Not to cite anyone in particular, but you notice a lot that some people don't want to post on a board because it's dead, and the board is in turn dead because nobody posts on it. I find this effect interesting; and it's understandable: if there's no threads to engage with, there's not much of a reason to go to a board, no?

 

Well, then I asked myself; how would one model expected board speed? How does number of posters affect it? What's the correlation? Of course, posters have very different levels of postings individually: some are prolific, some are more prone to making new threads while others generally just reply – that's a lot of variables. But let's just assume that there's not much difference between bernds, and let's assume that, since bernd doesn't go outside and has a fucked up sleeping schedule, there's no real power hours at any time. (Yes, I'm being a physicist here.) What kind of function of N – number of posters on a board – is posting speed? How does bringing a new poster affect board speed?

 

So, if we assume that all bernds are equally likely to create a thread, and will reply with equal likelihood to what they read (not necessarily reply to everything, just to things they find interesting, or have something to say) – bringing a new bernd over will 1) increase the number of threads (since he is OP of some of them now) as well as 2) increase the number of replies in each thread.

 

But his threads and replies, in turn, also make it more likely for all other bernds to post something: in reply to his posts. So if everyone reads everything and replies to everyone (when applicable) – number of threads goes as N, but number of replies, and thus posting speed grows much faster, since there's not only more posters, but also more content to reply to! Is it N² – N threads times N bernds who might reply? No – each new reply also makes every other bernd more likely to reply!

 

It's an infinite series: if probability of a bernd to reply is p, and if N bernds create N OPs: then there will be N*pN first order replies (N threads, and each of N bernds has probability of p to reply); then there's N*pN*pN second order replies (replies to first order replies), and so on and so on: N + pN² + p²N³ + p³N⁴ + ... = N/(1-pN) (which obviously makes sense only if p<1/N)

 

This has an interesting consequence. While number of bernds is small – the denominator is practically 1, and board speed grows roughly linearly with number of bernds. But as number of bernds approaches critical value: Ň=1/p, the board speed should, in this model, suddenly start diverging towards infinity. (Clearly, this shows that model assumptions are broken.)

 

Well, we assumed that all bernds can read everything, and will reply to everything they feel like replying to: but, can bernd really produce infinite number of posts? Not really: as the number of bernds approaches this critical value, suddenly the board becomes fast enough that there's constantly new posts, and bernds can no longer reply to absolutely everything. At higher speeds, there's not even enough time to read everything bernd might be interested in. But, we have seen that there's a critical number Ň when a board ceases being slow. At that critical number, the board is suddenly fast enough that, no matter when you come, there's new posts being made.

 

The key to getting the board alive is, thus, increasing the number of bernds past this critical number Ň.