Jump to content
IndiaDivine.org

Aryabhata I

Rate this topic


Guest guest

Recommended Posts

Dear

friends,

Namaskar!

The

following document was sent to me by Shri Niraj Mohanka, Indologist, sometime

back. It is a well researched paper and would therefore like to share it with

you for your views.

Regards,

A K Kaul

 

Aryabhata I

 

Aryabhata I (476-ca 550):

Indian astronomer and mathematician.

 

Using Hindu Brahmi (aka

'Arabic') numerals accurately calculates pi () to 3.1416, and the solar year to

365.3586805 days.

A thousand years before

Copernicus, Aryabhata propounds a heliocentric universe with elliptically

orbiting planets and a spherical Earth spinning on its axis, explaining the

apparent rotation of the heavens. Writes Aryabhatiya, history's first

exposition on plane and spherical trigonometry, algebra and arithmetic.

Aryabhata wrote

Aryabhatiya , finished in 499, which is a summary of Hindu mathematics up to

that time, written in verse.

Contribution to

trigonometry The first actual appearance of the sine of an angle appears in the

work of the Hindus.

Aryabhata, in about 500,

gave tables of half chords which now really are sine tables and used jya for

our sin. Jya (India)

became Jiba then Jaib (Arabs) which then became Sinus (Romans) which then

became Sine (modern terminology).

 

" All the planets

whether moving in the orbits or in eccentric circles, move anticlockwise from

their apogees and clockwise from their perigees. " This law was stated

before 500 C.E., over 1000 years before the first law of planetary motion was

given by Johannes Kepler in 1609 C.E.

 

(The

3100 B.C.E. date for the MBH War and start of Kali Yuga is a misinterpretation

of a date that astronomer Aryabhatta used to make a fixed reference in the past

which all astronomers could use to calibrate against. 3101 or 3102 B.C.E. has

no historical meaning in India’s

history as is validated by all the Puranas as referenced against the Vedas and

all the archaeological evidence we have.)

 

The blame for mixing up

the Puranic and the astronomical yugas rests squarely on the celebrated

astronomer-mathematician Aryabhatta (b. AD 476).

He introduced two changes

in the traditional yuga system.

1) He defined a kalpa as

a period of 1,008 mahayugas (instead of 1,000). Since 1,008 is divisible by

seven, each new kalpa would begin on the same week day.

2) He divided a mahayuga

into four equal rather than unequal parts so that each consisted of 108,000

years.

 

Aryabhatta started his

astronomical Kaliyuga at 6 A.M. on Friday, 18 February 3102 BC (Julian) at

Lanka, which is hypothetically placed at the intersection of the equator with

the meridian of Ujjain.

In astronomical parlance, this choice of epoch

defines the Aryapaksa, “the Arya school” of Siddhantic astronomy.

Aryabhatta also

propounded another system, in which the Kaliyuga began six hours earlier, that

is on the midnight of 17/18 February 3102 BC (Julian) at Ujjain. This is known as the

ardha-ratri-ka-paksa “the midnight school”. Since planets move,

their configuration cannot be the same at midnight and at sunrise.

In particular, the sun

and moon cannot remain aligned at two points in time, six hours apart. It is

thus clear that Aryabhatta’s Kaliyuga is a theoretical artifact, and not

the epoch of an actual astronomical observation.

 

How did Aryabhatta arrive

at this particular date? It seems that his starting point was the observed planetary

positions at a known epoch.

Since he knew the orbital

periods, he could calculate backwards the epoch when all the planets could be

taken to have been aligned at the beginning of the zodiacal sign Aries (Mesa). It is now known

that planetary orbits are subject to various kinds of perturbations, and a

theory depending on the orbital period as the sole parameter cannot give

accurate results.

According to modern

numerical simulations, on 17/18 February 3102 BC the five geocentric planets

were not aligned but spread over two neighboring zodiacal signs.

This again underlines the

inference that the significance of the date was hypothetical rather than real.

Even if Aryabhatta had chosen a slightly different epoch, it would not have

made much difference as far as the actual sky conditions are concerned.

 

The choice of 3102 BC,

however, had a special significance for Aryabhatta. Midday at Ujjain on the equinoctial

day 21 March AD 499 exactly corresponds to the beginning of the year 3600 of

his Kaliyuga. Since the ardharatrikapaksa starts its Kaliyuga six hours before

the Aryapaksa, Aryabhatta artificially made the duration of the year slightly

longer in the former case so that in both the schools the 3600th year starts at

the same time. We may recall that AD 499 is the year of the composition of

Aryabhatiya.

The acceptance of the new

date must have become universal by 634 C.E. for in that year we have the public

use of it in the Aihole Inscription of King Pulakesin II dating itself in the

Kaliyuga Era side by side with the Saka Era and referring to the Bharata War.

Unfortunately, while

talking of the passage of time, Aryabhatta did not explicitly say “before

the Kailyuga”. Instead, he used the term Bharatat Purvam, that is

“before [the] Bharata [battle]”, obviously alluding to the Puranic

yuga system. This is what gave currency to 3102 BC as the date of the battle.

The use of Aryabhatta’s epoch in the Puranic context is ironical in the

light of the fact that he was severely castigated by his student critic

Brahmagupta (b. AD 598) for deviating from smrti (“tradition”)

while formulating his own yuga system.

 

The date 3102 BC for the

Puranic Kaliyuga is not tenable. First, the Puranic and astronomical yugas are

widely different in length. The Puranas divide 94 generations from Manu to the

Bharata battle into three yugas, so that each yuga is approximately 31

generations or say 600 years. Aryabhata’s yugas, on the other hand, run

into hundreds of thousands of years.

Secondly, an astronomical

epoch begins at a precise moment which is chosen by the astronomer. In

contrast to the astronomical Kaliyuga, the beginning of the Puranic Kaliyuga is

not precise at all. According to Mahabharata Adiparvan (2.13), the battle

occurred at the junction of Kali and Dvapara.

The Bhagavata Purana, on

the other hand, gives two versions of the epoch. In one version (1.15.36),

Kaliyuga started the day Krsna died, while the second version (12.2.33) starts

Kaliyuga at the very moment Krsna died. One can see the feeling of discomfort

here. It did not look quite the right thing to have Krsna live into the

Kaliyuga. (According to the chronology of the Mahabharata, Krsna dies some 20

years after the battle. This was the time when Yudhisthira abdicated in favour

of his grand-nephew Parikshit.)

We thus see that the

Puranic Kaliyuga is a manner of speaking rather than a carefully chosen point

of time as in astronomy.

Finally, if the Bharata

battle indeed took place in 3102 BC, how was the epoch recorded? (It could not

have been in terms of eras that began later.) How and by who was the date kept

alive for 3,600 years? How did Aryabhata come across this date? If

Aryabhata’s predecessors had been asked about the battle’s

chronology, what date would they have mentioned in answer?

 

DATE OF THE BHARATA BATTLE

The Puranas do not

recognize Aryabhata’s date at all. They provide their own information on

the subject. It is possible to calculate the Bharata battle’s date from

statements within the Puranas. Unfortunately, one can derive not one but many

dates. The Puranas contain a bland statement that 1,015 (or 1,050) years

elapsed between Pariksit’s birth (shortly after the battle) and the

coronation of Mahapadma Nanda. Nanda’s coronation was a singular event

from the Puranic point of view because he was a son of a Sudra mother, and

exterminated all blue-blooded Ksatriyas.

 

The Jain Parisistaparvan

calls Nanda the son of a courtesan by a barber. The Greek historian Quintas

Curtius also says that Nanda was a barber who being handsome gained the

affection of the queen. Through her influence he obtained a position of royal

confidence which he treacherously used to murder the king.

The Matsya Purana assigns

88 years to the reign of the first Nanda. The figure is unreasonably high; 88

(astasiti) appears to be a mistake for 28 (astavimsati), which the Vayu Purana

quotes. The first Nanda was succeeded by his eight sons who, all Puranas

agree, ruled for 12 years, giving a total of 40 years for the Nanda rule.

(Ancient Sri Lankan chronicles reduce the figure to 22 years).

 

A hoard of coins

discovered from the Bhir mound at Taxila in 1924 contains 1,059 punch-marked

coins from Magadha.

These coins belong to three successive dynasties: Sisunaga, Nanda and the

Maurya. Significantly, while one can distinguish between coins issued by

different kings in the case of the Sisunagas and the Mauryas, the Nanda coins

all belong to a single ruler. This is consistent with the brevity of the Nanda

rule.

The Nandas were dethroned

by Candragupta Maurya whose date of coronation is known from independent

sources to be about 320 BC. Thus the Puranas

themselves suggest about 1400 BC for the Bharata battle.

 

Niraj Mohanka

Indologist

August 2006

Email: NewDharma2100

Websites: http://www.newdharma.org/ & http://www.dharmicscriptures.org/

 

Link to comment
Share on other sites

Dear Kaul ji,

I would say that the views about the same would come in a better

way than you expect. ;) A revived commentary for Aryabhateeya is

under preparation (No, Not by me) :). And that will put an end to

many controversies and confusions caused by half baked views. I hope

that the work will come out soon - you can guess by whom. ;). Yah,

from the same individual to whom you lack the caliber to answer using

the same mathematical or scientific views. :) So I am not much

interested as of now, in spending too much time on another

theoretical discussion, which won't be of much interest to the group

members.

Love,

Sreenadh

 

, " jyotirved "

<jyotirved wrote:

>

> Dear friends,

>

> Namaskar!

>

> The following document was sent to me by Shri Niraj Mohanka,

Indologist,

> sometime back. It is a well researched paper and would therefore

like to

> share it with you for your views.

>

> Regards,

>

> A K Kaul

>

>

>

> Aryabhata I

>

>

>

> Aryabhata I (476-ca 550): Indian astronomer and mathematician.

>

>

>

> Using Hindu Brahmi (aka 'Arabic') numerals accurately calculates pi

() to

> 3.1416, and the solar year to 365.3586805 days.

>

> A thousand years before Copernicus, Aryabhata propounds a

heliocentric

> universe with elliptically orbiting planets and a spherical Earth

spinning

> on its axis, explaining the apparent rotation of the heavens. Writes

> Aryabhatiya, history's first exposition on plane and spherical

trigonometry,

> algebra and arithmetic.

>

> Aryabhata wrote Aryabhatiya , finished in 499, which is a summary

of Hindu

> mathematics up to that time, written in verse.

>

> Contribution to trigonometry The first actual appearance of the

sine of an

> angle appears in the work of the Hindus.

>

> Aryabhata, in about 500, gave tables of half chords which now

really are

> sine tables and used jya for our sin. Jya (India) became Jiba then

Jaib

> (Arabs) which then became Sinus (Romans) which then became Sine

(modern

> terminology).

>

>

>

> " All the planets whether moving in the orbits or in eccentric

circles, move

> anticlockwise from their apogees and clockwise from their

perigees. " This

> law was stated before 500 C.E., over 1000 years before the first

law of

> planetary motion was given by Johannes Kepler in 1609 C.E.

>

>

>

> (The 3100 B.C.E. date for the MBH War and start of Kali Yuga is a

> misinterpretation of a date that astronomer Aryabhatta used to make

a fixed

> reference in the past which all astronomers could use to calibrate

against.

> 3101 or 3102 B.C.E. has no historical meaning in India's history as

is

> validated by all the Puranas as referenced against the Vedas and

all the

> archaeological evidence we have.)

>

>

>

> The blame for mixing up the Puranic and the astronomical yugas rests

> squarely on the celebrated astronomer-mathematician Aryabhatta (b.

AD 476).

>

> He introduced two changes in the traditional yuga system.

>

> 1) He defined a kalpa as a period of 1,008 mahayugas (instead of

1,000).

> Since 1,008 is divisible by seven, each new kalpa would begin on

the same

> week day.

>

> 2) He divided a mahayuga into four equal rather than unequal parts

so that

> each consisted of 108,000 years.

>

>

>

> Aryabhatta started his astronomical Kaliyuga at 6 A.M. on Friday, 18

> February 3102 BC (Julian) at Lanka, which is hypothetically placed

at the

> intersection of the equator with the meridian of Ujjain. In

astronomical

> parlance, this choice of epoch defines the Aryapaksa, " the Arya

school " of

> Siddhantic astronomy.

>

> Aryabhatta also propounded another system, in which the Kaliyuga

began six

> hours earlier, that is on the midnight of 17/18 February 3102 BC

(Julian) at

> Ujjain. This is known as the ardha-ratri-ka-paksa " the midnight

school " .

> Since planets move, their configuration cannot be the same at

midnight and

> at sunrise.

>

> In particular, the sun and moon cannot remain aligned at two points

in time,

> six hours apart. It is thus clear that Aryabhatta's Kaliyuga is a

> theoretical artifact, and not the epoch of an actual astronomical

> observation.

>

>

>

> How did Aryabhatta arrive at this particular date? It seems that his

> starting point was the observed planetary positions at a known

epoch.

>

> Since he knew the orbital periods, he could calculate backwards the

epoch

> when all the planets could be taken to have been aligned at the

beginning of

> the zodiacal sign Aries (Mesa). It is now known that planetary

orbits are

> subject to various kinds of perturbations, and a theory depending

on the

> orbital period as the sole parameter cannot give accurate results.

>

> According to modern numerical simulations, on 17/18 February 3102

BC the

> five geocentric planets were not aligned but spread over two

neighboring

> zodiacal signs.

>

> This again underlines the inference that the significance of the

date was

> hypothetical rather than real. Even if Aryabhatta had chosen a

slightly

> different epoch, it would not have made much difference as far as

the actual

> sky conditions are concerned.

>

>

>

> The choice of 3102 BC, however, had a special significance for

Aryabhatta.

> Midday at Ujjain on the equinoctial day 21 March AD 499 exactly

corresponds

> to the beginning of the year 3600 of his Kaliyuga. Since the

> ardharatrikapaksa starts its Kaliyuga six hours before the

Aryapaksa,

> Aryabhatta artificially made the duration of the year slightly

longer in the

> former case so that in both the schools the 3600th year starts at

the same

> time. We may recall that AD 499 is the year of the composition of

> Aryabhatiya.

>

> The acceptance of the new date must have become universal by 634

C.E. for in

> that year we have the public use of it in the Aihole Inscription of

King

> Pulakesin II dating itself in the Kaliyuga Era side by side with

the Saka

> Era and referring to the Bharata War.

>

> Unfortunately, while talking of the passage of time, Aryabhatta did

not

> explicitly say " before the Kailyuga " . Instead, he used the term

Bharatat

> Purvam, that is " before [the] Bharata [battle] " , obviously alluding

to the

> Puranic yuga system. This is what gave currency to 3102 BC as the

date of

> the battle. The use of Aryabhatta's epoch in the Puranic context is

> ironical in the light of the fact that he was severely castigated

by his

> student critic Brahmagupta (b. AD 598) for deviating from smrti

> ( " tradition " ) while formulating his own yuga system.

>

>

>

> The date 3102 BC for the Puranic Kaliyuga is not tenable. First,

the

> Puranic and astronomical yugas are widely different in length. The

Puranas

> divide 94 generations from Manu to the Bharata battle into three

yugas, so

> that each yuga is approximately 31 generations or say 600 years.

> Aryabhata's yugas, on the other hand, run into hundreds of

thousands of

> years.

>

> Secondly, an astronomical epoch begins at a precise moment which is

chosen

> by the astronomer. In contrast to the astronomical Kaliyuga, the

beginning

> of the Puranic Kaliyuga is not precise at all. According to

Mahabharata

> Adiparvan (2.13), the battle occurred at the junction of Kali and

Dvapara.

>

> The Bhagavata Purana, on the other hand, gives two versions of the

epoch.

> In one version (1.15.36), Kaliyuga started the day Krsna died,

while the

> second version (12.2.33) starts Kaliyuga at the very moment Krsna

died. One

> can see the feeling of discomfort here. It did not look quite the

right

> thing to have Krsna live into the Kaliyuga. (According to the

chronology of

> the Mahabharata, Krsna dies some 20 years after the battle. This

was the

> time when Yudhisthira abdicated in favour of his grand-nephew

Parikshit.)

>

> We thus see that the Puranic Kaliyuga is a manner of speaking

rather than a

> carefully chosen point of time as in astronomy.

>

> Finally, if the Bharata battle indeed took place in 3102 BC, how

was the

> epoch recorded? (It could not have been in terms of eras that

began later.)

> How and by who was the date kept alive for 3,600 years? How did

Aryabhata

> come across this date? If Aryabhata's predecessors had been asked

about the

> battle's chronology, what date would they have mentioned in answer?

>

>

>

> DATE OF THE BHARATA BATTLE

>

> The Puranas do not recognize Aryabhata's date at all. They provide

their

> own information on the subject. It is possible to calculate the

Bharata

> battle's date from statements within the Puranas. Unfortunately,

one can

> derive not one but many dates. The Puranas contain a bland

statement that

> 1,015 (or 1,050) years elapsed between Pariksit's birth (shortly

after the

> battle) and the coronation of Mahapadma Nanda. Nanda's coronation

was a

> singular event from the Puranic point of view because he was a son

of a

> Sudra mother, and exterminated all blue-blooded Ksatriyas.

>

>

>

> The Jain Parisistaparvan calls Nanda the son of a courtesan by a

barber.

> The Greek historian Quintas Curtius also says that Nanda was a

barber who

> being handsome gained the affection of the queen. Through her

influence he

> obtained a position of royal confidence which he treacherously used

to

> murder the king.

>

> The Matsya Purana assigns 88 years to the reign of the first

Nanda. The

> figure is unreasonably high; 88 (astasiti) appears to be a mistake

for 28

> (astavimsati), which the Vayu Purana quotes. The first Nanda was

succeeded

> by his eight sons who, all Puranas agree, ruled for 12 years,

giving a total

> of 40 years for the Nanda rule. (Ancient Sri Lankan chronicles

reduce the

> figure to 22 years).

>

>

>

> A hoard of coins discovered from the Bhir mound at Taxila in 1924

contains

> 1,059 punch-marked coins from Magadha. These coins belong to three

> successive dynasties: Sisunaga, Nanda and the Maurya.

Significantly, while

> one can distinguish between coins issued by different kings in the

case of

> the Sisunagas and the Mauryas, the Nanda coins all belong to a

single ruler.

> This is consistent with the brevity of the Nanda rule.

>

> The Nandas were dethroned by Candragupta Maurya whose date of

coronation is

> known from independent sources to be about 320 BC. Thus the Puranas

> themselves suggest about 1400 BC for the Bharata battle.

>

>

>

> Niraj Mohanka

>

> Indologist

>

> August 2006

>

> Email: NewDharma2100

>

> Websites: http://www.newdharma.org/ &

http://www.dharmicscriptures.org/

>

Link to comment
Share on other sites

hinducivilization , " Avtar Krishen Kaul "

<jyotirved wrote:

 

Dr. Anand M. Sharan ji,

Namaskar!

If by " alingment " you mean the mean longitudes of all the planets

having been zero, I am afraid right from 10000 BCE to 12030 AD,

there has not been/is not going to be any such moment when such

a " mishap " could have occured/can occur!

This can be verified by anybody from Ganpati etc. programs.

Thus, if we bave to bank on astronomical presumptions of all the

planets having been zero, Kaliyuga is yet to start!

So long live astronomical Kaliyuga without actually starting at all!

With regards,

A K Kaul

 

hinducivilization , " amsharanx "

<amsharanx@> wrote:

>

> Shree Kauljee:

>

> What I meant was - The Date, Time, and Place where any one could

have

> seen the event happening ? Obviously, latitude and longitude fix

the

> point on earth from where the observation is/was made.

>

> That book I am refering to - has a survey of many researchers who

> have given varius dates.

>

> Thanks.

>

> Anand M. Sharan

>

>

> hinducivilization , " Avtar Krishen Kaul "

> <jyotirved@> wrote:

> >

> > Dr. Anand M. Sharan ji,

> > Namaskar!

> > I do not understand what you mean by " Date and time of

observation

> > when it lines up " . Please clarify.

> >

> > Regarding the date of MBh war by Sarvashri Sathe, Deshmukh and

> > Joshi, I shall try to get the book from Pune, but in the

meantime,

> > could you kindly tell me the date/dates of the Mbh war according

to

> > them and the reason for their having arrived at that conclusion

in

> a

> > nutshell.

> > Regards,

> > AKK

> > hinducivilization , " amsharanx "

> > <amsharanx@> wrote:

> >

> > > Shree Kauljee:

> > >

> > > Possibly, I can check what you are saying myself.

> > >

> > > Pl write it down the following:

> > >

> > > 1. Date and time of observation when it lines up, preferably

the

> > > number itself.

> > >

> > > 2. Latitude of the place.

> > >

> > > 3. Longitude of place.

> > >

> > > Regarding all astronomers - I do not believe that only

> astronomers

> > can

> > > determine the date or they are the only ones who can find

> > solutions

> > > to this problem.

> > >

> > > Regarding the reference which has survey of other researchers

Pl

> > see

> > >

> > > " Sathe, S., Deshmukh, V., and Joshi, P., Bharatiya Yuddha:

> > > Astronomical References, Shri Babasaheb Apte Smarak Samiti,

(Pune,

> > > 1985). "

> > >

> > >

> > > Thanks.

> > >

> > > Anand M. Sharan

> > >

> >

>

 

--- End forwarded message ---

Link to comment
Share on other sites

Join the conversation

You are posting as a guest. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
×
×
  • Create New...