Mr. Finch and pi

March 14, Pi Day, is coming up. Is there any more to be said about $\pi$ that hasn’t been said?



In the January 3, 2013 episode of the TV show “Person of Interest” (“you are being watched ... ”), computer genius Mr. Finch says that since $\pi$ is an infinite non-repeating decimal, “contained within this string of decimals is every single other number. Your birth date, combination to your locker, your social security number ...”

Really? I didn’t think that is necessarily so. Mr. Finch doesn’t explain why.

There is a site that lets you search for a specific string of digits within the first 200 million digits of $\pi$, http://www.angio.net/pi/piquery, but of course just because your number doesn’t appear, doesn’t prove anything. 200 million is a long way from infinity.

Are the digits in $\pi$ truly random? There is something called a normal number, which is a real number whose infinite sequence of digits is distributed uniformly. See http://en.wikipedia.org/wiki/Normal_number which says it is believed that $\pi$ is normal, but this has not been proven.

So we think Mr. Fitch was right, but we’re not 100% sure.