In over twenty-five years of professional travel across the United States and the world, I have learned a few things, sometimes by experience, that have proven useful. They include
- If you can't lift your packed bags, discard things until you can, then repack. (Alternatively, visit the gym and work on your upper body strength. But – and this is really important – it must fit in that overhead compartment.)
- Checked baggage follows its own itinery, which only loosely resembles that of its putative owner.
- You can get a long way with a smile, pointing and gesturing, and the words "please" and "thank you" (even if they're the only words you can speak in the local language).
- If "please" and "thank you" seem overly limiting, learn how to say, "Sorry, I'm an idiot" or even better, "Sorry, I'm a dumb American" in the local vernacular. They have done wonders for me.
- You will get lost; it's part of the adventure, and you should try to enjoy it. (Remember, being lost and not knowing where you happen to be at the moment are not the same thing.)
- People really and truly are the same everywhere, with the same hopes and fears.
Integers and Reals
Despite the deep and broad similarities that transend regional and national cultures, uniting us as humans, I have observed wide variation in one one deeply individualistic trait. The frequency of this trait widely varies across regions of the United States, across countries and across cultures; it is preponderant in some, rare in others, but present everywhere. I speak, of course, about our philosophical approach to driving motorized vehicles.
I call the two extrema of this trait the integers and the reals, though there is a continuum between. Thought I have lived in both worlds, a deep chasm separates those who reside in the land of the integers (and who believe deeply in an integral number of lanes in the road) from the residents in the land of the reals (who believe equally deeply in a continuous, highly fluid number of proximate driving lanes).
The resident of integer land believes the road lane markings were created for good reasons, by thoughtful and knowledgable road engineers and government officials. Accordingly, they must be obeyed carefully, diligently and duitifully, even if there are no pedestrians or other motorized vehicles within 50 kilometers. Rules are, after all, rules, regardless of context, and they must be obeyed.
Conversely, the resident in real land believes equally passionately that lane markings were created by distant and uncaring bureaucrats who lack concern for the personal exigencies and superior skill of the vehicle driver. Accordingly, the markings are the merest suggestion that need not, indeed should not, interfere with the drivers freedom and flexibility. Indeed, even the sidewalks, should they exist, are available for use by vehicular transport, even if pedestrians might otherwise occupy them.
In integer land, the road lanes are discrete and denumerable, and traffic moves in integral multiples of lanes, with a one-to-one mapping of traffic steams to lanes. In real land, the road lanes are uncountably infinite, with a potentially unbounded number of traffic steams mappable to a single lane. Cantor would have been proud. (If you were wondering, you just experienced an example of situational learning, complete with set theory, an allusion to a diagionalization proof that the reals are uncountablly infinite, and a pointer to one of history's great mathematicians. Now back to our regularly scheduled programming.)
Many years ago in Canada, while attending a conference in Banff, Alberta, I was strolling down a street, taking in the scenery and architecture. I stopped at an intersection and waited for the light to change (this alone pegs me as an undisputed resident of integer land). I stepped off the curb with one foot, and then paused when something in the sky caught my eye. After a few moments, the silence interrupted my reverie, and I realized – to my chagrin – that I had paralyzed traffic at the intersection. With nary a car honk, the Canadians were waiting patiently for me to make a decision and move, for pedestrians always have the right of way. This is integer land in its purest form.
In the late 1980s, I was in Jakarta for three weeks to work with the University of Indonesia, as part of a World Bank program. While there, I was collaborating with the computer science faculty on curriculum issues. (I am delighted that one of my former Ph.D. students from the University of Illinois, Bobby Nazief, is now a member of that same computer science faculty and a senior IT advisor to the Minister of Finance in Indonesia.)
While in Indonesia, I stayed at the Hotel Indonesia in central Jakarta. Yes, it's the hotel that was famously the source for scenes from the Year of Living Dangerously book and movie. I had a truly delightful time in Indonesia. The people were incredibly friendly, the scenery was beautiful and food was fantastic – I learned to love nasi georing in all its forms.
After years spent living in the midwestern United States, though, I had become accustomed to the prairie, with open roads laid out on one mile squares. When I first stepped outside the hotel in Jakarta, I was both exhilarated and terrified by what I saw. (I was young and naive.) The traffic pattern looked like Brownian motion, but of course it was really a biased random walk – the steps were small but finite, and the vehicles were diverse.
(Ah, another teachable moment, Brownian motion is the continuous limit of a random walk, as the step size approaches zero. I have always loved the fact that the limiting probability of return to the origin is unity for one and two dimensional random walks, a result Polya proved many years ago. Here ends the second lesson.)
Drivin' the U.S of A.
Then there is my own, my native land, filled with integers and reals. We have the Boston left turn (edge into oncoming traffic, forcing it to stop, and then turn left) and the Michigan left turn (You wish to turn left, but all lanes are going right. You turn right, go one or two blocks, make a U-turn left, then you are pointed in the correct direction).
We are also blessed with the New York traffic jam, where you can learn English phrases that would make your mother cry and a Navy veteran blush. At the other extreme, we have the western states where the roads are straight and flat until they intersect the horizon, and drivers risk falling asleep because there are so few decisions to make.
Then there is Chicago, in my adopted home state, where you sometimes cannot even see the lanes due to the ice and snow. If it's Chicago and driving, you have to remember Jake and Elwood Blues and their "mission from God." You know where I'm going – work with me, here. Elwood says, "It's 106 miles to Chicago, we got a full tank of gas, half a pack of cigarettes, it's dark, and we're wearing sunglasses." Jake replies, "Hit it!" Prison, not surprisingly, followed.
Finally, there is Seattle, my current home. It's a place with lots of water and not enough bridges. Traffic backs up for miles on the bridges from Seattle to the eastside – Bellevue and Redmond – in ways that some days make the seven Bridges of Königsberg problem seem simple by comparison.
Look at the road ahead. Do you see a countable number of lanes or a continuous surface? Does your heart beat faster at the prospect of competition, or do you hope for carefree, laminar flow?