Induction Junction, What's Your Function?

I’m feeling much better after my two-week break. I still haven’t taken a break from trying to fix the world’s problems. It’s just that the problems seem to have become much simpler and easier to distribute. I will explain.

At the end of my break, my Dad and I were talking on the phone. He said, as he sometimes does, “Son, you don’t have to solve all the world’s problems.” He’s right, I don’t have to solve the world’s problems. I only have to find a single solution for each of the world’s problems, and then show that the solution is generic to that problem.

In mathematics, this is called “proof by induction”. Inductive proofs were one of the more magical things I studied in university. You start with a seemingly impossible problem, like proving that some equation holds true over an infinite range of input. Sure, you can try the equation out for a few numbers on your calculator, and see that it works, but how do you prove that it works for all infinity?

The first thing you do is throw away the hard problem and start with something much simpler: showing that the equation holds true for a single number. This usually would take a few seconds – plug in some simple input, like “x=1”, and see that the equation balances. Next, you solve a second problem: if the equation holds true for one number, then it must hold true for its neighbor. This is generally more difficult, but not infinitely so. Now, once you do these two simple things, you’ve achieved the impossible, and proven the equation over all infinity! Every number is a neighbor to two other numbers, and all together they create an infinite chain of solutions.

The same thing works in real life. Take the transit system of Curitiba, Brazil. The residents had to solve the problem of achieving subway-like mass-transit on a shoestring budget. The solution, called “Bus Rapid Transit”, indeed moves almost as many people as a subway system would, but for 1/10th the price. Curitiba proved that the solution would work for a single case. Since then, many people have described the aspects of the Curitiba system which make it a generic solution, and hundreds of similar systems have been built around the world. It was Curitiba's example which inspired both Bogota’s “TransMilenio” system and Vancouver’s “B-Line” system. BRTs have become a solution by induction.

To sum it up, Worldchanging Induction works like this:

1. Find something broken somewhere in the world and fix it, for just one specific case.

2. Prove that there is nothing special about your solution which makes it work technically for only the specific case you have solved. In other words, if your solution works for the case you solved, it will work for its neighbor.

Once you do these two things, “impossible” becomes merely a political statement.