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Subhash C. Kak
Department of Electrical & Computer Engineering
Louisiana State University
Baton Rouge, LA 70803-5901, USA
FAX: 504.388.5200; Email: kak at ee.lsu.edu
Indian Journal of History of Science, vol. 33, 1998, pp. 31-36
Abstract

In his commentary on the Rigveda, the fourteenth century scholar S¯
ayan.a mentions a specific speed for the sun which can be used to de-
termine the distance to the sun. Vartak has interpreted this statement to
stand for the speed of light but we cannot place that in any reason- able
historical context. The distance to the sun implied by S¯ ayan.a’s
statement suggests that there was another astronomical tradition in India
which is now lost.

KEYWORDS: Medieval astronomy, solar system, Siddh¯ antas 1

Introduction

S¯ ayan.a (c. 1315-1387) was a minister in the court of King Bukka I of
the Vijayanagar Empire in South India; he was also a great Vedic scholar
who wrote extensive commentaries on several ancient texts. In his
commentary on the fourth verse of the hymn 1.50 of the Rigveda on the sun,
he says

tath¯ a ca smaryate yojan¯ an¯ am . sahasre dve dve ´sate dve ca
yojane ekena nimis.¯ardhena kramam¯an.a namo ’stu ta iti

Thus it is remembered: [O Sun,] bow to you, you who traverse 2,202 yojanas
in half a nimes.a. We have no knowledge that S¯ ayan.a was an astronomer
and he acknowl- edges that he is only quoting from an old tradition, so we
label this note as “S¯ ayan.a’s astronomy” only in the sense of
what was known by his time in the fourteenth century.

Padmakar Vishnu Vartak in a recent book has argued that this state- ment
refers to the speed of light. He says, “One *Yojana* is equal to 9
miles, 110 yards = 9 1/16 miles = 9.0625, ...and according to Mah¯ abh¯
arata, 3

´ S¯ anti Parva, 231, half a nimes.a equals 8/75 seconds. If calculated
on this data the velocity of light comes to 187,084.1 miles per second...
Sir Monier Williams gives one *Yojana* equal to 4 Krosha = 9 miles. Taking
1 *Yojana* = 9 miles, the velocity comes to 186,413.22 miles per second.
The well accepted popular scientific figure is 186,300 miles per
second.”

This is astounding because it is in remarkable agreement with our cur-
rent knowledge about the speed of light! Vartak’s reference on the
nimes.a from the Mah¯ abh¯ arata, which is usually assigned to 400 B.C.
to 400 A.D., is correct. 4

The specific definition of a nimes.a is there given by 450 × 30.1 nimes.a
= 1 muh¯urta (48 minutes), which means that one nimes.a is 16 75.3 sec-
onds. The *yojana* is a well known unit of distance and the value ascribed
by Vartak is the usual one. 5

Even if one argues that there was no standardization of measures in the
ancient world and the specific values assigned by Vartak for *yojana* and
nimes.a were not used by all the ancient authorities, just the fact that
there could be mention of a finite speed of light three centuries before
that discovery by Roemer is not believable. Furthermore, we cannot place
such knowledge in context.

So should we take the statement of S¯ ayan.a as an amazing coincidence?

From all accounts, the passage is not an interpolation. There are those
who would suggest that consciousness reflecting on itself can obtain such
quantitative information. But if one discounted that possibility then,
wanting evidence of instrumentation that would have allowed an actual
measurement of the speed of light to have been made in medieval India of
S¯ ayan.a’s time, the only way Vartak’s interpretation can be
justified is to assume that the speed was a lucky guess.

We do know that in the Indian tradition a finite speed was associated with
the astronomical processes. Thus in the S¯ urya Siddh¯ anta 2.1-3, the 2
motion of the planets is described in terms of the action of cords of
“air”:

Forms of Time, of invisible shape, stationed in the zodiac (bhagan . a),
called the conjunction (´s¯ıghrocca), apsis (mandocca), and node (p¯
ata), are causes of the motion of the planets.

The planets, attached to these beings by cords of air, are drawn away by
them, with the right and left hand, forward or backward, according to
nearness, toward their own place.

A wind, moreover, called provector (pravaha) impels them toward their own
apices (ucca); being drawn away forward and backward, they proceed by a
varying motion. 6

The important point here is that gravitation is expressed in terms of a
force which is compared to a wind. One would assume, then, that light must
have also been compared to a wind and thus taken to have a finite speed.
It is possible that the speed of 2,202 *yojana* to half a nimes.a was
chosen just to make the time spent by light on its journey from the sun to
the earth equal a round number in some convenient units. Again, this would
make this choice just an astonishing coincidence.

On the other hand, if Vartak’s interpretation—that the statement
refers to the rays of the sun—is wrong, then should we take it to be the
speed of the sun? That this is likely is because the luminaries were taken
to move at speeds that were more or less fixed. For the other planets this
speed was considered to be 11,858.75 yojanas, 7 and there was a
corresponding tradition regarding the speed of the sun. In this note we
explore the implications of this interpretation that S¯ ayan.a’s
remarks referred to the speed of the sun in its orbit. 2

On nimes.a and *yojana*

Can one consider the possibility that nimes.a in S¯ayan.a’s statement
only means the “twinkling of an eyelid”– the usual non-technical
meaning of the term? This possibility is not credible because then S¯
ayan.a would have had no need to give a precise figure of 2,202 yojanas in
relation to a figure of speech. In such a situation, a “thousand (for
‘a large number’) yojanas in a 3 nimes.a (for ‘a twinkling of an
eyelid’)” might have been used. So it seems quite certain that a
specific meaning of the term nimes.a is meant here.

The definition of nimes.a in the Pur¯an.as generally agrees with that
given in the Mah¯ abh¯ arata. *Yojana* is an ancient measure which we
come across in the Rigveda. This is how the two units are defined in the
chapter 2.20 of the Artha´s¯ astra, 8 which is attributed to Kaut.ilya
(320 B.C.): *Yojana*. 8,000 dhanus (dhanus means bow, taken to be about 6
feet). A dhanus is also taken to be equal to one paurus.a, the height of a
person, so assigning about 6 feet to it is reasonable. One dhanus is
considered equal to 108 a ˙ngulas (fingers). It is a stage, 9.1 miles
approximately, and according to Kangle it has “reference to the
‘yoking’ of bullocks, i.e., distance covered before the yoke is taken
off.” Nimes.a. 150 nimes.as equal 1 kal¯a and 80 kal¯as equal one
muh¯urta (48 minutes). This means that one nimes.a equals 6 25 or about
one-fourth of a second.

We see the same definition of *yojana* in most astronomical texts over
several centuries, including in one commentary by Yallaya, who lived just
a century later than S¯ ayan.a in South India. 9

On the other hand, the definition of *yojana* by ¯ Aryabhat.a (c. 499) is
different. He takes nr. (man) to be equal to 96 a ˙ngulas and then he
considers a *yojana* to equal 8,000 nr..

This amounts to his *yojana* being equal to approximately 7 1 2 miles. 10

¯ Aryabhat.a takes the earth’s diameter to be 1,050 yojanas, whereas
his commentator Bh¯ askara I, writing a century later, uses another
definition of *yojana* so that the earth’s diameter is 1,600 yojanas.

Burgess provides the following commentary on the unit of *yojana*: 11

The usual reckoning makes the *yojana* equal 32,000 cubits [“cu- bit”
is hasta, hand, which ought to be close to 18 inches], but it is also
sometimes regarded as composed of 16,000 cubits; and it is accordingly
estimated by different authorities at from four and a half to rather more
than ten miles English.

Nevertheless, one can speak of what should be the “standard” unit of
*yojana* and nimes.a by considering astronomical texts. 12

According to these sources, a *yojana* is 8,000 dhanus or 32,000 hastas,
which is approximately 9 miles, and a nimes.a is given by the equation
that 18 nimes.as = 1 k¯as.t.h¯a 4 30 k¯ as.t.h¯as = 1 kal¯a 30 kal¯
as= 1 muh¯ urta (48 minutes).

This amounts to one nimes.a being equal to 8 45 seconds. In the various
definitions, nimes.a is approximately one-fifth to one-fourth seconds: the
four variants being 1 5 , 16 75.3 , 6 25 , and 8 45 . 3

The Distance to the Sun

We first note that there exist many traditions regarding the distance to
the sun. The earliest of these is the statement in the Pa˜ ncavim . ´sa
Br¯ ahman . a 16.8.6 that the heavens are 1,000 earth diameters away from
the earth. Since the sun was taken to be half-way to the heavens this
indicates a distance of 500 earth diameters. There are other references in
the Br¯ ahman.as that indicate that the Indians knew that the orbit of
the sun was not perfectly symmetrical. 13

Here we are interested in reviewing the tradition about the distance to
the sun during the Siddh¯ antic period. ¯ Aryabhat.a, in his ¯
Aryabhat.¯ıya 1.6, gives the distance of the sun, R s , to be 459,585
yojanas. But remember that ¯ Aryabhat.a uses a measure of *yojana* which
is 96 108 of the standard *yojana*. 14 S¯ ayan.a’s statement can be
used to determine the distance R s to the sun.

We have π × R s = speed/hour × 12 hours.

This amounts to the distance to the sun being equal to R s = 2202 × 90 ×
60 × 60 × 12 8 × π ≈ 340.6 × 10 6 yojanas.

This is approximately 740 times larger than the estimate during ¯
Aryabhat.a’s time, assuming the same yojanas were used. The correct
value for the distance is 93 million miles. If S¯ ayan.a was using a
short measure of *yojana* then his estimate was only 10 times greater than
the modern value. On the other hand, ¯ Aryabhat.a’s estimate—and a
similar estimate by Ptolemy,—which was typical for the ancient and the
medieval world until the time of Copernicus and Brahe, 15 was about 1 27
of the correct value. 5

If we use the standard *yojana*, the distance of the sun by S¯ ayan.a’s
state- ment becomes approximately 3,000 million miles which is almost as
far as the far reaches of the solar system. 4

Concluding Remarks

Even considering the “standard” measures of *yojana* and nimes.a,
S¯ayan.a’s statement, if interpreted as the speed of light, comes
pretty close to the true value. If we take this to be no more than a
coincidence and interpret S¯ ayan.a to mean the speed of the sun, then we
get a distance to the sun which is much greater than anyone could have
imagined before the speed of light was actually computed by Roemer. This
second interpretation also leaves us with an unresolved puzzle.

Perhaps, the resolution of this puzzle lies in the recognition that there
existed astronomical ideas in India other than those which have survived
as the extant Siddh¯ antas. The Indian books also speak of lost Siddh¯
antas. S¯ ayan.a appears to quote from one such lost tradition. This
tradition may have considered the solar system to be enormously large
trying to reconcile this size to the huge numbers related to the cycle of
8.64 billion years in the Pur¯ an.ic theory of the kalpa.

Collecting astronomical references in the various Indian texts that do not
fit into the standard Siddh¯ antic models may lead to the recovery of
some of the lost traditions. The referee of this paper notes that S¯
ayan.a’s brother M¯ adhava wrote two books on astronomy, the K¯
alanirn . aya (also called the K¯ ala-M¯ adhava) and a commentary on the
Par¯ a´sara-Smr.ti known as the Par¯ a´sara-M¯ adhav¯ıya; these may
be two sources to begin looking for non-Siddh¯ antic and
“non-standard” astronomical notions current in the four- teenth
century.

References and Notes

1. M¨ uller, Max (ed.), 1890. Rig-*Veda*-Samhita together with the
Commen- tary of S¯ ayan . a. Oxford University Press, London.

2. Vartak, P.V., 1995. Scientific Knowledge in the Vedas. Nag Publishers,
Delhi.

3. Mah¯ abh¯ arata (G¯ıt¯ a Press Edition), ´ S¯ anti Parvan,
chapter 231, verse 12.

4. Ganguli, K.M., 1970. The Mah¯ abh¯ arata. Munshiram Manoharlal,
Delhi, vol 9, page 155.

5. Basham, A.L., 1967. The Wonder that Was India. Sidgwick and Jack- son,
London, page 504.

6. Burgess, E., 1989. The S¯ urya Siddh¯ anta. Motilal Banarsidass,
Delhi, page 53.

7. D¯ıks.it, ´S. B., 1896, Bh¯arat¯ıya Jyotis.a. Translated from
Marathi into Hindi by ´ S. Jh¯ arkhand¯ı. Hindi Samiti, Lakhanau,
1963, page 422.

8. Kangle, R.P., 1986 (1972). The Kaut.il¯ıya Artha´s¯astra. Motilal
Banar- sidass, Delhi.

9. Shukla, K.S., 1976. ¯ Aryabhat.¯ıya of ¯ Aryabhat.a. Indian
National Science Academy, New Delhi, page xliii.

10. Shukla, 1976, page 19.

11. Burgess, 1989 (1860), page 43.

12. Basham, 1967, pp. 505-506.

13. This whole question will be discussed in a separate paper.

14. In the ¯ Aryabhat.a-siddh¯anta, ¯ Aryabhat.a uses another measure
of *yojana* which is two-thirds the one in the ¯ Aryabhat.¯ıya.

15. Neugebauer, O., 1975. A History of Ancient Mathematical Astronomy.
Springer-Verlag, Berlin. 7