What I’m Thinking:
I started dating my wife when I was seventeen years old. We ended our second or third date with a moonlit walk along the beach– not so much because I was a romantic as because it was close, it was free, it was private, and I was loathe to let an enjoyable night end.
At some point in the conversation, I picked up a seashell off the beach and grandly declared that I’d keep it forever to remember this night. And then I did, keeping the seashell with me through nine moves in ten years.
I took to keeping it in the coin tray in my car so that I would periodically stumble across it and think back to the early nights of our relationship. The seashell (like the relationship) outlasted two cars with no signs of wear.
Until one day when I took my car in to get it detailed. I drove off only to realize the next day– too late– that when cleaning out the trash in the console they had mistakenly thrown away the seashell, too.
And that’s the 100% true story of why to this day car washes make me sad.
(There’s perhaps a parable here about how the physical reminder of an event eventually became more interesting and memorable than the event itself, but I’ll leave that to you to puzzle out. Sometimes a story is just a story.)
What I’m Reading:
“The Birthday Paradox” is a famous problem in probability. The basic question is: assuming birthdays are evenly distributed and ignoring leap years, there’s a 1-in-365 chance that two randomly-selected individuals will have the same birthday. How many people would you need until it’s more likely than not that two of them share a birthday?
Usually, the easiest way to work out the probability of something happening is to take 1 minus the probability of it NOT happening. The odds that two people do *NOT* share a birthday are 364-in-365, or ~99.7%. The odds that a number of pairs don’t share a birthday are 99.7% * 99.7% * 99.7% * … * 99.7%, one for each pair. (Or rather, they’re 99.7% ^ n, where n is the number of pairs.)
You need 253 pairs before it becomes more likely than not that one of them shares a birthday. How many people are needed to make 253? Surprisingly, only 23. A group of 23 people gives you 253 pairs exactly– person 1+2, person 1+3, person 1+4, … , person 1+23, then person 2+3, person 2+4, … , person 2+23, and so on. Any group of size N gives you (N-1)+(N-2)+(N-3)+…+2+1 pairs.
And that’s the birthday paradox. Individually, the odds of sharing a birthday are incredibly low (less than 0.3%). And yet in most elementary, middle, and high school classrooms in America today it’s more likely than not that two people share a birthday.
Interestingly, a couple years ago one of my cousins had his first child. She was the 23rd person on my mom’s side of the family. And she and I just happen to share a birthday.
I love how tidily this illustrates the birthday paradox. (I also love that the rest of my family doesn’t find this anywhere near as interesting, which means they always forget and every year I get to amaze them anew with the fact that I remembered my niece’s birthday.)
What I’m Working On:
Updated returner projections for FootballguysArticle: “Are Dynasty Leagues the Right Fit for You?”- Buying a house!