Random Occurrences That Don’t Happen By Chance

Things the Laws of Probability Can’t Explain

You walk into a room and flick the light switch. The light doesn’t come on. Someone else walks into the room, flicks the light switch and the light comes on.

This happens frequently enough that you begin to wonder, “What’s this about?”

“There must be something in your light switch flicking technique that’s not completing the circuit,” they tell you, trying to be helpful.

There’s nothing the matter with your light switch flicking technique. If only there were.

I’ve written scores of notes, letters, documents, articles. Time and again, the final line of text laps over onto the next page. Rarely, if ever, is it two lines. Just one regardless of the length of the piece.

It’s annoying. It looks crummy. I edit the piece or adjust the font to eliminate the single overlapping line.

This single overlapping line happens so frequently I’ve almost come to expect it. But is it happening more frequently than the laws of probability can account for?

I’m told that in order to know, I’d have to compose thousands of pieces of various lengths, count the number of single overlapping lines and run the appropriate statistical test.

When you flip a coin, the chance of heads or tails is fifty-fifty assuming a valid coin and toss. Yet a series of ten flips could yield eight or nine heads, leading you to imagine that heads occur more frequently than tails when, in fact, the sample is too small. A large enough sample will yield the fifty-fifty split.

Statistically, with 35 to 40 lines per page, depending on margins and choice and size of font, my single overlapping line would occur, by chance, about 3% of the time. I’ve kept track. It occurs 18% of the time.

Still, I’m assured that I haven’t composed a sufficient number of notes, letters, documents and articles to arrive at what would eventually be the random 3% overlap.

When we’re in a rush, we may imagine that red lights last longer than they do when we’re not in a rush. I’ve timed it. The lights change at uniform intervals, but my wait is longer when I’m pressed for time.

There’s a traffic light at the end of the access road where I turn onto the main drag. When I pull up to the light, regardless of where I may be in the queue, I begin counting the seconds on the dashboard clock until the light turns green. I’ve done it hundreds of times. I pull up at this light at least once, often twice and, on occasion, three times a day.

It turns out that the wait is longer when I’m in a rush. It happens often enough so that both the average and the median wait is far from the fifty-fifty balance you’d expect. Again, I’d have to run this exercise thousands of times to gauge whether or not there might be statistical significance between wait times when I’m in a hurry and when I’m not.

Two vehicles approach one another on a long stretch of a lightly traveled, nearby road. They happen to meet, an uncanny number of times, at the local railroad underpass where the road narrows so that one vehicle has to slow down to let the other vehicle through as both vehicles can’t pass through the underpass side by side. Dozens of instances during the years that I’ve been driving along this lightly traveled road have brought this phenomenon to my attention.

I’d hazard a guess that the reason these odd serendipities don’t get more attention is because they’re trivial and — here curiosity gives way to paranoia — they may not affect everyone equally.

Cultures have employed astrologers, magicians, soothsayers, readers of entrails and tea leaves to divine future occurrences that are statistically random yet experientially predictable. If there’s a purpose to such statistically random but apparently non-random occurrences, it would seem to be a whimsical one.

Let’s Put It To The Test

Consider the following experiment for which we’ll enlist the assistance of an eccentric millionaire:

Imagine a sunny weekday morning on a quiet street in a quiet residential neighborhood. Assume, as in the old days, that the kids are in school and moms and dads are at their places of employment.

The street is 28 feet wide, the typical width of a residential street. There are no sidewalks. The street is straight and flat from one end to the other and sees very little traffic.

Across from the home in the middle of the street, there’s a flat, open field.

A snappy late model car in the hundred-foot-long driveway sits backed up against the garage. A camera atop the garage records the presence of pedestrians, whether on foot or bicycle, who pass by the driveway as they walk or bike along the street. A pedestrian walks or cycles past the driveway, on average, in 3.52 seconds.

We select, at random, a ten second interval. Let’s say we choose 10:32 on a weekday morning. We’ll make this ten second interval last from 10:32:17 to 10:32:27. The camera will record any walker or cyclist who happens, during this ten second interval, to walk or cycle past the driveway.

We’ll record this ten second interval every weekday for three years. That’s 783 weekdays.

Let’s say that during this three year interval, six walkers/cyclists are recorded walking or cycling past the driveway during the ten second interval that elapses between 10:32:17 and 10:32:27.

Remember that this is a quiet suburban street in a neighborhood where, five days a week, on most weeks of the year, the kids are in school and moms and dads are at work so you’d expect few people to be out walking and cycling at 10:32 in the morning.

Based on our three year sample, what are the chances that on any given weekday, between 10:32:17 and 10:32:27, a pedestrian or cyclist will be walking or cycling past the driveway?

.0076 (6/783.)

That’s 7 ½ tenths of one percent.

Which is to say that on any given weekday, between 10:32:17 and 10:32:27, the odds of a pedestrian or cyclist not walking or cycling past the driveway is 99.25%. In other words, there’s less than one chance in a hundred that, on any given weekday, between 10:32:17 and 10:32:27, a pedestrian or cyclist will be walking or cycling past the driveway.

You’ve lately fallen on hard times. You’ve had to apply for an extension to pay your kid’s private school tuition. You’re coming up on your twenty-fifth wedding anniversary. You’ve promised your spouse a vacation, and now you may have to renege.

You’ve just gotten notice from the bank that your adjustable rate mortgage is going to ratchet up next month which means you may have to decide whether to pay the mortgage or pay the auto loan which installment you’d otherwise miss for the second time, risking the repossession of your SUV. And there’s the upcoming medical procedure that your plan won’t cover.

In short, you’re strapped.

Our eccentric millionaire owns the snappy car parked in the driveway. The steering wheel is locked. The brakes have been disabled. The accelerator is operated by a button on the dashboard. You press the button and the pedal jams to the floor.

As the car reaches the lip of the driveway, it’s going sixty mph. It takes 1.2 seconds for the car to hurtle across the street at which point the accelerator pedal releases and the car gradually slows to a gentle stop in the open field across from the driveway.

Mr. Moneybags asks you how you’d like thirty thousand dollars.

Here’s all you have to do.

At 10:32:22., midway between 10:32:17 and 10:32:27, on this quiet, sunny weekday morning, you get into the driver’s seat and place your hands firmly on the locked steering wheel.

Then you’re blindfolded.

You press the accelerator button and off you go. Twenty seconds later, in the open field across from the driveway where the car has come to a stop, our eccentric millionaire hands you a satchel containing thirty grand in cold, hard cash.

That’s all you have to do.

Would you do it?

The odds of a pedestrian or cyclist walking or cycling past the speeding car as it leaps out of the driveway and flies across the road, in that 1.2 second interval, are less than one in a hundred.

On the astronomical chance that someone happens to be walking or cycling past the driveway at that precise instant, you’ll take that person’s life and would spend the rest of your life in prison not to say that you’d inflict inconsolable grief on an innocent family.

But you badly need the money, and it’s a near certainty that the coast will be clear.

Would you do it?

If you wouldn’t do it, why wouldn’t you do it? You desperately need the money, and you take greater risks every day. So where’s your hesitation coming from despite your extreme need and the odds being, for all practical purposes, totally in your favor?

Could it be that we sense that the laws of logic, science and probability aren’t truly the laws of life, that, in this case, the real chance of hitting and killing someone may be a good deal greater than one in a hundred?

Why should this be so? More than that. What if the odds for one person might be one in a thousand while the odds for someone else might be one in twenty or even one in ten although there’s no logical explanation for the difference?

Regardless of the piece that I’m working on, that last lousy line of text should lap over onto the next page no more than once in thirty-five to forty times. Yet it happens once in every eight or nine times. It’s so vexing. There’s no reason for it.

Maybe we really do wait longer at traffic lights when we’re feeling rushed and it’s not just our imagination. Some of us anyway.

The town planner says there’s no reason why vehicles approaching each other on that barely traveled stretch of road should meet at that railroad underpass as often as they do. (Much the same thing happens when making a left turn. I’ll pass one vehicle in a 1.7 mile stretch; yet it will pass so as to make me come to a full stop precisely where I’m making the turn.)

The universe has no apparent need to play such games so why does it? Of course there’s the faery world with its own laws and logic, but this is the everyday, mundane world in which the non-randomness of random events would seem to serve no purpose.

Yet we disregard the non-randomness of the random at our peril.

Thank you for reading. I hope you enjoyed this piece.