Author: Paramu Kurumathur

My Book on Indian Calendars

My upcoming book on Indian Calendars

Happy to say that I am making good progress with this project. I am titling the book

Conversations with Āryabhaṭa: about Indian Calendars (and Astronomy) 

(any comments on the title?)

I hope to complete the writing of the book in the next 3 to 4 months. The book should run to around 80,000 words. It will have a lot of figures, so it may go to between 300 and 400 pages.

Will keep you informed on progress.

Here is a table that gives a schema of the book.

Calendar Category / Description Calendar Mechanism / Description Calendars Discussed Reference (for the reader) 
Empirical (Observational) 
 
Direct visual observation: The immediate, real-time sighting of natural phenomena 		Phenological / Ecological 
 
Dynamically track the physical, organic rhythms of the local ecosystem (monsoons, winds, flora blooming, animal migrations and the stars). 		Calendars of the Chola Naikens; Gonds; Santalis; Ao Naga; Khasi; Baiha; Birgor; Juang; Soligas; Todas; Nicobarese Chapter 2 
 Stellar 
 
Track time and seasons by observing the rising and setting of specific stars or constellations relative to the night sky. 		Some ancient Vedic calendars,  
Santhal and Munda calendars,  
Calendars of the Gond people, the Oraoan and the Toda people. 		Chapter 3 
 Solar / Horizon Astronomy 
 
Synchronize with the Sun based on its observed position relative to physical, geographic landmarks on the horizon (solstice markers) 		Megalithic stone circles in India (e.g., Brahmagiri sites, Hanamsagar). Chapter 4 
 Lunar 
 
Mark time and months by the first visual sighting of the new crescent moon in the night sky 		The Hijri Calendar Chapter 5 
 Lunisolar 
 
Synchronize with both the Sun and the Moon based on direct observation of their physical positions and seasonal markers. 		Ancient Vedic Calendar Chapter 6 
 Planetary 
 
Align with the repeating orbital geometries of the planets based on systematic, recorded sky sightings 		Bṛhaspati Saṃvatsara Cakra Chapter 7 
Calendar Category / Description Calendar Mechanism / Description Calendars Discussed Reference (for the reader) 
Algorithmic (Arithmetic / Rule-based) 
  		Synchronizes with the tropical (Sayana) Sun or the Moon using a fixed mathematical formula and pre-programmed cycles, ensuring absolute calendar predictability. The Tabular Hijri Calendar 
Indian National Calendar 
The Gregorian Calendar 		Chapter 8 
Ephemeris (Calculational) 
 
True celestial coordinates. Precision calculations of shifting planetary orbits 		Lunisolar 
 
Synchronizes with both the sidereal (Nirayana) Sun and the Moon based on their calculated positions 		Some Pañcāṅgas 
Śaka Varṣa (Sauracāndramāna), Vikrama Saṃvat, Śālivāhana Śaka, Yudhiṣṭhira Era, Kali Yuga Era, Nepāla Saṃvat, Lakṣmaṇasena Era, The Saptarṣi Calendar 		Chapter 10, 11 
 Solar (Sidereal) 
 
Synchronizes with the sidereal (Nirayana) Sun based on its calculated position 		Some Pañcāṅgas,  
Kollam Era (Malayāḷam), Tamiḻ (Sauramāna), Oḍiā, Vaṅgīya (Bengali), Asamīyā, Punjabi (Nānakśāhī Solar), Cālukya Vikrama Era. The Sāyana Śaka Calendar 		Chapter 10, 12 
 Solar (Tropical) 
 
Synchronizes with the tropical (Sayana) Sun based on its calculated position 		The Sāyana Śaka Calendar, Tārīkh-i-Ilāhī. Chapter 13 
Linear / Epochal (Continuous Count) 
 
Unbroken tally of days. Pure, uninterrupted sequence from a fixed starting point. 		A running tally of days from a fixed epoch, completely unanchored from the immediate tracking of any single heavenly body. Kaliyuga Calendar (Ahargaṇa), Julian Day Calendar Chapter 14 

I am also thinking of adding 3 other chapters: About Time and Timekeeping in India (Chapter 15); Indian Astrological Systems (Chapter 16) (Only the theory, nothing about predictions); Some non-Indian calendars (Chapter 17) (if size allows).

You will see that Chapter 1 and 9 are missing in the above schema. Chapter 1 is (as you would have guessed) an introduction called Calendrical Questions. Chapter 9 is on astronomical calculations: It gives details of how positions of the Sun, the Moon and the planets are calculated by modern methods, by early western methods and early Indian methods.

Your comments on the above and your pointers to what is missing and need to be added are welcome.

The Vedic months – Twelve plus intercalary and suppressed months:

mádhuś ca mā́dhavaś ca 

śukráś ca śúciś ca 

nábhaś ca nabhasyàś 

ceṣáś corjáś ca 

sáhaś ca sahasyàś ca 

tápaś ca tapasyàś ca \ 

upayāmágr̥hīto ‘si 

saṁsárpo ‘si \ 

aṁhaspatyā́ya tvā // 


(Thou, Soma, art) 

Madhu and Mādhava; 

Śukra and Śuci; 

Nabha and Nabhasya; 

Iṣa and Ūrja; 

Saha and Sahasya; 

Tapa and Tapasya. 

Thou art taken with a support. 

Thou art Saṃsarpa. 

To Aṃhaspatya thee! 

(Taittirīya Saṃhitā (Kṛṣṇa Yajurveda) 1.4.14)

(A.B. Keith’s translation) 

Here’s the Prologue to the book:

It was in the twenty-eighth year of the reign of Emperor Bhāskara Ravi Manukulāditya that Śaṅkara’s father was murdered, stabbed through his left eye. Now, though five years had gone by, Śaṅkara could not forget it. He knew, deep inside, that Kṛṣṇa had done the foul deed. No one, including Kṛṣṇa, disputed the fact that he did have a strong motive. But Śaṅkara could not prove that he had the opportunity. Kṛṣṇa had an iron-clad alibi. 

Śaṅkara’s father had been killed on the first of the month of Siṁha (Ciṅṅaṁ as they called it in Malabār where he lived). Some of the people in his village thought that they had seen Kṛṣṇa lurking around Śaṅkara’s house that morning. But the headman of Kṛṣṇa’s village, about ten miles north of Śaṅkara’s village, was certain that Kṛṣṇa was in their village the whole day of the first of Ciṅṅaṁ. In fact, he had asked Kṛṣṇa to run some errands for him and he had seen Kṛṣṇa many times that day. And who was Śaṅkara to question the word of the headman? 

But Śaṅkara could not let go. He wanted to be sure. He decided that he would question Kṛṣṇa one last time. And if Kṛṣṇa’s story checked out, he would drop the issue from his mind once and for all. He therefore sent word to Kṛṣṇa to come and meet him on the fifteenth of that month. 

Kṛṣṇa did not keep the appointment. Śaṅkara waited the whole day, but Kṛṣṇa did not come. Śaṅkara was furious, but what could he do? 

However, the next day, come lunch time, there was Kṛṣṇa at Śaṅkara’s house asking for him. 

Śaṅkara said, “I thought I asked you to come yesterday?” 

Kṛṣṇa said, “No, your messenger said the fifteenth.” 

Śaṅkara felt like he had been hit by a bolt of lightning. It all made sense now. He now knew for sure that Kṛṣṇa had indeed killed his father. Kṛṣṇa had no alibi at all. 

Śaṅkara had not paid close attention to the calendars… 

Full-Stack Leadership: New book published: You are invited to the launch of the book

Full-Stack Leadership: New book published: You are invited to the launch of the book

This is to announce that I have published (as part of PM Power Consulting’s offerings) a new book called Full-Stack Leadership.

The book is being launched on August 22, 2025. Please click here to see details of the launch. In this site you can start off by playing the Full-Stack Leadership game, and explore the book in details using an AI companion to the book.

The book is available for purchase at the sites mentioned below.

Flipkart; Amazon.com; Amazon.in; Notionpress

For a synopsis of the book click here

For endorsements of the book from industry experts click here

Book Launch. You are invited

Book Launch. You are invited

If you are a stakeholder or change agent looking at steering an organisation through an Agile transformation journey, this book is for you. It examines the specific practices that need to be adopted and enabled within the organization to fully realize the Values/Tantras of Agile. It does this by looking at the outcomes expected/desired by the three main stakeholders of a successful enterprise – Customers, Associates, and Shareholders – and describing the practices that drive these outcomes. The contents of the book are based on the authors’ discussions with various industry leaders who have implemented, driven or guided Agile transformations and with PM Power experts who have more than 1000 years of collective experience in the area. The outcomes and practices are presented as responses to certain situations and episodes that have arisen in a fictitious organisation that is a combined entity embodying various organisations that PM Power has worked with. The conversational style and the touch of humour makes reading easy.

My upcoming book has been renamed. Here is the new cover. The contents remain the same.

My upcoming book has been renamed. Here is the new cover. The contents remain the same.

Click on the links below to visit summary pages of the book

Summary

Summary – Section 1

Summary – Section 2

Summary – Section 3

Summary – Section 4

Summary – Section 5 (1)

Summary – Section 5 (2)

Summary – Section 6

Summary – Section 7

Summary – Section 8 (1)

Summary – Section 8 (2)

Summary – Section 9

To write or not to write…

To write or not to write…

Do you have to be an expert to author a technical book?

A fable:

Once in the Champakaranya forest there lived a troop of monkeys. The head monkey was an expert at detecting any approaching predator, whether it was an eagle in the air or a leopard on the ground, and of any monkey-traps on the ground. However, the head monkey thought it was undignified of him to shout even when he sensed that danger was nearby. He expected the troop monkeys to observe him and hide or run away when he did. But, of course, this was never perfect. The troop lost many a member to predators and traps because they did not get an early warning of the danger.

Over time, a young monkey started learning the techniques to sense the approach of an oncoming predator and any traps set in the ground. He was not an expert as the head monkey was, but as soon as he sensed that danger was nearby, he shouted and alerted the other monkeys. Of course, he made mistakes and sometimes gave false alarms. But as time passed, he got better.

The monkey troop was very happy and decided that it was better to have as head a semi-expert who informed them of oncoming danger rather than an expert who kept silent and kept the knowledge to himself. So, they dethroned the head and made the young monkey their head.

Note: This fable and accompanying picture are taken from the book, The Five Tantras of Enterprise Agility, published by PM Power Consulting.

Experts in a field pass on their knowledge to others in various ways. Some consult, some coach, some give talks and some write books.

But what if you are not an expert?

I know many people who hold themselves back from writing and authoring books in technical areas because they feel that they are not ‘experts’ in the field. They perhaps feel that they are frauds, writing about an area that they are not at the top of. Another fear many people have is that if they are not ‘experts’ and write and publish a book, they may be caught out when somebody opens a discussion on the topics covered in the book.

[Let us get the difference between an author and a writer out of the way. A writer is someone who writes anything: a log, a book, any sort of content etc. A journalist is a writer. An author is a person who has written and published a book that is credited to their name. The author owns the copyright to the book. When I use the term ‘write’ a book, I mean writing it with the intention of getting it published, with the writer getting the credit and owning the copyright.]

I think that these fears are unfounded. If you can write well, you can write about anything, provided you get inputs from experts, either by interviewing and interacting with them or reading their published works. Remember a book is not like a research paper. In a research paper you are putting forward new ideas or coming to new conclusions. But a book’s purpose is basically to put into easy language known ideas and conclusions. [Indeed, if the book being written is on a completely new idea, and there are no experts around, then you better be the expert also.]

But the reverse may not be true, even if you are an expert, if you cannot write well, you cannot write a book on the topic. 

With apologies to the good bard, I write good words while others think good thoughts.

The basic idea of writing is to share with people what you know and what you can get from others. This is the basic dharma of a writer: inform the reader. As long as you are able to do this, whether or not you are an expert, you are OK. The real purpose is connecting with your readers and informing them. Of course, one thing that is important to note is that as a writer you can form your own opinion about the subject and put that forward too. You don’t have to be restricted to what ‘experts’ have put forward.

Another idea of writing a book is that even if you are not an expert when you start writing the book, by your association with experts while writing the book, you become an expert yourself! [This aspect, by the way, should put to rest fears that you may not be able to answer questions on the topic.] What, after all, is an expert? Lexico.com powered by Oxford defines an expert as A person who is very knowledgeable about or skilful in a particular area. It is not clear how much knowledge you need in a particular area to be called an expert. The expert is a relative one. Writing a book on a topic will certainly take you very far into being an expert in the topic.

So, I say: Write, if you can, whether you are an expert or not.

But whoever is writing a book, one thing is clear. Writing a book takes a lot of commitment. Only a writer will know the amount of work involved in writing and getting a book published. For every book that is written and published there may be hundreds that are left incomplete.

[Note: Writing a book is only one way an expert informs others. There are many other ways, as I said before, like coaching, consulting, speaking and so on.]

Calendars of India: Theory and Practice – Book in the Workshop

Calendars of India: Theory and Practice – Book in the Workshop

Suggestions for topics for inclusion (or exclusion) are welcome.

(This book is in the workshop. I am right now gathering materials for this book. Am looking at six to nine months for the completion of the book. Then another year for publishing it?)

A synopsis

A YouTube version is available here.

(Note that these are the first thoughts. Subject matter [and title] may undergo changes as time passes. Any suggestions in this area are welcome.)

These days, there is an upswell of interest in Indian mathematics, Indian astronomy and Indian religions, observances and festivals. Most of these observances and festivals are celebrated on particular dates of one calendar or the other. For example, the birthday of Lord Rama, one of the most important deities of veneration among Indians, is celebrated on the ninth day of the bright half of the month of Chaitra. What does that mean?

In India, while we follow the western (Gregorian Calendar) for civil and official purposes, at home, for religious and liturgical purposes we follow a myriad of calendars based on the region we are in, based on our religion, our community etc.. This gives rise to many questions that an average person is faced with:

  • Why is Lord Krishna’s birthday celebrated on different dates in different parts of India? Why even in the same place, Iyers and Iyengars have different dates for Krishna’s birthday?
  • Why do we hear people saying “While my actual birthday is today, my birth star / birth tithi is next week” What does it mean when someone says my birth star is today?
  • Do time zones make a difference to the star you are born under? [That is, does a person born at the same instant in the US and in India fall under the same star, tithi etc?]
  • Why is Makar Sankranti which is supposed to be the start of Uttarayana, celebrated nearly 24 days after the actual event of the start of Uttarayana? What is Uttarayana?
  • Why are there so many year-beginning dates in India? How many “new-years” are there in India and why?
  • How are months reckoned in the various calendars? Why do some months in some calendars have 32 days?
  • What is the concept of an added month? That is, why do some years have 13 months? And rarely only 11 months?
  • How do Christians fix the date of Easter?
  • Why does the Muslim festival of Ramadan migrate across the seasons? That is, why does Ramadan come sometimes in summer and sometimes in winter?
  • Why do Shraaddhas (death anniversaries)  and birthdays of the same star or tithi fall on different days?
  • What are the five “limbs” of the Panchanga? And what is the significance of each of those?
  • What is Raahu Kaala? And why is it bad? What are the other Kaalas?
  • What is a “muhurta”? What do we mean when we say that the “muhurta” for a wedding is such and such a time?
  • What is the meaning of a birth chart and how do you cast it?
  • Does the day begin at sunrise, sunset or any other time?
  • What is the effect of an eclipse?
  • What is Kali Yuga and Kali day number?
  • What is the history of the calendar?
  • What is the astronomy behind calendars?
  • What are the various calendars followed in India and how are they organised?
  • What is the meaning of a solar calendar, a lunar calendar, a luni-solar calendar etc?
  • Why don’t we have leap years in Indian calendars?
  • Why are there 30 tithis but only 27 stars?
  • What is yoga in the panchanga?
  • Why is there a difference between the beginning and ends of the birth signs (Aries, Taurus etc.) between western and Indian systems?

These are some of the kinds of questions that people of India grapple with every day when it comes to celebrating any religious festival.

This book Calendars of India: Theory and Practice strives to answer all the above questions and do much more.

The first part of the book looks at the origin of calendars and how calendars are intimately tied to the positions of the Sun, the Moon and the planets. It then goes into the astronomy of calendars, touching upon the following, among others:

  • The Solar System – the revolution of the earth round the sun, the movement of the sun, the moon and the planets as seen from the earth; 
  • The rotation of the earth – time, reckoning of days and hours minutes etc.
  • Sunrise, sunset, equation of time, mean solar day, sidereal day
  • Coordinate systems, the ecliptic, celestial equator, equinoxes, solstices; precession of the equinoxes and ayanamsa; obliquity of ecliptic, nutation etc. etc.
  • The year, days from equinox to equinox, the tropical year, the anomalistic year, the sidereal year etc
  • Days of the week
  • The sky, the stars, constellations, signs, the path of the ecliptic, the position of the sun
  • The moon, position of the moon, the phases of the moon and Eclipses
  • Notes on Indian astronomy, the various siddhantas (Surya Siddhanta, Brahma Siddhanta and Arya Siddhanta) and the various karanas associated with them, 
  • Epochs, Julian Day and Kali Yuga and Kalidina.
  • The changing sky and star orientations over the ages.

The second part looks at the Gregorian Calendar, its evolution and the logic behind it with respect to the astronomy discussed in the first part. The Gregorian calendar serves as a baseline for looking at other calendars. It also looks at the history of calendars.

The third part looks at the basic logic of Indian calendars and how the astronomical facts discussed in the first part affect them. Some of the topics discussed in this part are:

  • Types of calendars and the logic behind them – Solar calendars, lunar calendars, luni-solar calendars, equal-month calendars etc.
  • Solar months – stars, day numbering/naming, sankranthi, rule for beginning a month
  • Lunar months – Amaanta (new-moon last) and Puurnimaanta (full-moon last) systems, half-months/pakshas, tithis, day numbering/naming, month names, added (adhika) months, suppressed (kshyaya months), day additions, day suppressions, day repetition, length of months, adhika, kshaya tithis etc.
  • Lunisolar month 
  • Yuga, kalpa, mahayuga etc. samvatsaras, cycyles, kshaya and adhika samvatsara jupiter cycle
  • Mentioning dates; 10th day of the 8th month or 10 days after 8 months. Count up from the first of the month (like we do now) or count down to an event (like the roman counted to the ides etc.)

The fourth part looks at the various calendars of India and how they are organised:

  • the various Indian Panchangas and calendars – Kollam era, tamil era, vikrama era, saka era, gupta, bengali, Kannada/Telugu era, oriya, muslim era, maratha and many more
  • Calendars during the Vedic times
  • Chinese calendar, iranain calendar
  • Mathematical calendars (computed purely mathematically) and astronomical calendars (based on the position of the sun, moon etc.) ; Observational calendars (based on sighting of moon etc.)

The fifth part looks at the mathematics and astronomy (not predictions!) behind the astrological systems of India

  • Birth charts, Rashis (signs), positions of the planets, what is Rahu and Ketu, What is Gulika etc. effect of time zones
  • Navamshas and other amshas
  • What is ascendant (lagna)
  • What is the meaning of houses, aspects etc.
  • What is retrograde motion of planets?
  • What are muhurtas (times, good times etc.), Raahu kaala and other kaalas etc. dashas; balance of dashas

As I mentioned before, these are initial thoughts. As I get more and more into details of the book, subject matter and the order and format they are presented in may change.