How much of what is going around us do we understand? Surprisingly little. If not completely blind, our vision is obscured by the cobwebs of our mind, which include false assumptions, beliefs, and expectations. How can we think straight and make intelligent decisions if our mind can easily lead us astray? The answer is awareness. We must be aware of the problem and alert to the conclusions we make. We need to question them. Are they based on facts or our imagination? Often, rather than see what is there, we see what we hope to see, want to see, and expect to see.
Just because we have children it doesn’t necessarily follow that we know how to raise them. Intelligent parents will study parenting, and the skills they acquire will result in many rewards. Similarly, just because we can think, it doesn’t mean we know how to think properly. You wouldn’t drive a car without first learning how to drive, would you? So, why are we so comfortable thinking without first studying how to draw proper conclusions and avoid faulty thinking?
An awareness of some of the thinking pitfalls will help us make better decisions and gain a greater understanding of reality. There are many “mind traps” to beware of but here I will focus on one called, The Clustering Illusion. For example, let’s say you and a bunch of friends are flipping coins to see how many heads you can get in a row. A few friends have tried with unimpressive results. Now it’s Tom’s turn. He flips and gets four heads in a row. What would you think? Would you be impressed? Surprised? Many people would conclude Tom is ‘lucky’.
In this example we had a group or cluster of four coin tosses that led to an unexpected result. The ‘surprising’ result is called The Clustering Illusion. Tom’s ability to get four heads in a row led some to suspect he was lucky, has eery occult or magical skills, or that he cheated. What led some to come to a false conclusion? Why is this effect called an illusion? And what are the facts?
When we flip coins, we should get random results, some heads, some tails, but not a streak of heads or tails. Isn’t that correct? Yes, it’s true over the long term. For instance, if we flip the coins 10,000 times, we should come up with an average of heads and tails 50% of the time. But that average also contains streaks or runs of heads and tails. In fact, in a series of 20 flips, there is a 50% chance of getting four heads in a row!
So, Tom’s friends were surprised because they did not have the facts. Without the facts, the illusion was created that Tom was lucky or had a special gift. His friends mistakenly believed four heads in a row was against the laws of probability. But it wasn’t. Now, let’s take a look at an example of The Clustering Illusion that recently appeared in the news.
The death of Amy Winehouse on July 23, 2011 came as a double shock for the singer-songwriter’s fans. First, this promising talent died so young. Second, she died at age 27, the same age that six other famous musicians died. Here is the group or cluster of famous musicians who died at the same age:
Amy Winehouse has been added to the list of what some music aficionados call The 27 Club, The Forever 27 Club, Club 27 or The Curse of 27. Fans find it spooky that seven of the biggest names in rock music have all died at age 27. And if we expand the list to include lesser known musical artists who died at the same age, we can add 41 more names!
Doesn’t it seem mystical that ‘so many’ professional musicians have died at the same age? But that’s why it’s called The Clustering Illusion. What are the facts? Simply this: if you get a large enough sample you will find examples of any combination you are looking for. It’s just coincidence, nothing mystical. At first glance, the deaths of 48 musicians at age 27 may seem like a large number, but remember, the first member of “The 27 Club”, Robert Johnson, died 73 years ago. When compared to the number of musicians who have died since then, 48 is a small number.
To get a better sense of what is likely or unlikely, let’s look at three examples. First, imagine walking into a room full of people; what are the chances that at least two people in the room share the same birthday? Of course it depends on how many are in the room, but does it surprise you to learn that all it takes is a group of 23 people to have a better than 50% chance that two members of the group will have the same birthday?
Second, suppose you dream that a friend died and later learn that he died on the same day of your dream. How likely is that to happen? If it does happen, is it evidence of ESP, precognition, or some other paranormal ability? Well, British statistician Christopher Scott who considered the population of his country, the death rate, and other factors concluded there would be about one accurate death dream in England every two weeks. From the point of view of an expert on probability, such dreams are insignificant and prove nothing. However, can you see how those who have such dreams would feel otherwise?
Third, a highly unlikely golf story made the British press… Richard and Mark Evans (unrelated) both got a hole in one with successive shots. The likelihood of this occurring? According to William Hartston, International Chess Master and expert on odds, the odds are 1.85 billion to one. Doesn’t that make this feat impossible? Surely synchronicity or some unearthly force must be at work here, right?
Wrong says Hartston, “There are about two million golfers in the country (England) who play an average of two rounds of golf a week each. That’s more than 200 million rounds of golf a year, amounting to a total of 3.6 billion holes. That 1.85 billion to one shot doesn’t look so unlikely any more, does it?”
As a senior citizen, I have many elderly friends. One of the worries I often hear is that they may be getting Alzheimer’s disease. “I often forget things. I’m afraid I may be getting Alzheimer’s.” they say. “You often forgot things when you were young,” I explain, “and if forgetting things while you are young is not a sign of Alzheimer’s, why do you think it is a sign now?”
This, too, is an example of The Clustering Illusion. You see, our brain does not like randomness. It always tries to connect, link, and relate random data in order to find meaning. But like it or not, the world is filled with randomness or chaos, and the sooner we come to terms with it, the better. My elderly friends were connecting isolated, random moments of forgetfulness and imagining that they may be on the verge of getting Alzheimer’s disease. The result? Unnecessary anxiety and fear.
The consequences of not considering The Clustering Illusion can have much more dire results. It can, for example, lead to innocent people going to prison, or worse. Take the case of Sally Clark, for instance. In 1999 this British woman was sentenced to life imprisonment for the ‘murder’ of her two baby sons. At first, the death of her first son was considered to be a crib (cot) death, which is more formally referred to as sudden infant death syndrome (SIDS). Fortunately, SIDS has a fairly rare occurrence, and two incidents of SIDS in the same family are even rarer. The prosecution’s expert witness, who was a pediatrician and not a statistician, was swayed by The Clustering Illusion (“If there’s one crib death in the family, it’s suspicious; if there are two, it must be murder.”) The ‘expert’ witness incorrectly calculated the odds of two consecutive crib deaths occurring in the same family as 73 million to one. This ‘evidence’, which was wildly off the mark, was enough to convince the average person of Sally’s guilt.
Happily, Sally was freed and exonerated after serving three years in prison. However, her suffering took its toll and she died during her sleep at age 42. You can read her complete story here.
Today, we are more subject to The Clustering Illusion than ever before. Because of the Internet, Facebook, and Twitter, for example, we are exposed to such a large volume of information that we can easily find coincidences to support our favourite theories. The vast amount of web sites devoted to conspiracy theories, UFOs, psychics, synchronicity, and other paranormal phenomena attest to the widespread influence of The Clustering Illusion. By the way, finding meaningful patterns or connections in random or meaningless data is called apophenia.
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