October 12, 2010
Today's edition of Krulwich Wonders, an NPR science blog run by Robert Krulwich, reveals how the Buddha guessed the size of an atom--and got it right. Krulwich and his friend Ezra Block discuss George Ifrah's book The Universal History of Numbers which recounts a story from the Lalitavistara Sutra (completed around the third century) in which the Buddha estimates the size of an atom during a competition for the hand of Gopa, a woman that the Buddha (then Prince Siddhartha) hoped to marry.
Robert: So tell me about the math competition...
Ezra: Well there's this episode about a counting contest between the Buddha and a mathematician named Arjuna where the prince is asked to calculate both a very big number and, yes, a very, very small number.
Robert: Is that hard?
Ezra: Well, the small problem was to count the number of — I guess you could call them — atoms, the smallest possible unit, in a yojana.
Robert: What's a yojanda?
Ezra: According to Alex Bellos, a journalist who included this tale in his new book Here's Looking at Euclid, a yojana is an ancient unit of length equivalent to around 10 kilometers.
Robert: So the question is, roughly: How many atoms are there in a line 10 kilometers long?
Ezra: Kind of. And here, courtesy of the ancient texts, is his solution:
A yojana, the Buddha said, is equivalent to:
Four krosha, each of which was the length of
One thousand arcs, each of which was the length of
Four cubits, each of which was the length of
Two spans, each of which was the length of
Twelve phalanges of fingers, each of which was the length of
Seven grains of barley, each of which was the length of
Seven mustard seeds, each of which was the length of
Seven particles of dust stirred up by a cow, each of which was the length of
Seven specks of dust disturbed by a ram, each of which was the length of
Seven specks of dust stirred up by a hare, each of which was the length of
Seven specks of dust carried away by the wind, each of which was the length of
Seven tiny specks of dust, each of which was the length of
Seven minute specks of dust, each of which was the length of
Seven particles of the first atoms.
So here's the neat part: According to Alex Bellos, it turns out the Buddha's calculation got the size of an atom very close to right!
This was, in fact, a pretty good estimate. Just say that a finger is 4 centimeters long. The Buddha's "first atoms" are, therefore, 4 centimeters divided by 7 ten times, which is 0.04 meter x 7 to the minus 10 or 0.00000000001416 meter, which is more or less the size of a carbon atom.
Read the full Krulwich Wonders entry here.