237. Complexity Creep & The Birthday Problem

<p>Here’s a brain teaser for you: Imagine we’ve got a room full of people. We’re trying to figure if any two people in the room have the same birthday.</p> <p>For us to reach a fifty-percent probability that there are two people in the room with the exact same birthday, how many people need to be in the room?</p> <p>I told you this was a brain teaser, so suffice to say that the answer -- to how many people need to be in a room for there to be a fifty-percent probability that two people have the exact same birthday -- is not what you would intuitively expect.</p> <h3 id= "the-birthday-problem-tells-a-lot-about-how-we-fail-to-see-hidden-complexity"> The “birthday problem” tells a lot about how we fail to see hidden complexity</h3> <p>For the sake of this puzzle, let’s assume there are no twins, no leap year birthdays, and there are no seasonal variations. No spike in birthdays nine months after Christmas or some big snowstorm.</p> <p>Most people start with a rough calculation like this: There’s 365 days in a year, so for there to be two people in the room with the same birthday, take 365, divide it by two -- you’ve got about 180, give or take. With 180 people in a room it seems you’d have about a fifty-percent chance that two of them have the same birthday.</p> <p>This intuitive calculation is wrong. It’s very wrong. If you had 180 people in a room, the chances that two of them will have the same birthday is damn close to 100%. Even if there were only 100 people in the room, rather than 180, the chances that two of them would have the same birthday would be 99.99997%.</p> <p>The actual answer is fun to know, but it also tells us a lot about our minds. It tells us a lot about how bad we are at understanding complexity. It tells us a lot about how complexity tends to get out of hand, and weigh us down, and cause us to stagnate. Complexity creep.</p> <p>If we know the answer to what is known as <a href= "https://en.wikipedia.org/wiki/Birthday_problem">the birthday problem</a>, maybe -- just maybe -- we can fight again