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Mar 3, 2010

The meaning of π

In Carl Sagan’s novel Contact, Jodie Foster’s character, Ellie---Jodie Foster played Ellie in the movie adaptation (1997)---is looking for messages from God in the decimal expansion of π. As the π-page demonstrates, π is a very long number---infinitely long, in fact (we show only the first 100,000 digits). 

To find this message, Jodie writes a program that computes the digits of π to record lengths. In the novel (I don’t think it's in the movie) she does find a special pattern 1020 digits down the line. The sequence stops varying randomly and unfolds well-ordered 1s and 0s in a very long string. GOTCHA! 
Ellie’s discovery is just fiction, but Professor Sagan covered his rear by putting her finding at a place where no mathematician has treaded (yet). Calculating the decimal expansion of π is a mathematical cottage industry, and in January this year, 2.7 trillion digits had been calculated. To reach Ellie’s soft spot, we need to go 100 million times further, roughly.
Now, what if Ellie succeeds, and some meaningful sequence of numbers eventually pops up? Wouldn’t that be something? Some coded message, which would tell us, when deciphered, that “Donald Duck is the nephew of Dagobert Duck?” That would prove the existence of God, right? 
 Stay tuned.

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