The Indic MathematicaL Tradition

Transcription

1 The Indic MathematicaL Tradition Monthly Planner 2007,2008 With Panchangam Data Compliments Of Indic Studies Foundation Designed By Kosla Vepa

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3 The Indic Mathematical tradition Aryabhata I (the elder) आयर भट Born 2765 BCE (based on modern research) conventional dating ( CE) astronomer mathematician of the ancient world

4 Ancient Vedic Astronomy First mentioned in the Vedas The Vedas can be dated to the 5th or 6 th millennium BCE using techniques now considered as a part of a discipline known as Archaeo Astronomy One of the observations that the ancients made was the day and the location of the Sun when it makes its way past the Celestial equator to the northern half of the Celestial sphere. This is known as the Vernal equinox. When this occurs the number of hours of daylight equals 12 or half the modern calendar day The Astronomy and the Astrology of India is based upon sidereal calculations. Sidereal astronomy uses the distant stars as the frame of reference and the sidereal period is the time that it takes t the object to make one full orbit around the Sun, relative to the stars. This is a more accurate computation of the true orbital period of any planetary body.

5 January 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 New Year's Day 2 3 Purnima Makar Sankranti,, Uttarayana Punyakalam Martin Luther King, Jr. Amavasya Vasant Panchami Republic Day of India Dec 2006 Feb

6 The Indic Mathematical tradition The Armillary or Celestial sphere (Gola) depicts the way the ancients saw the universe,as they gazed at the sky. Armillary spheres have concentric rings to indicate planetary orbits, the zodiac band of constellations, and terrestrial and celestial measurement circles such as the Tropics of Cancer and Capricorn and the equator. Sometimes they are mounted with an Orrery inside. Sometimes they are mounted as garden sundials. A Ptolemaic armillary sphere has an earth globe at the center, surrounded by celestial circle and zodiac armillary rings, demonstrating the geocentric theory of the universe developed by Ptolemy and others in ancient Greece and Rome. The latest view is that Ptolemy was certainly not the first or the only oneto develop a calculation algorithm based on a geocentric model. The Indics were already there, no pun intended, as were probably the Chinese

7 February 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Jan 2007 M ar 2007 W S M T T F S Purnima Groundhog Day Lincoln's Birthday Valentine's Day Maha Shivaratri Amavasya Yugabda 5109 President's Day Washington's Birthday

8 The Indic Mathematical tradition The Celestial sphere Known also as the Armillary sphere or Gola in Sanskrit) Showing the ecliptic and its inclination to the celestial equator and is the inclination of the earths axis to the axis perpendicular to the plane of the ecliptic About 23.5 degrees

9 March 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Feb Apr Parti al Lunar Eclipse Holi Purnima Daylight Saving Time Begins St. Patri ck's Day Solar Eclipse Chaitra, Ugadi,Hindi, Telugu New year Vernal Equinox Ramayana week Sri Ram Navami

10 The Indic Mathematical tradition The structure of Vedic Literature (continued) EachVeda consists of Samhitas, Brahmanas, Aranyakas - speculation in the solitude of wilderness eventually taking shape as the Upanishads, To these were appended what were later called the Vedangas comprising of Shiksha (phonetics) Sandhi rules Chandas (meter) Nirukta (etymology) Vyakarana (grammar) Jyotisha (astronomy and calendric functions) KalpaSutras(Ritual procedures and the associated mathematics) Note the emphasis on brevity throughout, sandhi to make the content more compact, phonetics for mnemonic purposes. Panini s Ashtadhyayi is a tour de force as the worlds oldest Grammar text and Nirukta for associativity in remembering the meaning of words

11 April 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday April Fool's Day Purnima Mahavira Jayanti Tamil New Year, Baisakhi, Vishu Partial Lunar Eclipse Ramanuja Jayanti Sankara Jayanti Narasimha Jayanti Mar May

12 The Indic Mathematical tradition Proposed chronology of the Vedics A work in progress Event Individual Date Birth Veda Vyaasa ~3300 BCE Birth Apastambha 3200 BCE Birth Baudhayana 3200 BCE Era Kaliyuga 3102 BCE Birth Aryabhata 2765 BCE Lifespan Gautama Buddha BCE Coronation Chandragupta Maurya 1554 BCE Coronation Asoka Maurya 1472 BCE Coronation Kanishka BCE Era Andhra Satavahana 833 BCE -327 BCE Coronation Chandragupta of Gupta dynasty 327 BCE Pancha Siddhanta VarahaMihira 123 BCE Reign Vikramaditya 102 BCE to 78 BCE Birth Brahmagupta 30 BCE Writings Bhaskara II Siddhanta Siromani 486 BCE

13 May 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Apr Purnima 1 Buddha Purnima 2 Annamacharya Jayanti Hanuman Jayanti Mother's Day Amavasya,Jyeshta first of 2, adhik maas Armed Forces Day Memorial Day Poornima 31 Jun

14 The Indic Mathematical tradition Precession of the equinoxes At the end of a tropical year from one vernal equinox to the next with respect to the fixed stars, the earth appears to fall short by seconds of longitude. That means it takes approximately years for the precession to complete 360 degrees or 1 revolution of the vernal equinox as it traverses a different Nakshatra every 955 years. Voila, here we have a year clock and by noting the Nakshatra in which the vernal equinox occurred we can tell when the event occurred. By dividing each Nakshatra into 4 padas we can refine the unit of time to 240 years. This is a fairly reliable method of dating events such as the composition of the Rg or the date of the Mahabharata war Precession of the equinoxes and the pole star

15 June 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 2 May 2007 Jul Flag Day Adhik Maas last day Amavasya,Jyeshta shukla Father's Day Summer Solsti ce Purnima

16 The Indic Mathematical tradition Precession of the Equinoxes

17 July 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Independence Day Amavasya, Asadha shukla Dakshinayana Punyakala Guru(Vyaasa) Purnima Jun 2007 Aug

18 The Indic Mathematical tradition Deciphering the age of an event Observations about the Nakshatra in which the Vernal Equinox occurs tell us the era in which the observations took place (Archaeo-Astronomy) This is only one of the possible astronomical markers Look to manuscripts written by Astronomers and Mathematicians, since they have a penchant for precision in their observations and remarks We are at the beginning of discovery of our forgotten past

19 August 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Jul 2007 Sep Amavasya,Sravan shukla Independence Day Varalakshmi Vratam Purnima Raksha Bandhan

20 The Indic Mathematical tradition Dating of the Vedas Hermann Jacobi John Playfair In 1790, the Scottish mathematician John Playfair demonstrated that the starting-date of the astronomical observations recorded in the tables still in use among Hindu astrologers (of which three copies had reached Europe between 1687 and 1787) had to be 4300 BC.3 Playfair s argumentation, Remarks on the astronomy of the Brahmins, Edinburg 1790, is reproduced in Dharampal: Indian Science and Technology in the Eighteenth Century, Academy of Gandhian Studies, Hyderabad 1983 (Impex India, Delhi 1971), p

21 September 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Aug 2007 Oct 2007 W S M T T F S Labor Day Krishna Janmashtami Amavasya, Bhadrapada shukla Ganesh Chaturthi Autumnal equinox Purnima 30

22 The Indic Mathematical tradition The difference between the sidereal day and the solar day from Wikipedia. For the same reason the sidereal year is longer than the solar or tropical year by about 20 minutes. We will come back to this when we discuss the precession of the equinoxes

23 October 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Columbus Day (Observed) Amavasya,Aswina shukla Navratri begins Saraswati Puja Madhva Jayanti Vijaya Dashami Purnima Karva chaturthi (Karva chauth) Halloween Sep Nov

24 Western Asterism name Indian Nakshatras (Sidereal Zodiac) Sector in deg,min deg,min 1. Beta Arietis Aswini Arietis Bharani Eta Tauri Karthika Alpha Tauri Rohini Lamda Orionis Mrigasira Alpha Orionis Aridra Beta Geminorum Punarvasu Delta Cancri Pushya Alpha Cancri Aslesha Alpha Leonis Magha The Indic Nakshatra System attributed to Gargeya in the Atharva Veda 11. Delta Leonis Pubba Beta Leonis Uttara Delta Corvi Hasta Alpha Virginis Chitra Alpha Bootis Chothi Beta Librae Vishakam Delta Scorpi Anuradha Alpha Scorpi Jyeshta Lamda Scorpi Moola Delta Sagittari Poorvashad Delta Sagittari Uthrashad Alpha Aquilae Sravana Alpha Delphini Dhanishta Lamda Aquar Satabhisha Alpha Pegasi Poorvabhadra Alpha Andromeda Uttrarabhadra Zeta Piscium Revathi

25 November 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Oct 2007 Dec Daylight Savings Time Ends Election Day Naraka Chaturdasi Deepavali Amavasya,Kartika shukla Vikram New Year 2064 Veterans Day Thanksgiving Purnima

26 The Indic Mathematical tradition Dating of the Mahabharata The following key dates are found to be consistent with the sky inscriptions observed by Veda Vyasa: Krishna's departure on Revati Sept. 26, 3067 BCE Krishna's arrival in Hastinapura on Bharani Sept. 28, 3067 BCE Solar eclipse on Jyeshtha amavasya Oct. 14, 3067 BCE Krittika full moon (lunar eclipse) September 29, 3067 BCE War starts on November 22, 3067 BCE (Saturn in Rohini, Jupiter in Revati) Winter solstice, January 13, 3066 BCE Bhishma's expiry, January 17, 3066 BCE Magha shukla ashtami A fierce comet at Pushya October 3067 BCE Balarama sets off on pilgrimage on Sarasvati on Pushya day Nov. 1, 3067 BCE Balarama returns from pilgrimage on Sravana day Dec. 12, 3067 BCE On the day Ghatotkaca was killed moon rose at 2 a.m., Dec. 8, 3067 BCE

27 December 2007 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Nov 2007 Jan 2008 W S M T T F S Amavasya,Margas shukla Gita jayanti Vaikunta Winter solstice Purnima Christmas New Year's Eve

28 The Indic Mathematical tradition Month Months according to Indian Panchang Suns Longitude Deg min Duration days Gregorian 2007/ Vaisakha Apr Jyestha(adhika) Asadha Sravana Bhadrapada Asvina Kartika Margasirsa Pausa Magha May 17,16 June 15 July 13 Aug. 18 Sept. 12 Oct. 10 Nov. 10 Dec. 24 Jan. 19 Synchronization and Leap Months The fundamental problem with the Indian panchang as with all lunisolar calendars is the synchronizaton (or a lack thereof) between the solar and lunar periodicities and just as we add a leap day every four years to the Gregorian calendar m we have to add a leap month or adhika maas every 2.5 years. There are 2 synchronization cycles known as the Metonic Cycle and the Saros. According to the Metonic cycle (Meton. was a Greek of 430 BCE), every 2.5 years an extra lunar month, will have to be added to keep up to 365 days. In 19 years,7 lunar months are aided to make it more accurate, i.e. 19 x = 235 lunar months. Since a lunar month is about days which gives a total of 235 x = days. However Yajnavalkya was the first to demonstrate a 95 year (19*5)synchronization cycle in the Satapatha Brahmana. Yajnavalkya was another one of those who could be termed a Man for all seasons,a multi faceted personality, a species of Homo sapien that appeared to populate the pages of ancient Indian History in much profusion 11. Phalguna Feb Caitra Mar. 19

29 January 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Dec New Year's Day Amavasya, Pausa shukla Makar Sankranti Martin Luther King, Jr. Purnima Feb

30 The Indic Mathematical tradition In the 5th Mandala of Rig Veda, the 40th sukta and 5th Rik, Rishi Atri describes a total solar eclipse. Rig Veda- HYMN XL. 5. Indra. Surya. Atri. O Surya, when the Asura's descendant Svarbhanu, pierced thee through and through with darkness, All creatures looked like one who is bewildered, who knoweth not the place where he is standing. Vedic astrology refers to moon s ascending node or descending node at time of potential solar eclipse as Rahu or Swarbhanu, a demon. The passage certainly describes a total solar eclipse, magically imposed by Rahu, and people and animals being scared of the solar eclipse event.the same material is expanded in Kaushitiki or Sankhyayana Brahmana Dr.S.Balakrishna

31 February 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 2 Jan 2008 Mar 2008 W S M T T F S Groundhog Day Amavasya, Magha shukla Vasant panchami Lincoln's Birthday Valentine's Day President's Day Purnima Washington's Birthday

32 The Indic Mathematical tradition Definitions (see figure) Ecliptic - the great circle on the celestial sphere that lies in the plane of the earth's orbit (called the plane of the ecliptic). Because of the earth's yearly revolution around the sun, the sun appears to move in an annual journey through the heavens with the ecliptic as its path. Celestial sphere or armillary imaginary sphere enveloping the earth appears to turn as the earth rotates Celestial equator equinox (ē kwĭnŏks), क त त त त (Kranthivruth) either of two points on the celestial sphere where the ecliptic and the celestial equator intersect. Periodicity of the saptarishi or Great Bear constellation or the Ursa Major equatorial coordinate system Line of Declination Line of right ascension

33 March 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Feb 2008 Apr 2008 W S M T T F S Amavasya,Phalgu shukla Vernal Equinox Holi St. Patrick's Day Easter Sunday

34 The Indic Mathematical tradition Some more definitions Sidereal Day An apparent sidereal day - the time it takes for the Earth to turn 360 degrees in its rotation; more precisely, is the time it takes a typical star to make two successive upper meridian transits. This is slightly shorter than a solar day. There are sidereal days in a tropical year, but solar days, resulting in a sidereal day of 86, seconds (or: 23 hours, 56 minutes, seconds). The reason there is one more sidereal day than "normal" days in a year is that the Earth's orbit around the Sun offsets one sidereal day, giving observers on Earth 365 1/4 days, even though the planet itself rotated 366 1/4 times (the Earth rotates in the same direction around its axis as it does around the Sun: seen from the northern sky, counter-clockwise). Midnight, in sidereal time, is when the First Point of Aries crosses the upper meridian. A mean sidereal day is reckoned, not from the actual transit, but from the transit of the mean vernal equinox (see: mean sun).

35 April 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday April Fool's Day Amavasya,Chaitra shukla, Chandrama na uga di Daylight Saving Time Begins Hindi Telugu New Year (Cha itra) Ram Navmi Hanuman jayanti Mar May

36 The Indic Mathematical tradition Comparison of The Àryabhatiya of Àryabhata and Astronomic values. Astronomy Constants AD Aryabhatiya 1604 BC Rotations per solar orbit Days per solar orbit Days per lunar orbit Rotations per lunar orbit

37 May 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Apr 2008 Jun 2008 W S M T T F S Amavasya,Vaisak shukla Mother's Day Armed Forces Day Buddha jayanti Memorial Day (Observed)

38 The Indic Mathematical tradition ASTRONOMIC AUTHORITY Àryabhata (from Clarke and Kay) Surya Siddanta Years in Cycle 4,320,000 4,320,000 Rotations of the earth 1,582,237,500 1,582,237,828 Days 1,577,917,500 1,577,917,828 Lunar Orbits 57,753,336 57,753,336 Kay notes 57,753,339 lunar orbits rather than 57,753,336 per Clarke. Synodic Months 53,433,336 53,433,336 Mercury 17,937,920 17,937,060 Venus 7,022,388 7,022,376 Mars 2,296,824 2,296,832 Jupiter 364, ,220 Saturn 146, ,568

39 June 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Amavasya,Jyeshta shukla Flag Day Father's Day Purnima Summer Solsti ce May 2008 Jul

40 The Indic Mathematical tradition Dating of the Vedas Koenrad Elst In a rather shoddy way, Friedrich Max Müller launched the hypothesis that the Rg-Veda had to be dated to about 1200 BC, and even though he later retracted it, that arbitrary guess has become the orthodoxy. A precursor to the habitual circular reasioning adopted by current day European indologists Maurice Winternitz remained skeptical of his own assumptions - We cannot explain the development of the whole of this great literature if we assume as late a date as round about 1200 BC or 1500 BC as its starting-point. 1 Hermann Jacobi John Playfair see next slide B G Tilak Orion Cosco Publications, reprint 1984, original 1895 S Balakrishna Vedic Astronomy articles

41 July 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Jun Amavasya,Asadha shukla Independence Day Guru Purnima (Veda Vyaasa) Aug

42 The Indic Mathematical tradition English calendar weekdays Indian calendar weekdays Sunday Monday Tuesday Wednesday Thursday Friday Saturday Raviwar Somwar Mangalwar Budhwar Guruwar Shukrawar Shaniwar (Chandrawar) Chaitra Vaishakh Jeshta Ashadh Shrawan(Sawan) Bhadrapad(Bhado) Ashwin Kartik Margshirsh Paush Magha Falgoon (Fagan)

43 August 2008 Monthly Planner Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 Jul Sep Done Priority Description Due Date Amavasya, Sravana Shukla Purnima, Raksha Bandhan Krishna Janmashtami Amavasya, Bhadrapada shukla 31

44 The Indic Mathematical tradition Zodiac sign Sanskrit Name Sector begin Sector end Aries Mesha Taurus Vrishabha Gemini Mithuna Cancer Karka Leo Simha Virgo Kanya Libra Tula Scorpio Vrishchika Sagittarius Dhanus Capricorn Makara Aquarius Kumbha Pisces Meena

45 September 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Labor Day Purnima Autumn begins Amavasya,Aswina shukla 30 Aug Oct

46 The Indic Mathematical a region of the sky, within official borders set in 1928 by the IAU. Often recognizable by a pattern or grouping of stars. Some patterns, like the Winter Triangle, span several constellations. tradition A Constellation is

47 October 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sep 2008 Nov Vijaya dasami Columbus Day (Observed) Purnima Karva chaturthi Daylight Savings Time Ends Naraka Chaturdasi, Deepavali Amavasya,Kartika Shukla Vikram New Year 2065 Halloween

48 The Indic Mathematical tradition Asterisms (Sapta Rishi as an example) The big dipper Actually part of Ursa Major The Big Bear Or Big Raccoon? Bharateeya Jyotishya shaastra states that each Nakshatra name corresponds to a group of stars called star mansions or Asterisms. Image fom:

49 November 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday Oct 2008 Dec 2008 W S M T T F S Election Day Veterans Day Purnima Amavasya,Margas shukla Thanksgiving 30

50 The Indic Mathematical tradition Precession of the equinoxes and the pole star

51 December 2008 Monthly Planner Done Priority Description Due Date Sunday Monday Tuesday Wednesday Thursday Friday Saturday , Gita Jayanti Purnima Winter solstice Christmas Amavasya,Pausa shukla New Year's Eve Nov Jan

52 The Indic Mathematical tradition I dedicate this research to the Goddess Sarasvati And the river that bears her name And the Brahmi civilization that flourished on the banks of the river for over 3000 years giving rise to the first phonetic and syllabic script Om Sarveshaam Swastir Bhavatu Sarveshaam Saantir Bhavatu Sarveshaam Poornam Bhavatu SarveshamMangalamBhavatu