#### 20 Jul 2006 apenwarr»(Master)

Brooks' Singularity

In The Mythical Man-Month, Fred Brooks explains that the amount of communication necessary for a project time is n(n-1)/2, where n is the number of people on the team. Eventually, the communications effort begins to overshadow the actual productive effort. This is the primary factor limiting team sizes, which is why people start breaking into multiple teams, hierarchies, etc beyond a certain size - hierarchies may not be all that efficient, but at least it reduces the need for huge amounts of communication.

Now, this efficiency decrease is some kind of decaying function. If I add 5 people to a 5-person project, it'll be pretty hard on efficiency. If I add 5 people to 100-person project, I probably won't notice the difference. People tend to focus on the 100-person part of the curve (Brooks did, since he was talking about a massive project at IBM), which is why they summarize Brooks' Law as "Adding manpower to a late software project makes it later."

The converse, of course, is not necessarily true: removing manpower from a late software project doesn't necessarily make it earlier. Wouldn't that be nice!

But what if you tried? Eventually you would get back to the early part of the curve, where n is some small number. What if n=1: you're working all by yourself? Then n(n-1)/2 = 0, with zero communications effort! Awesome! I can get infinite work done in zero time!

Well, no, of course not. When n is large, communications efficiency becomes the controlling factor in your overall efficiency. If you take the simplified formula towards n=0, it will give you a "singularity," that is, a place where the number explodes because you're dividing by zero.

In real life, as the number of people on the project decreases, effects other than communications become the limiting factors. This means that if you're going to try to produce more work with fewer people than anyone else, you will have different problems than everyone else. (Of course, this makes it an inherently interesting question.)

So what are those limiting factors? Well, as a person who has worked on quite a few solo projects, I can give the top two that I've found: first, working totally alone, there's no chance for mutual motivation. Second, you run a greater risk of groupthink effects, where you don't have enough diverse opinions and you might end up going on terrible, inefficient tangents and failing to find anything like an optimal solution. For example, a one-man company run by a programmer will probably lack any business sense, and thus fail to make money even if the programmer is a genius.

What's interesting is that nowadays, smaller teams can produce much more than ever before. That's because something is already mitigating the most serious of these effects. Motivation? Well, if more people can do what they love, motivation is easier. Groupthink? Well, the Internet. QED.

I wonder how far you can take that model?

Side Note

The technological singularity can be expected to follow a similar pattern to what I called "Brooks' Singularity" above. Eventually, we will find out that our formula isn't complex enough and there is a speed-limiting factor on technological progress. Believe it or not, the time between "paradigm shifts" can't actually proceed linearly through zero until it takes negative time to do a shift.

Completely Offtopic

Q: So, how are you feeling about everything that's been happening lately?
A: Um... resigned?