Reinventing Discovery_ The New Era of Networked Science - Michael Nielsen [19]
Can someone help me with this dumb question?
Suppose A = B are the family of sets not including the last element n. Then A and B have density about 1/2 within K Nn,n/2−k/2. (We’re thinking k(n) → ∞, k(n)/n → 0 here, right?) [. . .]
That’s just the beginning of the question; it’s a far cry from “What’s the price of bread?” O’Donnell’s question is far too specialized and context-dependent to be addressed by a conventional offline market. He could, perhaps, have taken out an advertisement in a mathematics journal asking for help, but the bother would have been greater than the benefit. In an online collaboration such as the Polymath Project such a question can occur to someone,be broadcast to other participants, and answered, all within minutes or hours. Online tools thus combine the dynamic division of labor and designed serendipity found in markets with the flexibility and spontaneity of everyday conversation. This combination makes them a big step forward from offline markets, and, in particular, makes them well suited to attacking hard creative problems.
So far I’ve focused on conventional offline markets. Of course, in recent years markets have adopted the internet and other modern communications technologies, and as they’ve done so they’ve changed and become more complex. Increasingly, they too can be used to address very specialized and context-dependent questions. In this sense online tools are gradually subsuming and extending markets. Something similar is also going on in the conventional organizations we discussed in the last section: online tools are increasingly used as the command and control infrastructure in those organizations. And so online tools can subsume and extend both conventional markets and conventional organizations. And, as we’ll see shortly, they can also subsume and extend the third historical form of collaboration, small group conversation. In each case, the online tools are enabling architectures of attention that go beyond what is possible in offline methods of collaboration.
How Online Collaboration Compares to Offline Small-Group Conversation
In many respects online collaborations such as the Polymath Project and Kasparov versus the World resemble offline small-group conversation. As we’ll see, in some ways offline conversation is actually genuinely better than online collaboration, while in other ways, it is distinctly inferior. But before we compare the two, let’s first clear the air by disposing of two common but fallacious arguments that purport to relate online collaboration to offline conversation.
The first fallacy is to think that online collaboration is somehow similar to dreary committee work. Sometimes people hear about a project such as the Polymath Project, and their mind leaps to the unflattering stereotypes we associate with committees—“A camel is a horse designed by committee,” and so on. It’s true that many committees squelch creativity and commitment. But it doesn’t follow that online collaboration has the same problems. When you look closely at projects such as the Polymath Project and Kasparov versus the World, they don’t seem much like dysfunctional committees. Instead, they are vibrant communities filled with creativity and commitment.
How do such collaborations escape the problems of dysfunctional committees? Understanding why some groups work well while other don’t is a complex problem, and I won’t comprehensively address this question here. But there are two powerful factors that help explain why online collaboration often works well where a committee would not. First, committees are often made up of people who’ve been dragooned to sit on them, while collaborations such as the Polymath