Footpathology

April 10, 2010

Why do footpaths not go in straight lines ? But first the prologue…

I had the pleasure of returning to Leicester this week, where many moons ago I did my PhD.  Luckily it was indeed a pleasure as the PhD thesis I went to examine was v.good. (Well done Agnese.) Others who want to indulge in Leicester Space Physics nostalgia will want to be going to the groovy Leicester-50 Extreme Universe Conference.  Of course I have been back to Leicester many times, but for some reason I had not for many years found myself approaching the University by foot from the Victoria Park side, as opposed to from the centre of town, or by taxi from EMA. As I approached I had an odd twinge of nostalgia for a footpath I used to follow every day – but it had disappeared, to be replaced by a proper paved path with trees and stuff.

The old path, created organically by thousands of student feet, used to fascinate me – because it was very narrow, less than the width of two feet – and because it did not go in a straight line, but rather a kind of graceful swerve. Why ?

Most people I ask say, well, everybody follows the path, Andy. But they don’t. (Or rather didn’t). I would watch people walking across the park (is that sad ?) and very few were on the path. They tended to walk somewhere near the path, but few people were right on it. I would say the FWHM was about twenty feet. Nontheless walkers are guided by the central narrow path of course, so statistically that central patch gets trodden on more.  So why is the worn patch so narrow ? I guess it has to have something to with the physiology of grass, or the stability of roots. Somehow the probability of grass destruction must be a very non-linear function of grind frequency. So this aspect – the narrowness of the path – seems fairly obvious at first, but highly non-obvious in detail.

So what about the graceful swerve ? Two possibilities come to mind.

The first is that it is determined by features in the environment. Now Vicky Park is completely flat. We are not talking about following topology, or minimum energy paths etc. As you set off, you don’t know the globally optimum path. So why isn’t the result random ? Maybe just everybody thinks “I can see the Charles Wilson building, I’ll head towards that”, and then halfway across thinks “hang on, I can see the gate now, better swing left”.

The second possibility is that starting direction is actually random, but chance concentrations in a particular direction get re-inforced as the grass starts to wear. This is rather like forming large scale structure in the galaxy distribution by the growth of random fluctuations.

Those two possibilities must in principle be testable. In the first case, the graceful swerve would be the same every year. In the second, a new path would form each academic year : the average would be a straight line, but each individual realisation would be a wiggle. Maybe rather than a new path each year, the path could meander from month to month. That brings us back to biology – what is the grass recovery timescale ?

Anybody know the answer ? Sounds like a good research project. Too late for Vicky Park, but there must be countless other examples around, and people who have thought about this seriously. Google failed me but maybe I didn’t try a cunning enough search. Gordon Stewart told me thought there was some scholarly study somewhere, but he couldn’t remember where…