The Run-In Hypothesis

On a lazy Sunday afternoon, I dragged my lazier friend out in the blistering cold to whet the artsy thirst in me. How could I not have visited a museum three months after landing in this metropolis?

Thus I found myself in the middle of a thick crowd, talking about the good old times with my friend, who I was meeting after exactly two years. We were on our way to 86th Street station on the Upper East Side to raid the premises of the Guggenheim Museum. The train came to a crunching halt and we let ourselves get pushed out by the crowd. As we were walking out of the cavernous station, a familiar face flashed across the 180 degrees of my vision. It was ABC (name changed), who was a year senior to me in college in good ol' Singapore! Not that we were buddies exactly, but she immediately recognised me even though I was covered from head to toe and resembled an unsuccessful bank robber.
"Hey! It's you!"
"Yes, it's me! And you...I had no idea you were here", I quipped back.
"Are you still working at ... "
"Yeaha, very much there! Very lucky to still be on the payroll! Got a transfer to this city a few months back..."
"Good! Are you on Facebook?"
"Ofcourse!"
"Cool! We shall connect there!"
"Alright! See ya!"

The conversation was shorter than a minute and as we walked out into the sleepy sunshine, I remarked to my sleepier friend - "Wow! What are the chances? Bumping into someone who I last saw a few years back thousands of miles away, in the middle of New York!" Then I could not stop myself from uttering the cliche - "It IS a small world!"

Ten minutes later, we were inside the very elegant Guggenheim building, with tickets in our hand. We had already seen the first floor exhibits, which were a super flim-flam in the name of ground-breaking photography. What amused me more were how most people roamed about without gathering a clue about the photos of empty roads labelled "Vision of a Dream","The Path to the Inner Soul", etc. At the same time, they were furtively casting glances at others around them, attempting to understand if they were the only ones lost while trying to portray a deep look of comprehension at the same time.

While I was entertaining myself watching my now-awake friend pretending to be someone like that, there flashed another familiar face across my eyes. It was XYZ (name changed again, but you have probably guessed that out by now), a colleague from Sydney! Her face lit up on seeing me.

"Hiiiiii!!"
"Hello...", I answered back with what I imagine is a suave smile which makes guest appearances at such moments.
She was with a guy, and they were obviously relieved to find someone who was not bowled over by the flat displays.
"Hey Mike, this is Suryanshu, who works for DB in Singapore", she introduced me to her companion.
"Hiya! Ummm XYZ, I am actually now in New York. Got myself transferred a few months back."
Expressions of surprises followed with a minute's chatter ending with the traditional Apache pledge to meet up for drinks one of these days. Then they carried on with their tour, obviously determined to maximise every penny they had paid.

Twenty minutes later, I had dragged my friend out of the building, utterly let-down by the contents on those walls, with the exception of the floor that had Van Gogh's works and a really beautiful usher.

But what tickled my mind was how I had bumped into ABC and XYZ in a span of thirty minutes, half-way across the globe from where I had seen them last. Quick calculations at Kryptonic speeds led to a rough hypothesis (cannot call it a theorem yet, because it's yet to be proved), which is best expressed as a formula with a few variables. What are the chances of running into known people unexpectedly in a new city?

This formula will give you that. Suppose you are X and the other person is Y.

Then the probability of X running into Y without expecting that is given by Z, where:

Z = (((No. of X's acquaintances * No. of days since X saw Y) + (No. of Y's acquaintances * No. of days since Y saw X) - (Product of their respective no. of days since they both went out)) * (Probability of rain that day)^2 + No. of museums they have both seen in their lives - No. of movies showing on HBO at home that day which hey haven't seen) * Q / ((Sum of X and Y's acquaintances * Least of no. of hours they like to sleep on a Sunday afternoon) - (No. of friends they have visiting them each)^2 + (1/Probability of X feeling like taking the train)(1/Probability of Y buying a new jacket that day which she or he wanted to show off))

Obviously, as your naked eye can see, the formula still has the unknown variable Q.

If you can provide me the value of Q, I could plug it in and confirm the hypothesis. If not, I will have to take strolls on Sunday afternoons to figure that out.