"Miracles" happen all the time. Mathematics demands them.

Here's an amazing sign of the supernatural that happened to me recently. Except, it wasn't really amazing. Or, supernatural. Just seemed like it could be.

Four days before I'd contacted the yard maintenance company that episodically helps us out with chores we need to do in our non-easy care garden. When I didn't hear back from them after a few days, I phoned again. 

The woman who answered my call said she'd send another email to the maintenance supervisor, Chris. But two days later I still hadn't been contacted by Chris.

So I looked up his email address on the company's web site. I'd just started composing a message to him. All I'd done so far was put "Chris" in the address line. Then the phone rang. Instantly I thought, "I bet that's Chris."

Amazingly, it was. He phoned me at almost exactly the same moment I'd decided to email him.

Most, if not all, people have had experiences like this. Thinking of someone just before they phone, text, email, or whatever. Visualizing something happening, and then it does. Running into someone you know from your home town half a world away.

David J. Hand, a statistician, explains this stuff away in his fascinating book, "The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day." 

Here's the Amazon description:

In The Improbability Principle, the renowned statistician David J. Hand argues that extraordinarily rare events are anything but. In fact, they’re commonplace. Not only that, we should all expect to experience a miracle roughly once every month.

But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of “miracle” is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough.

Together, these constitute Hand’s groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day.

Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective.

An irresistible adventure into the laws behind “chance” moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it’s in the world of business and finance or you’re merely sitting in your backyard, tossing a ball into the air and wondering where it will land.

In my case, it didn't really require great mathematical insights to understand why my email message to Chris and his phone call to me coincided so precisely.

This happened on Friday morning. I'd been thinking that I wanted to get the garden maintenance issue settled before the weekend. Chris likely had the same idea. He may have been going through his list of unanswered emails at about the same time I was pondering my day's to-do list.

Yes, it felt strange to pick up the phone and hear "Hi, this is Chris" after I'd just started to write an email message to him. However, since I'd been reading The Improbability Principle, this didn't strike me as anything miraculous or other-worldly.

Hand points out that countless combinations of this and that are experienced by each person every day. Most of these events don't grab our attention. For example, every time someone unexpectedly phones or sends an email message.

it is only when we have a thought of that person just before a communication arrives that we have a sense of Wow! This is miraculous!

Many supposed miracles, of course, are outright frauds. But the rest are the result of what Hand calls the Improbability Principle. A key part of this principle is the law of truly large numbers, explained by Hand here.

One of the key strands of the principle is the law of truly large numbers. This law says that given enough opportunities, we should expect a specified event to happen, no matter how unlikely it may be at each opportunity.

Sometimes, though, when there are really many opportunities, it can look as if there are only relatively few. This misperception leads us to grossly underestimate the probability of an event: we think something is incredibly unlikely, when it's actually very likely, perhaps almost certain.

How can a huge number of opportunities occur without people realizing they are there? The law of combinations, a related strand of the Improbability Principle, points the way. It says: the number of combinations of interacting elements increases exponentially with the number of elements. The “birthday problem” is a well-known example.

The birthday problem poses the following question: How many people must be in a room to make it more likely than not that two of them share the same birthday?

The answer is just 23. If there are 23 or more people in the room, then it's more likely than not that two will have the same birthday.

Hand goes on to explain why. This relates to a tragic story in my home town, Salem, Oregon. 

In West Salem five young people were diagnosed with the same rare form of cancer. Understandably, there was an outcry for public health authorities to look for environmental factors that could have caused this seeming cluster of cases.

But the testing revealed nothing unusual. A story in today's newspaper discussed the study results, including this quote from a state representative:
Download Cancer analysis wont be made public OHA says

Greenlick, D-Portland, said the lack of a known cause for the cases shouldn’t stall the investigation.

“They’ve just sort of thrown up their hands because of that. I would like them to continue trying to puzzle this thing out,” Greenlick said. “I just don’t think that cluster could have happened by chance.”

Well, it could have. Just like so many purported miracles and other supposedly inexplicable events. We mistake improbable for impossible. Further, we fail to understand how our conceptions about probability are also mistaken.

Below I'll share a comment that I left on the above-mentioned newspaper story.

 

These five diagnoses of a rare cancer are tragic. But Greenlick is wrong when he is quoted as saying, "I just don’t think that cluster [of cases] could have happened by chance.” Actually, it could have. 

This is the point of a book I'm reading, "The Improbability Principle," by a mathematician. David Hand gives lots of examples of happenings that seem so unusual as to be more than coincidence, yet are expected by the law of large numbers and other mathematical truths.

For example, two sets of the same winning lottery numbers being drawn in succession by the same lottery. Given enough time, this indeed will happen. And it did.

Hand briefly discusses disease clusters. It's useful to visualize his "slider" notion when thinking about the five West Salem cancer cases. 

Imagine, say, a five square mile box that can be overlaid on a detailed map of the United States that shows the location of all of the diagnosed cases of this rare cancer. The box can be slid around anywhere in the country. As it moves, the number of cases within the box is shown.

This really is a three-dimensional situation, because time is involved. So also imagine time as well as geographic location being the variables. There are a huge number of five square mile box possibilities. It is akin to the difference between thinking there are only 12 thirty-day divisions in a year (the months, roughly), whereas actually there are hugely many more (again, imagine a 30 day "box" sliding over the 365 days in a year).

So finding five cases of the same rare cancer in a small geographic area is well within the laws of probability. Yes, environmental causes need to be investigated closely. But most of the time happenings like this are simply the result of The Improbability Principle. 

See:
http://www.slate.com/articles/health_and_science/science/2014/02/the_improbability_principle_rare_events_and_coincidences_happen_all_the.single.html

     -- Brian Hines, Salem, Oregon 

 

Comments

[Turan]

A timely blog. I have just read 'One Mind' by Larry Dossey where he draws upon many instances of coincidence, bird swarming, dreams etc. to illustrate that our individual minds are part of the One Mind.

A well researched book with some topics that overlap (though critically) with modern neuroscience studies. But I found his insistence that the mind is separate from the brain; the brain as just a 'receiver of consciousness and his drawing upon people's personal experiences a big turn-off; this after all was the gist of the book. Thought I'd check it out anyway though - but I'll stick with the improbability principle thesis at the moment!

[Willie R]

All 239 human beings aboard Malaysian Airlines Flight 370 are still alive.

That would be a miracle.

[Mike Williams]

I don't know anything.

[june schlebusch]

Mike your comment..I don,t know anything. How well I can relate to it..But dear friend you have been of tremendous help to me, in ways you can never imagine so I thank you.....

[Mike Williams]

Hi June,
The sad fact about life is even if you
do everything right, everything can go wrong.

When I look back at my life, over 50%
of my decisions were wrong. I did not
have enough correct information to make
an informed decision.

[june schlebusch]

Greetings Mike.....In the end we are always rewarded for our goodwill,our patience, fair-mindedness, and gentleness...With What is Strange...Friedrich Nietzche...The Gay Scientist.

[Mike Williams]

Strange mathematical facts by Ted Gunderson,
ex FBI director, Los Angeles.

In USA only;
82 children per hour go missing. 60,000
human sacrifices with death occur every year.

There are 4 million practicing
Satanists.