When is the last time that you wrong? Hugely, spectacularly wrong?

I’m wrong a lot. I’ve learned to live with it. Here’s an example of one of my biggest mistakes – the fundamental premise in my PhD research was completely wrong!

I had an idea when I read a paper by M. Angeles Serrano and Marian Boguna called Topology of the World Trade Web. In it, they showed that if you mapped international trade as a network, with countries as the nodes and trade relations as the links, it was a complex network (see Greg Satell’s excellent discussion of networks for more information on the basics of network analysis). I saw this, and I thought that if you could map international trade as a network over time, then that would be a great way to try to measure the impact of globalisation. After all, we all knew that globalisation was changing the fundamental structure of the international economy, right?

So that’s what I did for my PhD. I found international trade data from the International Monetary Fund that went back to 1938, and I mapped the networks as they changed over time. One of the key measures in all of this is In-Degree. For any particular country, this measures the number of other countries that send a significant percentage of their exports to that country. If you are an important trading partner for many other countries, your in-degree will be high. If few countries export goods and services to you, your in-degree will be low.

One of the important measures of the overall structure of the network is the distribution of degree. This is what the distribution of in-degree looks like from one of my sample years:

This shows that most countries have a very low in-degree. The majority of countries are clustered in the 0-5 range. In other words, the majority of countries in the international trade network are important trading partners for very few other countries. At the other end of the spectrum, you can see that a handful of countries have really big in-degree values on the right side of the graph. These are the hubs in the international trade network – countries like the US, UK, Germany, and Japan.

The physicists that started this line of research usually convert these histograms into a chart that shows degree probability distribution functions. This is what the PDF for the 1938 world trade network looks like:

Here’s where I was wrong. I thought that the shape of this distribution should change over time. We hear two stories about globalisation. The first is that everyone is trading with everyone else now. If that is the case, the degree distribution of the international trade network should be changing to more closely resemble the shape of the curved line in this figure:

However, other people say that globalisation leads to the rich getting richer. If this is true, then the shape of the degree distribution line should be changing to be more like a straight line – more closely resembling one of the lines in that figure.

I was pretty certain that my study would prove that one of these assertions was correct.

Here is what I found – this is the degree distribution of the international trade network as it evolved from 1938-2003:

What that shows is the shape of the degree distribution hasn’t changed at all. The lines have shifted to the right a bit as the number of countries in the network increased from about 100 to around 200, and that’s the only real change.

I was completely, totally wrong about the impact that globalisation would have on the structure of the overall network.

I was able to get a PhD out of that because that’s actually an interesting finding in and of itself (and I did a fair bit of work investigating other aspects of the network that have actually changed). But the core hypothesis that I had at the start of the research was wrong.

I thought of this when I was reading Where Good Ideas Come From by Steven Johnson. It’s a fantastic book. He includes one chapter discussing the importance of error in innovation, which includes this quote from William Stanley Jevons:

It would be an error to suppose that the great discoverer seizes at once upon the truth, or has any unerring method of divining it. In all probability the errors of the great mind exceed in number those of the less vigorous one. Fertility of imagination and abundance of guesses at truth are among the first requisites of discovery; but the erroneous guesses must be many times as numerous as those that prove well founded. The weakest analogies, the most whimsical notions, the most apparently absurd theories, may pass through the teeming brain, and no record remain of more than the hundredth part.

In other words, to be innovative, we have to be wrong a lot. Being wrong is the first step towards being right.

Don’t hide your mistakes, learn from them. If every idea that you try works, it’s a sure sign that you’re not trying enough ideas.

When was the last time that you were massively, gloriously wrong?

Note: I’ve got a couple of papers close to publication on this topic, but if you’d like to see it all explained, you can take a look at this conference paper from a few years ago.