Davide Castelvecchi writes for the Scientific American about how mathematician Timothy Gowers from the University of Cambridge used his blog to crack a complex Naughts and Crosses (Tic-Tac-Toe) problem. In an experiment to see if “spontaneous online collaborations could crack hard mathematical problems,” Gowers and commenters on his blog looked for a simpler proof for the density Hales-Jewett problem, (which asks, in a more complicated way than I am about to, how many squares can be removed from a naughts and crosses grid in N dimensions to make the game unwinnable).
It won’t be surprising to anyone familiar with social media that the answer turned out to be yes, you can crack complicated problems through discussion in a blog post’s comments. In this case, the new proof was derived in six weeks through hundreds of comments and was written up into a paper authored by the collective entity DHJ Polymath.
The methodology will be familiar to many bloggers too:
When trying to solve a problem, mathematicians usually make many failed attempts, in which they try lines of reasoning that can turn out to be “blind alleys,” after weeks or months of work. Often those lines of reasoning that seem promising to one expert look obviously fruitless to another. So when every attempt is exposed to public feedback, the process can become much faster.
Although not groundbreaking, what this experiment does do is throw up an interesting thought about the nature of problems. Castelvecchi draws a distinction at the top of the article between problems like the density Hales-Jewett problem which cannot be solved by breaking work up into smaller tasks, and those that can. In the distributed problem solving world, Galaxy Zoo is a great example, bringing together thousands of people to successfully classify millions of images of galaxies (and that’s just the start of their success!).
But the density Hales-Jewett problem also has key property that makes it amenable to collaborative solving which Castelvecchi doesn’t mention: It is possible to know when you have answered it. That means that there’s a specific end-point to which all participants are heading. Many problems that we seek to solve do not have such a neat solution, but the process of attempting to answer parts of the problem is valuable in and of itself. Wikipedia, for example, attempts to solve the problem of collating and verifying information and although it will never be “finished”, the process results in a very valuable information set. Some problems are even “wicked problems” which change their nature as we try to solve them. Wicked problems, and other problems with no solution, may yet still benefit from exploration.
So, we end up with this handy matrix:
Social media or specialised collaborative platforms can be used to in all instances to help find a solution to the problem, if it is possible to do so. Otherwise, it can at least provide an opportunity to discuss the problem which in itself is a valuable exercise. The only thing that surprises me is that more companies don’t turn to social media, internally or externally, to help them define, discuss and possibly solve business problems.