“There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.” William Shakespeare, Hamlet, Act 1, Scene 5
“One death is a tragedy, a million deaths are a statistic.” Unknown source, attributed to Josef Stalin
It would be my intention at this point to compare statistics to a world of dreams. Dreams are infinite. Statistics are static. To the modern scientist, one size fits all under the Bell-Shaped (Gaussian) Curve. Whatever size you are, we can find you a comfortable place under the Bell. All we have to do is locate your particular place in it and you will see how well our product can work for you. But—Believe me!—we will find a place for you and you will see how well our product really works. Unfortunately for the scientist and sometimes for the dreamer, dreams like people are not static. It is interesting to think that, considering the breadth of psychologists’ various practices, they may be educated in both worlds, the statistical world of phenomena and the mystical world of dreams. Depending on the individual psychologist’s training, experience, and predilection, a practitioner may pursue interests in either or in both worlds.
From my own world of dreams: I recall, as a child, being preoccupied with some real-life conundrums. Around the third grade, we were given the task of writing a composition about how to get from one place to another in the neighborhood. Someone wrote directions indicating that you “go straight”. During the subsequent discussion of our papers, the teacher pointed out that this description was not correct because the road that we were discussing curved. The question then became how you could write the directions accurately. Several of us offered our attempts at an answer before the teacher informed us of the correct one, “You follow the road.” I was involved in a similar exercise several years later, around the sixth grade, when I repeated what I had learned previously. However, on this second occasion, the teacher informed me that it was perfectly acceptable to give someone the direction to “go straight”. Wrong again!
This example doesn’t differ much from statistics in which an irregular or curved line can be made mathematically straight and, once mathematically straightened, any straight line can be determined to have its rightful place under the Bell. However you choose to analyze your walking in the real world, especially if you are seriously trying to go straight, you will find that your steps deviate somewhat, more if you have a limp or are dizzy. In this case, your steps might deviate more than most and it would take increasingly complex formulas to straighten the line of your steps, but, happily, statistics can do this using formulas and constructs like Standard Deviation. (At what point does any diversion from walking a straight line become significant? Statistics can be used like this in order to tell how much of a limp is worth noting, how much a lack of equilibrium, or how intoxicated you are by analyzing how far you divert from a straight line. You will need a tape measure or calipers to do the measuring and a calculator or computer to do the math.)
Considering how we can radically deviate despite the power of statistics, I am reminded of the girl in my second grade class who was making a Mother’s Day card along with the rest of us. But, in her case, her mother had died. At the time, I puzzled over why she was crying. I was even more confused when the teacher had her staple a black paper flower to the card instead of a red one. My puzzlement turned to concern when I saw that she was crying during the entire time that she was making the card. She broke down when she attached the flower, finishing her work. I am not aware of any scientific research that might help explain her upset.
Statistically, as the only one in the class who was crying while doing the project, she would be considered an outlier, that is, someone who was way outside the norm. Although statistics may not be able to analyze her plight, it should take little imagination for a sentient being to have some understanding of the girl’s dilemma. How do you give a Mother’s Day card to someone who is no longer there? Who is the card for? How does a child of her age cope at all? I am aware of no fixed parameters for grief. The answer is qualitative, not quantitative. For this reason, it cannot be answered statistically. It can only be understood with life experience and with empathy, which one may be able to analyze statistically, but that would likely provide little useful information.
One more example, this one from high school, reminds one of the Zen koan about the sound of one hand clapping. (In the case of the koan, I knew of a child schizophrenic years ago who like Alexander the Great and the Gordian knot conquered the riddle. He did it by flapping his hand, making a clapping noise. Everyone was intrigued by his novel solution. Pretty soon, everyone was trying it.) But, the question in high school was whether the number of grains of sand on a beach was infinite. We said yes, the teacher, no. This raised a series of additional questions some of which may be considered statistical. To me, the most important was whether the beach was bounded. How do we define the start and end of a beach? The answer has more to do with language and the imprecision of our understanding of the concept of a beach. How far does a beach extend into the water? How deep does the sand go to the sea before we run out of it? Does sand cease to be sand the deeper you go? If so, what does it turn into? How does a beach get there? Does sand reproduce or increase somehow with the occurrence of natural phenomena? Does it break down? Is there natural fluctuation in its numbers and does any fluctuation contravene the law of its finiteness?
If you can answer any of these questions to your own satisfaction, then you will likely have the makings of a modern scientist or statistician. I am sure that my high school science teacher’s answer would have been that, because the Earth is bounded, the number of grains of sand is finite, even if we don’t have the means to count them. Because the answer involves a definition, it borders on philosophy.
Indeed, I would argue that the Bell curve is a useful philosophical construct, but does not fit all the data to which it is applied, probably not even most of it. Still, I recall us discussing with the same high school science teacher whether we will run out of air one day. He hesitantly said, yes. In light of recent circumstances, it would appear that he might have been right about that as well. Maybe there are a finite number of grains of sand on a beach even though the number seems infinite to me because I am unable to count them. Maybe we will run out of air one day. (Inhale!) I get a headache whenever I think about it. Not much different than the headache I got while studying statistics.
