The Math to Enlightenment

by Jacqueline Verrilli

I believe that the formula above holds the answer to all of life’s problems.  This humble little formula is the most common of all formulas in mathematics and is actively used in every human endeavor of every kind in any discipline.  It is deceptively simple in nature, involving only addition and division to derive, and yet within this simplicity is a powerful beauty beyond any that can be achieved in painting, sculpture, or literature.  It has most certainly been around since shortly after we started counting things and so it shocks me that no one, outside of statisticians, has revered it or even so much as paid much attention to it.  I believe that it is the equation for life, the universe, and everything and I’m sorry that Douglas Adams won’t get a chance to read my blog, but hopefully the inter-dimensional beings are reading it now and will make this formula their new Supreme Being.

For those of you that haven’t used mathematical symbology since high-school or college (or ever), the weird looking set of hieroglyphs above is just the formula to calculate the average of a bunch of numbers, also known as the arithmetic mean.  Like most math, the calculations behind this scary-looking equation are actually relatively easy to do.  For example, the mean of the numbers 13, 5, 17, 22, and 20 is 15.4 and is simply calculated by adding the numbers up and dividing the total by the number of numbers.  If you had, say, a bunch of bushels of oranges, you could count the number of oranges in each bushel and find the average number of oranges per bushel.  And if you did this, as long as, the bushels were not filled by a super-accurate machine that put exactly the same number of oranges in each one, you would find that the number of oranges in each bushel varied a bit, so that there would be a distribution of numbers around the mean number of oranges per bushel.

Below is a graph of a distribution of numbers around a hypothetical mean.  This is a very typical graph that is often described as a bell-curve, for obvious reasons, but is known among the mathematically–minded as a “normal” distribution.  The conventional interpretation for bell-shaped distributions is that we tend to think of the right side as positive (or higher or “better”) and the left side as negative (or lower or “worse”).  I took this particular version of a normal distribution off of the internet and, as you can see, whoever created it was using it to show some distribution of “ability”.  We can think of this ability as just about anything.  We could, for example, make everyone in the world perform a standing jump, measure the height of each person’s jump and we would likely see a normal distribution across the population.  Most people would be able to jump, say, 18 inches off the ground, others would only be able to jump 8 inches, while other could jump 25 inches.  At the very extreme ends we might see a few souls who were able to jump, say 33 inches.  These people might fall into the tail of the bell curve on the right-hand side which would mean that they fall above 99% of the rest of the population in ability to jump high from a standing positon.  These would likely be your Olympians if you could find them in your country.  Others may only be able to jump, say ¼ of an inch.  These folks would fall into the tail on the left side of this distribution falling below 99% of the population in this particular ability.  Normal distributions occur around the mean, or average, of the population’s “ability”, so those of us who fall in the middle, jumping 18 inches, would fall on the line in the very center.  Let’s say ½ billion of us fall at exactly 18 inches, then the people who could jump 17.95 inches would fall just to the left of us, and the people who could jump 18.05 inches would be on a line just to the right of us.  So you can, hopefully, now see that this graph also shows the relative number of people (or things) that would fall into each level of the measurement.  That is why this is also called a density distribution function.

 The unbelievably amazing thing about normal distributions is that they occur in nature everywhere.  If we test the height of human beings worldwide, they fall into this pattern.  If we research people’s incomes, IQs, or the number of hairs on their heads, these figures will all tend to be distributed around a mean in this pattern. Even when we ask people subjective questions, and offer them an array of possible answers, their answers will tend to fall around a mean.  In recent years, economists, psychologists, and governments have been looking at a very subjective, yet extremely important factor in the advancement of humanity: well-being.  In the social sciences, we often use the term “Subjective Well-being” because an individual must report their level of well-being to an observer, like, say a social science researcher, since it cannot be observed and determined objectively like, say, the number of oranges in a particular bushel.  Since self-reports of well-being are considered subjective, it is said that researchers really shouldn’t compare one person’s reported well-being to that of another.  What I might call a “5 out of 10” as my feelings of satisfaction with some element of my own life, you might call a "9 out of 10" under the same circumstances, or vice versa.  It is also a matter of debate as to whether you can compare a reported level of well-being from one individual at a particular point in time to another reported by that same individual at a later time.  Human beings are known to be notoriously moody and often can’t shed that mood in order to answer subjective questions about their lives as objectively as possible.  And, of course, since neither of these comparisons is an ideal way to assess well-being, we social scientists do them anyway ‘cause, really, what in life is ideal?

Average is the New Awesome

Let’s look at a bell curve for “success”.  In point of fact, the definition of success is as subjective as all-get-out, but since this is an economics blog, let’s just use "wildly wealthy" as our definition of success.  The media LOVES to cover the lives of wildly wealthy people.  So we hear about them, ad nauseum.  We don’t often hear about people who are huge successes at just being decent human beings.  Our sample of "successful people" is, therefore, generally comprised of those who are in the tail ends of the bell curves, which are subject to availability bias.  For example, we might consider Warren Buffet or one of the Kardashians one of our success heroes.  But we, as consumers of the media, we, the average people, make up the market for information.  And if we stopped caring about those people in the tail ends of the “success” or “fame” bell curves and started watching only stories about average people, the media would have to respond in kind.  We simply don’t understand the power that we have in that opportunity!  My Econ Prof even pointed out the power that the average person has over the distribution of money.  Each time we click on an ad that has been placed with Google, Google gets money!  Can’t you feel that rush of power!  Imagine if we could just get rid of the Electoral College!  The point is, it is those of us in the tall and wide part of the bell-curve that have all the power.  We are the vast majority of the “normal” in Normal Distribution, after all.  And it behooves us to use that power in the most efficient and effective manner because, as we all know, with great power comes great responsibility. That’s why average is the new awesome!

Everybody Please Hold Hands and Take One Step to the Right

It is the average person that makes the world go ‘round, not the outliers.  The average person determines who wins an election, what prices prevail in markets, which goods and services are provided, and what team gets the good odds in Vegas.  We can argue that the monied and powerful people manipulate the systems and, yes, this is true, because we average people allow it.  We allow ourselves to be bought and manipulated and then place the blame outside ourselves.  It is an evolutionarily ingrained instinct to think of ourselves as autonomous and above influence, all the while allowing the outside world to effect our self-image, and our self-confidence, and, hence, our autonomy.  As much as we want to be viewed as special by everyone else, we are built to fit it so that we can be accepted and belong and enjoy the protection of the group.

But when even one of us does something that is a little different, even when we think we are doing it just for ourselves, like, say, sitting in the front of the bus, or wearing pants suits on the Congressional floor, or starting an internet search engine to help us find what we want more easily, the world actually gets better for everyone.  When a writer writes a great story, or an engineer designs a mechanical solution, or a teacher finds a way to help students understand chemistry, or a doctor describes a new illness, they feel proud of themselves because solving problems is fun.  And if one person improves their own well-being, it improves all well-being.  And you don’t even need to invent or discover anything to improve your own well-being or that of anyone else.  When my garbage haulers just do their jobs, it makes my life a WHOLE lot better because I don’t have to do anything other than drag the can to the curb!  When someone else teaches my children biology, I don’t have to; when someone drives a truck that delivers broccoli to my local grocer, I don’t have to; and when my husband takes the no-kill mouse trap out to the back yard, I don’t have to.  I would argue that they, thereby, improve my well-being.  Now, according to the calculation of a mean, if even one person under our bell-curve becomes better-off in terms of their well-being, it moves the entire mean to the right.  This shift may be ever so slight; so incredibly slight as to be unnoticeable to the casual observer, but the mean, nevertheless, has moved, and we can calculate the amount of the change.

Sure, But What's in it for Me?

I hope you’re as excited as I am at this point because here’s the BEST PART!  Remember that formula for the mean and how you add up all the numbers before you divide?  That’s why I believe that the mean is the math to enlightenment: it is an axiomatically logical and mathematically calculable function of what many people know to be true intuitively; that we are all interconnected to one another.  Our actions affect one another without us even necessarily meaning for it to happen!!!!  And wait!!  It gets even BETTER because of what that means to society as a whole.  It is everyone’s purpose in life to move the mean to the right.  And we all do it just be being ourselves!  Just imagine if we all started to actively help one another out!!  Holy compassionate actions, Batman!

Red Shift

When one person who might have dropped out of school instead stays in and completes a high school diploma or a college degree, the whole world is better off.  If a teacher or mentor helped to influence that outcome the whole world is even better off.  If even one person helps someone, anyone, that is even just slightly to the left of them on the bell-curve in any ability and that individual goes on to use this newly improved ability to their advantage, the mean for the world’s well-being moves to the right.  The graphic above is the latest assessment of an agglomeration of factors contributing to Subjective Well-being as reported via a survey given to the peoples of countries around the globe.  It is from a document quaintly entitled the “The World Happiness Report 2015”.  If you’ve heard anybody state recently that Switzerland is the “happiest” country in the world it’s because of the data contained in this report.  Don’t let the cutesy title fool you, though, the report is 87 pages long, involved the collection of thousands of data points, and involved statistical analysis of those points.  All to arrive at a mean level of well-being for each country, and that mean is then categorized and color-coded.  As is convention, red is worse than green.  I sincerely hope that everyone will read “The World Happiness Report 2015”.  It is an important document for individuals as well as world leaders and social scientists.  But even if you don’t read it, take a huge deep breath and go to work or send your kids off to school knowing that any little positive thing you do helps us shift away from the red.  And “The World Happiness Report” will thank you.

http://worldhappiness.report/ed/2015/

Helliwell, John F., Richard Layard, and Jeffrey Sachs, eds. 2015. World Happiness Report 2015.
New York: Sustainable Development Solutions Network.