Randomness

Last night, the weatherman told me that the next two days would be warmer than 'normal', with temperatures in the mid-nineties. By that, he meant that the temps would be above the average for this time of year. But, it does beg the question: If the temperature on any given day is above (or below) the average, is it therefore abnormal? If we were to get a string of above average days (say, 10 or so), would that also be abnormal, or is that something we should expect periodically?

Your favorite team has made it to the World Series (or Stanley Cup). You believe them to be the better team, although probably only slightly. Is 7 or 9 games enough to ensure that the better team wins the series? If one team sweeps the series 4-0, is that significant?

You family is uniformly tall. Your uncles are all above six feet, and even your aunts are close. Your grandparents are tall, as is your parents. However, you've topped out at 5'9”. Are you an aberration?

Each of these is an example of a distribution. In statistics, the standard distribution is an even curve around the mean, or average value. There are other distributions that are lopsided, with long tails to one side or the other. However, distributions are difficult to spot in our day to day lives: We have to keep records, and analyze those records to see the distributions, and they way they influence our lives.

Such analysis is the subject of Leonard Mlodinow's book: “The Drunkard's Walk: How Randomness Rules Our Lives.” In it, Mlodinow traces the development and understanding of probability and statistics from the early attempts to pinpoint the locations of the stars to recent studies of sports, finance, and medicine. Recognizing random distributions, and recognizing what they imply (and just as importantly, what they don't imply!) is a valuable skill.

The last example (height) demonstrates regression towards the mean – that given a sampling, even if there are outliers, most of the values will tend towards the mean (or average) value. It is actually important that tall people don't beget ever taller progeny: The human population would polarize to the very tall and the very short! However, the average height for a human male is in the 5'9”-5'10” range, and although the mean may be increasing slightly, there will be a greater concentration of people close to that height, and those very tall (or very short) are the outliers, and having them in your family tree is no guarantee of height.

The bad news on the World Series: If your team were 5% better than the other team (which might actually be unlikely in real life, the two best teams are likely even close in ability!); It would take something like 293 games to ensure that the better team won the majority. Is it possible for the lesser team to sweep the series 4-0? Not only possible, but likely, given to closely matched teams. (Think of flipping a penny: If you flip it enough times, you expect that half will be heads, and half tails, but if you flip it just 4 times, there is a reasonable chance that you will get all heads or all tails: 4 or 9 is just not enough flips to get the statistically expected outcome.)

And the weather? The weather, too, exhibits an even distribution about the daily means, both above and below. Where I live, the weather is regularly up to 10 degrees above or below the mean on any given day: Taken as a whole (365 days per year, 30 years worth of measurements, 10950 measurements total), the first standard deviation is 7 or 8 degrees of either side of the mean, indicating that 2/3's of the days are between -8 and +8 of the average. So, a day 5 or 6 degrees above average? Normal. 5 degrees below? Normal. 9 degrees below? Well...less common, but in something as variable as the weather, I'd say still normal.

In fact, the weather is one of those things that bedevils our senses. We have such short memories (and lives) that it is impossible from an experience standpoint to determine if the weather is warming, cooling, drying, or changing in a meaningful way. Given that the weather swings on a yearly basis over 50 degrees (and often over 30 degrees in a single day), has measured extremes 133 degrees apart, and yet exhibits a smooth yearly fluctuation of averages makes it the quintessential random distribution. As such, could any given year experience a (to our senses) long string of above or below average temps? Absolutely. In fact, as Mlodinow points out, it would be surprising if it didn't.

A Small Price

I stood in the shower, washing away three days' worth of dirt and sweat. Three days' of sunscreen and insect repellent. I wished I could just as easily wash away the fatigue and the bruises from an overloaded pack. As I did so, I contemplated why I would treat my body thusly.

Perhaps it was to experience the world as it was before electricity and the automobiles. To experience the quiet that only happens deep in the wilderness, farther away than the day hikers can go. To hear a rushing waterfall as the loudest sound.

It was to enjoy the smell of trees rather than the smells of industry. To watch the weather unfold, first warming, then cooling. To awake to the sounds of light rain striking the tent, and to rise to see the sun reflected on thousands of water droplets clinging to the grasses and trees of the forest.

It was to go on an early morning hike, and be surprised by, and perhaps surprise, a moose going about her business of eating breakfast. To be still, and watch as she decides we're no threat and lies down. To marvel that so large an animal can become virtually invisible lying just beyond that tree, and wonder at how many others we've missed.

Maybe to hike above timberline, and wonder at the stunted plants that grow in the alpine tundra. To see the jagged peaks surrounding the pass, with their patches of sheltered snow and flowers. To go on a hunt for ptarmigan, camouflaged and hard to spot.

Perhaps it was to observe the tenacity of a young fisherman, as he moved back and forth along the banks of the mountain lake, certain that if only he cast from there, he might get more than the nibble he just had.

It was to lie in our sleeping bags on the ground as darkness descended on a clear night, and watch as the stars appeared, the Milky Way unobstructed by pollution, brightly visible here, a surprising band of light crossing the sky. To watch as the first streaks of the Perseid meteors lit up the sky, amazing in their brightness.

It was to spend three days relaxing, and experiencing the world again through the eyes of a 9-year-old. I've become jaded, and unobservant of various things, but every animal, every plant, flower, mold, every jagged rock and every stream crossing are amazing things. Every bird must be identified, or at least guessed at: “Dad, quick! Give me the bird book again! That was a brown bird with a white tail, it will be in the brown section...” To positively identify some “That was a Hairy Woodpecker”, to leave others for another trip.

To hear the songs of birds unfamiliar, and strain to catch a sight of them in the trees. Then, to hear the sounds known, “There's a robin!” To marvel out how a squirrel runs, or a marmot ambles. To glimpse another moose as she angles up a slope.

A chance to spread the imagination about how each fallen tree got that way. To listen as my son wondered that if only that tree, now caught on another two, had instead fallen with more force might it have caused the next to fall, and the next, spreading in a fan to encompass all the forest like dominoes. To talk with him, no distractions, and strengthen the bonds we have.

A tent that needs cleaning and drying, sleeping bags that need to be hung and aired out.

Clothes that need to be washed.

Fatigue and bruises, dirt and sweat, sunscreen and Deet.

They seem like a small price to pay.