The mathematical formula that proves London is over

Some years ago, an Australian neurologist was in the habit of walking barefoot across his lawn. This being Australia, the lawn was slightly prickly, and the experience was painful but not intolerable; until one day, when one of the pricks in his heel was more pronounced than usual. He had been bitten by a snake and, again this being Australia, the snake was highly venomous. Doctors saved his leg and he made a complete recovery. But there was one lasting side-effect: he now found walking across his lawn agonising.

In terms of the stimulus to his feet, nothing had changed. What had changed was how his brain processed the stimulus. What was once a mildly aversive discomfort was amplified by a learned fear into something much more painful.

My contention is that a similar mental process may have taken place in relation to many forms of travel, especially commuting. The daily grind of the journey to work wasn’t quite so onerous when you saw it as unavoidable; but after two years spent learning of easier alternatives, our reaction to the pain and cost of commuting every day has gone from grudging acceptance to extreme irritation.

I would be surprised not to see an exodus from megacities over the next few decades. But this isn’t only driven by psychology: it’s driven by pure mathematics. Let me explain.

First, there’s that old chestnut A = πr2. Area increases exponentially with distance. Within one mile of work, there are three and a bit square miles of space available. Within 100 miles, there are 31,416. The odds of finding somewhere affordable and pleasant increase enormously with distance.

But there is also the Sutherland number.