Category Archives: Statistics

The Go No-Go Decision

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imagesSomebody decided to turn the world into ones and zeroes, and thus began the digital revolution.   Such a simple idea.   It’s either this or that.   Maybe the world really is black and white.   Maybe that whole idea that I have lived by all these years, that life is really analog, that understanding others and oneself is all about appreciating the subtlest shades of gray, the overlap between good and evil, the mysteries residing in the spaces between the lines, the sweet paralysis of ambiguity—maybe I had it all wrong.

Maybe the analog life is the illusion after all.   It really is now or never, and the hackneyed question “if not now, when?” really has currency.  Life would be so much simpler, wouldn’t it, if a person was all good or all evil, or if you are either in love or out of it, and if there really were only two sides to every story.   After all, it is probably indisputable that a person can’t be in two places at the same time, unless of course you’re struggling with one of Zeno’s paradoxes, in which case you might dispute the notions of place and time altogether.

Pilots call it the “go-no go decision.”  You either takeoff or you stay home.   It’s that simple.   As the paean to binariness that Rosie taught me goes: whether you like the weather you got, you gotta have weather, whether or not.  And if the weather is good enough, the airplane is working correctly, and you are physically and mentally capable, you go.   You crank up that engine and open the throttle and start rolling.   Or else, you go home, open a bag of potato chips, and watch TV or read a book. It’s that simple.   Ones and zeroes.

Now, I have nothing against ones and zeroes themselves; in fact, the invention of the zero, probably by ancient Olmecs in Mexico, is a milestone in mathematical history.   Even the ancient Greeks, who came later, struggled with the concept, wondering how nothing can actually be something, a question which many self-doubting adolescents ask themselves daily.

The notion of one, and its philosophical sibling oneness, is perhaps the biggest concept of all.   I would go so far as to say that the number one is like my friend Stephanie’s cheesecake– which is so delicious that it’s probably too sinful to eat, in that the number one is so profound that it’s probably too sinful to even talk about. It is, in Judaism, arguably the definition of God itself, in that every Jewish house has a little scroll wrapped up in a decorative case and affixed to the door that starts with the words—printed in larger type than the rest of the biblical excerpt: “Hear oh Israel, the Lord is God, the Lord is One.”   “Is” is the verbal representation of the mathematical “equals” sign, which is to say that, based on the principle of commutation, the Lord, God and the number One are all the same.

But while I have no problem with ones and zeroes, I also really like a lot of other numbers.   Thirteen, for example, has always been lucky for me.   Three is particularly romantic, and frankly quite mystical, being associated with the holy trinity and managing to represent both three gods and one simultaneously, while a lot of people believe that the third time you do something is “the charm.”

The magic of the digital revolution, I suppose, is the particular kind of alchemy that arises by stringing a bunch of ones and zeroes together into a byte, which as all you computer geeks know is eight bits.   A bit is a portmanteau for “binary digit,” which is generally coded as a one or a zero.   When you string together eight ones or zeroes, you can create all the letters of the alphabet, and a whole lot more.   But in order to do that, you are still bit-dependent, and so you still, ultimately, exist in a reductionistic, binary world.   No computer geeks worth their weight in kilobytes will tell you that the number eight is magical, because they know that it all really boils down to stringing together a series of binary digits.   Binary is where it’s at.

So the fact that you can perceive color or shades of gray on a computer screen is really an illusion based on making ones and zeroes dance to a programmer’s tune. Perhaps the purple salvia, brown rocks, light green and yellow leaves on the koelreuteria tree outside my window are all an illusion too, constructed out of bits of ones and zeroes, a carbon atom here or not, a bit of silicon or an empty space. Maybe the yearning to see my kids, the anticipation of an adventure, or the thrill of my airplane lifting off the earth is nothing more than a series of ones and zeroes, an electron jumping from one neuron to another or not.

I am, after all, either going to stop writing this now and check my email, or continue.   I am going to pour another cup of coffee before it gets too cold in the press, or not. I am going to face the chill of this Monday morning and get my ass off this chair, or I am going to sit here longer and try to craft something that you will enjoy reading, or I am going to get off my ass and unpack the backpack full of hopefully income-producing paperwork and have at it or not.   It’s go or no-go, now or never, this or that, yes or no.   The rest is an illusion.

 

 

 

 

 

 

 

The Big Sky Theory

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mathOn any given day, there are about 87,000 flights undertaken, and at any single moment, there are between 5 and 10 thousand airplanes (commercial and private) in the skies over the United States alone. According to the FAA, on an average day, controllers handle 28,537 commercial flights, 27,178 private flights, 24,548 “for hire” flights, 5,260 military flights, and 2,148 cargo flights.   And these numbers don’t include private pilots who choose not to talk to ATC, as I often do when out cruising the neighborhood or when flying around non-towered airports.

There’s so many airplanes up there at once it’s a wonder they don’t bump into each other more often.   They don’t, it seems, because relative to the sheer volume of atmosphere in which they fly, all those airplanes actually don’t take up a lot of space.   The relative volume of airplane to the volume of sky in which they fly being the reason that they don’t bump into each other more often is called the “big sky theory.”     And statistically, given the ratio, the chances of one airplane bumping into another should be close to zero.

But although it is happening less and less, it does happen, roughly a dozen times a year, especially in crowded airspace (such as busy airports) where airplanes are more likely to converge. The big sky theory, it appears, doesn’t work that well, because the statistical probability of it ever happening is very close to zero.

Once, at a party in the living room of the Victorian house I was renting as a student with several roommates in Santa Cruz, California the math instructor and brilliant folk music satirist Tom Lehrer entertained us by demonstrating statistically that it was impossible to get wet when walking through the rain.   Perhaps it was the blackberry brandy that mysteriously found its way from a bottle in my back pocket to my tummy that prohibited me from understanding the arithmetic, but his statistics appeared impeccable and his argument was compelling.

Now, I may not be able to tell you the formula for chi-square off the top of my head, but I can work my way around ANOVAs, MANOVAs, and one of my favorite statistics (and Russian movie stars)—ANACOVAs, with fluency. Compared to highly trained academic statisticians, I still sit at the kid’s table, but I retain some perhaps egoistic pride in my ability to do discriminant function analyses, and I can work my way around most research articles I read.

The big sky theory doesn’t work for similar reasons that you really can’t wet when walking through the rain.   It is very easy to misunderstand (to be generous) or deceive (to be cynical) with statistics.   (I am fond of “proving” to kids that I have 11 fingers by counting down from 10 on one hand and then adding five when I get to the other.)

That is why Joel Best’s book “Damned Lies and Statistics” and its subsequent editions should be required reading for anyone who reads anything, pretends to know something, and hasn’t studied statistics. It should also be required reading for journalists, with whom I have particular antipathy for perpetrating the most heinous of statistical misstatements.

Theories can be extremely convincing, especially when backed by statistics.   As an autism “expert,” I once described in detail the theory behind how the preservative thimerosal, used in the MMR vaccine, can cause autism.   I had a room full of family practice residents convinced, possibly because I sprinkled the explanation with statistics. (The proportion of thimerosal in vaccines, the multiples of mercury based on the FDA’s own limits of safety, the correlation between mercury poisoning and autism symptoms, etc.)   The theory can be made to look rather compelling, but it’s just wrong. These residents were smart cookies, but I could have just as easily convinced them that I had 11 fingers.

One of the many problems with statistics is that it is a very poor method for predicting low-frequency events, such as rain in California, earthquakes, violent behavior, or midair collisions. It is nearly impossible to account for all the variables required for a low-frequency (or extremely complex) event to occur.

The driveway to my domicile is located a half-mile up from a highway.   Although I typically drive that half-mile slowly, the other day I had to swerve to avoid a squirrel that decided to dart in front of my car.   Sadly for both me and the squirrel (but mostly the squirrel), we collided. If I had to create a statistical model that would attempt to predict the likelihood of me colliding with a squirrel down that half-mile stretch of road, I can assure you that it would reveal that colliding with a squirrel could not happen in thousands of lifetimes.   Statistics, it seems, cannot take into consideration the notion that squirrels appear to have a robust death wish, or have a secret ritual in which the transition to adult squirrelhood is marked by darting across a road in front of Lexus crossovers with balding drivers.

So, you see, it isn’t that difficult to prove, statistically, that it is nearly impossible to get wet when walking in the rain.   And really, it should never be necessary to look out your window when piloting an aircraft because the chances of bumping into another airplane are infinitesimal.   If you believe the statistics, that is.