Thursday, December 27, 2012

Shell Beach and Large Numbers

I am sometimes amused or at least entertained by large numbers.  Usually when I see a large number somewhere unexpectedly.  I recently saw a sign at Shell Beach that had a large number where I expected a larger number.  Shell Beach is part of Shark Bay in Western Australia.  I understand it is one of only two beaches in the world made entirely of shells.  I expected a lot of shells but I still thought there would be sand.  I was wrong.  Nothing but shells 5 meters deep (15 feet).  Shell Beach is a few hundred meters wide and many kilometers long.  An information sign on the beach said shells in the millions make up the beach.  I felt that number was a bit small.  With the help of Google Maps and Wikipedia I estimated number of shells to be around a quadrillion.  That’s 1,000,000,000,000,000 (1E+15), a billion million.  

I know the sign was just trying to convey the idea that there are a lot of shells on the beach.  It’s not easy to get our heads around big numbers, so I guess millions is as good as any number for that purpose.  

I like to look at large numbers in different ways to help grasp just how unimaginably large they are.  For example a few years ago I bought a few Zimbabwe One Hundred Trillion Dollar bills on eBay and gave them away for Chinese New Years in red envelopes (紅包, hong bao).  (They are the largest note ever printed.  Hyper inflation in Zimbabwe is another story.)  My nephew was particularly impressed.  He told me that was the coolest thing ever.  I told him if he was given $1,000 every second starting when he was born, in 16 minutes and 40 seconds he would have a million dollars.  However, he would have to live 3,171 years to get one hundred trillion dollars.  

One of my favorite examples of a large number in an unexpected place is a 40 digit tracking number for delivery confirmation from the US Post office.  I had to enter all 40 digits to get the confirmation.  I thought the US Postal service was being pretty optimistic to have 40 digit tracking numbers.  Why do they need so many digits?  Were they thinking they could possible deliver 10,000,000,000,000,000,000,000,000,000,000,000,000,000 letters? If each letter was 1 millimeter thick, a stack of this many letters would be over 1E+21 lightyears high!  That’s beyond the edge of the observable universe.  If each of these letters weighed just 10 grams, the mass of this many letters would be 50 billion times the mass of the sun.  

The sign said shells have been piling up on this beach for about 4000 years.  If that is correct and my estimate is not high by a factor of 10 or more (I tried to keep it conservative), then on average 684,000,000 shells wash up everyday.  One way or the other that’s a lot of little critters living and dying out in Shark Bay.