Excerpts from “Exact Science in The Srimad-Bhagavatam”
An encyclopedia article states that in early times
length was defined by the breadth of the palm or hand, and the length from
the elbow to the tip of the middle finger (the cubit). The article goes
on to say, “Such standards were both changeable and perishable, and only
within modern times have definite unchanging standards of measurement been
adopted.” (Microsoft Encarta)
The Middle Ages certainly saw many conflicting and poorly defined standards of weights and measures. But exact standards of measurement are not solely a modern invention.
Consider this example. In tenth-century England, King Athelstan decreed that the king’s girth, in which the king’s peace is in force, should extend from the royal residence for a distance of 3 miles, 3 furlongs, 9 acres, 9 feet, 9 palms, and 9 barleycorns. This sounds quaint. But it defines a circle with a diameter of 36,500 feet—almost exactly 1/10 of a degree of latitude in southern England.
Measuring with Latitude
To define a unit of length exactly, it is natural
to use latitude as a standard, because latitude derives from the size of
the earth, a constant that can be measured astronomically. So if a fire
or invasion destroys the standard measuring rod stored in some government
building, astronomical readings can be used to restore the lost standard.
Of course, it seems unlikely that accurate astronomical measurements were
being made in England in the days of King Athelstan. But if we look into
the history of weights and measures, we find that distances were gauged
in terms of latitude in ancient times, and medieval societies inherited
many exact standards of measurement. These included volumes defined as
length cubed and weights defined by filling such a volume with water.
The Greek astronomer Eratosthenes is usually credited with being the first to measure the size of the earth by observing latitudes (see Figure 2). He is said to have noted that the sun, when directly overhead at Syene at the Tropic of Cancer, casts a shadow of 7.2 degrees at Alexandria. Knowing the distance between Syene and Alexandria, he could compute the length of a degree of latitude and estimate the circumference of the earth.
But there is reason to believe that the size of the earth was known long before Eratosthenes. The Italian scholar Livio Stecchini has given extensive evidence that the ancient Egyptians laid out their country using latitude and longitude. He argues that they had accurate knowledge of the dimensions of the earth and that such knowledge was inherent in the design of the great pyramid at Giza. Since the great pyramid dates to about 2500 B.C., this implies that the earth was measured scientifically at least that long ago.
Defining the Yojana
Turning to India, we find a unit of distance—called the yojana—
that at first glance seems as ill defined as the medieval English furlong
or foot. The yojana is defined to be either 16,000 or 32,000 hastas,
where a hasta, or cubit, is 24 angulas, or fingers. That
there were at least two sizes for the yojana is upheld by the writings
of classical Indian astronomers. The fifth-century astronomer Aryabhata
used a yojana of about 8 miles, and the astronomy text Surya-siddhanta
a yojana of roughly 5 miles.
The first hint of the ancient history of the yojana comes from Strabo, who describes the experiences of Megasthenes, a Greek ambassador to India in the period following Alexander the Great. Strabo cites Megasthenes as saying that along the royal road to the Indian capital of Palibothra (thought to be modern Patna), pillars were set up every 10 stadia (see Figure 3). The British scholar Alexander Cunningham argues that the pillars marked an interval of one krosha. Since there are traditionally 4 kroshas per yojana, this implies 40 stadia per yojana. Stecchini gives 400 cubits per stadium, and this implies 16,000 cubits per yojana.
Since the smaller of the two definitions for the yojana assigns it 16,000 hastas, we can tentatively identify the hasta, or Indian cubit, with the Greek cubit. This unit is well known, and it enables us to compute the length of the yojana. The Greek cubit is 462.42 millimeters. This gives us a small yojana of about 4.6 miles, in rough agreement with texts such as the Surya-siddhanta. Stecchini points out that the stadium was defined as 1/600 of a degree of latitude. This would mean that there are 15 small yojanas per degree. Likewise, there are 60 kroshas per degree, or 1 krosha per minute. . . .
[Rest of Defining the Yojana and Familiar Numbers section skipped]
The Great Pyramid
Let us return briefly to our replacement of the Greek
cubit with a slightly smaller unit linked to a degree of latitude at the
equator. All the calculations above would go through if we used the Greek
cubit directly and did not make this substitution. But the errors would
be larger. So I prefer to match the two yojana lengths to the degree
of latitude at the equator rather than to Greece.
Curiously, we can find support for this in the design of the great pyramid of Egypt. In 1925 an engineer named J. H. Cole made an accurate survey of the great pyramid using up-to-date instruments. He found that twice the perimeter is 1,842.91 meters. For comparison, a minute of latitude at the equator—or 1 krosha of the small yojana—is 1,842.93 meters. In other words, the perimeter of the great pyramid is almost exactly 1 krosha. Likewise, we find that the hasta of the small yojana goes almost exactly 500 times into each of the sides of the pyramid.
The Greek cubit and stadium, however, fit the pyramid less closely. (There is a 0.4% error.) So it would seem that the great pyramid was designed using units linked to the degree of latitude at the equator. . . .
If the yojana was exactly defined as a fraction of the equatorial
degree of latitude, then the people who defined it must have known that
the earth is a globe. Indeed, they appear to have understood the dimensions
of the earth’s equatorial bulge.
Who were these people, and when did they live? The evidence considered here puts them at least as far back as the time of the great pyramid—a time when people supposedly believed that the earth is flat. Yet the correlation between planetary orbits and features of Bhu-mandala shows that the “earth mandala” of the Bhagavatam was far from being a naive flat earth. Its connection with planetary orbits shows that Bhu-mandala represents the plane of the solar system, which (if we discount the slight inclinations of the planetary orbits) is actually flat.
The Bhagavatam speaks of an ancient Vedic world civilization. Although the evidence we have looked at here does not prove that such a civilization existed, it does show that some people in the distant past attained an unexpectedly high level of scientific knowledge. Whether they lived in the East, the West, or both is hard to say. We do know that some evidence for this civilization is preserved in texts from India such as the Srimad-Bhagavatam, and other evidence may be found in ancient ruins of the West. Perhaps there was an advanced civilization that was worldwide in its influence. It is worth our while to be on the alert for other evidence that may shed light on this hidden chapter in human history.
Copyright © 2004 by Richard L. Thompson
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