Accident Prone People

I have to resist sleep till 4:00 in the morning and it is still a little more than 2 hours left. So I fire up my feed reader and I find an article that is shocking! Especially because the timing of the appearance of the article is just apt, according to what happened to me this morning.

Strikingly, it appears that there is a discrete group of people who suffer the most accidents: 1 in 29 people have a 50 per cent higher chance of having an accident than the rest of the population (Accident Analysis and Prevention, DOI: 10.1016/j.aap.2006.09.012).

Visser says the study doesn’t reveal which people in particular are most at risk, but it does show that a band of hapless people exists. Previous research suggests that children and people who work on oil rigs or as combat pilots, for instance, tend to have more accidents.

That was from this recent article in NewScientist.com.

So this made me wonder if I belong to that band of hapless people who are prone to accidents. To settle this question, I did a little analysis. First a few facts and then a bit of statistics and the analysis.

• This is what I was told about the scar at the top right hand side of my forehead: I was four. I was on my way to the school, particularly cheerful that day. I was walking ahead waving at my folks standing behind looking at me on my way to board the school bus. Something stopped my journey in between and I never reached the bus that day. A broken vase penetrated my forehead as I was left in blood flat on the ground. I got 6 stitches. The scar left there is always to be there as it went in the official records as my identification mark.

• I was seven. I somehow managed to put a spoon through my left cheek. That scar is almost invisible now.

• At nine I had an unfortunate confrontation with death. I came out clean with some injuries that healed soon after, but whatever else remained is not healed yet. I’d like to keep the details only to me.

• I was ten. In the process of trying to save a fellow from an accident, I ended up having a bus finding its way on my left arm. The poor little arm fractured at 13-16 places, exactly how many I do not remember now. The arm is fine now, except the occasional pain, and I can even bowl (in cricket) with it.

• I was twelve. I was carrying an electric voltage stabilizer that we use for ACs in India, and I let it slide. It fell on my right foot. So there is a scar of 4 stitches gracing my foot just where the thumb connects to the foot.

• I was fifteen. I dared playing hockey without shin-pads. A blow of an opposite team player chose to hit me, instead of the ball, 5-6 inches below the right knee. Everything surrounding the point of impact, within the radius of about 1 inch, became pulp. My friends in my school hostel enjoyed pressing it for a long time.

• I was a few months older than fifteen. I was batting (cricket) at 7:00 in the evening without proper gear. The bowler bowled, I took a front-foot stance to defend the ball and suddenly the ball rose more than what I, or anybody else for that matter, expected hitting me right on my chin. As a result, there is still a hard thing at that place.

• I was twenty-one, watching a live cricket match in a stadium. The ball came flying from nowhere and hit me smack on my right eye. That eye suffered a permanent damage. I can use the eye, but the eyesight worsened and it is +2.75 right now, irreparable, according to doctors.

Those were the accidents that left some parts of my body never to be what those should be. Accidents are very common to me. It happens quite often that I am walking and some pillar, wall or some door comes in my way to hit me. I was walking on one leg for 10 days a few weeks ago. This morning I was at a canteen in the campus thinking whatever, waving my hands vigorously as if I just arrived at some grand unification result. (I did not!) My hand hit a cup of boiling tea and the tea spilled over my body. Awesome!

So here I am with eight major mishaps and many-many more minor ones. I’m 27 years old. On an average, I encounter a major accident in 40 odd months, i.e., once in every (a little more than) 3 years. But if I plot the occurrences of the events against time, and observe the pattern, I find it relieving that the frequency will decrease as I get older. Do I suffer more accidents than most people? You decide.

Is it not a statistical proof that I’ll live longer than you, yes, YOU, whoever is reading this post? That is sad according to me! Sorry, I can’t come up with a concrete theory, for whatever happens in life has a very little or no control in my hands.

On xkcd goodness

My favorite web comic strip is xkcd. This is what I claim about xkcd:

My calculations suggest that xkcd is the best with the probability more than $(1 - O(1/N^2))$, where $N$ is the number of strips Randall publishes. So, if he or his successors publish forever, i.e., if $N \to \infty$, $Pr[xkcd\, is\, the\, best] \to 1$.

So he should keep publishing the strips with more frequency so that the goodness of xkcd converges to being almost surely the best of all time as fast as possible. 🙂

On the size of shoe racks

On a web discussion board, I conjectured the following:

The diversity of the size of women’s shoe-racks can be expressed in mathematical fashion as a distribution of a particular form, called a “power law“, meaning that the probability of a woman’s shoe-rack attaining a certain size $x$ is proportional to $(1/x)^y$, where $y \ge 1$.

When a distribution of some property has a power law form, the system looks the same at all length scales. Therefore, if one were to look at the distribution of rack-sizes for one arbitrary range, say, just racks with 100 to 1000 shoes, it would look the same as for a different range, say, 1 to 10 shoes. In other words, “zooming” in or out in the distribution, one keeps obtaining the same result. It also means that if one can determine the distribution of shoes per rack for a range of shoes, one can then predict the distribution for many other ranges.

Equally interesting, power law distributions have very long tails, meaning there is a non-zero probability of finding racks extremely large compared to the average. This finite probability of finding large racks is quite striking and can be illustrated by the example of the heights of individuals following the familiar normal distribution. It would be very surprising to find someone measuring two or three times the average human height of 5’10”. On the other hand, a power law distribution makes it possible to find a rack many times larger than average. Power laws also imply that the system’s average behavior is not typical. A typical size is one that is encountered most frequently; the average is the sum of all the sizes divided by the number of women. If one were to select a group of shoe-racks at random and count the number of shoes in each of them, the majority would be smaller than average.

A similar analysis can be carried out for women’s cloth cupboards, with $y \in [3, \infty)$.

Men don’t have shoe-racks! So an analogy between the show-rack size and the size of the cupboard would not be possible. But here is one fact that gives you the basic idea: I’ve two pairs of jeans, one is torn at several places. I have a few Ts, a few bought and a few won in different competitions held at my place. Apart from these prized possessions, I also have a couple of shorts and a track suite, a couple of towels, a few pairs of rotten socks and a few undies.