October 12, 2010

Did the Buddha correctly estimate the size of an atom?

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.

Image: himalayanart.org

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illarraza's picture

The hydrogen atom is 1/12 the size of a carbon atom, more nearly corresponding to the Buddha's prediction.

Alan Shusterman's picture

Beats me. I'm just reading what I read.

The last paragraph says how big the Buddha's atom is. If you want to change it to mean "seven particles", that's fine with me. For all I know, some part of the calculation is wrong (for example, 4 cm fingers seems much too short) and the Buddha nailed the size of the carbon atom.

All I wanted to do was share the conventional scientific wisdom on the size of the carbon atom.

tony's picture

Well, if you consider, according to this translation, that he said "seven particles of the first atoms", perhaps the size of one of such particles is close the this measurement that is 1/10th the size of an entire carbon atom?

Kenneth Elder's picture

The Theravada Sutta are about the only scripture everyone agrees are the original talks of the Buddha as given in the First Council by Arahat Ananda. I am not aware of Buddha giving an exact size of atoms in the Sutta. There are many interesting correct scientific concepts in the Sutta. In one Sutta Buddha gave a lesson in impermanence by describing the end of our planet. He said that in the future a second star would come join our sun in the sky and the water element would begin boiling away from the Earth. A third star would join our system and then more stars and then the air element would evaporate away (I forget at which no. of suns), finally the seventh sun is described as a world destroying star and it would destroy the earth element of our planet. Western scholars think that Buddha was talking about a black hole star in referring to this world destroying star. Half or more of the star systems in our galaxy are double or multiple star systems. If another star joins us before the sun expands to a red giant Earth’s orbit would widen thus the expanding sun would not be eaten up by our sun as predicted. There is a Sutta where Buddha talks about the dharma wheel world ruler & describes the disc shaped ship of the world ruler than can fly over the planet he says that it is intelligent like a living being but is not a living being. That is the only way Buddha could describe a computer system controlling a disc shaped anti-gravity ship to pre-tech folk. That was not guessing, that was his omniscient knowledge. Check search engine for the government/Lockheed anti-gravity ship, Project Aurora.

Alan Shusterman's picture

I don't want to be a killjoy, but the Buddha's estimate is a bit too small. 0.00000000001416 meter is 1.416 x 10 raised to the -11th power. The radius of a carbon atom (which is one of the smallish atoms in the periodic table) is about 10 times larger. The diameter of a carbon atom would be 20 times larger than the Buddha's estimate.

That said, Ezra Bloch makes an interesting point (see Krulwich blog for Bloch's commentary). The Buddha comes from a culture that is developing the ability to wonder about things that are much smaller (and much larger) than what a human can experience. So in place of a direct experience of the infinitesimal (which is beyond experience, but not beyond comprehension), the Buddha substitutes a procedure or algorithm that allows the mind to grasp the concept.

And, now that I think about it, having the Buddha substitute a logical algorithm for direct experience is deliciously ironic.