History & Culture  ·  Established  ·  Perspective

The priest sits down, and before anything else, he says when we are.

Not the year. Not the month. In the sankalpa, the spoken statement that opens a Hindu ceremony, he names the largest cycle of time first and works down to the ordinary date.

One number stands out: 4.32 billion years.

That is the traditional length of one day of Brahma, called a kalpa.

Modern science puts the age of the Earth at about 4.54 billion years. The two numbers are remarkably close.

So how did an ancient tradition arrive at a number so near the modern estimate?

4.32 billion was not measured. It was calculated from traditional units of time.

One year of the gods was taken as 360 human years. Four ages, or yugas, together made 12,000 divine years. That gives 4,320,000 human years — one mahayuga, or great cycle.

A day of Brahma was defined as 1,000 such cycles.

4,320,000 × 1,000 = 4.32 billion years.

The Laws of Manu sets out this calculation, and the Vishnu Purana gives the same scheme. No rock, no fossil, no observation of any physical thing enters the arithmetic.

There is a second point, and it settles the matter.

A kalpa is not the tradition’s age of the Earth. It is the length of a full day of Brahma, and the tradition places the present world partway through that day. Indian astronomical texts such as the Surya Siddhanta and Aryabhatiya give a reckoning in which roughly 1.97 billion years have elapsed in the current kalpa.

So the two numbers mean different things. 4.32 billion is the length of the whole day. About 1.97 billion is the part of it that has passed.

And 1.97 billion is the tradition’s own answer to how old the world is. That is not close to 4.54 billion. The gap is more than a factor of two.

The two figures came from unrelated methods. One was multiplied out of ritual units. The other came from radiometric dating — reading a rock’s age from the steady decay of the elements inside it. Clair Patterson’s 1956 work on meteorites put the figure at about 4.55 billion years, refined by later work to about 4.54 billion.

Once the apparent prediction is removed, something more interesting remains.

An ancient Indian tradition was comfortable describing time in billions of years. The billions were not a measurement of the Earth’s history. They were ordinary units in a scheme for describing very long stretches of time.

That is a very different achievement from measuring billions of years.

One requires instruments and physical evidence. The other requires the willingness to imagine a universe running on a scale far beyond ordinary experience.

The takeaway: The 4.32-billion-year kalpa was multiplied out of ritual time units, not measured from the Earth, and the tradition’s own reckoning of elapsed time — about 1.97 billion years — is nowhere near the Earth’s age. The closeness is a coincidence. What is not a coincidence is a culture that could think in billions of years long before anyone could measure them.

The priest finishes the sankalpa and moves on. He has just said something about time that no one in the room finds remarkable.

Glossary

• Sankalpa — the spoken statement of time and place that opens a Hindu ritual.
• Yuga — an age of the world. Four of them make one cycle.
• Mahayuga — a great cycle made up of four yugas, lasting 4,320,000 years.
• Kalpa — one day of Brahma: 1,000 mahayugas, or 4.32 billion years.
• Brahma — the creator god whose days and nights measure out time in this scheme.
• Radiometric dating — working out the age of a rock from the steady, measurable decay of certain elements inside it.

Sources

• The Laws of Manu, ch. 1, vv. 64–73, tr. Georg Bühler, Sacred Books of the East, vol. 25, Oxford, 1886.
• The Vishnu Purana, Book I, ch. 3, tr. H. H. Wilson, London, 1840.
• Surya Siddhanta, ch. 1, vv. 11–24, tr. Ebenezer Burgess, Journal of the American Oriental Society, 1860.
• The Aryabhatiya of Aryabhata, Kalakriya section, tr. Walter Eugene Clark, University of Chicago Press, 1930.
• C. Patterson, “Age of meteorites and the earth”, Geochimica et Cosmochimica Acta, vol. 10, 1956. Paywalled.
• Brent Dalrymple, “The age of the Earth in the twentieth century: a problem (mostly) solved”, Geological Society, London, Special Publications 190, 2001. Paywalled.
• Kim Plofker, Mathematics in India, Princeton University Press, 2009, ch. 3.