the Buddhists have an analogy they use to describe how rare it is to
attain an incarnation in human form

they say picture a sea turtle. he's rising up from the bottom of a
huge ocean and he just happens to poke his head through the hole of a
piece of driftwood on the surface of this ocean . . . those are the
odds that any particular sentient being would attain a human birth (as
opposed to birth in any one of the billions of other life forms on
this planet).

for the purpose of a writing project, I would like to get a
hypothetical ball park number for the odds of this happening.  Say the
ocean is the Pacific Ocean.  Say the piece of driftwood that is
floating aimlessly on the surface has a hole in it that is one meter
in diameter. Say the sea turtle is exactly half way between Tahiti and
Hawaii.  Disregard the effect of tides, season, the sea turtle's
aversion to driftwood, and other variables.

what are the chances (some number to one) of the sea turtle coming up through
the hole in the driftwood?

* * *

Hi timespacette,

First, sources disagree about the area of the Pacific Ocean,
presumably because they disagree about where the boundaries are.

The area is typically listed in millions of square kilometers. 
Numbers available on the Web include 155.557, 165.25, 165.384, 166,
and 179.7.  Wikipedia and the New American Encyclopedia (printed) have
the high number.

As kemlo-ga noted in the comments, assuming the hole is circular, the
area of the hole would be pi times the square of the radius.  The
diameter is one meter and the radius is half the diameter, so the
radius is half a meter, the square of the radius is 0.25 square meter,
and the area is approximately 0.785398 square meter.

There are 1,000 meters in a kilometer and a square kilometer is a
square with a kilometer on each side, so there are 1,000 x 1,000 or
1,000,000 square meters in a square kilometer.

So if we take the low estimate, the area of the Pacific Ocean is
155,557,000,000,000 square meters.  Dividing this number by the area
of the hole, 0.785398, we get odds of 198,061,365,065,864 to 1 that
the turtle will hit the hole.

If we take the high estimate, the odds are 228,801,193,789,645 to 1.

So it's roughly a couple of hundred trillion to one, good news if you
hope to avoid the annoyances of human life the next time around.


Additional Links

Pages with the area of the Pacific Ocean:

179.7 on Wikipedia
http://en.wikipedia.org/wiki/Pacific_Ocean

155.557 on Worldatlas.com
http://worldatlas.com/aatlas/infopage/oceans.htm

166 on Pacific Island Travel
http://www.pacificislandtravel.com/nature_gallery/pacificocean.html

166 on MSN Encarta
http://encarta.msn.com/encyclopedia_761564220/Pacific_Ocean.html

165.25 on Encyclopaedia Brittanica Concise
http://concise.britannica.com/ebc/article-9374340/Pacific-Ocean

--efn

"So it's roughly a couple of hundred trillion to one, good news if you
hope to avoid the annoyances of human life the next time around."

That's comforting.  I've always thought I'd like to be a Sea Otter
next time anyway.


* * * thank you!

Fret not, Timely One, all your friends are hard at work assembling the
necessary computer power to perform the calculations.

But first, tell us, does this event occur during the day or at night?

Note to Tisme, You do the easy stuff ... I'll do the difficult parts. OK?

Instead of driftwood can we make it a plastic six-pack holder that
then strangles the turtle? I see a cool irony to that scenario.

Area: total: 155.557 million sq km  
--http://geography.about.com/library/cia/blcpacific.htm

If the hole is 1m diameter then that is about 3.14 sq meters (Mmmm, I like pi).

So... 155,557,000,000 meters / 3.14 meters = 49,540,445,860.

So the odds are 1 in 49,540,445,860 (about 50 billion) that the poor
turtle would get his head through the hole in the driftwood.

I would of course like to join in this thread, however I have an
aversion to answers that might include the word COUNT.
Know what I mean?
Kemlo

If the hole is 1m diameter then that is about 3.14 sq meters   NO IT ISNT

pi times the radius squared 

0.785

155,557,000,000 divided by 0.785 is 198,161,000,000

Kemlo

oh no.

between jack_of_few_trades-ga and kemlo-ga . . .  I'm confoosed !

who is right?

and why would it matter, anyhow, that it happened in the day or in the night?

eh?


* * *

hi markvmd-ga

irony is good, yes.  but that would reduce the odds even more, poor turtle.

he would remain a turtle after all this!

we could say it was a plastic hoola-hoop (one meter in diameter)

how's that?

* * *

In daytime, the turtle would not be so stupid as to stick its head in
the hole .. so ZERO CHANCE!

At night, the turtle would be having a sleep ...

So if he drifted off, he might find the driftwood ...

And if he were to toss and turn in his sleep ...

Alas, I'm still waiting for tisme.

Hurry up tisme!

Yes, where IS tisme?

there's a question just WAITING for you over at Question ID: 755645 ! !

(not all that urgent, by the way, still . . . )


* * *

Phew, bad math with Jack.  Sorry about that guys (and thank you Kemlo
for catching it).  I guess the last time I worked with circles was
longer than I thought and I calculated perimeter 2pi(r) rather than
area pi(r squared).

I wonder if tisme has become a twasme?

Or a usedtobeme?

Or maybe it's a case of reincarnation and tisme will eventually
reappear as twillbeme?

Tis very frustrating.

I know nothing about circles...

I'm kinda "square", I guess...

Steph53