John Gottti Junior, fresh from his fourth mistrial on racketeering and murder conspiracy charges, reports a miracle: Over the past few days, two songs that remind him of his father (the late and legendary mobster John Gotti Senior) have come up on the radio at exactly 10:27 PM—and 10/27 is his father’s birthday.
From the New York Times:
Did the son feel that the father was was watching over him?
“How else do you explain it?”, he said.
This reminded me of a question that the mathematician J.E. Littlewood liked to ask: What is the most remarkable coincidence you have experienced, and is it remarkable given that it is the most remarkable coincidence you have experienced? It would, after all, be quite remarkable never to have experienced a remarkable coincidence, so coincidences of ordinary remarkability don’t count. If you have 100 memorable experiences a day, three or four in a lifetime should be of the one-in-a-million sort. But have you ever had a one-in-a-billion experience? Do share.
A few years ago, I had a dream in which I saw my father hit and killed by a car. It kind of shook me up. In the morning, while I was taking a shower, the phone rang. I stepped out dripping wet to answer it. It was a salesman wanting to know if I’d like to change my long distance carrier. My father lived more than 20 years after that and died in bed.
I realize we’re beyond all that here, but I felt an irresistible urge to draw attention to all the non-coincidences that no one ever talks about.
I’m a American mathematician, and while visiting Germany, I met another one. After inquiring about his background, it turned out that we had lived on the same block in the same town (Elmhurst, Illinois) for two years during grade school (about 1962), and had a friend in common. His house was behind ours and probably not more than 150 feet away.
Years ago I happened to go to the same hotel (a beautiful Tucson resort) twice in the same month, first for a Cato conference and later for a medical meeting. The first time, a good friend of mine was given a room with a great view. I therefore asked the front desk if I could have that room on my next visit in 2 weeks. They agreed. But when I got there, a slip up had been made and that room was not available. So they gave me the room immediately above it, with the same view.
The next day, I inadvertently got off the elevator on the wrong floor and ended up trying to enter the room below mine, the room my friend had been give 2 weeks earlier. The occupant heard my attempt as I realized my mistake, and opened the door as I was backing away. I began to stammer an apology while looking at my feet, and he said my name. Thinking it was a fellow medical conventioneer, I looked up. It was my old college roommate, whom I’d not seen or been in contact with in over a decade.
My diploid genome contains about 6 billion base pairs, according to Wikipedia. With four possibilities for each pair, the odds of me as a human being having the exact genome that I do have is therefore about one out of 6 billion to the 4th power. I don’t know how to translate that into normal numbers, but I do know that it’s inconceivably rarer than one in a billion. And, with close to 7 billion human beings on earth right now, each of whom is individually as unlikely as I am, the odds of the earth’s population consisting of the specific members it actually has is approximately one out of 6 billion to the 4th power to the 7 billionth power. And that doesn’t even consider the nurture side of the equation.
Alan,
6 billion base pairs with a choice of four different pairs is actually 4 to the 6 billionth power, not 6 billion to the fourth power. The probability is even smaller than you think.
This does bring up an interesting topic, though. What is the P(X|Y), where X = a specific DNA sequence and Y = being human> This is radically larger than the original 4^(-6,000,000,000), since every human shares over 98% of the same DNA sequencing. This of course leads to all sorts of various questions, that I can’t answer nor do I know of anyone who can. A couple are:
1) What is the variability human DNA? In other words, can we compute an answer to or at least get an upper and lower bound on the above P(X|Y)? Even more important than this question is at the what is the macro level of variability, not just this microlevel in the DNA? This, of course, can be worded as to define exactly, in terms of DNA, what it means to be human.
2. What is P(X|Y), where X = a DNA sequence and Y = a life form that uses DNA? In other words, how many DNA sequences DO NOT result in life?
Regards,
Ken
Alan, that is not a coincidence – conditional on surviving to you current age, you have to have had some genome and some sort of upbringing. In fact, the probability that you are the person that you are is 1.
Presumably if the average person has 3 or 4 “1 in a million” experiences a lifetime (presumably this is poison distributed), and 1000 people visit this blog we’d expect to hear about 3 or 4 “1 in a billion” experiences (assuming we’re calling 10^9 a billion as opposed to 10^12).
Two days ago, I sold an item on ebay, a gift card to a well-known restaurant. One of my very best friends won it. We didn’t realize this until ebay provided our contact info when the auction was finished. Probably not 1 in a billion…
CD -Luckily the coincidence ended where it did. It would have been even more of a coincidence if that friend had given you the gift card in the first place and you anonymously resold it to him.
Two stories…
Seven years ago I left my home country and went to the States to do my MA. A year after that, a guy from my country whom I met in the States goes back home for a summer internship. I geve him some stuff to take to my girlfriend. He calls her from work and her cell phone display shows “Marko’s Office”. She did not delete my old office phone number and it turns out that consulting company that he was interning with was implementing the project in the institution that I worked in and they gave him my old phone number (different office, though).
The second story… I fly from my country to Detroit over Frankfurt. I sit next to a guy in a flight to Frankfurt. After spending a couple of days in Detroit, I rent a car and drive to New York City. Walking down the 5th avenue at around 8:30 in the morning I meet a guy I was sitting with on an airplane a week ago, 4000 miles away. It turns out he flew to Boston and then came to NYC for a weekend.
Is any of these “one in a billion”? Probably not…
CD: My sister once attempted to buy a unique ceramic item on Ebay as a surprise birthday gift for a friend. She found herself in an intense bidding war for this item and somehow, after several rounds of bidding, figured out that the competing bidder was the friend for whom she was buying the item.
This left her in a deep quandary. She couldn’t reveal the situation to the friend, because this was a friend for whom she would not ordinarily buy a present, and to reveal that she was doing so this year would have effectively revealed that a surprise party was in the works. She didn’t want to walk away from the auction after having bid the price way up, leaving her friend to pay that high price. It seemed insane to prolong the bidding war, but she felt compelled to do so at least until she could devise an exit strategy.
I forget how this story ends. It’s also possible I’ve got some details wrong. My sister can fill in the ending and (if necessary) correct the details. This will be a good test to see whether she reads this blog.
My wife recently took a new job that is requiring us to move to Chicago area. We live in Detroit so this is a step up. We got the offer on Monday ( 4 days ago ). 2 days ago I was flying back to Detroit from Busan, ROK and the guy accross the aisle was chatty for some of it.
Talk about the economy moved the discussion to our move. And after a short time he realized that he had interviewed my wife the previous week and had made the hiring decision. I was chatting the VP my wife will be reporting to next week.
One in One Billion? dunno, Detroit and Chicago are both hub airports.
I don’t think I’ve ever had an even one-in-ten-thousand coincidence.
But here’s the interesting thing: Given 100 opportunities a day for a coincidence, all of us should have a 1-in-10,000 coincidence about three times a year. And yet not only have I not had any, I can’t remember the last time someone else told me about a coincidence that impressive.
I take this to mean that 100 “opportunities for coincidence” per day must be an overestimation. This is probably because even though I may have about 100 memorable experiences per day, for most of them I can’t imagine anything that would have turned them into a “coincidence”. Say I run into my friend at Starbucks. What could have possibly made that into an “impressive” coincidence? If they were wearing a sweater and jeans like me?
The most impressive coincidence that comes to mind was at a small party in Cambridge, England. There were two people at party who had been schoolmates in New Zealand, and did not know before then that they had both become graduate students in Cambridge.
I rate the coincidence at much less than 1 billion, because as a first approximation I divide (the number of human beings in the age range represented at that party, who have been to high school) by (the number of people in a typical high school class x the square of the number of people at the party /2). Or should that be (the square of the number of people in a typical high school class x the number of people at the party /2)?
When I was at university, I made some new friends obviously. Took one of them around to a high school friends’ place (they had never heard of each other before) and wiled away that afternoon playing pool in her basement. Midway through a game, she happens to say “you look like you were born in October”.
He started smiling.
She then says “the 23rd?”
He tells her to guess the year and she said 1979.
He pulls out his drivers license and shows her the exact date she had just said.
We were freaked out. A few hours later, her sister and parents come home and we ran upstairs to tell them.
Her sister then guesses the month correctly and didn’t want to proceed because it was kinda scarey for her (they claim that they have always had this psychic connection).
Anyway, under intense pressure, she reluctantly yells out the day and year correctly. We couldn’t believe it.
Now I’m the world’s biggest atheistic skeptic whatever but that did seem like it came down to more than just mathematical coincidence….not sure what the odds are of that happenning (can anyone help? I’ve been trying to work that out for 10 years now).
Maybe giant spaghetti monster told them?
I was in Paris about 12 years ago and was checking my email at a hostel. My mom had sent an email wishing me well and she closed by saying “keep an eye out for April, she’s travelling in Europe too!” April being our next door neighbours daughter. I was in the middle of writing my reply saying something like “there are 300 million people in Europe what are the chances….” when I looked up and saw April standing at the front desk. It blew me away.
I was once traveling in Europe for 4 months and staying in hostels. In Vienna I stayed in the same room with a guy from States. About a month later in Pula, Croatia, I saw the same guy in an internet cafe. About a month later after having traveled through Hungary, Romania, and Bulgaria, I ended up in the same room with this person in a hostel in Istanbul.
Richard Feynman once told a story that went something like this: On the way to work today I saw a license plate that read XRD-7352. What do you suppose the odds are of that?
My wife and I recently went on a trip to South Korea. My wife has a thing for the weird way Ostrich’s keep showing up in her life. We were staring out the window of the hotel on Jeju Island and she said “hey look horse racing”. She grabbed her camera and then said “no way, those are Ostrich’s”. The next morning we were visiting an old village and she disappeared to see if she could take a picture of the Ostrich’s which were in a pen next door. She found them and was taking pictures when a gust of wind blew her Bennie off her head and into the pen. The beanie was from “Nightmare before Christmas”. She took a picture of it in the pen. Two weeks later while back in the states she went to a Christmas craft fair with her mother and was looking at ornaments when she came across a wooden ornament with an ostrich on it and decided to buy it. When the clerk turned around to help her she freaked out since he was wearing the exact same beanie she had lost.
The more I think about probability, the less sure I am that I understand what it even means that something is incredibly unlikely coincidence in the real world. The problem is that we are trying to estimate the odds of a dice roll when we have no idea what the die look like: how many of them there are, how many sides they have, or even what numbers are on their faces. In fact, we don’t REALLY even know, and may not be ABLE to know, if questions like “is this or that feature of the universe probable or improbable?” even make sense.
This is why theologians with pat assertions about the likelihood or unlikelihood of the universe, taken from a misunderstood translation of physics into philosophy, always strike me as unimaginative: exactly the opposite of what they seem to think they are.
Yes, if the laws of the universe _that we know about_ were slightly different, we might have had a universe we wouldn’t recognize. But who is to say that the laws we know of are the only ones possible? Who is to say how much the constants could have varied, and why? Perhaps our universe is remarkable in that most have many MORE universal constants and laws and features that we cannot even imagine. Perhaps in the total number of possible universes (which is not the same idea as “multiverses,” take heed), what is so remarkable about ours is how unordered and lifeless it is. Perhaps instead of needing to wonder about the necessity of a great organizer, we really need to be trying to look to a great DISorganizer.
I don’t see how any philosopher or theologian can possibly nail down the ontological truth: doing so always seems to require making some remarkably unimaginative assumptions. Empiricism, in contrast, may not be fully or fundamentally reliable, but at least it is modest: it makes assumptions, but they happily happen to be basically the same ones that I require to treat the world around me as real. And we admit upfront that they are our best approximation, not some core truth. So, that’s okay. And then we work ourselves up from the there to figure out larger truths as best we can. And we are encouraged to stay humble, always checking our work.
But of course, without working from the top down, saying much of anything about ultimate probability and causality is really a crapshoot. For all we know, our universe is deeply flawed in such a way that we don’t have, as most possible universes would have had, nearly every event and characteristic neatly connected by incredible coincidences.
When I was 24 years old, I was hitchhiking from Butte to Missoula, Montana. I got a ride from someone, and over the course of our conversation I mentioned that I was from NYC. They only person the driver knew from NYC was his college roommate, who it turned out, I knew. From one perspective the odds are 1 in 7 million (the population of NYC at the time). However, given the number of New Yorkers I knew, and the fact that the driver and I were in the same relative age group (he was about 30), it really wasn’t that incredible a coincidence.
A friend of mine used to drive a cab in NYC. One morning he picked up a fare on the upper west side, going downtown to the financial district. While passing through the Village, my friend’s cab strikes another cab, which is running a red light. Virtually no damage, but they have to trade info a fill out an accident report, so the passenger pays his fare, gets out, and hails another cab. Around 5:00 that day, my friend drops a fare downtown, and shortly stops for another passenger. After the passenger gets in, he says “Broadway and 87th Street, and this time don’t hit anyone.” It was, of course, the same passenger.
Odds, actually not that remote. There are 11,787 yellow cabs in New York. During the day, almost all are out on the streets. If we knew the average number of taxi rides per day per person (not per cab), we could figure out the probability.
The most remarkable coincidence I experienced the other day was one of the license plates I saw parked on a nearby street. I don’t remember it, but it was an out of state car. And of all the ~300 million license plate numbers in the United states – the overwhelming majority of which are from other states, and are less often seen in my neighborhood than local plates – the chances that the car bearing that particular plate would be parked right where I was walking were, given what information I had at the time, extraordinarily small. I never could have guessed it if I hadn’t seen it!
I’m sure the person who parked it there had ample reason to, and might very well have not considered it much of a coincidence.
Then again, maybe the DJs who played those two songs at those times, also had their reasons, and didn’t consider the timing especially remarkable, either. They just had different knowledge of the situation beforehand.
Okay, I do have some stories of the kinds of coincidences you were actually looking for :) I posted several stories of coincidentally perfect timing several years ago, and your post reminded me of those.