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Happiness as a Sine Curve: Quantifying the Qualitative Life

April 15, 2011
It's pseudo-math!

Aristotle once wrote that you can only know if you lived a happy life after you are dead.  To be happy, quoth he, you need to be virtuous; at the end of your life, your life would be deemed more or less ‘happy’ depending on how virtuous you were and how much you lived up to your potential.  To be virtuous, you needed to live a life of balance, tending towards neither extreme.   In other words, ‘neither lender nor borrower be’… something like that.

In ‘You’re a Good Man, Charlie Brown,’ happiness is equated with finding a pencil, pizza with sausage and telling the time.  Not to mention knowing a secret, climbing a tree and five different crayons.  Apparently, if you are truly happy, you have to sing about it.

No offense to Aristotle (or Charles Schultz for that matter), but this seems like a very wishy-washy method of measuring happiness.  This is America, baby- we are results orientated.  Economic theories of happiness or bust!  Thus, I turn to those who are known to make quantitative magic out of qualitative nonsense: the happiness economists. (No, I don’t think that is the title they put on their business cards, but you never know).

Happiness economists use metrics to measure and do comparative analysis on how happy we are as a species, a demographic and as individuals.  Happiness is often labeled as ‘utility.’  Economists measure individual and societal utility. (I guess saying you are measuring happiness sounds a little too much ‘My Pretty Pony’ for economists).  This information is measured through concrete quality of life factors (how far above or below the poverty line someone is and other similar socio-economic indicators) as well as through more sweeping figures such as a nations GDP.   According to Wikipedia,

“Micro-econometric happiness equations have the standard form: Wit = α + βxit + εit. In this equation W is the reported well-being of individual i at time t, and x is a vector of known variables, which include socio-demographic and socioeconomic characteristics.”

There you have it, in pure and simple mathematics.  Your utility level, now new and improved with variables!  Don’t you feel more secure now that you don’t have to find mere fallible words to express your joy or angst?

Okay, you’re not feeling it.  I get it.  Not gaining much utility about this method of turning happiness into an equation.  Let’s look to other factors that affect happiness levels then.  Maybe I’m not convinced either.

Some other quickies: a belief in your own self of efficacy (the ability to produce a desire result) is key for feeling happy.  Having some type of ‘work’ (expending energy towards some goal or process that gives meaning to the effort and time allocated) is also essential for one to be happy.  Having relationships (did you know that the average number of ‘best friends’ someone at one given time has lowered to 1.2 from almost 3 nationally over the past 50 years?  That’s a little sad, people) creates an emotional safety net and a safe vent for strong emotions.

Psychology Today gives a few other interesting demographic factors: “The basic determinants of happiness –age (a U-shaped relationship with happiness with the low point in the mid forties), income, health, stable partnerships, and friendships, among others–are remarkably similar in countries and cultures around the world.”  It also goes on to state that uncertainty is something that people have a difficult time adapting to, and that uncertainty, more than poor conditions or low pay (people adjust) is the number one cause of unhappiness.

With that in mind, I (generous blogger that I am) have decided to lessen your uncertainty about two life equations.  I have drawn pretty graphs that pretty much explain that the meaning of life is not 42.  These graphs are designed to reduce stress levels but allowing you to calculate just how happy you will be in the future.  Take that, Aristotle.

It's pseudo-math!

Please note the life events that send one into a depressive cycle.

This graph clearly illustrates that happiness vacillates with a sine/cosine wave function.  The way to determine Aristotelian average happiness over a lifetime then is to take the derivative of the spaces above and below the curves, and see whether the number is ultimately positive or negative.    Positive: you have had more good times than bad, baby.

(Side note: notice that moody people are not actually unhappier than their more stoic brethren.  It is more that they experience higher amplitudes in general; the highs and lows are magnified.  Thus being emotional should not be equated with being susceptible to a life of angst and sorrow.)

The Law of Diminishing Marginal Returns

This second graph is just a freebie I decided to throw in there.  Basically, kisses do not equate happiness in the long run, but short term, they can’t be beat.  Not exactly crazy reasoning, but I decided I liked being able to measure the declining average utility of each individual kiss.  Try it on your significant other sometime.  Trust me, they’ll love you for it.

I’m going to close with a quote ascribed to Lincoln, our 16th president, and wiser words were never spoken: “Most people are about as happy as they make up their minds to be.”

2 Comments leave one →
  1. Daniel permalink
    April 15, 2011 10:43 AM

    For your first graph, I feel like the time-scale should really be more discrete. That is to say, it should be clear that the happiness at any given point is really just an average happiness over a period of time. Otherwise people might get the impression that you think 20-somethings are never happy, and they’ll call a hotline on you.

  2. Jesse permalink
    March 28, 2015 7:40 AM

    I found your thesis when I was thinking about how a happiness vs money graph might look. I too had decided that the curve would be parabolic like the positive undulation of a sine curve. However, I’m not so sure about your idea of integrating the happiness curve to find total happiness over a period. The integration would result in the total quantity of something which is the antiderivative of happiness. The question becomes: The slope of what function is equal to happiness? In other words: if f(x) = H, what is x? I think you could plug in many different variables for x. For instance x = daily ability to achieve intended outcomes. The function would be some exponential that peaks and subsides at a certain point due some damping function like the numbing effect of aging.

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