Wednesday, 6 August 2014

The geometric dog days of summer

The phone doesn't ring. Insects buzz through an open window. There's almost no traffic in town. Why does work feel more futile than usual in August?

Why don't business networks take off until they reach a certain size?

What have these got to do with each other? The effects of arithmetic versus geometric progression.

I run Principle Six co-operative business referral events, where people fulfil other network members' business 'asks' by making third party introductions to people from their own contact book.

If, every time a networking group added a new member, the number of referrals increased by the same amount, that would be a 'straight line', or arithmetic, progression. Let's say there are 10 people in the network, and each of them can make 5 possible referrals. That would mean 50 potential referrals. When the group grew to 6, you'd get 55 possibilities; and when the group expanded to 20, it would make 100 potential connections.

But in fact the progression isn't arithmetic - it's geometric. It goes more like this:

The number of potential referrals in a group of 5 people is represented by the sequence 4+3+2+1 = 10. In a group of 10, it's 9+8+7+6+5+4+3+2+1 = 45. On the same lines, for a group of 20 networkers it's 190, and for 40 it's 780. In other words, every time the group doubles in size, the potential benefit to the members increases roughly fourfold. And actually the number of potential connections in a group of 40 isn't 780, it's more of the order of 10,000.

A business network of 10 people is not worth the effort. A network of 20 is the minimum you really need, and 40 is probably ideal if you want the members to know each other and create lots of business interactions and opportunities.

The geometric principle also works in reverse. In August, when a quarter of the workers disappear to the beach or the park, the world of work seems to slow to a special grind. Those of us still toiling wonder what we're doing. The workers' battlecries "Never work!" and "Sous les pav├ęs, la plage!" resonate with awful meaning.