Archive for April 2008
The Infinite monkey theorem
An amusing if not likely debate culture occaisionally reoccurs - where if an infinite number of monkeys sit at an infinite number of typewriters and randomly press keys, they will eventually produce the complete works of Shakespeare.
I’m not sure they would eventually produce Shakespeare - but I do think they could come pretty close to reproducing the Bible… :)
In 2007, the theorem was listed by Wired magazine in a list of eight classic thought experiments.
My other favorite:
| Power laws for monkeys typing randomly: the case of unequal probabilities Conrad, B.; Mitzenmacher, M. Information Theory, IEEE Transactions on Volume 50, Issue 7, July 2004 Page(s): 1403 - 1414 Digital Object Identifier 10.1109/TIT.2004.830752 Summary: An early result in the history of power laws, due to Miller, concerned the following experiment. A monkey types randomly on a keyboard with N letters (N>1) and a space bar, where a space separates words. A space is hit with probability p; all other letters are hit with equal probability (1-p)/N. Miller proved that in this experiment, the rank-frequency distribution of words follows a power law. The case where letters are hit with unequal probability has been the subject of recent confusion, with some suggesting that in this case the rank-frequency distribution follows a lognormal distribution. We prove that the rank-frequency distribution follows a power law for assignments of probabilities that have rational log-ratios for any pair of keys, and we present an argument of Montgomery that settles the remaining cases, also yielding a power law. The key to both arguments is the use of complex analysis. The method of proof produces simple explicit formulas for the coefficient in the power law in cases with rational log-ratios for the assigned probabilities of keys. Our formula in these cases suggests an exact asymptotic formula in the cases with an irrational log-ratio, and this formula is exactly what was proved by Montgomery. |
What have you typed lately…?
Is it the destination, the journey, or both?
There’s a useful post on lifehack.org: “34 Tips for Your Younger Self.”
The advice I’d probably give my younger self is to appreciate while we don’t always control our lives or environments, we always have choices - even if our choice becomes figuring out where to go from the spot some external force put us in. Or, “when life hands you lemons, make lemonade.”
In a past life, I was lucky enough to land a job as a network administrator and legislative correspondent in the Washington, DC office of Mike Synar, who represented the 2nd District of Oklahoma in the US House of Representatives.
For the few months after I moved to DC, I lived with my aunt, uncle, and younger cousin Court, although my cousins Lore and Lindy were frequently over at the house too.
One night we all ate dinner together in the back yard; and the conversation steered towards why my Uncle attended West Point for college for mechanical engineering, rather than studying that at his first choice school, the University of Illinois in Urbana-Champaign.
His parents/our grandparents couldn’t afford to send him to college and pay for him to join/live in the fraternity he wanted to join, so he refused to go to college at all. Instead, he moved out of their apartment and moved in with his uncle (my great uncle). (Note: family legend has it he spent much of his time sleeping on my great uncle’s couch and only a little time attending classes at what eventually became the University of Illinois at Chicago.)
My grandfather was a staunch Republican precinct committeeman in Chicago during the reign of the first Mayor Richard Dailey, when being a Republican was a very lonely experience. But- while clearly a member of the minority party, my grandfather was still able to elicit help through one of his political connections and my uncle won an appointment to West Point, which he started the following fall as a new freshman.
That began a remarkable career. Eventually he became a career Foreign Service Officer who was mainly posted in active war zones, so we’ll never fully know what he did while at work.
Anyway – it came out during that dinner he was still angry over 25 years later he attended West Point because my grandparents couldn’t afford the fraternity dues as well as the tuition, but when it was time five years later for my mother to go to college, my grandfather again wasn’t working but my grandmother worked two jobs to send my mom to a private college.
Then the discussion ended abruptly, my uncle got up, took his plate into the kitchen, and didn’t rejoin us.
My aunt and cousins looked confused and asked “what was that about?” I’d heard that story before and so knew what he was talking about, and filled them in. They all shook their heads. Yes, his life turned out a lot differently - he’d had extraordinary opportunities which would not have been available to him had he stayed in Illinois.
I think it must have been an off day for my uncle; but at the same time, I understand at least some of his perspective that night.
One of my favorite poems is Robert Frost’s “The Road not Taken.” Even now, there are times I wish I’d made chosen a different path than the one I chose. While sometimes appealing, “re-do’s” are rarely real options for me.
Supposedly every experience we have in some way physically changes the wiring in our brains, but if nothing else, is imprinted in our short and/or long term memories. If we’re smart and/or lucky, we learn from each experience to keep moving forward.
I will always admire my uncle and appreciate what he achieved; especially since I didn’t inherit the genes to be a diplomat. I also appreciate the lesson I learned that night: even people who lead extraordinary lives may also regret choices they made/roads they took.
While I still sometimes struggle when choosing between two or more paths – I also know every exit is also an entrance to some place else.
“I may not have gone where I intended to go, but I think I have ended up where I intended to be.” - Douglas Adams


