Mar 4, 2010

The meaning of π (2)

-"Donald Duck is the nephew of Dagobert Duck,” you may ask? Yes, we were pondering whether this sentence, when found in the decimal expansion of π (appropriately coded in decimals), would prove something---say a message from the creator built into the fabric of mathematics.

But would it? Consider another setting, this time filled with diligent monkies and typewriters (a  typewriter was a machine to create ("type") text mechanically by hand, typically on a sheet of paper, kids, pictured). The monkeys are bored and type away on their machines. The first monkey starts typing: "ane uzv awu but seiw." But, wait, there is "but"...there is already one meaningful word in this sequence.

In fact, by sheer coincidence, some meaning is apt to crop into meaningless strings. Somewhere along the line some monkey will type "srv zgftj To be or sxew vdkt." (Much) later, some monkey will create the string "ljoh To be or not to dsr cvf.." And so on. How long will it take for a given group of monkey's to churn out the complete works of Shakespeare? By sheer happenstance? Very long. But it's not impossible. The first "To be" may crop up in a year. The first "To be or" might require a decade (we could employ lot's of monkeys that work in parallel). The first "To be or not to be" may require 100,000 or 1,000,000 years...but...you get the idea. The longer the monkies churn along, the longer the take on Hamlet's soliloquy will get, and with infinite time we should eventually arrive at the bard's complete works. 

But we don't have infinite time. Wait, don't we? π is infinitely long! Computers are infinitely fast, almost.

Stay tuned, and read up on the Infinite Monkey Theorem in the meantime.

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