## Too Many Twinkles

(Submitted by Skepticality listener Katharine Shade)

Today during my 7 year old’s violin lesson, I was reading a “Mr. Men” book to my 4 year old. He had selected it randomly from the teacher’s complete set of the books.

I had just finished a page which mentioned “Mrs. Twinkle”, when my daughter started playing “Twinkle Twinkle Little Star”.

It wasn’t as a direct result of my reading – she was working her way backwards through her repertoire of pieces, so that had been set in motion before I’d even started reading the book. And there was nothing to specifically draw my son to this book.

I often notice that I’m reading a word at about the same time I hear somebody say it, but that easily make sense considering the number of words I read. But my daughter only knows about 6 violin pieces by heart!

So what are the odds?

Below are the extended notes provided by mathematician Brian Pasko for use in Skepticality Episode 267.  Brian is on the faculty at a university in the southwestern United States. His interests include scientific skepticism, popular science books and improbable coincidences that makes one wonder just what the fates are up to. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

What a lovely vision: a young mother dramatically reading to the toddler in her lap while her daughter struggles through the elementary musical cannon. I can only hope that afternoon sunlight was streaming through the large windows of the studio…

How probable was your experience? I would say rather high! Of course, what questions we ask determines our estimate of the probability. Let’s start this way: the probability that a children’s book contains the word twinkle, fairly high; the probability that at some point during the lesson your seven year old daughter plays Twinkle, Twinkle Little Star I would say pretty close to one. (Probability is measured between zero and one with zero being cannot happen and one being cannot not happen.) In this case your experience is not that hard to believe.

Or, we could wonder what the probability is of reading a book with a character Miss Spider, Mr. Farmer, Ms. Wheels or, Madame Spaghetti (atop or otherwise) and noticing that your daughter plays one of the corresponding songs. In this case, your coincidence is even expected.

We can be a bit more specific, though we have to make some assumptions. There are numerous titles in the Mr. Men series but a box set of 50 books was issued in 2010, let’s suppose your son picked the book you read from one of these. I have been unable to determine the number of these books that include the character Mrs. Twinkle but let’s just assume two. (Yes, a bit arbitrary but it seems unlikely that she appears in only one title; if she is a regular character in the series, I expect a Google search would turn up some mention of her.) Twinkle, Twinkle Little Star takes about 30 seconds to play. Reading a Mr. Men book takes about 10 minutes and if the words ‘Mrs. Twinkle’ appears on three pages there is a 2 minute window that you could read the words ‘Mrs. Twinkle’ while your daughter is playing the song.

I wrote a short computer program to model the situation assuming the lesson was thirty minutes long. It turns out that the probability that you read the words “Mrs. Twinkle” while your daughter was playing Twinkle, Twinkle Little Star is about 0.27. Since two of the 50 books your son could have chosen include this character, I estimate the probability of your experience around 1.1%.

So, I think your improbable event is not all that improbable. Imagine the alternative: that one chooses a children’s book that does not have some similarity to a common children’s song.

## The Conference Coincidence

(Submitted by Skepticality listener Rob)

My first job after college sent me on a five-day training course in Boston, where I made fast friends with three other students. We were all traveling from different states (North Carolina, Nebraska, Michigan, & Missouri) and our ages ranged from 22 to mid 40s. Somehow we all hit it off in class and went to dinner every night before returning to our hotel.

Eight months later, I flew from NC to San Diego on a work conference. Checking into my hotel, I happened to bump into my Nebraska buddy hauling his luggage through the lobby. Amazed, we chatted for a few minutes, and I learned he was on a work trip of his own, unrelated to mine.

The next evening, I exited the elevator and passed none other than my Missouri friend, who was staying on my floor. He too was on a work trip, and after picking my jaw up from the carpet, I suggested we meet up with Nebraska guy and go out to dinner for old time’s sake. “What are the chances?” remained the theme of our conversation as we set off to find Mr. Nebraska.

Long story short, the three of us ended up at a seafood place, laughing, swapping stories, when suddenly our Michigan friend passed by our table, did a quadruple take, stared at us for a moment in silence, and burst out in laughter. Turned out he was a vendor at my conference, and was sent to demo a product that I would eventually take back to NC.

So, our impromptu gang had managed to assemble once again, from one coast to the other, from Massachusetts to California, eight months apart. I tell all my friends and dates this story, and none of them believe it. It’s certainly the most improbably bizarre event that’s ever happened to me, and I can’t even begin to calculate the odds.

You’d think I would’ve kept up with these guys, but honestly I never did. We never got together again after that fateful week in San Diego

Below are the extended notes provided by mathematician Brian Pasko for use in Skepticality Episode 263.  Brian is on the faculty at Eastern New Mexico University. His interests include scientific skepticism, popular science books and improbable coincidences that makes one wonder just what the fates are up to. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

Cool! The Drake equation is named for physicist Frank Drake. It provides important considerations to estimate the probability of extraterrestrial civilizations in the universe. Finding the probability of you four friends meeting seems hard. Let’s analyze your situation with Drake as inspiration. The probability that you all meet as you described is the product of the probabilities that:

1. You all happen to be in the same city (or, nearby) at the same time;
2. three of you get the same hotel (and actually see each other!); and
3. that the third person comes to the restaurant at which the others are eating (and actually see each other!).

This product is, let’s say, small. However, there are some interesting facets that affect this probability. The first is that I suspect you four are in the same industry. This may increase the likelihood of you all being in the same area at the same time. If this assumption is correct, you’re all likely in the same economic class as well. This narrows the selection of hotels you each choose and the restaurants you’re likely to patronize.

You could have met Michigan and Nebraska at the hotel instead of Missouri and Nebraska. So we need only that three of the four friends were at the same hotel. This increases the likelihood of a meeting by factor of three! Also, you could have seen any of the other two at any time during the day. In addition, you’re all on work trips and so probably are moving in and out of your rooms at the same times of the day, which increases the likelihood of a meeting.

Of course, the meet up could have happened in a lot of different ways. For example, two pairs of you could have met at two different hotels; or not at hotels at all but on the street getting the same cab; or at a pub after work hours… You get the idea.

A consequence of Drake’s ideas is that if we happened to find alien life in our solar system it would imply that the universe is positively rife with life! I suggest that if such a meet up happens again between you four, rather than lightening striking twice, it means that you’re often in the same place at the same time and just don’t see each other.