Stephen Wolfram, Examples, and Finally Answering the Question: How many miles of paved roads are there?

In a few days I will publish a short comment on the difference between Big Fixes in higher education and Small Fixes. Big fixes are things like policy changes at the federal and state level. When Big Fixes go wrong, there is no way to predict how systems will fail.  No Child Left Behind was a Big Fix, and the damages are still unfolding.

Technology innovations are Small Fixes. I’m not talking about new technology that force-fits a 16th century educational system into a hyper-techno contraption.  I’m talking about innovative things that are not obvious and may not even have an obvious application to education. Most iPad apps are Small Fixes for some bigger problem. Small Fixes are important precisely because you can assemble a lot of them and stand back while some invisible hand fishes out the ones that actually add value. Blogging is a Small Fix for higher education.

I was preparing for a class on nanotechnology a few years ago, and I needed an example to illustrate how much heat would be generated by a wide scale deployment of cell-sized nano-computers.  I wanted the class to calculate the energy dissipation of a film of these little computers on all paved roads in the US. But how many miles of paved roads are there?

I looked through atlases, online maps and more websites for departments of transportation than I care to remember.  In the end I took a stab at it:  2 million miles more or less. It was a case of misplaced priorities.  No one but me really cared what the right number was (or even if there was a right number).  I was anticipating that some wiseguy graduate student would want to know where the number came from.  That never happened.  It was a waste of time.

I was reminded at some point in this literal journey through the back roads of America that my old friend and colleague Alan Perlis had the knack of pulling computational examples like this out of thin air. “How many bricks are there in New York City?” he would ask during an oral exam, and then he would sit back and watch the gears turn. Well-oiled gears would tune in quickly to an interesting line of reasoning.  That was the point.  Not-so-well-oiled gears would cause of a lot of embarrassed thrashing.

I vaguely remember wondering, “What would be the value of being able to create and re-create many examples with a sort of search engine for computational knowledge?” I thought nothing more about it until I stumbled upon WolframAlpha, a “computational knowledge engine” from the company that distributes Mathematica. WolframAlpha is a website, and the first thing you should do when you land there is to type in a question.  So I asked how many miles of paved roads there are in the U.S. You can see the result above. In addition to the answer itself, you get a plausible chain of reasoning that leads you to that answer.

Here is what Stephen Wolfram says about WolframAlpha:

Realistically, though, we haven’t been “discovered” yet in even a small fraction of the areas we cover. We don’t know the whole process by which that happens (and it would make a fascinating study), but somehow, gradually, different areas of Wolfram|Alpha functionality do seem to be “discovered”, and progressively build up larger and larger followings.

This is really the essence of a Small Fix.  Wolfram points out that an engine like this has been the dream of philosophers for centuries.  An “assistant” who assembles knowledge in context. Leibniz’s idea was to accelerate the pace of inquiry. As one of the comments on Wolfram’s blog says:

Every once in a while I can’t help but think that Liebniz must be having a party in his grave!

What impact might WolframAlpha have on education?  Maybe none, but there’s almost no cost to finding out. I can’t help but think that Leibniz would have found a way to say, “Cool!”

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