I have long been fascinated by sewing machines and how they work—especially because my theories on the subject have always struck me as absurd. I knew that a thread came from above, through the eye of the needle, and another from below, from a device called a “bobbin”—a word that sounds so British it seems like a crime, or at least indelicate, for an American to use. And that was about it.

Sewing Machine

Those interested can find pretty much everything they would want to know about how sewing machines work at How Stuff Works and Threads Magazine. What I’m interested in here is how that two-thread mechanism works. I figure that most people understand the rest of the machine, anyway. After all, it doesn’t amaze anyone that the pedals in the middle of a bike make the wheel at the back go around. So it shouldn’t be amazing that the needle and bobbin work in synchronization. But what’s up with that threading thing?

Two Thread System

When I was younger, I thought that through some amazing bit of technology, when the needle penetrated the fabric, the upper thread was removed from the eye and the bobbin thread was inserted into the eye. And then reversed on the next penetration. Wrong, of course. I knew that even as a child, but that was the best explanation I could come up with. In my defense, my 5-year-old’s theories about household plumbing turned out to be spot on.

What is really happening is much more clever than my dubious thought experiments. In all sewing machines that I am aware of, the upper thread stays above the fabric and the the bobbin thread stays below. The trick is that they wrap around each other under the fabric—whether the machine uses a bobbin or not. This is illustrated in the image below that I made from screen captures of a Wikipedia animated gif. [caveat]

Six Stages of Sewing

1. This is the set-up, just as the needle breaks through the fabric.

2. When the needle reaches full penetration, the bobbin hook grabs the upper thread loop.

3. The bobbin hook rotates in the opposite direction of the taut bobbin thread.

4. The bobbin hook continues to rotate the upper thread so that it wraps around the bobbin core—catching on the bobbin thread.

5. After the bobbin hook has rotated once around, it releases the upper thread.

6. The fabric moves backward, effectively moving the needle forward, and thus tightening the stitch.

This evening, I wrote a letter to my nephew on his 18th birthday. I like to torture him, so I wrote:

Up to this point the world has been nothing but possibilities; you could walk through any door you want to an exciting future. This is true, if by “exciting future” you mean a future in which you struggle your whole life to get by and not despair so much that you finally just give up either via long drop and sudden stop or just by refusing to get out of bed. But the moment you walk through that door, you will hear all those other doors slam shut. And you will be looking at… It’s kind of like Let’s Make a Deal except there are more doors and a llama is behind every one of them.

This brought to mind Monty Hall (who is still alive) and the Monty Hall Problem and, unfortunately, Marilyn vos Savant. I say “unfortunately” because I find her annoying. She is exactly the kind of snarky intellectual that I hate. Here is my biggest complaint: she advertises herself as having the highest IQ in the world, but when anyone questions that claim, she responds that the IQ doesn’t really mean that much. That’s quite true: the IQ is a measure of a certain type of mental functioning; to say it is limited is to be charitable. But vos Savant’s whole career is based upon this claim. If it doesn’t mean much, why is it listed in everything she writes? All of this should not be taken to mean that I think she is stupid—just a PITA self-promoter.

I am grateful to vos Savant for introducing me to the Monty Hall Problem. Here it is: suppose you are on Let’s Make a Deal and there is a new car behind one of the doors and a llama behind each of the other two. You pick door number one. Monty says, “Are you sure you want to pick that door?” And to entice you to change your door, he opens door number three and shows that behind it is a llama. So now you have two doors: one has a car and one has a llama. Should you change to door number two?

This puzzle is counter-intuitive. My first guess (and yours too I bet) is that you shouldn’t change doors, or rather that it doesn’t matter: there is an equal chance of the car being behind each one of the doors. But this is utterly false. Think about it this way: at the beginning, there is 1/3 chance the car is behind door number one; there is a 2/3 chance that it is behind door number two or door number three. So after door number three is taken out of the equation, there is a 2/3 chance that the car will be behind door number two.

You don’t believe me though, do you? That’s okay; I wouldn’t either. But before you embarrass yourself, you should do what slow thinking Frank did: get out a deck of cards. Take three cards and define one of them as the car. Then run through the process. If you are smart (like vos Savant or even me) you will quickly (like after one or two deals) see it (in the religious sense). If you are not so smart, just do it ten or twenty times and you will see that by switching, you will win the car about 70% of the time. Q-E-fucking-D!

You might wonder why switching has this effect. I’m not as smart as Ms. vos Savant (although I’m more fun at parties), but I think I can help. By showing you one of the llama doors, Monty is adding information to the system. When you stick with your original choice, you are not taking advantage of the new information. There is always a 1/3 chance that the car is behind door number one; but there is a 1/3 chance it is behind door number two at the beginning and a 2/3 chance it is behind door number two at the end.

It is not considered ethical to torture people. This is why they invented probability theory. Luckily, I have my nephew to abuse.

Check out the excellent New York Times article/interview with Monty Hall that will explain it all, including some aspects that I have not talked about.

This is actually a field within Social Psychology. In general, I am trying to avoid it these days, but the Wikipedia article on Illusory Superiority is really good. The most interesting thing I learned from the article is that people find any member of a group to be above the median of the group itself. Also: people rate themselves less better compared to specific individuals than to the abstract “average”. I think this has something to do with how we find it easier to empathize with a single individual than with a group—even a group of two. (Sorry that I don’t have a reference for this; I heard it on On The Media last week.)

Worse Than Average Effect

There is another effect—the opposite of Illusory Superiority: The Worse Than Average Effect. This is the tendency for people to under-estimate their chances of doing something that they think they have a very low chance of doing. For example, people tend to underestimate how likely they are to find a $20 bill on the ground during the next two weeks.

After writing this article (when I had read about the WTA effect, but did not write about it), I thought, “Yeah, right; that’s not going to happen to me.” It had happened: four years earlier, but I expected it to never happen again. While writing, I estimated my chances of finding a twenty in the next two weeks at about one-half of one percent. That meant that I should find a $20 bill on the ground every four years, so if my estimate was right, I was due.

It turned out that nine days later, I found a $20 bill on the ground. Freaky cool.

Actually, 93% of a sample of American drivers rated their skill in the top 50%. This is from a 1981 paper “Are we all less risky and more skillful than our fellow drivers?” by O. Svenson in Acta Psychologica.

Many years ago, I was introduced to the snarky statistic that 80% of drivers believe they are above average. This annoyed me from the start. Initially, I thought it was just another useless statistic; its snarky meaning had to be explained to me, “You see—idiot—only 50% of drivers can be above average; so at least 30% of the people are fooling themselves!”

The statistic has the feel of an urban legend. It seems reasonable—but then such stories always do. In fact, it appeals to my prejudice (very common among the kind of people who would pass on such information) that people over-estimate their own skills and under-value those of others. Just like an urban legend. And, of course, there is no real reference, and one has to wonder who would pay to find out how many people think their driving is better than it really is. (It turns out that a number of people would; see the caveat at the end.)

The biggest problem is that the snarky aspect of this “fact” is incorrect. It is quite possible for 80% of a population to be above the average (mean). Just imagine if driver quality were rated on a scale of 0 to 100. Further, imagine that there were ten drivers with the following ratings: 0, 100, 100, 100, 100, 100, 100, 100, 100, 100. Clearly, the average would be less than 100 and so 90% of the population would be “above average”. (I’m slow, not stupid.) This is hardly a normal distribution, however. And you would think that driver ability would be a normal distribution, or something like it. (But maybe not; my father thinks that the road is filled with “idiots” and him.)

At this point, the worst case scenario is that someone comes forward with an actual study that shows, more precisely: 80% of drivers believe they drive better than the median. On its face, this cannot be factually true: 50% of a population must be above the median and 50% must be below; this is the definition of “median”. However, this too is a ridiculous claim and leads me to the whole point of this article.

What does it mean to be a good driver? We must know this before we can know if one driver is better than another. For one person, a good driver might be one who can control his car at high speeds. For another, it may be one who always drives the speed limit. Given that most people are rather good at the kind of driving they value—and thus practice regularly—it is surprising to me that only 80% consider themselves “above average”. [caveat]

People are foolish. And at least in political matters, people tend to under-estimate others. For example, Americans consistantly over-estimate how racist their neighbors are: almost always rating them as more racist than they rate themselves. But this is exactly the appeal of this little statistic: “I am not one of those silly people who think that their driving is better than it really is.” My driving, however, definitely is above average.

[Caveat: Illusory Superiority]