Tag Archive: Law of Large Numbers

TV – or Not TV

(Submitted by reader Jason Pope)

I was in college in 2000 or 2001, living in a house with four friends.  We were in the basement one day watching TV as we would do more often that I care to admit. I had the remote control and, as I often did, I would flip through channels at a pretty good clip.  I would assess whether a show was interesting or not in a second or less before flipping to the next channel; a practice which infuriates many people (my wife/former room mate included).

Here is where the oddity occurs.  At one point I flipped past a channel when, for reasons unknown to me, I thought I had recognized actor Kyle MacLachlan talking to somebody. Before changing channels again, I said out loud to my friends, “Is that Twin Peaks?” referring to the TV or movie starring Kyle MacLachlan.

I immediately returned to that channel with the same rapidity as I had skipped it. As soon as I settled on that channel, the character portrayed by Kyle MacLachlan without hesitation said on screen, “Yes, it is” as if answering my previous question.

Though I know he was not talking to me, the fact that I had asked such a specific question, out loud, and immediately been answered correctly by the onscreen character from a strange TV show was bizarre. With that I turned the TV off and told my friends I was going to bed.

My own thought on this is that it chiefly suffers from confirmation bias or selective recall. I have probably flipped through thousands upon thousands of channels and asked myself the exact same type of questions. However, I only remember this occurrence because of the peculiar dialogue.  In addition, it sadly might also be a product of the law of large numbers, with dialogue that was not perfectly responsive being ignored or forgotten. Way too much TV.  🙁

[EDITOR: I’d vote for the Law of Large Numbers. Channel surfing is a direct result of the feeling that there are 57 channels, and there’s nothing on, to paraphrase The Boss. The sane response was to turn the thing off and get some sleep, or listen to a podcast, instead of believing it was possible to have a dialogue with the TV set  🙂 – Wendy]

Below are the extended notes provided by Barbara Drescher for use in Skepticality Episode 187. Take a look and leave your comments below.

This a great story and I have to concur with the editor’s note by Wendy Hughes. It is more than simply a large number of channels available, although channel surfing is hard if you only have three. But if you surf through channels the way the author describes on a regular basis, you are bound to have an experience like this. I am actually surprised that the author does not have several stories just like it.

And as these things often do, it sparked a clear memory I have of a similar incident, so rather than a useless analysis, I’ll just add to the drama.

When I was in grade school, the teacher was reading to us for the first time. The story was a little bit creepy and she lowered her voice in a creepy manner to make it more dramatic. She read, “Slowly, the door creaked open and I heard footsteps approaching.”

Just then, the door to the classroom creaked open quite slowly and the principal tiptoed into the classroom.

I think we were all surprised that nobody screamed. The teacher was just as stunned as the rest of us and we had a great laugh about it afterward.

Last month an article on one of my favorite websites, io9.com, grabbed my attention. It included a discussion of studies and simulations which demonstrate (and provide evidence for) some of those things in life that lead us all to think that fate is trying to tell us something. Specifically, the adage we call “Murphy’s Law” states that what can go wrong will go wrong and it is supported by both mathematical proofs and observations.

“When it comes to long strands of string, from proteins in a person’s cells to the rigging in a ship, this means spontaneous knotting. People have written papers about how string knots up the minute it’s given a chance to jiggle around.”

The article goes on to discuss a simulation of a random walk (direction for each step is determined randomly) in 3-dimensional space with the restriction that no space can be occupied more than once. The path of the walk simulates the placement of a length of string – the beginning and end of the path are the ends of the string and no part of the string can occupy the same space as another part. What the researchers found was that any sufficiently long walk (string) must contain a knot. The longer the walk (string), the more knots.

This can teach us that tossing our Christmas lights into a box is almost certain to result in knots to untangle next year, but it can also teach us a lot about risks, coincidences, and how to think about those things.

Barbara Drescher

When I was nine years old my family lived on the Great Lakes Naval Station (on the shores of Lake Michigan) for about a year before buying a house off the base. Our home was in a cul de sac that was shared by several families. One of the families of which we were particularly fond was a widower with a boy and girl about the same ages as my brother and I. Fast forward to more than four years later, after we had moved twice and now lived 2,000 miles away in Sacramento, California. We drove the three hours from our home to a tiny fishing hole called Blue Lake for a weekend of camping and fishing. About an hour after we arrived, my mother suddenly blurted out, “Hey, isn’t that Bud Neighbor [not his real name]?” Sure enough, camped a few spaces down were our old friends.

I have had quite a few similar experiences, but none as bizarre or unexplainable as this one. Should we have been freaked out and considered some cosmic connection?

To find out, let’s turn back to the article I mentioned and Murphy’s Law. Is it true that anything that can go wrong will go wrong? Well, not exactly. You can get on that plane tomorrow and be confident that you will survive the flight (your odds are approximately 9.2 million to 1). However, if you “tempt fate” enough, even the least likely disaster will eventually happen. Of course, your plan to commit suicide via commercial airliner will require you to fly every day for more than 25,000 days to ensure success, and even then you have no guarantees.

The problem of spontaneous knotting is simply a matter of odds. It relies on something called “The Law of Large Numbers”, which dictates that any event which can occur will occur if given enough opportunities.* String knots up when there’s a lot of it because there are a number of ways in which it can be knotted.

Without going through a bunch of math, let’s look at how we determine probabilities. There are two properties to consider when determining whether an event is unusual (vs. expected):

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