effectively; it could be used as an effective tool for turn of events.

Let us pause for a moment and think about the word "curse". It does not even come close to convey the meaning of the actual word used in Samskrita - "shApa". The word shApa has so much overloaded context in it, the word 'curse' simply does not carry that. Just like dharma, papa, punya, guru do not have any direct translations, it is hard to bring out the complete meaning of shApa in "curse". I will try to use the word shApa throughout this blog.

In saying "Im giving you a curse" vs "Im giving you a shApa", the latter definitely sounds effective and more realistic. Try and say it in different Indian vernaculars. And try to use a mega-serial heroine (or a truly filmy mother) tone: 'mein tujhe shAp deti hoon, tum vinAsh ho jaoge'; 'unakku shAbam kodukkaren, nI nasamai povai'; 'ninage shApa kodtini, nI nAsavagi hogu'. All these certainly sound effective and make good one-liner cliches for mega-serials.

In the PurAnas every one or other is found to be giving shApa to others. To some extent one is lead to believe that ones fate is not in one's hands but in the mouth of others. There are certain characters in the purAnas, whose only job is to just give shApa to somebody.

The famous among them is durvAsa, who literally has a "template shApa" in his mouth. If somebody sneezes and he doesnt like it, poof, there is a shApa. If he comes for alms, and you are little bit late in giving it, poof, he lets another one. He is a very interesting character though; lot of stories would not have happened without him. Do you know the actual birth of durvAsa? Once Shiva was just getting angry at silly things. Parvati was getting very uncomfortable at Shiva's behavior. So she says to Shiva "durvAsam bhavati me" (Your presence is very difficult to me). Shiva realises it, feels ashamed and does a classic "spin off" of this anger into a new person and thus durvAasa is born. He appears in several purAnas, the primary aim being to give shApa to someone. The puranic writers have a convenient character in Durvasa where he is summoned at-will to alter the fate of any character.

Sometimes the shApa is very complex, other times the reasons are plain ridiculous. In general the rules of a shApa can be categorized thus:

• A shApa can be given for the silliest of reasons
• Every one - all mortals, gods, asuras, rakshasas, even the Supreme Lord are subjected to shApa; there is literally no-one guaranteed to be shApa-free.
• Once given, the shApa can never be taken back
• shApa-s cannot be amended directly, but an escape route can be provided, or 'eased-out' in phase
• - All shApa-s have a mandatory expiration date and ends in shApa-vimochana.
• At the end of the expiration period, the receiver can either be restored to original state or become somebody new
• In most cases, the shApa can be redeemed only by the giver, others cannot change this
• A shApa can be counter-shApa-ed. The reciever can in turn give another shApa to the giver

There are cases where A curses B and B curses A in turn. This is called a shApa-deadlock. They really have to timeout each other to obtain the shApa-vimochana. There are also cases where a subsequent shApa renders a previously given shApa ineffective (although temporarily) because of the impossibility of the event. Once Silavati was carrying her leper husband Ugratapas. Sage Mandavya sees the amorous state of Ugratapas and curses that he will die at sun-rise the following day. Silavati, now curses that sun will not rise the next day, thus making the first shApa impossible to happen.

Most purAnic characters are prompted to act only because they are given a shApa. In fact we see this even in Samskrita literature. The most original of Samskrita works, Kalidasa's mEghadhUta, starts off with a brilliant line: "A certain yaksha, because of some shApa put upon him, was separated from his love and lives in the foothills of rAmagiri in the vindhyA mountains". KalidAsa doesnt bother to say what is that shApa, but just a passing mention of it was sufficient enough to convince us that the yaksha had indeed done something miserable and is suffering from it. Think about it: just one word puts the whole poetry on course. If the concept of shApa was not that powerful, kAlidasa would either have to explain why that yaksha got stuck there, or give some other logical reason behind it.

Even though we think that shApa can be effecitvely given only by rshis, there are stories where any Ram, Shyam and Hari gives shApa to anybody. Were people's words that really powerful in those times? Why were the rishis the primary shApa-givers? Was their life-long meditation not helping them to restrain heir anger? And where is all that power now? Why is shApa not that effective in kali yuga?

Here are some of the popular shApa-s and the course of events:

Giver - Receiver - Course of events

• Durvasa - Sakuntala - Sakuntala forgets to invite Durvasa; Dushyanta forgets Sakuntala
• Gautama - Ahalya - Indra seduces Ahalya; Gautama turns her into stone; Rama rescues her
• Durvasa - Airavata - Airavata tears Durvasa's garland gift to Indira; Durvasa curses Gods will become old; Leads to finding of Amrutam
• Vasishta - Apa (Dyau) - Ashtavasus took cow Nandini by force; Vasishta cursed 7 would be born as men and die immediately except the main thief, who would live long (Bhishma)
• Bhrgu - Vishnu - Vishnu kills kAvyamata, mother of Sukracharya in a battle; Bhrgu curses Vishnu to have countless incarnations to atone the sin of killing a woman
• Some sages - Yadava dynasty - Yadavas make fun of some sages; they curse the whole dynasty will be destroyed, including Krishna
• Srngi - Parikshit - Parikshit puts a dead snake around a rishi; Rishi's son curses that Parikshit will be killed by snake Taksha in 7 days
• Matanga - Vali - Matanga curses Vali cannot enter RshyamukhA mountains; so it becomes a safe place for Sugriva

Avatar 9.5

Narada, the celestial sage was restless. It has been ages that he had done any "kalaha" in devaloka. I don't think that there is any better word than "kalaham" to describe Narada's acts. The closest I can come to translate is "mischief" though that word carries more connotations to it than just "mischief". If you know of any such word in English, let me know. But I bet there isn't.

Sage Narada is a composer and singer. Just as Lord Kartikeya got a favorite raga Shanmukhapriya, just as Goddess Lakshmi has a favorite raga Ramapriya, just as Nandi has a favorite raga Rishabhapriya, just as Lord Shiva has a favorite raga Rudrapriya, and Vishnu has a favorite raga Shri, Narada too has a favorite raga - "Kalahapriya". I dont know its arohana or avarohana - but I can take a guess to say that it has too much of vakra sancharas in it. He probably is the creator of this raga and therefore he is sometimes called as "Kalahapriya Narada".

When was the last kalaham he did? He couldnt even remember it. It was probably in Thiruvilayadal. But now he was determined. But the most difficult part is: "Where shall I start?".

"Ah! By the way Indra is throwing a party tonight. They had won a cricket match against the Asuras. In Krita yuga, devas and asuras fought over each other by churning the milky way. Now that those galaxies are already much dispersed and left with reduced density, there is nothing much to churn. As far as Kali yuga is concerned, a simple one day match could decide who won. Yugas have really changed. Whoa! That was a really exciting and gripping match. The Asuras fought really well, I should admit. Their coach Kripacharya is really shrewd one. And their tail-end is really good. The last pair of tail-enders, Rahu and Ketu batted out the final five overs. For the Devas, Agni was the best pick of the bowlers. His fiery first few overs stands a class apart. And Varuna's spell is worth mentioning.

"The devas chase really interesting. The physiotherapist Danvantri was around to heal the wounds if any caused by asura bowling. Anyway the devas have won and have a reason to celebrate. It would only be proper to imagine that they are all getting drunk over the victory". Thinking thus Narada reached the hermit of Tumburu.

Tumburu wasn't home. What happened to this guy? Has he gone to party out? He too has changed a lot in recent yugas. Earlier he used to be a lonely singer roaming in Himalayas. Now he has got a band! Imagine the nerve of him to form a band! It has a funny name too - "The Band Harvas".

The sound from the Indrasabha hall was loud and garrulous. Chanting the mantra "Narayana! Narayana!!" Narada reached the party. He stood in a corner and started observing the dancing devas and devis. Thumburu was on a podium with his Thambura, joined with a couple of Gandharvas from Chitrakoota. One had a veena attached with a strap hanging around his shoulders. Another was carrying a dholak on one hand, a WinZipped version of dumru on the other hand and some flute like instrument was in front of his mouth. Don't ask me how he was holding it. It is a gandharva magic. Chitrakoota, the capital of Gandharvas has now got a new sobriquet - "The Gandharva Motown". The people born there are prenatally skilled in music. When the citizens rise in music, take bath in music, go to bed in music and give birth in music, it is no surprise that everyone is skilled in music. "The Band Harvas" were singing a song that was hardly legible. Is the song really in Sanskrita? wondered Narada.

The devis were dancing in the center of the hall. Fresh faces were seen apart from the traditional Ramba, Urvasi and Thilothama. The Devas were also dancing scattered around the hall, some with devis and some alone. There in the corner is Indra, seated in a table, all alone. He had a large pitcher in his hand and seemed to be thoroughly enjoying the soma rasa. Well, his enjoyment is going to be short-lived, as Narada approached him.

"Narayana, Narayana, Congratulations on your win O Indra", Narada began in his inimitable style.

"Oh! Is it Sage Narada I see? Pranam O venerable sage! What is a sage doing in a party for Devas?" Indra too wasn't less political in his reply.

"Just checking on you, in case I have anything to report to Shiva, the God of Gods". Narada said in his inimitable sarcastic tone. Indra now realized that he was talking to Narada, the unbeatable in creating kalaham-s and is a favorite of Lord Vishnu. He thought to himself "If this guy reports to Lord Vishnu about the fun the other devas are having in this party, I could be in trouble. I better not mess with him". What he didn't realize was he had already fell for the sage's plot.

"What can I do for O veritable Sage" asked Indra.

"Nothing Indra, I just came to congratulate you. Your captain's knock helped the team win the trophy! I could not have imagined what would happen if the Asuras had won..."

"You are right! It is because of your support we won..."

Narada hadnt yet finished his previous sentence: "...especially when the stakes are high !"

Indra willing to change subject said: "Victory is all that matters! O Narada"

"You are right O Indra! But aren't you getting a little selfish?"

"Wh... what .. what? Can you explain me O Celestial Singer?" Indra stumbled a bit.

"Your bhaktas in Bharatavarsha are getting humiliated with defeats. The weakest teams, when they meet the Indian team on the field, emerge the strongest with greater self-confidence. Is it enough if you win against the Asuras? Should you not help the Indian Cricket team? They pray you and Agni for helping them. They even pray Varuna to bring rains when they are on the edge of defeat! But nothing seems to happen. If I may say so, Lord Vishnu is a bit upset that bhaktas are ignored..."

Indra was frightened. He remembered how Vishnu protects his bhaktas at anybodys cost. If this guy complains to Vishnu that he is ignoring the bhaktas and partying out, he may find himself in trouble. He quickly wanted to amend for that.

"O Narada, the giver of generous boons! It is due to my ignorance that I am in such an ignorance. Could you please advice me on what can I do?"

"I don't really know O the best among Devas! But I think its time for Indian cricket team to have some person who can really win matches. May be you can think something along those lines..."

Indra became cautious. What is this guy getting at? If I send some deva to play in the Indian team and if the team still loses, because of other 10 members, he would yet be blamed. If he didn't send any deva to join the team he would be blamed again for not taking care of bhaktas. A catch 22 situation. This Narada is very clever. But wait a minute, here is an idea...

"O Sage Narada! The Indian team loses consecutively and the commentators are heard saying that 'only Bhagavan can help them'. Why dont we ask Lord Vishnu to take an avataar to play for Indian team?"

Narada was smarter than Indra on any account. "O Indra! That is a fantastic idea! But dharma hasn't really been defeated yet. Vishnu is scheduled to take the Kalki avataar only at the end of the Kali Yuga. Measured in bhuloka-years there are about 427000 years left... But if you along with other devas can convince Vishnu to take a temporary avataar for the protection of his bhaktas, he may concede to your request. After all he is the all merciful Paramatma..."

Indra got the hint. The next morning he summoned all the devas and briefed them about the mission. The devas hadn't recovered from hang-over and so didn't have much to object. And so they all marched to "Kshirasagara" chanting the thousand names of Vishnu.

The dvArapAlakA-s were surprised to see the devas' sudden visit. Indra approached them and offered salutations "Pranam to dvArapAlakA-s"

"Pranam O Indra" they said in unision. "And congratulations on winning the trophy!"

"Why thank you" replied Indra. "I have come to offer my prayers to Lord Vishnu and talk to him about a burning issue."

The dvArapAlakA-s said "You are very welcome O King of the Devas"

Indra followed by other devas reached the sanctum sanctorum. "Namo Narayana" said the devas in unision.

"Welcome O Indra and Devas! I congratulate you on winning the trophy..."

"Its all your mercy O Lord! Without you can a ball swing or reverse-swing? Without you can a bat be wielded? Without you can a wicket be taken? Without you can the umpire raise his finger? Without you can a fielder catch a catch? Salutations to you whom the ball cannot beat, whom the bat cannot miss, for whom there are no boundaries. Salutations to you the effulgent one, who is neither the game played nor the game not played nor both, neither the victory nor the loss nor both! Salutations to you O Existence-Knowledge-Bliss!"

Lord Vishnu smiled and said "What brings you here O Indra?"

Indra said "O Lord! It is said that the wise ones should not lose their head on their victory. Even though we won against the asuras we still are not rejoicing. We are worried very much about how our bhaktas are being defeated day-in and day-out against all the opposition teams. We have come here to request you to help our bhaktas in re-strengthening the team and instilling confidence in them. We would like you to take an avataar to play for Indian cricket team"

Lord Vishnu smiled again and said politely "O Best among Devas! I take avataar only on purpose of defeating adharma and not because of the defeat of Indian cricket team. The Indian team doesn't win because they don't bat well, bowl well or field well. They are paying for their own karma. It is nothing that I can do about!"

Indra didn't relent "But is it not in your realms to take care of the suffering and the anguish of the bhaktas? If not for the Indian team you should at least take an avataar for the cricket fans. It is aching to see the fans spend money and cheer up for the team, but return back from the stadium disappointed. Is it fair? Even poor Indian families buy new TV sets to watch their team play, yet they are disappointed by their team due to lack of application? Is it not disheartening? At least for the sake of the fans you should take an avataar and play in Indian team! Only you can take an avataar so that not only will the Indian fans relish your game, but every cricket fan in the world would love to watch your game. It is possible only by you, O Lord of Lords, O Purushottama, not by us, mere devas!"

The All-merciful Paramatma was moved by the pleading of Indra and other devas. "Your wish will be granted O Indra! Even though I am scheduled to take Kalki avataar only by the end of the Kali Yuga, for the protection of the Indian cricket, and the defeat of other teams, and to establish the Cricket Dharma, I concede to take an avataar".

The Devas were pleased. They showered flowers on the Lord. They chanted mantras to please Lord Vishnu and shouted "Om Peace be with all Om".

As always, Narada's kalaham has ended in a good note. For Vishnu now has a job to do. For the Indians the Lord himself has arrived to save Indian Cricket.

And for the rest of the audience in the world - well, they simply have to watch Sachin Tendulkar bat.

(Note: I wrote this article almost 12 years ago when Sachin made a superlative century against Australia in Sharjah. I think the article still holds true and is a tribute to him for his 200 in ODI).

Fonetiks

Recently when I was driving my kid to school, I thought of playing on phonetics with him. With my increasing frustration and disillusionment with the amount of effort one has to put to spell English and remember the alphabet-sequence and my increasing understanding of Sanskrita, I wanted to see how kids react to phonetics of something they have not heard so-far.

The experiment contained of pronouncing a letter and finding out the origination of the letter in the position of the mouth. It also helped he was not seeing my face and just hearing the sounds. The SikSha SaStra (lit. science of phonetics) goes very deep into the subject and literature has been written around it over the span of 2500+ years.

The conversation went like this (all his responses were after some thought).

Me: Tell me where does the sound 'a' come from?
He: (after some thought) throat.
Me: Tell me where does the sound 'ka' come from?
He: throat
Me: Whats the difference?
He: the tongue touching.
Me: Tell me what happens with 'ca' ?
He: the tongue goes and touches up.
Me: Now repeat after me ka kha ga gha ~nga (like the ng in sing)
He: (repeats)
Me: Where does the sound ~nga come from?
He: throat
Me: where else?
He: (does not catch on first, then very doubtfully) nose?
Me: Tell me what happens with Ta (like T in Patrick)
He: tongue rolls up.
Me: Whats the difference? Stop the tongue at T and tell me
He: (thinks a bit more) tongue rolls back
Me: Now repeat ca, cha, ja, jha, nya, Ta, Tha, Da, Dha (I stop).. What comes after ?
He: (Repeats, keeps rolling the tongue backwards and pronounces Na) (Like the N in Pundit, Mandala, but not navy, nine)
Me: Now tell me what comes after pa.
He: (catches on to the pattern and says) pa pha ba bha ma.
Me: Finally now just repeat 'ka ca Ta ta pa'
He: (tries it, but does not catch on)
Me: Do you observe that the tongue travels from throat all the way to the lips?
He: (Nods, but i hardly think he understood)

But the point is how natural it is - I only make half the effort for him to understand the 'alphabets', he just latched on to others naturally (or analytically). I was not fully convinced about placement of varNa-s in Sanskrita, but I think I'm slowly beginning to see the originality and superiority. I still have confusions about Ra, La, Sa, zed, zha -- about placement/omission of these in the scheme, but that's only due to my very limited knowledge of phonetics.

The retro-flex is probably the most important and obvious difference between a "desi" pronunciation and a Westerner's pronunciation. Even among the Indians, you can see the Tamilians use the retro-flex a lot more than other South Indians because of the presence of the Ra and Zha, both of which are not present in other Indian languages. In fact there is even a Tamil adage that says the tongue has to roll for proper pronunciation. Sri DJ Vaidya-ji in his audio blog on phonetics mentions that Sanskrita retro-flex is most likely the effect of Dravidian languages on her.

kaalapramaaNa

Much is being made of 2012 as the end of the world. In the Hindu literature, the perception of time is completely different. There are various accounts of time with slightly differing measurements, but here is presented what is probably the most accepted. I also consulted the book Puranic Encyclopedia by Sri Vettam Mani.

Carl Sagan in his hugely successful and influential book/TV Serial Cosmos, mentions about how the early Hindu sages were thinking in terms of billions, when the rest of the world did not yet begin to count numbers. Clearly, the table goes from 1/3600 of a second to several billion years.

For the end of Kali yuga in the current cycle, we have about 427,000 years to go! And we are in the 28th cycle of the 7th manvantara. For this manvantara to end, we have 43 cycles to go. And for this kalpa to end, we have about 7 more manvantaras. The current manu is vivaSvata. We will see the future manu-s in the next post.

At it does not end here. When the lifetime of current Brahma expires, a new Brahma takes over.

count	of this	is 1	equal to this of	in modern units	Comments
30	alpakala	truti	1/3600	second	~ 0.3 milli seconds
30	truti	kalaa	1/120	second	~ 8.3 milli seconds
30	kalaa	nimisha	1/4	second	~ 250 milli seconds
4	nimisha	ganita	1	second
60	ganita	vinadi	1	minute
60	vinadi	ghatika	24	minutes
60	ghatika	ahoratra	24	hours	Day + Night
15	ahoratra	paksha	15	days	1 Moon cycle
2	paksha	chandramasa	1	month	1 Lunar month
12	chandra masa	varsha	12	months	1 Solar year
1	varsha	deva aho ratram	1	Deva day	1 Human year
360	varsha	devavarsha	360	human years
4800	devavarsha	kruta yuga	1,728,000	human years
3600	devavarsha	treta yuga	1,296,000	human years
2400	devavarsha	dvapara yuga	864,000	human years
1200	devavarsha	kali yuga	432,000	human years
12000	devavarsha	catur yuga	4,320,000	human years
71	catur yuga	manu	306,720,000	human years
14	manvantara	kalpa	4,294,080,000	human years	Deluge
1	kalpa	Brahma's night	4,294,080,000	human years	No action
1	kalpa	Brahma's day	4,294,080,000	human years	Creation
2	kalpa	Brahma ahoratra	8,588,160,000	human years	Brahma's day + night
360	Brahma ahoratra	Brahma varsha	3,091,737,600,000	human years	1 Brahma year
100	Brahma varsha	End of Brahma	309,173,760,000,000	human years	100 Brahma years