1 January 2006

32 ft. / sec. / sec.

--by Mike Murray

You remember the old science class example: Teachers explained that, if you were to drop a baseball and an anvil simultaneously from the top of the Empire State Building (instructors substituted the Terminal Tower here in the Cleveland area), the result should be that they would strike the sidewalk below at the same instant.

It's a simple matter of physics. The equation that represents our planet's gravity holds that objects (of any kind) fall toward the ground -- more precisely, toward the Earth's core -- at an accelerating rate of 32 feet per second per second (covering 32 feet during the first second, 64 during the second, 96 feet during the third, and so on). At the end of three seconds of free fall, then, any object should have traveled 192 feet (32 + 64 + 96).

Ah, if only it were that simple.

Fact is, the gravity equation only really works in a vacuum. Our atmosphere is loaded up with molecules, grouped in varying densities. Further, they are buffeted about by winds generated by the Sun's uneven heating of our myriad planetary surfaces. The irregular absorption and reflection rates of Old Sol's radiation by vegetation, by water, and by manmade surfaces (such as concrete and asphalt) generate turbulence in the Earth's atmosphere.

Think of a leaf and a baseball dropped together from that same skyscraper. Although they would be equally attracted to the ground by gravity, atmospheric resistance would certainly affect their respective rates of descent. The baseball would fall more directly, more quickly. On an even mildly windy day, the less-aerodynamically shaped leaf would encounter greater resistance, and would consequently float and flutter and drift -- and would surely reach the pavement much later than the baseball.

And so it is with life. Things are never really as simple as they first appear.

In helping a boy better understand basic algebra, Tom Hank's character in the movie Big posed this question to the struggling student: "If Michael Jordan scores 10 points in the first quarter, how many will he score for the whole game?"

The kid came up with the correct answer: 40. He was able to see that "40 is to 4 as 10 is to 1." Of course, most real-world outcomes cannot easily be predicted by mathematical formulas. Many more factors than points produced in one quarter of a basketball contest, for example, contribute to accurately guessing a player's probable offensive output for an entire game.

Still, it is impressive that quantitative representations come so easily to mind for most of us.

I recall that, as a child, some of the calculations (the underlying logic, anyway) of economics and physics were innately apparent to me. I remember a lemonade stand I operated one youthful summer. My brother and I sold tall glasses at 10 cents per.

As the pitcher drew down on one hot, sticky August day, I noticed that there remained but two or three servings. The line of waiting purchasers, however, still numbered 8 or 9 thirsty souls. It became perfectly clear to me that those few remaining portions could probably fetch something in excess of a dime each.

Likewise, on days when the temperature was more pleasant (and the line of would-be purchasers nearly non-existent), it was equally obvious to me that, perhaps, a reduction to a nickel a glass might be required to empty the pitcher.

I had no formal knowledge of the principles of supply and demand, or of the part they played in the breakthrough theory that John Nash Jr. established for calculating equilibrium pricing. But I was easily able to intuit their practical application. I "got" -- as has every other hawker of products and services since the dawn of time -- what Nash's character in the movie A Beautiful Mind termed the "governing dynamics" of the situation.

Similarly, I vividly remember my years playing pee wee football. I was average in height. But I was decidedly scrawny in build. (Oh, how I came to rue my desire to gain weight, to "fill out." I guess we really should be careful what we wish for.)

Anyway, my coach meant it as high praise when he shared this observation with my more physically developed, older brother. Speaking of me, coach said, "He isn't the biggest kid out there. But I gotta hand it to him; he isn't afraid to smash full speed into heavier players in one-on-one drills."

Poor coach. He just didn't get it. It wasn't bravery; it was survival. I was ignorant of the specifics of the physics concept that states that Momentum = Mass x Velocity. But I had learned that, if I got a full head of steam up before impact with a larger opponent, I could better survive the collision. My mass was lesser, but my velocity greater. Result: similar momentum, similar force ...fewer times getting "pancaked."

On the other hand, I proved to be ignorant of things quantitative when -- as a naive tadpole -- I fell for this query of my dad's: "What weighs more, a pound of feathers or a pound of lead?" I wore a dunce cap the rest of that day.

My error was obvious. My mind was stuck on expectation. There seemed to be an obvious answer implied in the question. I drew upon little more than a superficial review of the facts before coming to a (very wrong) answer.

Once again, so it is with life.

More times than I care to remember, I've jumped to a wrong conclusion when evaluating the behavior of another. Some of my miscalculations were sins of commission (inferring motives that did not exist); some were of omission (failing to consider factors that influenced behavior). In both cases, I made unfair judgments.

At times like this, when I force myself to ponder matters more carefully, I -- of course -- recognize my folly. It seems so obvious now. None of us can ever be fully aware of the things going on in someone else's life -- in someone else's head. None of us really knows for sure all of the elements that contribute to, that influence, another's behavior. Only an idiot (as I admit that I can, occasionally, be) presumes to fathom inexplicitly expressed intent.

Heck, for all the scientific breakthroughs in weather forecasting, meteorologists often err. Sometimes, they even get short-term predictions wrong. (Haven't you ever headed out the door, assured by your favorite weather person that the rain would hold off at least 10 hours or so, only to be drenched by a downpour only 60 minutes later? Or, as Cleveland-area weather guru Dick Goddard likes to put it, haven't you ever awoken to "six inches of partly cloudy?")

It's not that our friends in meteorology are idiots. It's not that their measurements aren't accurate, that their computer models aren't sophisticated. It's just that weather prediction is a complicated business. It's hard to identify all of the factors involved and to properly interpret their interactions.

It's one thing to learn how to calculate multivariate, curvilinear regressions; it's quite another to know how to develop complex formulae by establishing component variables and accurately representing interrelationships. Anyone with average intelligence and a modicum of training (or a calculator) can substitute and solve; only a precious few can see and construct the means of quantitatively getting at "new knowledge."

If weather forecasting is difficult, making sense of human behavior is downright confounding. More and more as the years go by, I'm aware of my ignorance in a variety of disciplines. (That's the way it works: the more you know, the more you realize you don't know.) Given that, what the heck makes me think I have a clue about what goes on in other people's heads?

It's finally sinking into my thick skull that, when it comes to understanding the behaviors of others, it is much the same as it is with trying to unlock the mysteries of meteorology. Odds improve with data accumulation. But there will always be some things that are unknowable, some contributing factors that will be unavailable to even the most careful of observers.

Ever walk through a cool spot in front of a window and get the sensation that cold air was wafting toward you? So long as no actual draft existed (that is, so long as there were no gaps around the window frame that permitted outside air to infiltrate), the sensation was an illusion.

Physics tells us that heat always transfers -- by conduction, convection, or radiation -- from warmer molecules to cooler ones. That means that what you actually experienced was counter-intuitive: you didn't feel cold coming toward you; you felt heat leaving your body, as it was being drawn toward the chillier window pane.

The "seems like" validity that sometimes holds up well in helping us to understand underlying notions of simple economics, of basic algebra, and of rudimentary physics at other times fails us completely. And so it is with people. There are no easy ways for us to quantify, to understand, the complex behaviors of our fellow humans.

In judging the actions of others, then, I have learned the hard way that it is sometimes best to cut people a little slack. Like icebergs that float ominously in the Earth's coldest waters, too much information is unavailable. In such cases, "what you see is [not necessarily] what you get."

Though I'm not much for New Year's resolutions, I will try to keep that simple truth in mind in 2006. If I don't, you remind me, hear? And, when you do, knock hard and talk loud; my noggin is pretty thick. I calculate your probability of successfully breaking through at 60%. But, hey, that's a definite improvement over 2005.

Now, let's get down to it. Just what am I going to have to do to sell you a tasty beverage today? I can cut you a rock-bottom price on a refreshing glass of lemonade, seein' as how it's the off season. On the other hand, if you'd prefer a delicious, steaming cup of hot chocolate (hold on a sec while I check the outside temp ...yes!) that'll run you a tad more.