Hooray for the likeliness of unlikely events!

Coincidences? Fate? Final Destination 5?
Are Nick Wren and I somehow cosmically connected?

Recently, Zena and Tim left the house to go back to Santa Clara for their last year of college. As a celebration, we all decided to go to a movie that Nelson really wanted to see: Final Destination 5. This movie's premise is that a group of people escape death, and death tracks them down, one by one, to fulfill their Final Destination 5!

Tim, me, Rosita, Zena, and Maribel (Nelson on the lens)

As the characters are brutally, grotesquely, and comically massacred in increasingly improbable ways, the characters and the detective in the movie say to themselves again and again: "There is just no way this could happen, it would be too much of a coincidence."

Nick Wren and I had never talked to each other before these past months. He and I independently decided to live at this house starting in August. However, improbably, we are both from Milwaukee, went to the same high school a year apart, Nick played soccer with my best friend Bryan, I played Sheepshead with one of Nick's best friends Mike, I got a ride to St. Louis this summer with Nick's girlfriend Beth's brother, Nick and I both are learning guitar, and we both seem to be 5's on the enneagram.

Although it is entertaining to think about connections like this, it really shouldn't surprise us if we take a look at the numbers. John Allen Paulos summarizes this idea in his book "Innumeracy: Mathematical Illiteracy and Its Consequences":

The paradoxical conclusion is that it would be very unlikely for unlikely events not to occur. If you don't specify a predicted event precisely, there are an indeterminate number of ways for an event of that general kind to take place (Paulos 28).

So, before meeting Nick, if I specified some connection in advance, like "What is the probability that Nick's grandma sang in choir with my grandma?", then the likelihood of this specific connection coming true upon meeting and asking Nick, is very low. However, the likelihood of any connection between us is actually very high.

As a classic example, take the probability that two people share a birthday. How many people must be gathered in a room to ensure this is true? Answer: 367 people need to be in the room. (there are usually 365 days in a year, plus February 29th, plus 1 to make sure two people share)

Now, how many people must be in a room to ensure that 50% of the time, at least two people share a birthday?

Only 23.

(The calculation is 1 - {365! / [(365-23)!*365^23]} which equals about 1/2. For a full explanation see Paulos' book on page 27, trust me it's easier than it appears)

Half the time that 23 people are in a room together, at least two of them will share a birthday. This shows that the likelihood of a broad range or category of individually unlikely events, is actually quite high. Plus, sharing a birthday is pretty specific compared to "connections" between me and Nick. A "connection" could be practically anything!

As Paulos points out:

A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence. If they anticipate someone else's thought, or have a dream that seems to come true, or read that, say, President Kennedy's secretary was named Lincoln while President Lincoln's secretary was named Kennedy, this is considered proof of some wondrous but mysterious harmony that somehow holds in their personal universe.

But seriously, it is pretty crazy that Nick and I happened to both come here from Milwaukee. I say: Hooray for the likeliness of unlikely events!