Math, how I love you, let me count the ways

Steven Strogatz is a new columnist for the NYT, and he talks about math and its conceptual foundations.

Sweet!

Here's a couple excerpts of his general awesomeness:

[from "Math and the City"]
"The mathematics of cities was launched in 1949 when George Zipf, a linguist working at Harvard, reported a striking regularity in the size distribution of cities. He noticed that if you tabulate the biggest cities in a given country and rank them according to their populations, the largest city is always about twice as big as the second largest, and three times as big as the third largest, and so on. In other words, the population of a city is, to a good approximation, inversely proportional to its rank. Why this should be true, no one knows...
Keep in mind that this pattern emerged on its own. No city planner imposed it, and no citizens conspired to make it happen. Something is enforcing this invisible law, but we’re still in the dark about what that something might be."

[From "Like water for money"]

"In the front right corner, in a structure that resembles a large cupboard with a transparent front, stands a Rube Goldberg collection of tubes, tanks, valves, pumps and sluices. You could think of it as a hydraulic computer. Water flows through a series of clear pipes, mimicking the way that money flows through the economy. It lets you see (literally) what would happen if you lower tax rates or increase the money supply or whatever; just open a valve here or pull a lever there and the machine sloshes away, showing in real time how the water levels rise and fall in various tanks representing the growth in personal savings, tax revenue, and so on. This device was state of the art in the 1950s, but it looks hilarious now, with all its plumbing and noisy pumps...
Though it’s tempting to view the Phillips machine as a relic of a bygone era, in one way it’s just the opposite; there’s something about it as fresh as the day it began gurgling. Look at its plumbing diagram. It’s a network of dynamic feedback loops. In this sense the Phillips machine foreshadowed one of the most central challenges in science today: the quest to decipher and control the complex, interconnected systems that pervade our lives."

[From "From fish to infinity"]
"As adults, however, we might notice a potential downside to numbers. Sure, they are great time savers, but at a serious cost in abstraction. Six is more ethereal than six fish, precisely because it’s more general. It applies to six of anything: six plates, six penguins, six utterances of the word “fish.” It’s the ineffable thing they all have in common."

[From "The enemy of my enemy"]
"Still, many of us haven’t quite made peace with negative numbers. As my colleague Andy Ruina has pointed out, people have concocted all sorts of funny little mental strategies to sidestep the dreaded negative sign. On mutual fund statements, losses (negative numbers) are printed in red or nestled in parentheses, without a negative sign to be found. The history books tell us that Julius Caesar was born in 100 B.C., not –100. The subterranean levels in a parking garage often have names like B1 and B2. Temperatures are one of the few exceptions: folks do say, especially here in Ithaca, that it’s –5 degrees outside, though even then, many prefer to say 5 below zero. There’s something about that negative sign that just looks so unpleasant, so … negative."