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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.

HairyPhil

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.”

3trendies

“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!).

SlideSheet

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

HairyPhilSlide

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.

Transportation

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.

(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.

KnightsTour1

KnightsTour2

KnightsTour3

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.

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.