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The Scientific Study vs. The Dream

I listen to a lot of science and skeptical podcasts and other media. Consequently I post breaking science news stories on my Facebook page regularly as they are “on my mind”. The story/anecdote told by my Facebook friend that follows this Facebook post is the one I wanted to submit. My post below was the result of a scientific study, to which his “the odds must be crazy” story was a refutation or denial/reason why he is unwilling to accept the truth value of the study’s conclusion. (This form of reasoning, single data point, confirmation biased anecdote trumps large population empirical study, is common among many in my community. It is employed by many smart, educated people to convince themselves not to vaccinate their kids.) SCIENCE CONFRONTS Paranormal Claims. Nine recently reported parapsychological experiments appear to support the existence of precognition. Three more recent independent studies set up to exactly replicate the experiments all failed to produce significant effects and thus do not support the existence of psychic ability. The nine studies it seems all suffered from false positive artifacts generated by poor methodology and statistics. MY FACEBOOK FRIEND’S rebuttal story, in response to the study below: “When I was about 10 or 11, I remember clearly my mother recalling for us one morning an incredibly detailed and vivid dream she had had during the night. She told us this at breakfast time before we went to school that day so it was probably about 7.30am-8am. She dreamed that the high school age daughter of a friend of hers had to rescue her two horses that had escaped from their paddock and were running amok in panic on the main highway through Wellsford, the small town in which we lived at the time. The paddock was at the bottom of a steep hill and the residential road on that hill led up to the main road which ran through Wellsford and was the State Highway between Auckland and Whangarei. That very afternoon, Kay Shepherd, (the teenage horse owner), was given urgent notification that her horses were running in a blind panic on that road and were endangering themselves and motorists. She had to leave class and rescue her horses in quite a frightening and distressing situation for her and her horses. This happened probably at some time between 2 and 3pm. It happened exactly as my mother had dreamed it some 6-7 hours after she told us about her dream.”

Coincidence Twins

I have two sisters, one of them my twin, the other a year older.

Years ago, my twin was in the Army and her first duty station was in South Korea. My older sister was going to school in Long Island, New York. Our family was home-based in Minnesota. One night, at about 3am, my older sister gets a phone call from my twin because she had just met a guy who was from the same town in Long Island where the older sister was and she was just curious if she knew the name. Of course, she did not. She had only been there a year or so at that time.

My older sister goes into school the next day where she worked in a lab. She had become good friends with the secretary of that lab and was complaining to her about having been woken by her sister so early and for a stupid question – how was she to know of some guy half way around the world? The secretary, having lived a long time in that town asked for his name.  My sister told her it was something like “Joe, Joseph, Joe Schmo or something”  (well, actually using the name my twin gave her…)

My sister’s friend responded, “JOE SCHMO???!! His parents live right next door to me, I knew that kid as he grew up!”  It turned out she was right, it was the same guy and my twin and Joe Schmo have been married for nearly 15 years now.

Reconnecting in Rio

When I was in college, I spent a portion of my junior year on a study abroad program in Rio de Janeiro, Brazil. On the weekends my roommate, another American exchange student from a different university, would often travel to nearby towns and cities to explore the country.

On one of our first trips we headed to a small city in the interior of São Paulo state. On the bus ride Alberto and I spent the time getting to know each other by sharing stories of where we grew up. His father had been an executive for a large American company and he had spent several years growing up in Thailand where the company had a manufacturing plant. He recalled that there was a man from Brazil who worked for the same company who lived there with his family that had left Thailand the year before he and his family returned to the US (you can already guess where this story is going).

As the bus pulled into the station of our destination, Alberto looked out at the town square across the street and said something like, “Oh, my god.” Sure enough, the family he had just been telling me about were sitting on a park bench there enjoying lunch (if I recall). We grabbed our backpacks, got off the bus, and dashed across the street.

As we approached, the wife looked up at saw us.  The expression on her face was priceless! Then her husband and daughter turned to see what she was staring at. Being the outsider, I had the best view of this reunion as they marveled at the coincidence. Turned out, they lived in the city of São Paulo and were on a short getaway in this same small city. We ended up spending the weekend with them and later visiting them at their home in São Paulo.

Exhausting Coincidence

I have no idea whether this story will be applicable or not, as I have no idea how to evaluate the odds.

Back in the ’90s, I was driving an old Buick from 1968. (This is relevant because it was well before the age of computerized ignition.) I had known the exhaust was leaking, but I didn’t know how badly. One day, as I arrived at work, basically the whole exhaust fell off, onto the street.

After much soul-searching, I finally made the decision to bite the bullet and replace the entire exhaust from the Y-pipe* back. Deciding to invest nearly $1000 took some doing, as I had only paid $400 for the entire car.

Anyway, the day after I got the car back with its nice new (quiet!) exhaust, I drove it to work again, and on my way out of the parking lot that evening, it suddenly started running badly. It started coughing and spluttering, culminating in a huge, violent backfire, and stalled. I investigated, and discovered that the top hose of the radiator had developed a pinhole leak, and was shooting a jet of water across the engine, and intersecting both posts of the coil, shorting it out. (In pre-computerized ignitions, the coil was the source of the spark to the plugs. In my car, it had + and – top posts, much like a battery) The aim required to make this contact bordered on miraculous: An eighth of an inch in any direction, it wouldn’t have hit both posts. If the location of the hole in the hose had been half an inch in any direction, there wouldn’t have been any angle at which it could hit both. But it did, and the backfire it caused blew up my shiny new (less than a day old) muffler like a balloon, splitting the seams on both sides.

Again, I have no way to evaluate how unlikely it is for a pinhole jet of water to make this incredible sniper shot. I can’t think of any two parts more unrelated than a radiator hose and a muffler. If I had any tendency to assume supernatural agency, I’d have taken this as concrete proof that I wasn’t allowed to have nice things.

* (Irrelevant footnote: If you’re not aware, the Y-pipe is where the exhaust from the two banks of cylinders in a V6 or (in this case) a V8 come together into one.)


(Submitted by Skepticality listener and friend of the blog Christopher Brown.

Hi all:

My son, Ethan Brown performs a Mental Mathematics stage show. A few months ago, he developed a new piece for his act. It’s a version of an old presentation puzzle known as The Knight’s Tour.

Traditionally, performers have allowed audience volunteers to select a square on a Chessboard. The performer then begins on that square and theoretically moves a knight around the board using only legal knight moves (which are “L” shaped). The goal is to land on every single square on the board without landing on any square twice.

Ethan adds an additional twist to this trick by allowing the audience to also select the final square on which the knight must land, finishing the puzzle.

Since debuting this new trick, he has had a chance to perform it 5 times. 3 out of those five times, the two audience members selected the exact same two squares (only they were reversed in one of those times). Our back of the envelope calculations place the Mathematical odds at 1 in 107,374,182, though I suspect something else might be going on here. We have video of 2 of the performances if you’d like to see it. Could there be something psychological that causes people to gravitate to these squares much like people often pick “Ace of Spades” when asked to randomly think of a card?

I have attached photos of the three final Knight’s Tours. Note where the numbers 1 and 64 are.




 Thanks! Let me know if you have any questions at all.

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 244.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog.

These notes are a bit dense for the podlet, but maybe you can use the story and just skip most of the math.


First, let’s assume that the choice of square is completely random in all cases.

We are not particularly interested in the odds that the audience would choose those squares because it’s not the squares themselves that are interesting. It’s the fact that the audience chose the same squares the second time Ethan performed the trick. Therefore, we are given the squares by the first audience and we want to calculate the probability that the second audience would choose those particular squares.

To calculate the odds of choosing those particular squares, we must first note the odds for each, which are pretty easy. The odds of choosing the first square are 1 in 64, or .015625. The odds of choosing the second square are 1 in 32 (since you are limited to only white squares and all white squares are available), or .03125. The odds of choosing both is:

.015625 x .03125 = .00048828125 or 1 in 2,000

1 in 2,000 is the probability that the audience will choose the same squares on the second round that it did on the first round.

The third instance is a bit different because, although the audience chose the same squares, the starting and ending squares are backwards. The calculation is partially the same, but if we allow either square to be the starting square, we are now asking a different question. We now want to know the probability of choosing that specific black square to start and white square to end, or that particular white square to start and black square to end. So, we start with the probability of each scenario, which we know to be about 1 in 2,000, then double it (it is not possible to choose both, so there is no joint probability to subtract). So, the probability of choosing either the same squares or the same squares in reverse on any subsequent game is about .00098 or about 1 in 1,000.

Since each time Ethan performs this trick, there is about 1 in 1,000 chance that the audience will choose those same squares as start/end points, the probability that it would happen on the 3rd, 4th, or 5th time that he performed it is about 3 in 1,000, or .003.

So, taken as a whole, the probability of the audience repeating the first (exact) choices on the second performance and choosing the same squares on one of the three subsequent performances is about .0000015, or 1.5 in a million. So not quite one in a million…

But that is all assuming that the choices were random. I saw nothing in Ethan’s posture or delivery that would suggest any given square as a starting point. However, we do know that human beings don’t do anything at random. I doubt that anyone has conducted studies to determine which squares someone is likely to choose if they are in this particular situation, but I think it is fairly safe to say that they are at least twice as likely to choose squares in the middle of the board than on the edges. I would be interested to find out if that is true, but let’s assume that number is accurate.

That changes the entire game.

We could simply double the probability of choosing those same squares in the second performance, but that wouldn’t give us the whole picture. Now we have to consider the probability of choosing those squares in the first round, because it is no longer a uniform distribution.

If we consider that someone is twice as likely to choose a square that is not on the edge, the probability of choosing that particular square is now .02, or 1 in 50. Likewise, the probability of choosing an ending square that is not on the edge is about 1 in 25. So the probability of choosing those particular beginning and ending squares is:

.02 x .04 = .008 or 1 in 125.

And now the probability of choosing the same squares, with either as the starting square, is about 2 in 125.

And that makes the probability of this scenario about 1 in 31,250.

But I think it is worth noting that the probability of those two squares being chosen at any given performance is independent of the outcome of other performances. It ranges from 1 in 1,000 to 2 in 125, which isn’t exactly “crazy”. But if it keeps happening, I’m going to think seriously about setting up a betting pool.

Road Rage!

(Submitted by Skepticality listener Michael Farese.

I have less of a story and more of a question. My girlfriend is from New Jersey and has a very, um, animated personality. While driving, she often gives people certain gestures, honks, flashes headlights, etc.

I always tell her that she needs to be careful and that she shouldn’t do things like that because there are crazy people out there who might try to run her off the road (or worse) in a fit of road rage. She tells me that I’m being ridiculous and that she has a better chance of getting struck by lightning.

My question is: does she have a better chance of getting struck by lightning? Am I worrying about something that has only a negligible statistical chance of occurring?

Looking forward to some insight!

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 243.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog.

Hmmm…. Well, finding statistics about road rage is difficult, mostly because the definition of “road rage” is fuzzy. However, after looking at several different sources, I believe it’s safe to say that it seriously injures or kills around 1500 people in the U.S. per year, and that doesn’t include incidents in which only minor injuries or property damage are involved.

By contrast, the number of people who are injured by lightning in the U.S. each year is fewer than 300. On average, the number killed is 33.

Several websites echoed this sentiment written in About News:

“Statistics tell us that most all of us have been involved in an aggressive driving experience either as the victim or the aggressor at some point in our lives.”

Yet the lifetime chances of being struck by lightning at some point in one’s life are about 1 in 12,000. So I’d go with the author on this one.

Watch This Coincidence

(Submitted by reader who prefers to remain anonymous.)

I grew up in Alaska, and didn’t move to Michigan until 1990. After a few years of marriage, my wife and I decided to buy a new house (2002). We just contacted a realtor and looked on the internet ourselves. We finally decided on a house in a town about 10 miles away, because we thought it was a great deal.

I was a construction worker at the time.  About 5 years later, I got into watchmaking, and 4 years after that I opened my own watch repair shop in town.  There were many open storefronts for rent, and we finally decided on the one that looked like it was in the best condition. Soon after, I started researching the local watchmaker who lived and worked in town (he died in 1910). Long story short… not only am I in a storefront literally across the street, but I’m related to both him, and one of the founders of the town.  I don’t think I need to tell you that watchmaking is not a common profession. My great-grandfather was the watchmaker’s second cousin. And I’m a descendant of the brother of one of the founders of the town.

The only thing that makes the story sound less coincidental is if I admit that my mother grew up in another town about 40 miles away, and that her family has lived in this area since the 1830’s.

Holy Comical Coincidence, Batman!

As I have 2 monitors, I like to watch something on one while surfing the web on the other. I decided to re-watch Batman the Animated Series.

While browsing through stuff in an artist community website, I came across a little fan comic derived from one of the episodes of Batman (coming across comics isn’t rare, but this is the first one I’ve seen derived from a specific episode). I was about to pass it by until I noticed that the comic supposedly took place during the exact episode that I happened to be watching!

The Spooky Cab Ride

(Submitted by Skepticality listener Celestia Ward

Greetings. I had a strange coincidental experience a couple of decades back that, unfortunately, wasn’t cute or funny. My odds-must-be-crazy story is actually kind of gruesome and not for the weak of heart. So if you don’t mind a change of pace from your typical stories, I’ll tell you mine.

Some years ago, in Baltimore, I worked part-time with a small crew of artists in the tourist district. There were maybe eight of us. After night shifts I would routinely take a cab home; as a young female, waiting for a bus late at night could feel a bit lonely and dangerous. I would walk across the street to the large hotel taxi stand and usually there would be one or two cabs waiting.

One Sunday night I hopped into the one waiting cab and the driver told me he had just gotten paged by one of his “regulars” and would need to go pick her up–but if I wanted to ride along he’d drop me off afterward for a reduced fare. I had never had a driver offer this before, but there were no other cabs at the stand and a cheaper ride sounded good to me. I was in no hurry.

This regular client was a nurse who was just getting off her ER shift at the major hospital in the city center. We chatted as we rode, and she described the victim of grisly crime that had come in the previous night. An eighty-year-old woman had been attacked by her adult son, who lived with her and had a history of mental illness. He had come home from a drinking binge, accused her of stealing his money, and beat her up–even cut into her lips and cheeks, the nurse said, convinced, in his psychotic state, that she was hiding money in her mouth.

The cab driver and I were horrified. She said that the police had this man in custody and were expecting to charge him with murder. The old woman was in very bad condition and not expected to recover.

The nurse was dropped off at her house, then the cab driver took me home at his promised discount, and I just assumed that would be the last I heard of that awful scenario, unless the local news was covering it.

I went to work the next night and saw a couple of coworkers with grim expressions on their faces. They told me that Joe (I am changing his name) wouldn’t be working with us anymore. I first assumed that he’d finally been fired–Joe was kind of a jerk, had some issues and drank too much. No one really liked Joe.

It hit me sideways when my coworkers told me he had been arrested–for killing his mother! Out of the whole city, out of all the times I had taken a cab, I had ended up in the one taxi cab that–unknown to me at the time–got me a firsthand account of a murder committed by a coworker.

Tell me, what are the odds??!

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 242.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog.

It’s hard to say what the odds are without more information. The population of Baltimore at the time would be helpful, but not entirely, since the odds are increased a great deal by geography–the proximity of Joe’s home to his work place and the hospital where his mother was taken are not coincidental. So, I can say that the odds are much higher than one might think, but it is still quite a coincidence, and similar to stories I have heard before (I even have a similar story myself).

It is a gruesome story, and that gruesomeness enhances the chill and eeriness of the coincidence.

John’s New TV

(Submitted by TOMBC Team Member John Rael)

The day I went to my bank in order to get a personal loan, I came home, turned on my LCD TV (Westinghouse LVM-47W1), which I’ve owned for six years, and started seeing random ‘snowlike’ pixels on the screen. I turned it off in order to turn it on again… it would not turn on again.

I unplugged it and replugged it. Nothing. It was officially dead. Even though its standby light was on, and it kept making a slightly high pitched hum sound.

Keep in mind, without the loan I had just received (that very day), I would not have been able to afford another television until at least October. Anyways, I’m not sure how relevant any of that is to the coincidence, but there you go. Feel free to incorporate any info you happen to know about me personally (career, lifestyle, etc.). Also, feel free to ask me any questions.

Below are the extended notes for use in Skepticality Episode 241 provided Edward Clint.  Ed Clint produces the Skeptic Ink Network and writes about Evolutionary Psychology, critical thinking and more at his blog Incredulous. He is presently a bioanthropology graduate student at UCLA studying evolutionary psychology.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

TV used to be pejoratively called the “boob tube”, until computer monitors became the rightful heir to that meaning, partly because televisions used to be cathode ray tubes. The cathode tubes of our primitive low-def ancestors were electron guns firing away at the screen one pixel at a time. Today’s liquid crystal display (LCD) TV technology is much more reliable, having fewer moving parts, and no electron gun. Thanks to this tubal migration, today’s tube-less TVs can have a mean-time-between-failure of 100,000 hours. This means that, on average, if you watched 5 hours of TV a day, it would take 54 years for the device to fail. A bit less if you like Peter Jackson movies.

TV failure in general is pretty rare. Then again, John, you’re probably not an average user. I’m told you spend a large amount of time and energy on making and consuming videos for the internets and whatever other media outlets still exist. I assume that means you work with lots of footage of cats and people falling off of things. So maybe you really put that Westinghouse through its paces. Even if you used it 24/7, it would probably take 11 years to reach the statistical breaking point.

What’re the odds you’d just happen to be able to replace a broken set on the day it breaks? A fairer question is, how many different expensive things breaking that day could have seemed like a strange coincidence? I have not been to your house, John, but I know you don’t drive, and I will assume it is populated with a variety of large fancy cameras that aren’t compensating for anything, some high end editing equipment, and at least two fancy blenders with way more settings than anyone could possibly need. I’m not sure why I assume there’re blenders, it just feels right. The breakage or loss of any of these items on a given day still isn’t too likely, but the odds are more moderately unhinged than crazy, which seems about right for John Rael.