Subject: Re: [HM] Indian astronomy and mathematics
From: Dinesh Maheshwari (dsm@cypress.com)
Date: Fri Feb 11 2000 - 22:44:21 EST
Dear HM list members,
Forgive me for answering some what belatedly; my "employer's demands"
take precedence over my personal interest.
Let's examine again the data we do have about Aryabhata's system from
recorded history.
*1. He believed in a rotating earth and that the daily stellar movement
was because of the rotation of the earth.
*2. He used the concept of sighrocca and the mandocca, the period of
sighrocca for inferior planets in his model is the time taken by the
planet around the sun.
Compare this with Ptolemy's model.
*1 . Earth is stationary, no rotation and no revolution.
*2. Has the concept of epicycles for the planets; I do not know as to how
the period of epicycles in this system correspond with actual planetary
periods around the Sun (if some one knows the actual numbers,
please let me know.)
Let's first consider the implications of the rotating earth. If the earth
rotates such that the daily movement of the stars is accounted for
by the rotation then the period of the rotation has to be the approximately
same as a day. Therefore, day and night are also caused by the rotation of
the earth and not by the revolution of the sun around the earth.
Thus by the Occam's Razor principle, rotating earth and
geocentric, homocentric, topocentric (and also Tycho-Brahic hybrid )
solar systems are not compatible. It is for this reason we see the notion
of rotating earth only in heliocentric models- Copernicus' as well as
Aristarchus', although the rotation of the earth was proposed by another
Greek astronomer (Anaxagoras ? ) before Aristarchus.
Now critics can object that the earth can be rotating in a geocentric
model if the period of the Sun around the earth is taken to be a year
and not 24 hours. However, this model cannot explain the time and position
of the planets, even approximately, as observed from the earth. And
certainly this is the less intuitive model than earth rotating in a heliocentric
model.
Ergo, a rotating earth such that sighrocca for inferior planets is
the time taken by the planet around the sun implies a presence of
a heliocentric model from which the geocentric rendering is obtained.
And we know that armed with the concept of epicycles one can
perform this mapping from the heliocentric model to the geocentric
model for rendering time and position of the heavenly bodies
to the observers from earth.
Brahmagupta does not believe in a rotating earth and therefore
could have also not believed in a heliocentric model. However, he can
still use the sighrocca method to perform "corrections" to planetary motions.
Could it be that Aryabhata was trying to reconcile the two systems
by equating the "apogee of an eccentric orbit, or the point on a
concentric orbit from which an epicycle moves", as KP has cited
from _Aryabhatiya_ (Kalakriya 17--21), because he could
derive the epicycles from the heliocentric model more easily than
the "apogee of an eccentric orbit".
BTW, it is also interesting that one of the most important Vedic
astronomical treatises, _SuryaSiddhanta_ is named after the Sun
("Surya" means Sun in Sanskrit) and not the earth. Could it be that
the ancient Vedic conception was indeed heliocentric as suggested
in _Satapatha_Brahamana_(SB 8.7.3.10) which says -
"The sun strings these worlds - the earth, the planets, the atmosphere-
to himself on a thread. This thread is the same as the wind"
And that when the summaries of the five surviving siddhantas (of the
18 from the ancient Vedic times, as corroborated by references to them
in the later commentaries, 13 are deemed to be lost) were written down
in the early part of the first millennium CE that there was some ambiguity
(perhaps due to some Hellenic influence, for instance we know that the
Greek Zodiac names were used in India for a brief period after which
they reverted back to the Sanskrit names "implying" the
dominant constellation in the 12 lunar months used in Vedic times).
This ambiguity could have been the cause of different interpretations by
Brahmagutpa and Aryabhata vis-a-vis the heliocentric and geocentric
system and perhaps this is what the rivalry was really about.
Why should there be a need for a heliocentric solar system in ancient times?
*1. As Milo Gardner has correctly pointed out, the ancients were aware
of the sidereal motion and calculated the sidereal year etc. In Vedic times
in India, three different years were computed simultaneously (as recorded
in Vedanga Jyotisa[prior to 1350BC]) :-
1. naksatra year (sidereal year) (BTW, divided into 12 months).
2. lunar year
3. solar year
And two different days were used : solar days and the tithi -lunar
day (lunar_year/360).
They used a 95 year cycle to synchronize the naksatra and solar years and
this was also manifested in the design of the fire altars.
(Even today, the Indian lunar and Indian solar calendars are used in India,
although in different parts of India. )
The sidereal motion can be more easily and accurately explained by the
heliocentric model than the geocentric model. BTW, Aryabhata calculated
the sidereal year to be 365days, 6 hours, 12 m, 30 secs which is within
3 min 30secs of the actual sidereal year of 365 days, 6 hr, 9 min, 9.5 sec
of mean solar time.
The Greeks however were not as concerned with the sidereal motion, so
Aristarchus' heliocentric notions "could have been" inspired by the notions
of the rotating earth put forth by Anaxagoras (?).
*2. A heliocentric model is simpler and simpler is always better in Vedic
philosophy. Vedic philosophy promotes simplicity and coherence with as
few boundary conditions as possible. (e.g. notions of non-duality etc.)
BTW, my understanding is that the Copernicus' system had less epicycles
than employed in Ptolemic system(80 circles), but a recent post suggests
otherwise; can someone please clarify.
Also, I remember reading somewhere (I apologize, I cannot remember
where) that Galileo was able to see the different phases of Venus using
the telescope and was thus able to confirm that the earth was moving.
Can someone corroborate this ?
Best Regards,
Dinesh
PS: Yesterday, while watching a documentary on Roman history, my wife
asked me if the Romans had made any significant contributions to math
and science DURING the Roman empire.
[She is from an ancient town, Boves, (from the Roman times) at the foothill
of Alps in Northern Italy and from time to time you can still unearth stone
pieces from the Roman times - inspiring people, like my wife, to dig deeper
into Roman history]. Unfortunately, I could not recall any significant Roman
contributions to math and science (although I am quite aware of their
engineering feats and the mathematical, artistic etc. achievements in the
post Roman-empire period).
Can someone please shed more light on the Roman contribution ?
--
Dinesh Maheshwari
Advanced Design Methods
Cypress Semiconductor
San Jose, CA, USA
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