Re: [-BAS-] Digest for b-a-s@googlegroups.com - 25 Messages in 8 Topics
Balachandra Rao
The post on the great Indian astronomer and mathematician
Bhaskara II (born
1114 C.E.) is welcome. But one has to be very careful while using
posts on the internet. Often there are hypes and unauthentic claims
and assertions. In the case of Bhaskara II, his birth place
"V(B)ijjada- v(b)ida" is not yet identified conclusively.
Sanskrit commentaries on his works don't throw much light on that
though one or two clues are there. Our Karnataka scholars proudly
associate him with Bijapur. But this is not possible since the place
is nowhere near the Sahyadri range of mountains. Another place often
cited is "Bidduru" identified with modern Bidar in Karnataka. Again,
the said mountain range does not pass near this town.
Maharashtrian scholars, as is traditionally usual, contradict the
Karnataka's claim! They identify one or two places called "Bid" or
"Beed" in their region. A copper plate inscription is discovered which
states that Bhaskara's grandson Changadeva was granted funds by a
certain king to run a centre to propagate
Bhaskara's system of maths and astronomy.
Further, claims about Bhaskara's association with Ujjayini are
mot authenticated. As regards the story of Lilavati being daughter of
Bhaskara is a myth calculatedly popularized by practitioners and
believers of astrology to earn authenticity to the non-science!
While it is true that Bhaskara's works are excellent, both for
content and style,
generally his predecessors Brahmagupta (628 C.E.) and Sripati Bhatta
(of 10th-11th Cent.) are held in great esteem as original
contributors to naths & astronomy. However, Bhaskara II gets the
credit for popularizing the discipline in a big way.
Balachandra Rao
On Wed, Feb 1, 2012 at 11:15 AM, <b-...@googlegroups.com> wrote:
> Today's Topic Summary
>
> Group: http://groups.google.com/group/b-a-s/topics
>
> [OT] Happy Birthday Vivek!! [1 Update]
> {OT} - [WTB] - Used EQ6 Mount [1 Update]
> Orion and his surroundings [5 Updates]
> Flaming Star [5 Updates]
> Astro planner for 2012 [2 Updates]
> sombrero galaxy [6 Updates]
> Bhaskaracharya [3 Updates]
> CCD Nights ! [2 Updates]
>
> [OT] Happy Birthday Vivek!!
>
> lavanya koushik <lavanya...@gmail.com> Jan 30 06:38PM +0530
>
> hi vivek,
> many hapy returns of the day:)hav a gr8 year:)
>
>
> --
>
> Lavanya Koushik M N
>
>
>
> {OT} - [WTB] - Used EQ6 Mount
>
> keerthi kiran <info...@gmail.com> Feb 01 09:07AM +0530
>
> Hello All,
> I am planning to buy a used EQ6 GoTo mount. If somebody has one and
> planning to sell it, please let me know by personal mail.
>
> Regards,
> Keerthi
>
>
>
> Orion and his surroundings
>
> keerthi kiran <info...@gmail.com> Jan 31 11:07PM +0530
>
> Hello All,
> Two weeks back we went to Agumbe for BAS star party. On the
> astrophotography front, nothing went right... Still managed to get this one
> pic...
> Wide field Orion with Barnard's loop.
> https://picasaweb.google.com/lh/photo/PJ9Ide_JOYeTFWGVSYEVXdMTjNZETYmyPJy0liipFm0?feat=directlink
>
> Regards,
> Keerthi
>
>
>
> Amar Sharma <amar_u...@yahoo.com> Jan 31 11:03AM -0800
>
> It would be fun and challenging to get the same shot with manual tracking on
> a film camera, right? Just like the good old days.
> This photo reminded me of a similar one, by one of our earliest member
> Shashank's shot of Orion region using his film camera and manual tracking
> scope. And he got a similar result ! He was an avid film user on his manual
> tracker for a long time.
>
> --- On Tue, 1/31/12, keerthi kiran <info...@gmail.com> wrote:
> Hello All,
> Two weeks back we went to Agumbe for BAS star party. On the astrophotography
> front, nothing went right... Still managed to get this one pic...
> Wide field Orion with Barnard's loop.
>
>
>
> Akarsh Simha <akars...@gmail.com> Jan 31 08:26PM -0600
>
> Hi Keerthi,
>
> That's a wonderful picture. It seems to me, however, that you are having
> some vignetting. It might prove useful to take some flats with the same
> lens and try dividing them out.
>
> Regards,
> Akarsh
>
>
>
> keerthi kiran <info...@gmail.com> Feb 01 08:09AM +0530
>
> Thanks Akarsh... You are right. I need to apply flats. But I am not happy
> with the way stars look. So I am going to redo this shot again...
>
>
>
>
> Suresh Mohan <drsure...@gmail.com> Feb 01 08:59AM +0530
>
> Where is the pic ?
> Suresh
>
> Sent from my iPhone
>
>
>
>
> Flaming Star
>
> Subhankar Saha <subhank...@gmail.com> Feb 01 01:03AM +0530
>
> Hi,
>
> Here is first of the two objects I captured from Ramanjeri, along with
> Doc. The other one is Jellyfish, yet to be processed. I captured 15
> frames with not-so-perfect polar alignment. As a result, ImagesPlus
> through away 8 of them, and stacked only 7 good frames. It was kind of
> difficult to get the faint nebula out. But I am extremely happy with
> the result.
>
> http://nakshatralok.blogspot.com/2012/02/flaming-star.html
>
> Doc: thanks for all the hospitality! :) It was a pleasure as always.
> My 10" needs more of your attention. I am yet to image through it :(
>
> Regards,
> Subhankar.
>
>
>
> keerthi kiran <info...@gmail.com> Feb 01 08:12AM +0530
>
> Very nice... It looks like a cobra ready to attack :)
>
>
>
>
> keerthi kiran <info...@gmail.com> Feb 01 08:13AM +0530
>
> And Nice blog!
>
>
>
>
> Deepak Arya <z_a...@sify.com> Feb 01 08:52AM +0530
>
> Hi
>
> Amazing - I had seen such photos only in books, too good.
>
> Deepak Arya
>
>
> --
> Deepak Arya
>
>
>
> Suresh Mohan <drsure...@gmail.com> Feb 01 08:56AM +0530
>
> Lovely Subhankar
> Suresh
>
> Sent from my iPhone
>
>
>
>
> Astro planner for 2012
>
> "Sunil G.R." <super...@gmail.com> Jan 31 12:24PM +0530
>
> Nice Calendar :). I think you would have put lot of effort on creating this
> Calendar.
> Hope an excel sheet can be made similar way on Planets rise and set.
>
> Thanks,
> Sunil.
>
>
>
>
> Arun Venkataswamy <aru...@gmail.com> Feb 01 07:53AM +0530
>
>
>> Nice Calendar :). I think you would have put lot of effort on creating
>> this Calendar.
>> Hope an excel sheet can be made similar way on Planets rise and set.
>
> Thanks Sunil.
> I wanted to put in a lot more information, but had to trade it off for a
> single page printable size.
>
> Regards,
> Arun
>
>
>
> sombrero galaxy
>
> Suresh Mohan Neelmegh <drsure...@gmail.com> Jan 31 09:47PM +0530
>
> last weekend we were pleasantly accompanied by Subhanker who drove all the
> way from bangalore, he brought his beautiful telescope 10 inch with him. WE
> set up our scopes and were all the time chatting thill almost midnight when
> the session began. I did try thor s helmet and later in the night sombrero
> galaxy , here is the link and thanks for looking .
> Suresh
> *http://tinyurl.com/6m2hdzu*
>
>
>
> keerthi kiran <info...@gmail.com> Jan 31 09:52PM +0530
>
> Nice pic... Looks like a UFO from a 60's movie ;)
>
> On Tue, Jan 31, 2012 at 9:47 PM, Suresh Mohan Neelmegh <
>
>
>
> parag kulkarni <mip...@gmail.com> Jan 31 09:55PM +0530
>
> nice dust lane, but doc why there is so much color noise? (because of only
> 15 subs?)
>
>
>
>
> Suresh Mohan <drsure...@gmail.com> Jan 31 10:03PM +0530
>
> Yes yes it dawned actually 13
> Suresh
>
> Sent from my iPhone
>
>
>
>
> Suresh Mohan <drsure...@gmail.com> Jan 31 10:36PM +0530
>
> Also colour noise is due to the fact I've zoomed so much and my scope is
> only 500 mm focal length
>
> Sent from my iPhone
>
>
>
>
> Akarsh Simha <akars...@gmail.com> Jan 31 05:46PM -0600
>
>> Yes yes it dawned actually 13
>
> Oh, no wonder. I was going to make a blunt, but frank and honest
> comment that I've had visual views that have been as good, if not
> better. That explains it. This is extremely good for 13 frames!!
>
> Regards
> Akarsh
>
>
>
> Bhaskaracharya
>
> Dhinakar Rajaram <rdhi...@gmail.com> Jan 31 11:34AM +0530
>
> Thanks to : http://veda.wikidot.com.
>
> This post is just a introduction to one of the greatest astronomer of India
> Bhaskarachārya ! I am in search for his works in detail, will post them
> here later. I am taking a small step to bring out the works by Indians on
> field of Astronomy especially solar astronomy.
>
>
> *Life Cycles of the Universe*
>
> The Indians view that the Universe has no beginning or end, but follows a
> cosmic creation and dissolution. Hindus are the only one who propounds the
> idea of life-cycles of the universe. It suggests that the universe
> undergoes an infinite number of deaths and rebirths. Hindus views the
> universe as without a beginning (anadi = beginning-less) or an end (ananta
> = end-less). Rather the universe is projected in cycles. Hindu scriptures
> refer to time scales that vary from ordinary earth day and night to the day
> and night of the Brahma that are a few billion earth years long.
>
> According to Carl Sagan,
>
>
> * "A millennium before Europeans were wiling to divest themselves of the
> Biblical idea that the world was a few thousand years old, the Mayans were
> thinking of millions and the Hindus billions".*
>
> Continues Carl Sagan,
> *
> "… is the only religion in which the time scales correspond… to those
> of modern scientific cosmology."*
>
> Its cycles run from our ordinary day and night to a day and night of the
> Brahma, 8.64 billion years long, longer than the age of the Earth or the
> Sun and about half the time since the Big Bang". One day of Brahma is worth
> a thousand of the ages (yuga) known to humankind; as is each night." Thus
> each kalpa is worth one day in the life of Brahma, the God of creation. In
> other words, the four ages of the mahayuga must be repeated a thousand
> times to make a "day ot Brahma", a unit of time that is the equivalent of
> 4.32 billion human years, doubling which one gets 8.64 billion years for a
> Brahma day and night. This was later theorized (possibly independently) by
> Aryabhata in the 6th century. The cyclic nature of this analysis suggests a
> universe that is expanding to be followed by contraction… a cosmos without
> end. This, according to modern physicists is not an impossibility.[/i]
>
> Bhaskara II or Bhaskarachārya was an Indian mathematician and astronomer
> who extended Brahmagupta's work on number systems. He was born near Bijjada
> Bida (in present day Bijapur district, Karnataka state, South India) into
> the Deshastha Brahmin family. Bhaskara was head of an astronomical
> observatory at Ujjain, the leading mathematical centre of ancient India.
> His predecessors in this post had included both the noted Indian
> mathematician Brahmagupta (598–c. 665) and Varahamihira. He lived in the
> Sahyadri region. It has been recorded that his
> great-great-great-grandfather held a hereditary post as a court scholar, as
> did his son and other descendants. His father Mahesvara was as an
> astrologer, who taught him mathematics, which he later passed on to his son
> Loksamudra. Loksamudra's son helped to set up a school in 1207 for the
> study of Bhāskara's writings
> Bhaskaracharya.jpg
>
> [image: Bhaskaracharya.jpg]
> *Bhaskara (1114 – 1185)
> (also known as Bhaskara II
> and Bhaskarachārya*
>
> Bhaskaracharya's work in Algebra, Arithmetic and Geometry catapulted him to
> fame and immortality. His renowned mathematical works called Lilavati" and
> Bijaganita are considered to be unparalleled and a memorial to his profound
> intelligence. Its translation in several languages of the world bear
> testimony to its eminence. In his treatise Siddhant Shiromani he writes on
> planetary positions, eclipses, cosmography, mathematical techniques and
> astronomical equipment. In the Surya Siddhant he makes a note on the force
> of gravity:
>
> * "Objects fall on earth due to a force of attraction by the earth.
> Therefore, the earth, planets, constellations, moon, and sun are held in
> orbit due to this attraction."*
>
> Bhaskaracharya was the first to discover gravity, 500 years before Sir
> Isaac Newton. He was the champion among mathematicians of ancient and
> medieval India . His works fired the imagination of Persian and European
> scholars, who through research on his works earned fame and popularity. It
> is stated Chinese and Mayans too had that idea some 2000 years before him.
>
> *Birth and Education of Bhaskaracharya*
>
> Ganesh Daivadnya has bestowed a very apt title on Bhaskaracharya. He has
> called him ‘Ganakchakrachudamani’, which means, ‘a gem among all the
> calculators of astronomical phenomena.’ Bhaskaracharya himself has written
> about his birth, his place of residence, his teacher and his education, in
> Siddhantashiromani as follows, ‘A place called ‘Vijjadveed’, which is
> surrounded by Sahyadri ranges, where there are scholars of three Vedas,
> where all branches of knowledge are studied, and where all kinds of noble
> people reside, a brahmin called Maheshwar was staying, who was born in
> Shandilya Gotra (in Hindu religion, Gotra is similar to lineage from a
> particular person, in this case sage Shandilya), well versed in Shroud
> (originated from ‘Shut’ or ‘Vedas’) and ‘Smart’ (originated from ‘Smut’)
> Dharma, respected by all and who was authority in all the branches of
> knowledge. I acquired knowledge at his feet’.
>
> From this verse it is clear that Bhaskaracharya was a resident of
> Vijjadveed and his father Maheshwar taught him mathematics and astronomy.
> Unfortunately today we have no idea where Vijjadveed was located. It is
> necessary to ardently search this place which was surrounded by the hills
> of Sahyadri and which was the center of learning at the time of
> Bhaskaracharya. He writes about his year of birth as follows,
> ‘I was born in Shake 1036 (1114 AD) and I wrote Siddhanta Shiromani when I
> was 36 years old.’
>
> Bhaskaracharya has also written about his education. Looking at the
> knowledge, which he acquired in a span of 36 years, it seems impossible for
> any modern student to achieve that feat in his entire life. See what
> Bhaskaracharya writes about his education,
>
> ‘I have studied eight books of grammar, six texts of medicine, six
> books on logic, five books of mathematics, four Vedas, five books on Bharat
> Shastras, and two Mimansas’.
>
> Bhaskaracharya calls himself a poet and most probably he was Vedanti, since
> he has mentioned ‘Parambrahman’ in that verse.
> Siddhanta Shriomani
>
> Bhaskaracharya wrote Siddhanta Shiromani in 1150 AD when he was 36 years
> old. This is a mammoth work containing about 1450 verses. It is divided
> into four parts, Lilawati, Beejaganit, Ganitadhyaya and Goladhyaya. In fact
> each part can be considered as separate book. The numbers of verses in each
> part are as follows, Lilawati has 278, Beejaganit has 213, Ganitadhyaya has
> 451 and Goladhyaya has 501 verses.
>
> One of the most important characteristic of Siddhanta Shiromani is, it
> consists of simple methods of calculations from Arithmetic to Astronomy.
> Essential knowledge of ancient Indian Astronomy can be acquired by reading
> only this book. Siddhanta Shiromani has surpassed all the ancient books on
> astronomy in India. After Bhaskaracharya nobody could write excellent books
> on mathematics and astronomy in lucid language in India. In India,
> Siddhanta works used to give no proofs of any theorem. Bhaskaracharya has
> also followed the same tradition.
>
> Lilawati is an excellent example of how a difficult subject like
> mathematics can be written in poetic language. Lilawati has been translated
> in many languages throughout the world. When British Empire became
> paramount in India, they established three universities in 1857, at Bombay,
> Calcutta and Madras. Till then, for about 700 years, mathematics was taught
> in India from Bhaskaracharya’s Lilawati and Beejaganit. No other textbook
> has enjoyed such long lifespan.
> Bhaskara's contributions to mathematics
>
> Lilawati and Beejaganit together consist of about 500 verses. A few
> important highlights of Bhaskar's mathematics are as follows:
> Terms for numbers
>
> In English, cardinal numbers are only in multiples of 1000. They have terms
> such as thousand, million, billion, trillion, quadrillion etc. Most of
> these have been named recently. However, Bhaskaracharya has given the terms
> for numbers in multiples of ten and he says that these terms were coined by
> ancients for the sake of positional values. Bhaskar's terms for numbers are
> as follows:
>
> eka(1), dasha(10), shata(100), sahastra(1000), ayuta(10,000),
> laksha(100,000), prayuta (1,000,000=million), koti(107), arbuda(108),
> abja(109=billion), kharva (1010), nikharva (1011), mahapadma
> (1012=trillion), shanku(1013), jaladhi(1014), antya(1015=quadrillion),
> Madhya (1016) and parardha(1017).
> Kuttak
>
> Kuttak is nothing but the modern indeterminate equation of first order. The
> method of solution of such equations was called as ‘pulverizer’ in the
> western world. Kuttak means to crush to fine particles or to pulverize.
> There are many kinds of Kuttaks. Let us consider one example.
>
> In the equation, ax + b = cy, a and b are known positive integers. We want
> to also find out the values of x and y in integers. A particular example
> is, 100x +90 = 63y
>
> Bhaskaracharya gives the solution of this example as, x = 18, 81, 144, 207…
> And y=30, 130, 230, 330…
> Indian Astronomers used such kinds of equations to solve astronomical
> problems. It is not easy to find solutions of these equations but Bhaskara
> has given a generalized solution to get multiple answers.
> Chakrawaal
>
> Chakrawaal is the “indeterminate equation of second order” in western
> mathematics. This type of equation is also called Pell’s equation. Though
> the equation is recognized by his name Pell had never solved the equation.
> Much before Pell, the equation was solved by an ancient and eminent Indian
> mathematician, Brahmagupta (628 AD). The solution is given in his
> Brahmasphutasiddhanta. Bhaskara modified the method and gave a general
> solution of this equation. For example, consider the equation 61x2 + 1 =
> y2. Bhaskara gives the values of x = 22615398 and y = 1766319049
>
> There is an interesting history behind this very equation. The Famous
> French mathematician Pierre de Fermat (1601-1664) asked his friend Bessy to
> solve this very equation. Bessy used to solve the problems in his head like
> present day Shakuntaladevi. Bessy failed to solve the problem. After about
> 100 years another famous French mathematician solved this problem. But his
> method is lengthy and could find a particular solution only, while Bhaskara
> gave the solution for five cases. In his book ‘History of mathematics’, see
> what Carl Boyer says about this equation,
>
> ‘In connection with the Pell’s equation ax2 + 1 = y2, Bhaskara gave
> particular solutions for five cases, a = 8, 11, 32, 61, and 67, for 61x2 +
> 1 = y2, for example he gave the solutions, x = 226153980 and y =
> 1766319049, this is an impressive feat in calculations and its
> verifications alone will tax the efforts of the reader’
>
> Henceforth the so-called Pell’s equation should be recognized as
> ‘Brahmagupta-Bhaskaracharya equation’.
> Simple mathematical methods
>
> Bhaskara has given simple methods to find the squares, square roots, cube,
> and cube roots of big numbers. He has proved the Pythagoras theorem in only
> two lines. The famous Pascal Triangle was Bhaskara’s ‘Khandameru’. Bhaskara
> has given problems on that number triangle. Pascal was born 500 years after
> Bhaskara. Several problems on permutations and combinations are given in
> Lilawati. Bhaskar. He has called the method ‘ankapaash’. Bhaskara has given
> an approximate value of PI as 22/7 and more accurate value as 3.1416. He
> knew the concept of infinity and called it as ‘khahar rashi’, which means
> ‘anant’. It seems that Bhaskara had not notions about calculus, One of his
> equations in modern notation can be written as, d(sin (w)) = cos (w) dw.
> A Summary of Bhaskara's contributions
> image005.jpg
> Bhaskarachārya
>
> A proof of the Pythagorean theorem by calculating the same area in two
> different ways and then canceling out terms to get a² + b² = c².
>
> In Lilavati, solutions of quadratic, cubic and quartic indeterminate
> equations.
>
> Solutions of indeterminate quadratic equations (of the type ax² + b =
> y²).
>
> Integer solutions of linear and quadratic indeterminate equations
> (Kuttaka). The rules he gives are (in effect) the same as those given by
> the Renaissance European mathematicians of the 17th century
>
> A cyclic Chakravala method for solving indeterminate equations of the
> form ax² + bx + c = y. The solution to this equation was traditionally
> attributed to William Brouncker in 1657, though his method was more
> difficult than the chakravala method.
>
> His method for finding the solutions of the problem x² − ny² = 1
> (so-called "Pell's equation") is of considerable interest and importance.
>
> Solutions of Diophantine equations of the second order, such as 61x² +
> 1 = y². This very equation was posed as a problem in 1657 by the French
> mathematician Pierre de Fermat, but its solution was unknown in Europe
> until the time of Euler in the 18th century.
>
> Solved quadratic equations with more than one unknown, and found
> negative and irrational solutions.
>
> Preliminary concept of mathematical analysis.
>
> Preliminary concept of infinitesimal calculus, along with notable
> contributions towards integral calculus.
>
> Conceived differential calculus, after discovering the derivative and
> differential coefficient.
>
> Stated Rolle's theorem, a special case of one of the most important
> theorems in analysis, the mean value theorem. Traces of the general mean
> value theorem are also found in his works.
>
> Calculated the derivatives of trigonometric functions and formulae.
> (See Calculus section below.)
>
> In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along
> with a number of other trigonometric results. (See Trigonometry section
> below.)
>
> Arithmetic
>
> Bhaskara's arithmetic text Lilavati covers the topics of definitions,
> arithmetical terms, interest computation, arithmetical and geometrical
> progressions, plane geometry, solid geometry, the shadow of the gnomon,
> methods to solve indeterminate equations, and combinations.
>
> Lilavati is divided into 13 chapters and covers many branches of
> mathematics, arithmetic, algebra, geometry, and a little trigonometry and
> mensuration. More specifically the contents include:
>
> Definitions.
> Properties of zero (including division, and rules of operations with
> zero).
> Further extensive numerical work, including use of negative numbers and
> surds.
> Estimation of π.
> Arithmetical terms, methods of multiplication, and squaring.
> Inverse rule of three, and rules of 3, 5, 7, 9, and 11.
> Problems involving interest and interest computation.
> Arithmetical and geometrical progressions.
> Plane (geometry).
> Solid geometry.
> Permutations and combinations.
> Indeterminate equations (Kuttaka), integer solutions (first and second
> order). His contributions to this topic are particularly important, since
> the rules he gives are (in effect) the same as those given by the
> renaissance European mathematicians of the 17th century, yet his work was
> of the 12th century. Bhaskara's method of solving was an improvement of the
> methods found in the work of Aryabhata and subsequent mathematicians.
>
> His work is outstanding for its systemisation, improved methods and the new
> topics that he has introduced. Furthermore the Lilavati contained excellent
> recreative problems and it is thought that Bhaskara's intention may have
> been that a student of 'Lilavati' should concern himself with the
> mechanical application of the method.
> Algebra
>
> His Bijaganita ("Algebra") was a work in twelve chapters. It was the first
>
>
>
> Dhinakar Rajaram <rdhi...@gmail.com> Jan 31 12:09PM +0530
>
> Last mail before I could make the corrections, was accidently sent due to
> some issues with system. I rue for that. I have given below the corrected
> version of that post.
>
>
> *Thanks to: http://veda.wikidot.com.*
>
>
>
> *This post is just an introduction to one of the greatest astronomer of
> India Bhaskarachārya! I am in search for his works in detail, will post
> them here later. I am taking a small step to bring out the works by Indians
> on field of Astronomy especially solar astronomy.*
>
>
>
> Life Cycles of the Universe
>
>
>
> The Indians view that the Universe has no beginning or end, but follows a
> cosmic creation and dissolution. Indians are the one who propounds the idea
> of life-cycles of the universe. It suggests that the universe undergoes an
> infinite number of deaths and rebirths. Indians views the universe as
> without a beginning (anadi = beginning-less) or an end (ananta = end-less).
> Rather the universe is projected in cycles. Hindu scriptures refer to time
> scales that vary from ordinary earth day and night to the day and night of
> the Brahma that are a few billion earth years long.
>
>
>
> According to Carl Sagan,
>
>
>
>
>
> *"Millenniums before Europeans were willing to divest themselves of the
> Biblical idea that the world was a few thousand years old, the Mayans were
> thinking of millions and the Indians billions".*
>
>
>
> Continues Carl Sagan,
>
>
>
> *"… is the only religion in which the time scales correspond… to those
> of modern scientific cosmology."*
>
>
>
> Its cycles run from our ordinary day and night to a day and night of the
> Brahma, 8.64 billion years long, longer than the age of the Earth or the
> Sun and about half the time since the Big Bang". One day of Brahma is worth
> a thousand of the ages (yuga) known to humankind; as is each night." Thus
> each kalpa is worth one day in the life of Brahma, the God of creation. In
> other words, the four ages of the mahayuga must be repeated a thousand
> times to make a "day to Brahma", a unit of time that is the equivalent of
> 4.32 billion human years, doubling which one gets 8.64 billion years for a
> Brahma day and night. This was later theorized (possibly independently) by
> Aryabhata in the 6th century. The cyclic nature of this analysis suggests a
> universe that is expanding to be followed by contraction… a cosmos without
> end. This, according to modern physicists is not impossibility.
>
>
>
> Bhaskara II or Bhaskarachārya was an Indian mathematician and astronomer
> who extended Brahmagupta's work on number systems. He was born near Bijjada
> Bida (in present day Bijapur district, Karnataka state, South India) into
> the Deshastha Brahmin family. Bhaskara was head of an astronomical
> observatory at Ujjain, the leading mathematical centre of ancient India.
> His predecessors in this post had included both the noted Indian
> mathematician Brahmagupta (598–c. 665) and Varahamihira. He lived in the
> Sahyadri region. It has been recorded that his
> great-great-great-grandfather held a hereditary post as a court scholar, as
> did his son and other descendants. His father Mahesvara was as an
> astrologer, who taught him mathematics, which he later passed on to his son
> Loksamudra. Loksamudra's son helped to set up a school in 1207 for the
> study of Bhāskara's writings
>
>
>
> [image: Bhaskaracharya.jpg]
>
> *Bhaskara (1114 – 1185) (also known as Bhaskara II and Bhaskarachārya)*
>
>
>
> Bhaskaracharya's work in Algebra, Arithmetic and Geometry catapulted him to
> fame and immortality. His renowned mathematical works called Lilavati" and
> Bijaganita are considered to be unparalleled and a memorial to his profound
> intelligence. Its translation in several languages of the world bear
> testimony to its eminence. In his treatise Siddhant Shiromani he writes on
> planetary positions, eclipses, cosmography, mathematical techniques and
> astronomical equipment. In the Surya Siddhant he makes a note on the force
> of gravity:
>
>
>
> * "Objects fall on earth due to a force of attraction by the earth.
> Therefore, the earth, planets, constellations, moon, and sun are held in
> orbit due to this attraction."*
>
>
>
> Bhaskaracharya was the first to discover gravity, 500 years before Sir
> Isaac Newton. He was the champion among mathematicians of ancient and
> medieval India. His works fired the imagination of Persian and European
> scholars, who through research on his works earned fame and popularity.
> Some say Mayans and Chinese too know of gravity some 2000 years before him.
>
>
> *Birth and Education of Bhaskaracharya*
>
>
>
> Ganesh Daivadnya has bestowed a very apt title on Bhaskaracharya. He has
> called him ‘Ganakchakrachudamani’, which means, ‘a gem among all the
> calculators of astronomical phenomena.’ Bhaskaracharya himself has written
> about his birth, his place of residence, his teacher and his education, in
> Siddhantashiromani as follows, ‘A place called ‘Vijjadveed’, which is
> surrounded by Sahyadri ranges, where there are scholars of three Vedas,
> where all branches of knowledge are studied, and where all kinds of noble
> people reside, a brahmin called Maheshwar was staying, who was born in
> Shandilya Gotra (in Hindu religion, Gotra is similar to lineage from a
> particular person, in this case sage Shandilya), well versed in Shroud
> (originated from ‘Shut’ or ‘Vedas’) and ‘Smart’ (originated from ‘Smut’)
> Dharma, respected by all and who was authority in all the branches of
> knowledge. I acquired knowledge at his feet’.
>
>
>
> From this verse it is clear that Bhaskaracharya was a resident of
> Vijjadveed and his father Maheshwar taught him mathematics and astronomy.
> Unfortunately today we have no idea where Vijjadveed was located. It is
> necessary to ardently search this place which was surrounded by the hills
> of Sahyadri and which was the centre of learning at the time of
> Bhaskaracharya. He writes about his year of birth as follows,
>
> ‘I was born in Shake 1036 (1114 AD) and I wrote Siddhanta Shiromani when I
> was 36 years old.’
>
>
>
> Bhaskaracharya has also written about his education. Looking at the
> knowledge, which he acquired in a span of 36 years, it seems impossible for
> any modern student to achieve that feat in his entire life. See what
> Bhaskaracharya writes about his education,
>
>
>
> ‘I have studied eight books of grammar, six texts of medicine, six
> books on logic, five books of mathematics, four Vedas, five books on Bharat
> Shastras, and two Mimansas’.
>
>
>
> Bhaskaracharya calls himself a poet and most probably he was Vedanti, since
> he has mentioned ‘Parambrahman’ in that verse.
>
> Siddhanta Shriomani
>
>
>
> Bhaskaracharya wrote Siddhanta Shiromani in 1150 AD when he was 36 years
> old. This is a mammoth work containing about 1450 verses. It is divided
> into four parts, Lilawati, Beejaganit, Ganitadhyaya and Goladhyaya. In fact
> each part can be considered as separate book. The numbers of verses in each
> part are as follows, Lilawati has 278, Beejaganit has 213, Ganitadhyaya has
> 451 and Goladhyaya has 501 verses.
>
> One of the most important characteristic of Siddhanta Shiromani is it
> consists of simple methods of calculations from Arithmetic to Astronomy.
> Essential knowledge of ancient Indian Astronomy can be acquired by reading
> only this book. Siddhanta Shiromani has surpassed all the ancient books on
> astronomy in India. After Bhaskaracharya nobody could write excellent books
> on mathematics and astronomy in lucid language in India. In India,
> Siddhanta works used to give no proofs of any theorem. Bhaskaracharya has
> also followed the same tradition.
>
>
>
> Lilawati is an excellent example of how a difficult subject like
> mathematics can be written in poetic language. Lilawati has been translated
> in many languages throughout the world. When British Empire became
> paramount in India, they established three universities in 1857, at Bombay,
> Calcutta and Madras. Till then, for about 700 years, mathematics was taught
> in India from Bhaskaracharya’s Lilawati and Beejaganit. No other textbook
> has enjoyed such long lifespan.
>
> Bhaskara's contributions to mathematics
>
>
>
> Lilawati and Beejaganit together consist of about 500 verses. A few
> important highlights of Bhaskar's mathematics are as follows:
>
> Terms for numbers
>
>
>
> In English, cardinal numbers are only in multiples of 1000. They have terms
> such as thousand, million, billion, trillion, quadrillion etc. Most of
> these have been named recently. However, Bhaskaracharya has given the terms
> for numbers in multiples of ten and he says that these terms were coined by
> ancients for the sake of positional values. Bhaskar's terms for numbers are
> as follows:
>
>
>
> eka(1), dasha(10), shata(100), sahastra(1000), ayuta(10,000),
> laksha(100,000), prayuta (1,000,000=million), koti(107), arbuda(108),
> abja(109=billion), kharva (1010), nikharva (1011), mahapadma
> (1012=trillion), shanku(1013), jaladhi(1014), antya(1015=quadrillion),
> Madhya (1016) and parardha(1017).
>
> Kuttak
>
>
>
> Kuttak is nothing but the modern indeterminate equation of first order. The
> method of solution of such equations was called as ‘pulveriser’ in the
> western world. Kuttak means to crush to fine particles or to pulverize.
> There are many kinds of Kuttaks. Let us consider one example.
>
>
>
> In the equation, ax + b = CY, a and b are known positive integers. We want
> to also find out the values of x and y in integers. A particular example
> is, 100x +90 = 63y
>
>
>
> Bhaskaracharya gives the solution of this example as, x = 18, 81, 144, 207…
> And y=30, 130, 230, 330…
>
> Indian Astronomers used such kinds of equations to solve astronomical
> problems. It is not easy to find solutions of these equations but Bhaskara
> has given a generalized solution to get multiple answers.
>
> Chakrawaal
>
>
>
> Chakrawaal is the “indeterminate equation of second order” in western
> mathematics. This type of equation is also called Pell’s equation. Though
> the equation is recognized by his name Pell had never solved the equation.
> Much before Pell, the equation was solved by an ancient and eminent Indian
> mathematician, Brahmagupta (628 AD). The solution is given in his
> Brahmasphutasiddhanta. Bhaskara modified the method and gave a general
> solution of this equation. For example, consider the equation 61x2 + 1 =
> y2. Bhaskara gives the values of x = 22615398 and y = 1766319049
>
>
>
> There is an interesting history behind this very equation. The Famous
> French mathematician Pierre de Fermat (1601-1664) asked his friend Bessy to
> solve this very equation. Bessy used to solve the problems in his head like
> present day Shakuntaladevi. Bessy failed to solve the problem. After about
> 100 years another famous French mathematician solved this problem. But his
> method is lengthy and could find a particular solution only, while Bhaskara
> gave the solution for five cases. In his book ‘History of mathematics’, see
> what Carl Boyer says about this equation,
>
>
>
> ‘In connection with the Pell’s equation ax2 + 1 = y2, Bhaskara gave
> particular solutions for five cases, a = 8, 11, 32, 61, and 67, for 61x2 +
> 1 = y2, for example he gave the solutions, x = 226153980 and y =
> 1766319049, this is an impressive feat in calculations and its
> verifications alone will tax the efforts of the reader’
>
>
>
> Henceforth the so-called Pell’s equation should be recognized as
> ‘Brahmagupta-Bhaskaracharya equation’.
>
> Simple mathematical methods
>
>
>
> Bhaskara has given simple methods to find the squares, square roots, cube,
> and cube roots of big numbers. He has proved the Pythagoras theorem in only
> two lines. The famous Pascal Triangle was Bhaskara’s ‘Khandameru’. Bhaskara
> has given problems on that number triangle. Pascal was born 500 years after
> Bhaskara. Several problems on permutations and combinations are given in
> Lilawati. Bhaskar. He has called the method ‘ankapaash’. Bhaskara has given
> an approximate value of PI as 22/7 and more accurate value as 3.1416. He
> knew the concept of infinity and called it as ‘khahar rashi’, which means
> ‘anant’. It seems that Bhaskara had not notions about calculus, One of his
> equations in modern notation can be written as, d (sin (w)) = cos (w) dw.
>
> A Summary of Bhaskara's contributions
>
> A proof of the Pythagorean Theorem by calculating the same area in two
> different ways and then canceling out terms to get a² + b² = c².
>
>
>
> In Lilavati, solutions of quadratic, cubic and quartic indeterminate
> equations.
>
>
>
> Solutions of indeterminate quadratic equations (of the type ax² + b =
> y²).
>
>
>
> Integer solutions of linear and quadratic indeterminate equations
> (Kuttaka). The rules he gives are (in effect) the same as those given by
> the Renaissance European mathematicians of the 17th century
>
>
>
> A cyclic Chakravala method for solving indeterminate equations of the
> form ax² + bx + c = y. The solution to this equation was traditionally
> attributed to William Brouncker in 1657, though his method was more
> difficult than the chakravala method.
>
>
>
> His method for finding the solutions of the problem x² − ny² = 1
> (so-called "Pell's equation") is of considerable interest and importance.
>
>
>
> Solutions of Diophantine equations of the second order, such as 61x² +
> 1 = y². This very equation was posed as a problem in 1657 by the French
> mathematician Pierre de Fermat, but its solution was unknown in Europe
> until the time of Euler in the 18th century.
>
>
>
> Solved quadratic equations with more than one unknown, and found
> negative and irrational solutions.
>
>
>
> Preliminary concept of mathematical analysis.
>
>
>
> Preliminary concept of infinitesimal calculus, along with notable
> contributions towards integral calculus.
>
>
>
> Conceived differential calculus, after discovering the derivative and
> differential coefficient.
>
>
>
> Stated Rolle's theorem, a special case of one of the most important
> theorems in analysis, the mean value theorem. Traces of the general mean
> value theorem are also found in his works.
>
>
>
> Calculated the derivatives of trigonometric functions and formulae.
> (See Calculus section below.)
>
>
>
> In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along
> with a number of other trigonometric results.
>
> Arithmetic
>
>
>
> Bhaskara's arithmetic text Lilavati covers the topics of definitions,
> arithmetical terms, interest computation, arithmetical and geometrical
> progressions, plane geometry, solid geometry, the shadow of the gnomon,
> methods to solve indeterminate equations, and combinations.
>
>
>
> Lilavati is divided into 13 chapters and covers many branches of
> mathematics, arithmetic, algebra, geometry, and a little trigonometry and
> mensuration. More specifically the contents include:
>
>
>
> Definitions.
>
> Properties of zero (including division, and rules of operations with
> zero).
>
> Further extensive numerical work, including use of negative numbers and
> surds.
>
> Estimation of π.
>
> Arithmetical terms, methods of multiplication, and squaring.
>
> Inverse rule of three, and rules of 3, 5, 7, 9, and 11.
>
> Problems involving interest and interest computation.
>
> Arithmetical and geometrical progressions.
>
> Plane (geometry).
>
> Solid geometry.
>
> Permutations and combinations.
>
> Indeterminate equations (Kuttaka), integer solutions (first and second
> order). His contributions to this topic are particularly important, since
> the rules he gives are (in effect) the same as those given by the
> renaissance European mathematicians of the 17th century, yet his work was
> of the 12th century. Bhaskara's method of solving was an improvement of the
> methods found in the work of Aryabhata and subsequent mathematicians.
>
>
>
> His work is outstanding for its systemisation, improved methods and the new
> topics that he has introduced.
>
>
>
> Harish Kamath <bharis...@gmail.com> Jan 31 10:02PM +0530
>
> Thanks for this Wonderful information. I have been looking for similar
> information.
>
>
>
>
>
>
> CCD Nights !
>
> Suresh Mohan Neelmegh <drsure...@gmail.com> Jan 31 12:02PM +0530
>
> @ Doc : "But capturing photons is to do with f ratio" --- Yes. These are
> taken with f/6.9. Hope to try out a faster scope sometime.
> i meant that if there were two scope of equal focal length but different
> size lets say 10 inch but 4000 mm fl vs 14 inch 4000 mm fl both will have
> equal signal to noise ratio , but resolution will be more in lieu of light
> gathering capacity
> Suresh
>
>
>
>
> Amar Sharma <amar_u...@yahoo.com> Jan 31 04:48AM -0800
>
> Just to let you know there are few backlogs which I should be submitting
> here once I am at home and have some decent internet connection.
> I have taken prime focus shots of Comet Garradd with a DSLR, last week. I
> would be passing the RAW files onto someone like Keerthi who should be able
> to stack and further process them. Since I have not yet ventured into DSLR
> imaging and especially its processing. Hope some data could be extracted
> from those
> shots.
> Some FITS images of comets taken earlier are to be analyzed in a software
> like Astrometrica.
> As of now I am sitting awaiting for the 433 Eros event tonight. Knowing that
> I have gotten very restless and saturated cos of some GOTO pointing problem
> I will have a very hard time centering the point of light called Eros into
> the small f.o.v. of the CCD. Will have to rely hard on visual experience and
> tricks. In any case if the foggy weather doesnt play spoilsport I am willing
> to spend most part of the night for just the upcoming historic asteroid
> event, getting some CCD shots for analysis further.
> Lets hope for the best tonight.
> --- On Sun, 1/29/12, Amar Sharma <amar_u...@yahoo.com> wrote:Okay...Now
> inspite of after having clicked some not-often-clicked objects, I feel like
> its time to bring about a challenge and change in what I am doing. There's
> no point in just clicking images; there should be some value to it.
> I would have loved to click some bright asteroids and learn astrometry, but
> as mentioned earlier the scope is giving me a
> really *hard* time due to its bad GOTO functioning, inspite of having done
> complete star alignment several times. I have to painfully star hop every
> time to the difficult positions in the 50mm finder scope and attempt to
> center the objects in the very small CCD field of view (fov) :-(
>
>
>
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keerthi kiran
>>Bhaskara is a myth calculatedly popularized by practitioners and
>>believers of astrology to earn authenticity to the non-science!
At least, is it true that the book was named after his daughter and written for his daughter?
Another question always haunts me. Our ancestors did a lot of observations and research to calculate and predict the positions of the "grahas" as accurately as possible. This shows that they had a scientific mentality. With this being the case, why did they believe in Astrology? What made them believe that the positions of the planets may decide a person's fate? Why dint they ever question this belief?
Regards,
Keerthi
Balachandra Rao
You have asked: while our Indian astronomers did a lot of
observations and calculations
to predict correctly planetary positions and had the scientific
attitude, why did they believe in astrology?
This is truly a highly involved question and rather
sensitive to answer. All the same this is how I have tried to analyze
the issue:
1. Top Indian astronomers like Aryabhata, Bhaskara I, Brahmagupta and
Bhaskara II did not compose any work on astrology while they did
contribute their masterpieces on Astronomy! This shows that they had
no respect for that "discipline"!. Nor have they brought in astrology
in their astronomical works.
2. Hindus unfortunately have linked the theory of "karma" and fate or
destiny with the so-called influence of the planets for long. They did
not commit the mistake of thinking that the planets have "physical"
influence
(like gravitation, ultraviolet rays etc) on our day-to-day trivia-
the way modern believers rationalize!
3. However, brilliant Vedantins, saints and "vicharavaadins"
(taarkikas), chaarvaakas etc did not believe either in astrology or in
destiny.
4. Lord Buddha decried the practice of astrology and related divinations.
5. Unfortunately practising science and having a scientific attitude
are often different as we do notice among many modern scientists! Have
we not read in the media about a top scientist of space research in
this country expressing his gratitude to the Lord of Guruvayur by
offering "tulaabhaara" and the same organization deputing high level
officers (scientists!) to Tirupati to pray for the success of their
launchings?
5. How many scientists, including a former director of IISc, have not
surrendered themselves, mortgaging their brains, to the likes of Satya
Sai Baba et al ?
6. As I had mentioned earlier, it was mainly Varahamihira (505 CE) who
institutionalized and popularized astrology in India, fully conscious
of its being imported from "yavanas".
7. Most often astronomers, even in the West, unwillingly practised
astrology for livlihood since they could easily get royal patronage
for astrology but surely not for astronomy
8. For a detailed analysis of belief in astrology I recommend the
book "Astrology - Believe it or Not?"
(Navakarnataka Publications, Embassy Centre,Crescent Rd, B'lore-1)
l
On Fri, Feb 17, 2012 at 6:09 PM, keerthi kiran <info...@gmail.com> wrote:
> Dear Sir,
> Thanks for all your replies to my earlier questions. I had some more
> questions related to our ancestors. I had mailed them some time back (in the
> mail below). Can you please answer them whenever you are free?
> Our ancestors did a lot of observations and research to calculate and
> predict the positions of the "grahas" as accurately as possible. This shows
> that they had a scientific mentality. With this being the case, why did they
> believe in Astrology? What made them believe that the positions of the
> planets may decide a person's fate? Why dint they ever question this belief?
>
> Regards,
> Keerthi
>
Rakesh Nath
> 6. As I had mentioned earlier, it was mainly Varahamihira (505 CE) who
> institutionalized and popularized astrology in India, fully conscious
> of its being imported from "yavanas".
more than glad to hear about this.
Applause for a fine answer, sir, I am glad we have such a fine
personality in BAS. Really heartening to see.
--
Thanks and Regards
Rakesh Nath
"It is far better to grasp the Universe as it really is than to persist in delusion, however satisfying and reassuring."
Carl Sagan
Balachandra Rao
Thank you. In fact, in Varahamihira's "Brihad-jaataka" the
twelve raashis are introduced not
with their Sanskrit names like Mesha,Vrishabha etc but with Greek
names and his text is full of such Greek
words. Not only that, he gratefully acknowledges the superiority of
the 'yavanas' when he declares in his another popular text,
'Brihat-samhita': "The yavanas are of course 'mlecchaa' (uncultured
aliens) but this shaastra (astrology) is well established among them.
Even they are worshipped as rishis......".(Mlecchaa hi yavanaah teshu
samyakstitham:shaastramidam / rishivat te api poojyante kim punah
daivavid dvijah // ).
On Fri, Feb 17, 2012 at 9:44 PM, Rakesh Nath <rak...@gmail.com> wrote:
> Brilliant answer sir!
>
> I am really glad we have educated and knowledgeable academics in India
> and in BAS.
> You might already know that I take a keen interest in history of
> Astronomy and have been time and again baffled by people like Subhas Kak
> not doing justice to the astronomy in India. Its really hard to sift the
> real science from made up ideas. I hope at sometime I can study with you
> about some ideas in astronomy.
>
> Glad to have access to you.
>
> On 02/17/2012 09:07 AM, Balachandra Rao wrote:
keerthi kiran
From: keerthi kiran <info...@gmail.com>
Date: Mon, Feb 20, 2012 at 11:31 PM
Subject: Re: [-BAS-] Digest for b-...@googlegroups.com - 25 Messages in 8 Topics
Hello Sir,
Thanks a lot for the wonderful answer. But this changes the point of view I always had about the Indian Astronomy.
1. I always thought that our classical astronomers did astronomy so that they could accurately predict the future.
2. I always thought that the Kingdoms gave them land and infrastructure so that they could master the art of fortune telling.
3. In all the mythological stories (Ramayana, Mahabharata, Story of Buddha, Shankaracharya and so on) we have seen that based on the janma nakshatras and Kundali of the protagonists, thier future is foretold by a famous Jyothishi of their time.
So my question now is, What was the need for our ancestors to observe the planets? Was it sheer curiosity? Or was it a method to measure time? Or was it only for the astrology?
I am sorry if I am asking stupid questions without knowing anything. Perhaps, I should first read the material you have suggested and then will be able to better understand the past.
Regards,
keerthi
Balachandra Rao
Glad that you have a big stock of questions and hopefully these
get cleared by and by. (1) It is not true that ancient Indians
practised astronomy so that they could predict the future (of humans)
accurately. The question of astrological predictions, based on
planetary chart, came to India much later - by about 2nd or 3rd
cent.CE. (2) Partly it is true that monarchs gave patronage to
astrologers since most of the rulers believed in that non-science.
Don't we see our 21st century chief-ministers spend all their time
with soothsayers, mumbo-jumbo charlatans and visiting every
street-smart "godman" and "godwoman" - except attending to
administration of the state?
(3) It is true that in our epics and "vijayas" of acharyas there are
references to "jyotishis" predicting the great achievements of their
heroes. But most of these predictions are later fabrications
incorporated into the texts.
(4) The need for our ancients to develop astronomy was mainly (i)
natural curiosity shared by all ancient civilizations, (ii)
requirements of navigators; you may know that ancient India developed
mature technology of navigation, "naukaashaastra",
(iii) to keep time - newmoons,fullmoons,eqinoxes & solstices and seasons;
Vedaang Jyotisha calls astronomy "Kaala-vidhaana-shaastra" - the
science of procedures of time and of course, (iv) ability to make
astrological predictions "accurately" even as chemistry emerged from
the practised-for-centuries alchemy.
In fact, this is how astronomy developed in ancient Babylonia
(motherland of astrology!), ancient Egypt and Greece - how can we
ignore Ptolemy's "Tetrabiblios", the treatise on planetary astrology?
But what was unique of ancient India is their preoccupation with
performing "yaagas" and "yajnas" prescibed for special times. This
necessity was equally resposible for our Indian geometry thro' the
"Shulva sootras" eight to nine centuries before Euclid!
In passing let me tell you, our ancients' incorrigible faith in
things religious was greatly responsible for their continuously
seeking accuracy - without cooking up - in their astronomical
procedures, parameters and mathematical methods (e.g. determining the
value of "pi" as accurately as required, infinite series for sine,
cosine etc) centuries before the Europeans! This subtle psychological
trait of
ancient (if not modern) Indians passes above the heads of western
critics. (It is incidental that I am a non-believer!).
Have I bored you too much?
On Mon, Feb 20, 2012 at 11:31 PM, keerthi kiran <info...@gmail.com> wrote:
> Hello Sir,
> Thanks a lot for the wonderful answer. But this changes the point of view I
> always had about the Indian Astronomy.
> 1. I always thought that our classical astronomers did astronomy so that
> they could accurately predict the future.
> 2. I always thought that the Kingdoms gave them land and infrastructure so
> that they could master the art of fortune telling.
> 3. In all the mythological stories (Ramayana, Mahabharata, Story of Buddha,
> Shankaracharya and so on) we have seen that based on the janma nakshatras
> and Kundali of the protagonists, thier future is foretold by a famous
> Jyothishi of their time.
>
> So my question now is, What was the need for our ancestors to observe the
> planets? Was it sheer curiosity? Or was it a method to measure time? Or was
> it only for the astrology?
>
> I am sorry if I am asking stupid questions without knowing anything.
> Perhaps, I should first read the material you have suggested and then will
> be able to better understand the past.
>
> Regards,
> keerthi
>
>
> On Fri, Feb 17, 2012 at 8:37 PM, Balachandra Rao <balacha...@gmail.com>
Pavan Keshavamurthy
Thanks for your wonderful inputs. It's a pleasure to follow you on this
list!
> (3) It is true that in our epics and "vijayas" of acharyas there are
> references to "jyotishis" predicting the great achievements of their
> heroes. But most of these predictions are later fabrications
> incorporated into the texts.
This is a recurrent motif in most hagiographical accounts, Indian
or otherwise. A literary idiom of sorts to establish somebody's
importance by giving weightage to archetypal mythic episodes and
foretelling of future destiny.
I don't think they may be called fabrications; They're just not to be
interpreted literally.
> In passing let me tell you, our ancients' incorrigible faith in
> things religious was greatly responsible for their continuously
> seeking accuracy - without cooking up - in their astronomical
> procedures, parameters and mathematical methods (e.g. determining the
> value of "pi" as accurately as required, infinite series for sine,
> cosine etc) centuries before the Europeans! This subtle psychological
> trait of
> ancient (if not modern) Indians passes above the heads of western
> critics. (It is incidental that I am a non-believer!).
> Have I bored you too much?
I understand that there was very little of organized religious hegemony
over matters of science, philosophy and spirituality, but how exactly
does incorrigible faith correspond to seeking accuracy?
Regards
--
/P
http://grahana.net/
praveen kulkarni
This sincerity coupled with the Obsessive Compulsive trait of piety must have been the driving force in the pursuit of "accurate" values that Balachandra Sir mentioned.
Anthropological studies across various cultures show that ritualistic behavior is common world-over. It's part of the Schizotypal Personality.
I understand that there was very little of organized religious hegemony
over matters of science, philosophy and spirituality, but how exactly
does incorrigible faith correspond to seeking accuracy?
Signature /-
