Subject: Re: [HM] Indian astronomy and mathematics
From: Kim Plofker (Kim_Plofker@Brown.edu)
Date: Wed Feb 09 2000 - 21:13:27 EST
>> We've already gone through these points and discussed which of them
>> are supported by textual sources from what's known of Aryabhata's work
>> and which are not. A reference to MacTutor that provides no verifiable
>> citations of primary textual sources will not further the discussion
>> much, I'm afraid.
>
>Well, MacTutor does indeed list 30 books and articles as references
>and in the very top section you find "Shukla, Kripa Shankar Glimpses
>from the 'Aryabhata-siddhanta', Indian J. Hist. Sci. 12 (2) (1977),
>181-186."; the same author who co-authored "Aryabhatiya", [New Delhi
>1976] that KP has referred to, in her posts.
Thank you! I'm glad to know that.
>> The Sanskrit texts we see quite definitely assign to all seven planets,
>> including the sun, orbital periods and orbital distances with respect to
>> the earth.
>
>As I had mentioned in the previous post, there appear to be two systems.
>One for measurement and primary observation (heliocentric) and another
>for rendering time and position of the heavenly bodies with respect to the
>earth, earth being the vantage point of the observers(geocentric) with
>mapping done from the former to the latter.
My concern is only to make quite clear that the first of these "two
systems" is confined to modern inferences such as the one being discussed
in this thread. The actual statements of Sanskrit astronomical texts
referring to planetary motions indicate that they consider them to be
geocentric. Here, for example, is a quote from the _Aryabhatiya_
(Gola 2): "The nodes of the star-planets and of the Moon incessantly
move on the ecliptic. So also does the Sun." If we're going to say
that Indian astronomy was "really" heliocentric, we must acknowledge
that that inference is not based on any explicit statements to that
effect in the primary sources.
(And personally, I don't see why an ancient heliocentric model
should be considered a laudable achievement anyway; before the ability
to observe stellar parallax, there was simply no good physical reason
to assume the counterintuitive proposition that the earth might be
flying through space. Anachronistic thinking on the part of historians
has set up the foolish premise that somehow "anticipating" current
theories is a sign of merit in an ancient civilization, and so the
history of science has turned into a retroactive race for priority.
(And yes, it was the arrogance and often outright racism of
half-informed European scholars cheerleading for the Greeks that
started the whole process, and nobody regrets it more than I---if
this nasty and unscholarly competition had never started, we could
all spend less time arguing and more time working!) Rightly considered,
I think, the complex geocentric system of Ptolemy is a much more
remarkable accomplishment than the heliocentric speculations of
Aristarchus.)
>> If we assume that the existence of the sighra-correction
>> implies a truly heliocentric cosmology, we will have to assume that
>> almost all ancient astronomy had a heliocentric system too: for example,
>> Babylonian astronomy was based on synodic planetary periods, which also
>> computationally link the position of the planet to that of the sun.
>
>First, as I understand sighrocca, it is a mapping of the motion of the
>planets around the sun to an imaginary point moving around the earth.
Well, what the sighrocca is stated to be in astronomical siddhantas
is the apex (ucca) of the fast (sighra) anomaly (there is also
an ucca of the slow (manda) anomaly). As Aryabhata
points out in the _Aryabhatiya_ (Kalakriya 17--21), this apex, which
has an orbital motion with respect to the earth, can
equivalently be considered as the apogee of an eccentric orbit, or
the point on a concentric orbit from which an epicycle moves. Either
way, the planet can be considered for computational purposes to be either
actually on one of these non-concentric circles or on the concentric orbit
and displaced from its mean position by the "pull" from the ucca.
(This latter physical model is the one explicitly described by the
_Suryasiddhanta_, for instance.) Here are Aryabhata's verses, in
Shukla's and Sarma's translation:
"All the planets, whether moving on their orbits or on the eccentric
circles, move with their own (mean) motion, anticlockwise from their
mandoccas and clockwise from their sighroccas. The eccentric circle of
each of these planets is equal to its own orbit, but the centre of
the eccentric circle lies at a distance from the centre of the solid
Earth. The distance between the centre of the Earth and the centre
of the eccentric circle is (equal to) the semi-diameter of the epicycle
(of the planet). All the planets undoubtedly move with mean motion on
the circumference of the epicycles. A planet when faster than its ucca
moves clockwise on the circumference of its epicycle and when slower than
its ucca moves anticlockwise on its epicycle. The epicycles move
anticlockwise from the mandoccas and clockwise from the sighroccas. The
mean planet lies at the centre of its epicycle, which is situated on the
(planet's) orbit."
So indeed, the sighrocca is a point moving around the earth, and the
computed effect of its position upon that of the mean planet does
account for what modern astronomy calls "the motion of the planets around
the sun." But I repeat that it's not necessary to interpret that as
a deliberate "mapping" of an explicitly heliocentric model to a geocentric
one. And if it is so interpreted, then much other ancient astronomy
should be interpreted the same way: see below.
>Second, equating the concept of sighrocca to synodic planetary periods
>in significance is tantamount to seriously (perhaps purposefully)
>undermining the significance of the concept of sighrocca; synodic
>planetary periods is a very primitive concept compared with sighrocca.
Here I think you are being somewhat unfair to the Babylonians;
although the concept of synodic periods is not _geometrically_
sophisticated (in fact, it has no intrinsic geometrical implications
at all), the computational models involving them (at least the ones
dating from the end of the last millennium BCE) are quite complex
and elegant. They represent a system in which anomalies of planetary
motion are related to the motion of the sun, which is exactly the same
function performed by the Indian sighrocca.
But if only geometrically sophisticated systems count, then just look
at Ptolemy. Here's what he says in _Almagest_ IX, 5 (trans. G. J. Toomer,
Springer-Verlag 1984): "There are likewise two apparent anomalies
for each [star-]planet: [1] that anomaly which varies according to its
position in the ecliptic, and [2] that which varies according to
its position relative to the sun." He goes on to describe how the
"diameter of the epicycle rotates uniformly about the centre [of the
eccentric]...with a speed corresponding to the planet's return [i.e.,
period] in longitude...the planet, for its part, moves with uniform
motion on the epicycle...with a speed corresponding to the mean
period of the synodic anomaly." This eccentric/epicycle system is
accounting for the same phenomena that the Indian manda/sighra system
does, and the motion on Ptolemy's epicycle is just as much a "mapping" of
heliocentric to geocentric motion as the sighrocca-correction is. No
plainer illustration could be found of the fact that a sun-dependent
anomaly does not have to imply the hypothesis of literally sun-centered
motion.
>> Recall, after all, that Brahmagupta and many later authors,
>> who all used the sighra-correction as a matter of course, strongly
>> rejected Aryabhata's notion that the earth might even rotate;
>
>I am not surprised to see Brahmagupta disagreeing with Aryabhata,
>the two schools of astronomy (from two different geographical
>locations in India) were rivals and were competing with each other.
But both were working with the same basic Indian system of positional
astronomy (including the manda- and sighra-corrections) that had
originated prior to both of them, appearing in the _Paitamahasiddhanta_
("astronomy of Brahma") dating probably from the mid-fifth century CE.
Both Aryabhata and Brahmagupta explicitly claim to be preserving a
true version of the "astronomy of Brahma" (although you're right that
they used different parameters, hence the rivalry!), which Nrsimha
and Kamalakara and others identify with this _Paitamahasiddhanta_ of
the _Visnudharmottarapurana_. So the sighrocca-correction in itself
was evidently not offensive to the stationary-earth convictions of
Brahmagupta or anyone else: _they_ apparently did not think that it
implied a heliocentric model, and surely their opinions should count
for something.
>Perhaps, there is a preconceived notion that the ideas of "time and
>space" in ancient India were the same as in contemporary Europe.
>Let me quote from Yoga-Vasishta(YV) composed by Valmiki,
>author of the epic Ramayana. YV is a book of philosophy and describes
>instructions given to Rama, the hero of the epic Ramayana.
[...]
>As I mentioned in the previous post, there are hints of an idea of a
>heliocentric system in _Satapatha_Brahamana_(SB)
[...]
>The above citations should give you an idea that the Vedic people did not
>consider the earth to be the central element of importance in the spatial
>or temporal reference of the universe.
I don't mind at all if anyone wishes to infer support for heliocentric
or other "anticipatory" theories from philosophical or religious texts, as
many Western scholars have also done with Pythagorean and Neoplatonist
concepts, for example. But for myself, I think the best source of real
information about Indian astronomy is the evidence actually appearing
in Sanskrit astronomical treatises, and that's the only aspect of the
argument on which I can venture an opinion.
With best wishes,
Kim Plofker
Department of History of Mathematics
Brown University
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