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Sea Turtles

The ocean + a blind turtle + some driftwood = lucky to be human

A friend of mine, Sandeep, loves to tell this story about how long a kalpa is. Kalpas are the unit of time by which things are measured in Buddhism, and it doesn’t particularly matter how long they are in years, per se, but that a kalpa is a very, very long period of time. This is to give the sense that Buddhism is concerned with the eternal, recurrent universe, that things like an individual’s life are fleeting and small – to place one in context.


Sandeep’s Story of the Blind Turtle

Sandeep’s story goes as follows. So there’s a blind turtle living at the bottom of the sea, who surfaces for air once every five billion years (the turtle is, well, pretty old). There’s a piece of driftwood, with a little hole in it, floating on the ocean surface, tossed about by wind and currents, waiting for the turtle. A kalpa is as long as it takes for the turtle to happen to pop its head through the hole in the driftwood one of the times it comes up for air.


Fig. 1 – Buddhism is like waiting for this blind turtle to find this wooden neck-hole in this great blue yonder. ‘And they think finding a needle in a haystack is tough’. Screen Shot 2016-01-17 at 12.12.07 PM




That’s a long time, and moreover a beautiful metaphor. Fascinated by this anecdote after I’d heard it, I looked it up. Sandeep has a graceful way with fudging the details, and it appears this particular anecdote is no exception: all the better if you ask me. We’ll be interested in the story as it actually goes, though, which requires some revision (cue: the noise of a record scratching as we start the whole thing from the top).


The Story of the Blind Turtle, As it Actually Goes

In Hinduism and certain writings of Buddhism, a kalpa is indeed a long unit of time, about 4.32 billion years – curiously close to the 4.54 billion years old the earth is thought to be, and probably where the 5 billion years in Sandeep’s story comes from. There is a story about a blind turtle, too, with the driftwood and all, but rather than illustrating how long a kalpa is, it illustrates something far more fundamental to the Buddhist ethos: how being human is special.


Fig. 2 – Revision: being human is like this blind turtle finding this wooden neck-hole in this great blue yonder. Maybe Barney was right… Screen Shot 2016-01-17 at 12.12.07 PM




The actual story, found in 129 Balapandita Sutta, is that there is a blind turtle, innumerable kalpas old, living at the bottom of the sea and surfacing for air every 100 years, and a wooden cattle-yoke waiting for it amongst the waves. The likelihood that the turtle pops its head through the hole in the cattle-yoke when surfacing is said to be greater than the likelihood of being reincarnated as a human. Being born human is luckier than a blind turtle popping its head through a cattle-yolk. The implication, then, is that you better get busy becoming enlightened while you’ve got the chance – only human beings are said to have the capacity to attain enlightenment.

Now, the fun part is that to a scientist, this looks like a comparison of two simple questions about oceanography and biology, respectively; how likely is it for the turtle to pop its head out in the wood, versus how likely it is for something to be reincarnated as human when it dies? We can estimate and compare these probabilities; we have ourselves a testable hypothesis! What is the probability of a turtle surfacing through a cattle-yoke’s hole, and what is the probability of being reincarnated as a human?


Two Simple Calculations, One Surprising Result

Let’s take the yoke first. A cattle-yoke hole typically measures 16” by 8”, so if we think of it as an ellipse, that’s about 400 square inches of hole to fit through. Then the total surface area of the oceans, added all up, is about 360 million square kilometers. If you assume that after 100 years the location of the turtle and the yoke are sufficiently randomized from their moving around, which seems reasonable, the probability that the turtle would poke its head out is just the ratio of these two areas, which after converting inches to kilometers is about P(turtle sticks head through yoke) = 7.2 x 10^-16.

How about reincarnation? This one seems possibly trickier, as that’s a lot of creatures to account for, but we’re in luck. It’s often thought by Buddhists that one can only be reincarnated as a multicellular organism, and by far the most abundant organisms are nematodes – rather gross tubular little roundworms. These reproduce about 1150 times faster than human beings; we live about 67 years, and they live about 3 weeks. Then there are about 7.4 billion humans on earth, and 10^22 nematodes. So if I die and I’m up for reincarnation, the probability I get reincarnated as human can be accurately estimated as the ratio between the number of humans and the number of nematodes, divided by that factor of 1150 to account for how much faster nematodes are born and die. That probability ends up being P(reincarnated as human) = 6.5 x 10^-16.


Fig. 3 – You might rather be the one holding the nematode than be the nematode, but I’d rather not hold a nematode at all, thank you very much.

Screen Shot 2016-01-17 at 12.13.17 PM










Those probabilities are remarkably similar – the metaphor is in fact precise! I wouldn’t mind a piece of whatever wisdom was available to the Majjhima Nikaya (who told the story in this Sutta). Another interesting consideration, though, is that this comparison wasn’t as close when the Majjhima Nikaya spoke it; there used to be far fewer humans on earth. Back then, though, there was no way to estimate the total area of the oceans, or the number of organisms on earth! Thus, the comparison only becomes precise once it is testable – a sort of inverse Uncertainty Principle. What will happen once there are 9 billion people on earth, and the comparison stops being true?


All in all

Thanks to a couple of neat modern estimates about the global extent of the oceans and the big picture numbers of life on earth, we can test the veracity of an ancient spiritual anecdote, which turns out to be strikingly accurate. Whether this demonstrates something miraculous about Buddhist sages, humanity, or science is up to you, but certainly it does feel a bit miraculous.

Cael was once told by a professor that applied mathematicians are ‘intellectual dilettantes,’ which has been a proud self-identification for Cael since that moment. Cael is a graduate student at MIT & Woods Hole, & studies the ocean from a mathematical perspective; right now Cael is trying to figure out how detailed our measurements of phytoplankton communities can be if we detect them from space. Otherwise, Cael plays accordion, gardens, & reads instead of sleeping like it’s still fifth grade.


One Response to “The ocean + a blind turtle + some driftwood = lucky to be human”

  1. Thanks for the fun, interesting article!

    Posted by harold | January 19, 2016, 11:13 am

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