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Monkey’s Uncle

(Submitted by Skepticality listener Brian Hart)

I’m taking college level courses at UCLA to complete my education. I was sitting, an hour before class, and reading in our Anthropology book, a chapter about primates. I had no idea there were so many species around the globe. Anyway, one of the Old World species I had never heard of before, the Vervet Monkey, native to Africa, was mentioned in the book along with it’s picture. The chapter I was reading was about sexual reproduction, populations, groups, etc.

I closed the book and headed on to my Anthropology class and put George Hrab’s skeptical show, The Geologic Podcast, episode #383. In the amusing segment called, Interesting Fauna, Geo started talking about a species of primate and it’s mating habits. Can you guess which species? Yep, the Vervet Monkey.

I’ll be a Monkey’s Uncle (or, I share about 96% of my DNA with my Monkey Uncle)!

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 254.  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 ICBS Everywhere, and Insight at Skeptics Society.

It’s a cute story, but there is absolutely no way to calculate the odds of this happening. It’s highly likely that the author would read about vervet monkeys in an anthropology book, but the likelihood of the topic being discussed on a podcast is a pretty difficult thing to quantify. George is not an anthropologist, zoologist, or any other profession that would be expected to talk about primates. He is a musician by trade and his podcast is about science and skepticism. There are many potential topics for his show and while monkeys certainly aren’t a strange thing to discuss, it’s not exactly a commonly-discussed topic, either.

I think we just have to tip our hat to nature for this one and accept that this is one of those funny, unlikely coincidences that we just can’t quantify.

That and thank the coincidence gods or the opportunity for endless puns about monkeys.


Numbers Sometimes Lie

(Submitted by Skepticality listener  Stephen Hayko.)

I do clerical work for a company that uses part numbers that are six digits long and begin with either a 5 or 6. When we order parts, our ordering system generates a purchase order (PO) that is six digits long and sequential.

We’ve been using this ordering system for about a year, and throughout the company, we typically place about 45-50 orders in the system every week, in my branch. We’re one of 25 branches in the US that uses this system, and we are one of the higher-volume branches – most other branches use about 30-35 orders per week.

In March, I placed an order for part number 649384. This is a relatively common piece and we typically sell 8-10 of this part per week – so it accounts for 16-20% of our orders. Lo and Behold! The PO was 649384.

Given that information, what are the odds that PO 649384 was attached to an order for part number 649384?


Below are the extended notes provided by contributing editor Mark Gouch for use in Skepticality Episode 253. Mark is a wastewater treatment system operator and engineer living in Smithtown, NY (Long Island). He started to become interested in coincidences after recognizing the series of events that conspired to get him employment on Long Island many years ago. Two of Mark’s recommended books include “The Drunkard’s Walk: How Randomness Rules Our Lives” by American physicist and author Leonard Mlodinow, and “The Hidden Brain: How Our Unconscious Minds Elect Presidents, Control Markets, Wage Wars, and Save Our Lives” by Shankar Vedantam.

Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

This problem seemed very straightforward at first, but on closer review it seems that there is something interesting hidden in the details Steve provided. Estimating the total number of POs generated company-wide using the average of the ranges you gave comes to about 780 POs per week. That’s about 3,586 per month, and 43,030 annually. Steve said the numbers generated automatically are six digits long, and are sequential. So if 43,030 are generated annually, it would take 649,384 / 43,030 years to hit number 649384, or about 15 years, one month. So barring any large increase or decrease in business, in about 15 years you may see this happen again. But wait, Steve also stated that the company has been using this system for a year. Something is fishy here. If the numbers are sequential, and they’ve used this for a year, then they must not have started at 000 001. They must have started somewhere around 649,384 – 43,030 = 606,354. That is, if the numbers Steve gave were close to correct. Starting to wonder if this is some sort of trick question here Steve. Something does not add up. Literally.

So either Steve submitted a trick question which he knows is impossible, or someone, for some reason, decided to covertly tamper with the automatic PO number generating software to make it start at some number other than 000001. Perhaps someone thought PO numbers like 000001, 0000002, etc. would make the company look like a startup, or just would look odd. PO number 606354 makes the company look like they’ve been in business for a long time, and/or process quite a lot of POs. So this great mystery deserves some investigation. Inquisitive minds want to know what was the first PO number generated, who determined what that number was, how did they determine it, and why? And was it part of a conspiracy, or did this mysterious person act alone? A reasonably thorough investigation is certainly in order. There must be a logical explanation.

A number starting in 60 does not look like someone used their birthdate, which would be weird anyway. Does Steve know the last six digits of the CEO’s social security number? Well, there could be a mundane explanation, like the numbers were sequential for many years, maybe kept on a clipboard or something, and only a year ago was it computerized. Let’s go with that, and forget the conspiracy theory. In fact, everyone please forget all conspiracy “theories.”

So back to the actual question. It seems that Steve already knows the answer to his question. He said that this common part accounts for 16 to 20% of their orders. So the odds of any one order having this part number on it should be approximately……16 to 20%! Grab any random order out of the pile (or computer system) and there will be a 16-20% chance that it has this part number on it. That goes for any PO number: 650000, 700000, 131313, and also for 649384. Steve knew the answer; he just did not know that he knew. This is certainly not a criticism. It is better to not know that you know something than to think you know something that you do not. The fallacy was that he thought the odds would be different for that one special PO number, but they are not. The odds are the odds. The odds, in this case, are perfectly rational – but not sequential.

(Submitted by Skepticality listener Misty Wegman.)

First of all, I do not believe in horoscopes or any such nonsense but in this situation it makes the story better. Feel free to take it out if it gets too messy.

I was born on June 2nd and my dad was born on June 3rd. This makes our astrological signs “Gemini” or Twins. He is an identical twin. I gave birth to fraternal twins. He is a twin-twin and I am a twin that had twins.

It gets better. My Aunt (father’s-sister) had identical twins. My mother’s Aunt had fraternal twins too (which is where I got them from). After my mother divorced my father, she married the boy of boy/girl fraternal twins. So I have twin second cousins, twin cousins, 2 twin dads and I’m an astrological twin that had twins.

What are the odds of more twins being born in my family?

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 000.  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 ICBS Everywhere, and Insight at Skeptics Society.

Well, I would say that the odds of more twins being born might be pretty good, but not much higher than in anyone else’s family. Of course, one would have to define and learn quite a few things before even trying to come up with an actual number, including what is meant by “family” (siblings? offspring?) and the ages and intents of those involved.

But there are a few things to talk about nonetheless.

First, the author notes that two of the cases of twins are identical, and one case is a step-father. Identical twins occur as randomly as astrological signs and one has no blood ties to a step-father, so these factors are independent–they have no influence on whether twins will occur in a family. Fraternal twins, on the other hand, do run in families, as hyperovulation is a genetic trait, although one does not receive genes from aunts/uncles. If genetics are to blame, the author’s chances of having fraternal twins on a subsequent pregnancy is now double. In addition, the age of the mother is a factor–the older the mother is, the more likely fraternal twins will occur.

All of that said, fraternal twins can also be the result of fertility treatments. This introduces a controllable factor that can increase the odds of twins dramatically. If fertility treatments are involved, genetics can’t be blamed.

According to and several other online sources, the most recent data shows about 1 in every 30 births today are twins (about 3.3%), with only a about 10% of those being identical. So, about 3 in every 1,000 births will be twins born under Gemini.

Having that many twins in a family depends on many factors such as the size of the family, but I do love the idea of introducing someone as a twin twin with twins (yes, I know author isn’t a twin herself, but I took some license).

(Submitted by Skepticality personality and friend of the blog Bob Blaskiewicz.)

What are the odds? I mean, they must be CrAzY!!!!
Bob :)
Two players die at world chess event in Norway
Competitor dies in the middle of a match during Chess Olympiad in Norway and another is found dead in hotel room
By Esther Addley

The most prestigious international tournament in chess, at which the world’s top players compete alongside amateurs to win honours for their country, has ended on a sombre note after two players died suddenly within hours of each other, one while he was in the middle of a match. Hundreds of spectators attending the 41st Chess Olympiad in Tromsø, Norway, and countless others watching live TV coverage on Norway’s state broadcaster, reacted with shock after Kurt Meier, 67, a Swiss-born member of the Seychelles team, collapsed on Thursday afternoon, during his final match of the marathon two-week contest. Despite immediate medical attention at the scene he died later in hospital.Hours later, a player from Uzbekistan who has not yet been named was found dead in his hotel room in central Tromsø. Norwegian police and the event’s organisers said on Friday they were not treating the deaths as suspicious.

“We regard these as tragic but natural deaths,” said Jarle Heitmann, a spokesman for the Chess Olympiad. “When so many people are gathered for such a long time, these things can happen.

The Olympiad involved 1,800 competitors from 174 countries, accompanied by more than 1,000 coaches, delegates and fans.

The event sees players compete in national teams over 11 rounds, often playing matches that last for up to six hours, and claims a worldwide online audience of tens of millions.

There were brief scenes of panic in the hall after Meier’s collapse, when spectators reportedly mistook a defibrillator for a weapon. Play was briefly suspended before his death was marked with a minute’s silence during the closing ceremony.

While the causes of the two men’s deaths are still unknown, they will raise questions about the mental and physical stress that tournaments place on players.

Meier is not the first player to die in the middle of a match; in 2000 Vladimir Bagirov, a Latvian grandmaster, had a fatal heart attack during a tournament in Finland, while in the same year, another Latvian, Aivars Gipslis, suffered a stroke while playing in Berlin from which he later died.

One of Australia’s leading players, Ian Rogers, retired abruptly from chess in 2007, saying he had been warned by his doctors that the stress of top-level competition was causing him serious health problems.

Tarjei J. Svensen, a reporter for who attended the Olympiad, said the event had a reputation for heavy drinking. “There are two rest days during the competition, and particularly the night before the rest days there tends to be a lot of drinking,” he said.

A favourite attraction for delegates was the now-legendary “Bermuda party”, he added, hosted at each Olympiad by a member of the Bermudan delegation.

The Olympiad was big news in Norway, with the state broadcaster, NRK, carrying hours of live coverage each day, and the country’s government paying 87m kroner (£8.5m) for the privilege of hosting the event.

Last week the women’s team from Burundi were disqualified after failing to show up for their round six and seven matches; they remain unaccounted for, Heitmann said on Friday.

“It has been an eventful Olympiad, certainly,” said Svensen.


Below are the extended notes provided by contributing editor Mark Gouch for use in Skepticality Episode 251. Mark is a wastewater treatment system operator and engineer living in Smithtown, NY (Long Island). He started to become interested in coincidences after recognizing the series of events that conspired to get him employment on Long Island many years ago. Two of Mark’s recommended books include “The Drunkard’s Walk: How Randomness Rules Our Lives” by American physicist and author Leonard Mlodinow, and “The Hidden Brain: How Our Unconscious Minds Elect Presidents, Control Markets, Wage Wars, and Save Our Lives” by Shankar Vedantam.

Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

A sad story, and surely it must have been a shock to those involved in the chess tournament. Well, we do not have a lot of information about the cause of death of the two men, so that limits what we might say about the probability. The best we can do is a very general estimate of the odds of the death of any person out of a thousand random persons. According to the ECOLOGY Global Network ™ web site, as of 2011 the global daily death rate was about 151,600 deaths per day. And in round numbers world population is about 7.3 billion.

So it would seem we should estimate the odds of one person out of a thousand at any conference, or any group of a thousand people should be somewhere around 151,600/7,30,000,000  * 1000= 0.0215, or about 2.15%. The odds of two persons in the group dying would be 0.0215 * 0.0215=0.00046, or about 0.046%. I think most people like to think of odds in terms of per million. So 0.0046% odds is 46,200 per million. This means that for every million conferences, meetings, etc. that have about a thousand persons in attendance, there would be over 46,000 of those events.

Accident Down Under

(Submitted by Skepticality listener  Craig.)


I have this story this is totally legit, happened to me a few months ago.

Basically one Sunday night we heard a big crash out the front of our house. Turns out a car had crashed through our neighbour and my front fence with three young occupants (2 males, 1 female). The police came and took the relevant details and while getting names we realised the driver lived right next door to my sister, who lives two suburbs away (Melbourne, Australia). She always said they were dodgy neighbours!

Then when the my neighbours daughter in law came around to see if everything was fine she realised that she knew the female occupant of the car (who then begged not to tell her parents). Her sister was the god mother of the girl.

So it was to co-incidents in the one crash. The odd’s must be crazy!



Below are the extended notes provided by contributing editor Mark Gouch for use in Skepticality Episode 249. Mark is a wastewater treatment system operator and engineer living in Smithtown, NY (Long Island). He started to become interested in coincidences after recognizing the series of events that conspired to get him employment on Long Island many years ago. Two of Mark’s recommended books include “The Drunkard’s Walk: How Randomness Rules Our Lives” by American physicist and author Leonard Mlodinow, and “The Hidden Brain: How Our Unconscious Minds Elect Presidents, Control Markets, Wage Wars, and Save Our Lives” by Shankar Vedantam.

Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

There is an old adage that says most car accidents happen close to home. We’ve all heard this, and it seems reasonable that since we drive to and from our homes quite often, that we probably spend a lot more time driving near our home than far away, so we would expect to have more accidents close to home.

According to DrivingToday web site , this kind of data is surprisingly not typically gathered by law enforcement or insurance companies, but the Progressive Insurance company completed a survey in 2001 to try to find out. (Gather a decent amount of data, analyze the data, and learn something. What a progressive thing to do! )

According to the site, they gathered information from people who were involved in 11,000 accidents, and found 52 % occurred within 5 miles of home and 77% within 15 miles. (Isn’t it nice when actual statistics confirm what we thought we already knew? This seems to be not usually the case. So much of what people think is true turns out not to be true when researched objectively. But that is another story).

Craig said his sister lived two suburbs away. Suburbs is not a standard unit of distance in the U.S., so we are not sure how far that is. It’s probably safe to assume the distance is 15 miles or less. If so, then the person driving had really good odds of having an accident within a radius that includes his house.

So the fact that the driver lived only two towns away has to be considered as unremarkable. Or actually: pretty likely. It would be highly unlikely for a person who lives in Canada or Argentina to have crashed into your yard.

Your neighbor’s daughter-in-law knows one of the people in the car. So let’s restate this: Not your neighbor, not his child, but the child’s spouse knew someone in the car. So the acquaintance had three “degrees of separation”, so to speak, half way to Kevin Bacon (not sure if your part of the world will get that reference).

It seems that this coincidence should be calculated by the number of acquaintances that your neighbor’s family has compared to the number of people living in the greater Melbourne area. The number of acquaintances that people have on average has been estimated by various methods to be in a wide range of between 150 and 300.

A very cool teenage acquaintance I asked said 1,500 minimum, in this, the social media age. But I think that is high. According to Robin Dunbar on the Social Science Space Web Site, a good estimate is 150. In this case we are talking about acquaintances of family members, who will have some overlap in the people they know, so let’s conservatively use 100.

So if your neighbor knows 100 people and each one of those 100 knows 100 people, then the total number of acquaintances of your neighbor and his acquaintances is 100 * 100 or 10,000. Assume your neighbors have two children, and both are married. So we have your neighbor and his wife, their two kids, and their two spouses, for a total of 6 people. Those 6 people should have about 60,000 acquaintances. Wikipedia (the source of all knowledge) indicates that about 4.5 million people live in the greater Melbourne area . So it seems that the odds of this coincidence would be about 60,000/4,500,000 or about 1.33 out of a hundred. That’s not all that low. (if we used 150 the odds come out to 3.0 out of a hundred.


Clear as Glass

(Submitted by Skepticality listener  Bill Walker.)

Hi, I am a contractor in New Jersey. I recently ordered 14 windows for a job. They only had 11 of the windows in stock so I agreed to accept the 11 and get the other 3 when they became available.

A few days later when the 11 windows were delivered to the jobsite I paid for them with my business credit card. They completed the transaction by having the driver call the home office and give them my credit card information. The driver gave the secretary the 6 digit total for the windows and then proceeded to give her my credit card number.

Business & Finance

As he was giving her the credit card number I heard her stop him before he finished so I asked what was wrong. It turns out that the first 6 numbers of my credit card were the exact same 6 numbers, in the same order, as the total for the delivery. She thought he was giving her the total again. And since my card grouped the first 4 numbers together there was even a space where the decimal in the total is located.

I would be interested in knowing what the odds of that happening might be. Even throwing aside the fact that I didn’t receive the complete delivery and that I chose to use that particular card it must be a very rare event.

Business & Finance

I have recounted this story to a few friends since it has happened and, to a man, the response has been “You should play those numbers”. (in the NJ Pick 6 Lottery)

When my wife suggested that to me I responded by saying that of course I should play those numbers because the same super natural force that had created the coincidence was surely going to exert it’s powers over the lottery for me too. I didn’t play the numbers.

It’s easy to see how someone who has a tendency to believe that there is no such thing as a coincidence and everything that happens has meaning would assign special significance to an event like this. And apparently even for people who seems completely rational their first response was to suggest that the numbers on my credit card and a receipt for some windows could somehow influence the outcome of a lottery.

Hopefully I won’t fall into that trap. Knock on wood.

Below are the extended notes provided by contributing editor Mark Gouch for use in Skepticality Episode 248. Mark is a wastewater treatment system operator and engineer living in Smithtown, NY (Long Island). He started to become interested in coincidences after recognizing the series of events that conspired to get him employment on Long Island many years ago. Two of Mark’s recommended books include “The Drunkard’s Walk: How Randomness Rules Our Lives” by American physicist and author Leonard Mlodinow, and “The Hidden Brain: How Our Unconscious Minds Elect Presidents, Control Markets, Wage Wars, and Save Our Lives” by Shankar Vedantam.

Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

We’re sure it must have been at first a confusing, then a weird experience to realize that the sequence of numbers in your credit card matched the sequence of numbers in the cost for the windows. Determining the probability of this happening seems to be a pretty straightforward process. Bill also asked a few related questions that are interesting.

First of all, Bill did not mention the cost of the individual windows. Assuming they cost somewhere in the range of $120 to $500 each (based on a quick web search for single hung windows), the range of costs would be from $1,320 to $7,000. The low number in the range is estimated using the low range of cost of windows and only 11 being available. The high end of the range is estimated using the high range of the unit cost and assumes all 14 windows were available. Almost forgot this: If we assume NJ state tax of 6%, the maximum cost would be $7,420.00. This demonstrates that regardless of whether 11 or 14 windows were available, the cost would be less than $ 9,999.99, so the cost including pennies will contain six digits (Thousands, hundreds, tens, and dollars, and two decimal, or cents digits). Therefore, the fact that only 11 were available does not change anything in the probability estimate. Anything we determine is true for 11 windows available, will be true for the case of 14. We will still be talking about a series of 6 digits. Make sense?

So the question is what is the probability of a six digit series of numbers matching a different series of six digits. The possible range of six digits is 000000 to 999999. (Writing it as either digits with commas or using dollar figures makes it easier to see there are six digits). So there are one million possible sequences of numbers of six digits. And the odds would be 1 in 1,000,000, one in a million.

Now considering how many thousands of contractors there are, and how many pay for supplies in the same cost range with credit cards would be tough to estimate. But it is reasonable to expect that there are well over one million such purchases in the U.S. annually. So this probably happens at least once a year in the U.S., and probably much more often than that.

Bill mentioned the decimal point in the cost matched up to a space in the sequence of digits on the credit card. This seemed like an addition to the coincidence. He did not mention the lack of a space in the card sequence where the comma would be in the cost, which, if you consider a space in the place where the decimal was to be noteworthy, one would assume you would think that the lack of a space where the comma would be to be noteworthy also. This may be a case as Dr. Michael Shermer has pointed out many times that our brains “remember the hits and forget the misses.” But in general, we’re talking about a sequence of numbers, so let’s ignore the decimal point and comma. (Plus, in Europe they use decimals and commas in the opposite functions as we do, so thinking more globally, lets agree it is ok to ignore them.).

Now to the question of whether it is sound advice to suggest that based on this coincidence that it would be wise to purchase a lottery ticket with the same sequence of numbers. It would not. In probability these are referred to as independent events. What the sequence of numbers in a credit card number and/or an invoice amount are, will have absolutely no effect on the random numbers generated by a lottery ticket. The odds will be the same for your lottery number. But if that series of numbers were to win the lottery for you, you’d have a heck of a story to tell. It would still only be a coincidence, but a good story. So if you want to choose the same numbers for a lottery, do it for fun, but don’t do it expecting any advantage or disadvantage in your odds of winning the lottery.

Lastly, the question of whether some supernatural entity had an impact on the coincidence. Bill offered no evidence for the existence of, or the potential observed impact of a supernatural entity on the coincidence or any other event that has occurred in the real world. So it would be impossible to estimate the odds of that. We are skeptical enough to demand evidence.

Three Trendies

(Submitted by Skepticality listener Michael McClure.)

I’ve been working at Disney Animation now for more than 18 years. My son was 11 months old when I started my career at the mouse. He’s now a 19 year old sophomore in college.

We were working on Tarzan a year or so after I started at Disney Animation. I got to know the Artistic Coordinator on the show, a fellow Scot musician named Fraser. One morning he called Support (where I was working at the time), so I took the ticket and went to see him. I had brought in some of my slides in a sleeve (16 slides per sleeve) a few days earlier, because I had a shot of the composer on Tarzan, one Phil Collins. However, instead of the short-haired, balding Phil of the early ’80s, my shot was from a Genesis gig in 1977 at the San Diego Sports Arena, with hirsute Phil (long hair, beard and all!) decked out in the jersey of the farm hockey team from the town that he threw on for the band’s encore of the evening, singing his heart out in a pool of red light. I’d shot the picture 20 years prior, and of course hippie Phil would be relatively unrecognizable to most folks in the late ’90s. The Tarzan production admin folks put out a printed newsletter each week containing the goings on in production-land, and I thought it would be fun to put this picture of Phil into the newsletter, to see if anyone could guess who it was.


Phil Collins, San Diego Sports Arena, 1977 Genesis Concert

I brought the sleeve of slides with me to Fraser’s office, I pulled out the slides to show to him, to see if maybe my musical brethren could guess who the hairy man in the slide was.

Fraser held the sleeve up to the light, and he pondered the picture of Phil for a moment, but I saw his glance drift to one of the other slides in the sleeve. Fraser couldn’t guess who it was, and was amazed when I told him that it was a picture of Phil Collins, but he kept looking at a different slide in the sleeve. Finally, Fraser said, “Can I pull this slide out?” pointing at some random slide I had in the sleeve along with my Genesis concert pictures. I said sure, and he pulled out a picture I’d shot of some random people along Princes Street in Edinburgh, Scotland when I was there with the California Repertory Theater in the summer of 1980 for the Edinburgh Fringe Festival, a huge, yearly theatrical festival held in the city. Fraser inspected the slide very closely, and then looked me in the eye, and said, “This is my best friend Graham.”

“What? Really?”

“Yes. No doubt about it. This is Graham.”


“3 trendies”

Well, that was stunning right there. The picture, as you can tell, shows three trendies (as I wrote on the edge of the slide) whom I stopped on the street that sunny day in August of 1981, and asked in my California twang if I could take their picture. The girls were fine with it, but the boy in the shot was huffy. I think he was annoyed by this ‘foreigner’ bothering them, and showed that by being annoyed and petulant in the picture (but, he was still in the picture!).


The sheet of slides, showing where the two pictures were located.


The “P. Collins” slide

3trendiesSlide (1)

The “3 trendies” slide (dated SEP 80).

Fraser and I had a great can-you-believe-it moment about this, a good laugh, and then we went about our day.

Within 20 minutes, Fraser had called back down to my offices, asking for me. I went back to his office, where I found him, looking even more stunned. After seeing this now 16 or 17 year old picture of his Best Friend, shot by his Support Guy at Disney Animation, he just had to call Graham to tell him about it. So, he did. And things got REALLY weird.

Graham apparently picked up his phone and said hello to Fraser. Fraser explained about the photo, and Graham shrieked in his ear on the phone and hung up. I mean, Fraser said he really SHRIEKED at him, and then abruptly hung the phone up. That was it.

So, Fraser called him back.

Fraser got Graham back on the line, and after a few moments, he drew the story of the shriek and the ensuing hang up out of him. Graham was completely beside himself the entire time they were on the phone. But, in the end, it made perfect sense.

Graham told Fraser that just a few hours earlier THAT SAME DAY, he had had a conversation with his old friend — let’s call her Carol — the small brunette in my photograph. He was attempting to refresh her memory of their other friend — let’s call her Alice — the blonde in the picture. But, Carol wasn’t remembering her. She couldn’t quite place her. Apparently Alice had left Scotland not too long after I’d taken the picture of the three of them in Edinburgh, to marry the bass player of the Bay City Rollers, a then very popular pop group/boy band. She’d gone all the way to New Jersey to marry this guy, apparently. In any case, Graham was trying to remind Carol of this other girl Alice, when he said something to the effect of, “Do you remember when that Yank stopped us on Princes Street years ago and took a picture of the three of us?” hoping that would jar her memory. Maybe it did, or maybe it didn’t — I don’t remember that part. But, Graham hung up with Carol eventually, and then Fraser rung him up from the States soon after that call and said over the staticky international land line, “You’re not going to believe the picture I just saw of you and two girls on Princes Street from the summer of 1981…”

I think I would shriek, too.

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 247.  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.

There are some factors that increase the probability that Fraser would recognize someone in one of the pictures, namely the shared interest in a genre of music and probably the artist. However, it’s a pretty amazing and impressive event. I’ll add that if I was in Graham’s shoes, I would probably shriek, too. These things are bound to happen from time-to-time, of course, so there’s nothing supernatural about it, but that wouldn’t keep my jaw from hitting the floor if this had happened to me.

(Submitted by Skepticality listener  Mark Gouch relayed to The Odds Must Be Crazy by Barbara Drescher.)

Here is the article (includes video) by Barry Wolf, WKYC.

Holiday & Seasonal

But how can we say this is unbelievable as they do in the article? Sorry, but I can’t help myself here…

The odds would be one out of 365 * 365 * 365, or about one out of 48.6 million births. With 7 billion people on the planet, odds are that this has probably happened about 143 times ( to living persons. many more to those in the past). So rare, fun, and interesting, but not unbelievable.

I believe it happened based on the evidence (their claim that it did, which is good enough).

Actually since everyone has to have a birthday, we can ignore the first birthday, that of the man or the woman. So the odds someone marries someone with the same birthday (date of the year) as them is 1/365.

Then the odds their baby has that same birthday would be 1/(365 * 365) or 1/133,225. So with ~7 billion people this probably happened 52,543 times to persons living on the planet now.

The error in the first calculation is that the date was selected first. That calculation is correct for any specific date, whether it is January 1st or July 4th, or March 15th, or July 22nd. Anyone with better knowlege of probability please correct me if any of the above is incorrect.

As often happens, things that seem unbelievable are quite believable and things that are believed without evidence are not believable.

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 246.  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.

Good job!

You are correct with both calculations. It depends on how you frame it. If you’re wondering the odds of two people with the birthday of January 1st marrying and having a baby on January 1st, then the first is correct, but as you pointed out, that’s not really what’s interesting.

The only thing I would add is that these calculations also assume some things that we know are not true, such as that births are uniformly distributed across the days of the year. Even if natural births were (they aren’t), we’d see fewer births on days like January 1st simply because the number of scheduled C-sections and inductions is lower because it’s a holiday. However, figuring those few things in requires data that probably isn’t available.

Littlewood’s Law

(Submitted by friend of the blog Jonathan MS Pearce)

I recently reviewed Randal Rauser and John Loftus’ debate book entitled God or Godless. I have also responded to Randal’s post on why I am an atheist as well as posting an article critiquing Randal on why he is a Christian. During my review, I noted that I was particularly frustrated at Randal’s prayer chapter.

Randal’s chapter recounted an anecdote involving prayer. In simple terms, this is it:

  1. Pastor Kent Sparks, living in North Carolina with wife, were pursuing adoption with House of Ruth
  2. No luck in year and a half, so pursued private adoption in Georgia
  3. After adoption of daughter Emily went through, Kent called House of Ruth to leave message to suspend their file
  4. Staff were in meeting to discuss with a client who had chosen Sparks for a child
  5. Meeting ended, staff called Cheryl Sparks to tell her good: news – another child for adoption
  6. Cheryl called a friend to ask her for prayer
  7. Kent returned from work and Cheryl asked him to conduct a devotion without telling him of the news
  8. Kent opened Bible and read Proverbs 3:27: “Do not withhold good from those to whom it is due,
    When it is in your power to do it.”
  9. Cheryl’s friend later phoned with a Bible verse, Proverbs 3:27
  10. They adopted their second child, Cara

And this was the main evidence to support his argument that prayer works.

Kent and Cheryl’s case evinces these same hallmarks of contingency, complexity and specification. While these events are obviously contingent, they are also complex since they involved multiple factors timed together (e.g., Kent’s call concurrent with the adoption meeting), and they included specified information (e.g., two independently confirmed referenced to Proverbs 3:27). Consequently, Kent and Cheryl (and we) are fully justified in drawing the conclusion of divine action in confirmation of the adoption. (p. 142)

When I read this account and the rationalisation of it thereof, I was staggered. Randal is an intelligent guy who claims he is conversant with cognitive biases and suchlike (I think he has written a book about them). This example is so very easy to dismiss. Let me refer you to the chapter on prayer in my book The Little Book of Unholy Questions:

The subject of prayer provides several problems for the believer, if thorough critical questioning is followed through. Part of the issue of perceived success of prayer is down to religious people interpreting coincidence as divinely purposed, and this is very common. I am aware of this, and am constantly amazed at the amount of seemingly dauntingly huge coincidences that I go through on a daily basis. Most of these are so innocuous as not to even stick in the memory. Usually, this will entail reading a book, and a certain word that you haven’t heard for ages, and then hearing it five seconds later on the television in the background. Wow! Who would have believed it? The problem is, we see things as much bigger coincidences than they really are because we are unaware of the frequency involved in calculating the probability. For example, buying a lottery ticket might mean that the probability of winning the lottery is staggeringly small, say one in fourteen million. However, if you bought fifteen million tickets, then it becomes likely. Also, if you look at the frequency of tickets bought as a whole, then someone winning is a statistical certainty. To translate this across to the word scenario, then the number of words I read or use per year, and the amount of words I hear in the background per year, means that the occurrence of these weird coincidences actually becomes a statistical certainty too. Don’t just look at the incident in isolation, but in the greater context of everything around it.

Now, as mentioned, these are innocuous cases. However, let’s look at something that happened to me the other day. I am the proud father of newly born twin boys. These two delights give us great joy, and yet they can also be a great challenge. When we introduced them to solids recently, they had a week of screaming the house down at night. This led my partner and me to have some degree of sleep deprivation, as they were waking every two hours to be breastfed. We sat down one Sunday afternoon and discussed this for about four hours. We had all the books out, and were scouring the internet for different routines, opinions and helpful tips. We were fairly stressed, and this was really important for us, especially as the boys were pretty stressed too. After all the talk and worry, we simply couldn’t conclude what to do – there were so many options. It was at this point that, had we been praying people, we would almost certainly have joined hands and prayed for strength and insight; for an answer.

Giving up, I walked myself down to the local shop for some milk, as we had some surprise guests over for a cup of tea. Just walking out of my local shop as I got there, on a random Sunday afternoon, was a woman we knew from Twins Club. I had never seen her on this road before, or even outside of Twins Club. And there she was. I stood and talked to her for half an hour. She had had exactly the same problem with her twins, gave us a routine and some ideas, and hey presto, we were sorted and so much happier. What were the chances!

Of course, had I prayed, this would have been bona fide proof that prayer works, that God listens to me, that my faith works. Imagine the joy in God’s works that I would have experienced, and imagine the evangelising I would have done at the church in telling my Christian friends of the ‘miracle’. I didn’t pray, and don’t hold that faith. What to a Christian in exactly the same sort of situation, and who has a real spiritual moment of transcendent evidence of prayer and faith, becomes just another funny coincidence to someone like me. For someone who prays frequently every day, the chances of a ‘successful prayer’ are very high.

These coincidences happen all the time. But when they happen to a religious person, they take on a whole different religious meaning derived from the religious context. Prayer works for a lot of people who follow a lot of different religions. At least most of those gods don’t exist, so something must be up. “My God and my prayers work, but yours are just coincidences,” seems like special pleading to me. The chances are, in my opinion, that most (if not all) incidences of prayer working can be put down to coincidence. We do and say an awful lot of things every day, and we wish for an awful lot of things every day. Some of them are bound to actually happen.

Besides, I’ve never seen an amputee grow back their limb after prayer. I have seen evidence of cancer naturally go into remission without prayer. Enough cancer patients get prayed for, for there to eventually be a correlation. Not, may I add, a causal relationship.

Let me now refer you to Littlewood’s Law:

Littlewood defines a miracle as an exceptional event of special significance occurring at a frequency of one in a million. He assumes that during the hours in which a human is awake and alert, a human will see or hear one “event” per second, which may be either exceptional or unexceptional. Additionally, Littlewood supposes that a human is alert for about eight hours per day.

As a result a human will in 35 days have experienced under these suppositions about one million events. Accepting this definition of a miracle, one can expect to observe one miraculous event for every 35 days’ time, on average – and therefore, according to this reasoning, seemingly miraculous events are actually commonplace.

Ever since learning about Littlewood’s Law I have been cognisant of coincidences and ‘wow’ moments and I have to admit, I have bloody loads.

Archbishop of Canterbury William Temple once observed, “When I pray, coincidences happen, when I do not pray coincidences do not happen.” Many Christians can resonate with Temple’s wry reference to God’s providence. But atheists demur, charging that such experiences only evince a selection bias that counts the hits and ignores the misses.

And I would say that Randal’s example simply does not represent a specified complexity which would prove God. Cheryl’s friend is likely to find some such relevant passage, and Kent would have such issues of the adoption at the forefront of his mind whilst choosing passages. As in my own case, things like this happen all of the time to people who don’t believe and don’t pray. They get forgotten, or not even seen as significant in any way.

Here is an excerpt which I posted on my previous blog to illustrate the point further:

I have an analogy which I hope will illustrate why at least a lot of examples of alleged successful prayer or interventions of God take place.


Yesterday I was pumping up the tyres to my twins’ buggy. I have an old bicycle pump which I bought probably seven years ago. I bought it for £3 – peanuts. This pump has been very hard working – two bicycles and a buggy at regular intervals (the buggy particularly often needing pumping up). The pump has worked tirelessly (pun intended).

For the first time ever, whilst pumping the tyres up to the buggy in the kitchen, I wanted to talk about this pump, and laud its efficiency, reliability and value for money to my partner.

“This pump is brilliant. I’ve had it for seven years now, and it’s never let me down. I only paid three quid for it and it has been such a good bargain. Basically, it’s genius.”

And like a Greek tragedy, surprise, surprise. What amazed me was the timing. No sooner had I finished the ‘us’ of ‘genius’ than the mechanism of the pump twanged and it broke in my hands. The two of us burst out laughing at the sheer amazing coincidence of it. The first time, after very regular use for seven years, that I had ever even mentioned the pump, after singing its praises in my over-exuberant manner, it broke in my hands. Really, what were the chances!? It was like there was some supernatural force making that happen.

It was like there was some supernatural force making that happen… And that made me think.

Let me now change the analogy around – shift the paradigm. Let me now put myself in the position of being a praying Christian.

I am said Christian. I am on my way to work, and am late for an important meeting for the first time. The level crossing that I cross very often is always down. As I approach, I fear it is down. But suddenly, I see it is UP! I race through it thanking God for doing that! Woo Hoo! Now imagine, just before I approach it, I give a little prayer. When it is up, and I race though, I think to myself, “God listened! I won’t be late for that crucial meeting! Thank you God!”

Now imagine that same crossroad which is always down, is open after a little prayer with my critically ill partner on the way to the hospital. That small amount of time could be the difference between life and death. That same prayer has a massive consequence. Now God really is listening and I will remember that for the rest of my life.

But let us return to the original event. The pump breaks after an amazingly coincidental exuberant display of affection for the pump. Hey-ho, I forget about it after a week.

If I was a fervent believer, I would be praying multiple times a day, asking for things very often. The sheer volume of prayer means that many of them, by the laws of statistics, will be ‘successfully acted upon’.

The sheer volume of things we do every day, every week and every year (considering we are often doing many thing simultaneously – driving to work whilst listening to the radio and thinking of my twins) means that, statistically, HUGE coincidences will happen remarkably often. If you attach a prayer prior to that, a remarkable event will seem to happen at the will of God in answering your prayer.

And just in case you aren’t convinced, here is an example of me comparing my experience further above to my Christian friend who produced a very similar example and argument to Randal. This is an email I sent a couple of years ago using the same twins example used above:

With regards to last night’s session in the pub talking of miracles, we used a miracle claim of Colin to steer the talk. Colin has claimed a miracle of answered prayer occurred whose specified complexity points towards it being a miracle. It went something like this (apologies if I misrepresent you here, Colin):

  1. Colin had a specific problem which was affecting him badly with regards to a biblical passage.
  2. He was going away for the weekend to a Christian retreat / party
  3. He, the next day or two, had an image in his mind of a golden sword.
  4. The next day he was in a book shop and the second or third book he pulled out had an image of a golden sword on the front. He opened it to a page in the book which answered all his worries.
  5. He claims this had such a specified complexity as to be best explained by it being a second-order miracle (one that does not violate natural laws).

Andy and I both came back with some ‘incredible coincidence’ stories. Colin claimed these did not have the same level of specified complexity. I will now attempt to show you that he was wrong.

Here is the quote from my last book to explain the scenario:

[I use the quote above to give the case involving the twins.]

So what we have here is this:

  1. We had a problem that was affecting us which we sought the answer to.
  2. Some surprise guests turned up unannounced
  3. We had run out of milk and I had, at that particular moment, to go to the shop to buy some.
  4. At the shop I met a mother of twins who I have never seen before or since on my road.
  5. She gave us all the answers we needed to our massive relief as she had been through EXACTLY the same issues.

Now let’s compare these two stories for probability. At the end of the day, miracles deal in probability and specified complexity is merely a reflection of probability.

First of all, we have the problem. Colin is a Christian, there are many Christians and many have issues with passages in the bible. This problem we had involved not one, but four people, thus the probabilities that must exist to conspire to all of us being there to have that problem are higher. However, as an individual starting point, these probabilities are less relevant.

The catalyst: Colin had an image over a 2-3 day period which coincided with the cover of the book. We had a situation where we were discussing the problem at length and right afterwards some unannounced guests arrived. The actions of two other people must now be calculated such that the chances of them coming to our door, from living in London, are very low indeed. Suddenly they are there. AND THEN we had to have run out of milk in order for me to need to go to the shop. Just on the catalyst front, my story appears far more improbable, statistically.

Next, Colin is in a book shop and picks out a book which corresponds to his image. I walk to the shop and find not just anyone, but the EXACT person who had experienced THE EXACT SAME THING, there with her twins. I had and have never seen her there before. Had we prayed, she literally would have been the answer to our prayers. The probability of her being in that exact place at that exact time, of being a mother of twins with exactly the same problem (and for me to need to go to the shops at that time due to milk running out and unexpected guests) is astronomically more improbable that a book detailing information on a biblical passage being in a Christian bookshop full of other Christian books.

As I was pointing out to Colin , I don’t think there is often an understanding of the massive improbability of coincidences like mine, and there is often a desire to make the calculations for probabilities which seem to involve purpose much lower due to intuitive belief that the events are purposes. At the end of the day, If Helen and I had held hands and prayed before my friends came to the door, that chain of events would have seemed more powerful, I posit, than Colin’s miracle claim. Heck, I would have been praising the Lord!

Using Littlewood’s Law, of course, we know that highly improbable events take place with alarming regularity since the frequency of things we do and experience is phenomenal. Littlewood calculated you would experience a ‘miracle’ once a month.

Thus I hope to have shown that massive coincidences happen regularly and have just a low probability, and often lower (as in this case), than many religious miracle claims. Just because there is no perceived purpose does not mean the probability is any higher.

So, given these points, I think that Randal’s case is exceptionally weak. It certainly does not evidence God. Think of all the ways in which prayer could work which would leave one with no doubt. The complexity which Randal invokes is simply not strong enough or specified enough to do what he wants it to do. Only if you overload it with copious amounts of cognitive bias. Again, we could talk of growing back limbs and what have you. What do we have instead? Events which look extraordinarily like coincidences.

A Tippling Philosopher is a blog dedicated to the philosophy of religion, with a popular, easy to digest approach. The name comes from the casual philosophy and theology group that author and blogger Jonathan MS Pearce frequents in Hampshire, UK. This blog is an extension of that, with guest posts by other thinkers with the same questioning vein from around the world. What started with Socrates, in challenging the legitimacy of religious beliefs of his time, will hopefully be continued several thousand years later with the lively community of critical thinkers in the Skeptic Ink Network.

As an author, Pearce writes about the subjects which fascinate him hugely. His first book “Free Will?” is a work dedicated to investigating free will and determinism, presenting a wealth of evidence to support a deterministic worldview. His second book “The Little Book of Unholy Questions” is a cumulative case against the existence of God written in the form of a set of questions asked directly to God. His last book “The Nativity: A Critical Examination” is a synthesis of the work detailing the analysis of the infancy narratives in the New Testament, showing that the two Gospel accounts are clearly a-historical.

Visit JP’s blog here.

Checking the Check

(Submitted by Skepticality listener Paul)

I live on one side of town, and I’m currently taking a college class one day a week on the other side of town about 40 minutes away. Today we got out of class about 2 hours early, so I decided that since I’m rarely on the other side of town I would use the extra time to stop by the new beer warehouse that was opened earlier this year by my wife’s former co-worker. I had never been there before but I had heard good things about it, and so I was really looking forward to checking it out.

Once inside, I chatted with my wife’s former co-worker and toured the store, sampling some beer and picking out some interesting bottles to bring home and try. Okay, so I went a little overboard and wound up with nearly a case of various microbrews and hard ciders I had never tried. I also added a growler of one of the beers I had sampled and enjoyed, and as I was at the checkout my wife’s former co-worker came over and gave me a 10% discount. I signed the credit card receipt as we talked some more, then I thanked him and departed for home.

When I got home I checked the mail and found an envelope from the New York State Tax Board. My stomach sank, and I assumed the worst: we owed some back taxes. I put off opening it for the time being while I fed the dog and let her outside to relieve herself.

Finally I decided to open the envelope to see what bad news might be awaiting me. The letter inside informed me that the state was refunding home owners a percentage of their property taxes if their school district had kept taxes capped below a certain level for the year. Ours had, and so we qualified for the rebate.

Sure enough, there was a check inside! I immediately looked at the amount to see what our windfall was. The check was in the amount of $77.26. That seemed familiar to me, as I seemed to recall the total at the beer warehouse had been seventy-something dollars but I hadn’t really been paying attention because I was distracted while talking with my wife’s former co-worker. So I pulled out my receipt and checked the amount. I did a double-take when I saw that the total was $77.26!

I had just paid $77.26 at a store, and within 30 minutes had opened an unexpected refund check from the state for the exact same amount! So I ask you: what are the odds?!?!

Below are the extended notes for use in Skepticality Episode 245 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.

There is a mysterious power in the universe bending time and space, the very fabric of existence, creating amazing, inexplicable patterns. We may never fully discern its inscrutable purpose, but obviously it’s so some people can get some free beer, and occasionally scratch their heads and say “huh, how ’bout that?” Thank goodness it’s not wasting time preventing epidemics or something stupid like that.

Okay, that may have been a tad sarcastic, but their really is a mysterious force creating coincidences, and it sits between the ears. A couple of pounds of grey goo that can do amazing things, like feel bad about eating the last donut, seems pretty mysterious, to me, at least.

To understand why apparently astronomically unlikely coincidences are fairly mundane, I suggest an exercise in doing what minds are ordinarily a bit crap at: look at it from the opposite point of view, in this case, the universe’s. Imagine the mysterious cosmic power is you, except that your job is to prevent apparent coincidences that occur during random events in human affairs. Think about how much work you would have to do. Whenever a number crosses a person’s path twice or more in one day, you’d have to intervene. Whenever a popular song, movie, tv show, book (or part thereof) is referenced more than once in a short time frame, whenever two humans (who just love talking to each other) call each other at almost the same time, when two people meet and happen to share any significant detail such as hometown or favorite sports-ball team, et cetera.

That’s just a sample of the hundreds of ways people connect unconnected events. Your cosmic civil servant self would be working overtime. You would probably need to intervene in the life of every single human daily (hourly, for the numerologists).

That is, until someone says to someone else, “hey you ever notice two of the same number never show up on the same day? What’r the odds?” Then you’d have to start creating coincidences, to mimic what the universe already does. Or alternately, you could just quit, since that’s the way the universe works anyway.