all solids, only looks solid to the human eye. In fact, at the atomic level it’s mostly empty space, and the neutron can travel a long way before it encounters the nucleus of another uranium atom. In a small piece of uranium—say, half a kilogram (about a pound)—the chances are pretty good that the neutron will never encounter another nucleus, and will instead fly all the way out of the piece of uranium, and just keep going. But if the piece of uranium is just a little bit bigger—say, a kilogram—the chances are a fair bit higher that the neutron will smash into the nucleus of another uranium atom. That nucleus then disintegrates, and, it turns out, releases three more neutrons. Now there are four neutrons whizzing through the uranium—it’s four because we need to include in our count the original neutron that started the process, which continues to move, even after smashing into the nucleus. Each of those neutrons is, in turn, likely to smash into four other nuclei, with the result that 16 neutrons are now on the loose. They are likely to crash into still more nuclei, and things rapidly cascade out of control: after 40 collisions like this, we have a trillion trillion neutrons whizzing around. It’s because of this incredibly rapid rate of growth that the process is called a chain reaction. Below a certain mass, called the critical mass, a piece of uranium is simply an inert lump of rock. Atoms inside are occasionally decaying and releasing neutrons, but for each such neutron the average number of so-called daughter neutrons caused by further collisions is less than one, and any possible chain reaction quickly dies out. But with just a slightly larger piece of uranium, larger than the critical mass, the average number of daughter neutrons is slightly more than one. And if the average number of daughter neutrons is even a tiny bit larger than one then the chain reaction will take off, and cascade out of control. If the average number of daughter neutrons is 1.1, then after just 200 collisions the uranium will have more than 100 million neutrons flying around inside, causing still more collisions. This is why two apparently similar pieces of uranium will behave in completely different ways. One will lie inert, while another just slightly larger piece will explode with the force of thousands of tons of dynamite. A small increase in size can cause a complete qualitative change in behavior.
Something similar goes on in a good creative collaboration. When we attempt to solve a hard creative problem on our own, most of our ideas go nowhere. But in a good creative collaboration, some of our ideas—ideas we couldn’t have taken any further on our own—stimulate other people to come up with daughter ideas of their own. Those, in turn, stimulate other people to come up with still more ideas. And so on. Ideally, we achieve a kind of conversational critical mass, where the collaboration becomes self-stimulating, and we get the mutual benefit of serendipitous connection over and over again. It’s that transition that is enabled by designed serendipity, and which is why the experience of designed serendipity feels so different from ordinary collaboration. It occurs when collaboration is scaled up, increasing the number and diversity of participants, and so increasing the chance that one idea will stimulate another new idea. In the Polymath Project, for example, Tim Gowers commented that the main thing that sped up the process was that he and other participants often “found [themselves] having thoughts that [they] would not have had without some chance remark of another contributor.” In Kasparov versus the World the same thing happened, with an idea from one team member often sparking ideas from others, enabling the World Team to explore many different directions.
Of course, the chain reaction model shouldn’t be taken too literally as a model of collaboration. Ideas aren’t neutrons, and the goal of collaboration isn’t simply to go “critical,” producing a rapidly ballooning number of ideas. We need to, at least occasionally, have the right ideas,