## Sunday, January 8, 2017

### Birthday Weekend

Another year, another birthday. I spent the evening before my birthday at the opera and hanging out with friends, and also making some new friends - everyone wants to buy you a drink when it's your birthday. So yesterday, the actual day, was really low-key: sleeping in, Netflix, reading, takeout. I opened gifts from my family and went to bed early. It was the perfect counterpoint to my wild Friday night. Today, I'm doing more reading, and hopefully doing some long-overdue writing, before going to one of my favorite restaurants this evening.

Birthdays have always been tough for me. Being the coldest time of the year, it's usually difficult to organize outings. Years ago, a cousin committed suicide on his birthday, and when I reached his age, every birthday after that was a reminder: I'm older now than he will ever be. In fact, I'm sure birthdays - turning a year older - are hard for most people. A friend on Facebook said wishing someone happy birthday is like cheering at regular intervals while someone's life runs out. That's not really how I think about, but I suppose it's accurate.

Growing up, one of my good friends had the same birthday as me, though she was a few years younger. And several years ago, at a friend's wedding, I met a true birthday buddy: someone born the same day and year as me. There's an interesting concept known as the birthday paradox, which is a great demonstration of probability.

The birthday paradox is essentially that in a room of 23 people, the chance that two people will have the same birthday is about 50%. How could this possibly be? Better Explained offers a post that demonstrates the math behind this concept. But to summarize, most people get hung up on the probability that a specific day will be someone's birthday: 1/365. But the math behind the birthday paradox deals with paired comparisons. The chance of two randomly selected people having different birthdays is 1-1/365, or 0.9973. When we have 23 people to choose from, we have 253 paired comparisons. And when we examine this kind of probability, we use exponents. The probability that all 23 people have different birthdays is (1-1/365)^253, or 0.4995. Meaning the probability that at least 2 people have the same birthday is 1-0.4995, or 0.5005.