Complexity_ A Guided Tour - Melanie Mitchell [108]
I will give the last word to physicist (and ahead-of-his-time model-building proponent) Phillip Anderson, from his 1977 Nobel Prize acceptance speech:
The art of model-building is the exclusion of real but irrelevant parts of the problem, and entails hazards for the builder and the reader. The builder may leave out something genuinely relevant; the reader, armed with too sophisticated an experimental probe or too accurate a computation, may take literally a schematized model whose main aim is to be a demonstration of possibility.
PART IV
Network Thinking
In Ersilia, to establish the relationships that sustain the city’s life, the inhabitants stretch strings from the corners of the houses, white or black or gray or black-and-white according to whether they mark a relationship of blood, of trade, authority, agency. When the strings become so numerous that you can no longer pass among them, the inhabitants leave: the houses are dismantled; only the strings and their supports remain.
From a mountainside, camping with their household goods, Ersilia’s refugees look at the labyrinth of taut strings and poles that rise in the plain. That is the city of Ersilia still, and they are nothing.
They rebuild Ersilia elsewhere. They weave a similar pattern of strings which they would like to be more complex and at the same time more regular than the other. Then they abandon it and take themselves and their houses still farther away.
Thus, when traveling in the territory of Ersilia, you come upon the ruins of abandoned cities, without the walls which do not last, without the bones of the dead which the wind rolls away: spiderwebs of intricate relationships seeking a form.
—Italo Calvino, Invisible Cities (Trans. W. Weaver)
CHAPTER 15
The Science of Networks
Small Worlds
I live in Portland, Oregon, whose metro area is home to over two million people. I teach at Portland State University, which has close to 25,000 students and over 1,200 faculty members. A few years back, my family had recently moved into a new house, somewhat far from campus, and I was chatting with our new next-door neighbor, Dorothy, a lawyer. I mentioned that I taught at Portland State. She said, “I wonder if you know my father. His name is George Lendaris.” I was amazed. George Lendaris is one of the three or four faculty members at PSU, including myself, who work on artificial intelligence. Just the day before, I had been in a meeting with him to discuss a grant proposal we were collaborating on. Small world!
Virtually all of us have had this kind of “small world” experience, many much more dramatic than mine. My husband’s best friend from high school turns out to be the first cousin of the guy who wrote the artificial intelligence textbook I use in my class. The woman who lived three houses away from mine in Santa Fe turned out to be a good friend of my high-school English teacher in Los Angeles. I’m sure you can think of several experiences of your own like this.
How is it that such unexpected connections seem to happen as often as they do? In the 1950s, a Harvard University psychologist named Stanley Milgram wanted to answer this question by determining, on average, how many links it would take to get from any person to any other person in the United States. He designed an experiment in which ordinary people would attempt to relay a letter to a distant stranger by giving the letter to an acquaintance, having the acquaintance give the letter to one of his or her acquaintances, and so on, until the intended recipient was reached at the end of the chain.
Milgram recruited (from newspaper ads) a group of “starters” in Kansas and Nebraska, and gave each the name, occupation, and home city of a “target,” a person unknown to the starter, to whom the letter was addressed. Two examples of Milgram’s chosen targets were a stockbroker in Boston