Why the grass is greener
By Lewis Dartnell
Centre for Mathematics and Physics in the Life Sciences and Experimental Biology (CoMPLEX), University College London, UK.
Introduction
Summer is rubbish for two fundamental reasons. One: wasps set about stinging anything with two legs without doing anything useful with their time like making honey or pollinating stuff. Two: girlfriends always want to go off on picnics.
Avoiding having to eat al fresco was the sole reason our ancestors stopped messing about in trees and found some good caves instead. Picnics are inherently stressful; the apple juice invariably leaks into the bag, the sports section blows away, and it is always impossible to find a spot good enough to settle down on.
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But I can now reveal the facts behind this illusion, and help spare you picnicking anguish. It’s all to do with selective biases, which are also lurking behind other annoyances like always seeming to be in the wrong queue at a supermarket or the slowest lane in a traffic jam on the motorway.
Method
Grass is not distributed uniformly and there are often scattered patches of bare earth, especially if everyone else has recently been blackmailed by their girlfriend into going for a picnic and the park/unspecified recreational land area is becoming scuffed and worn out.
The majority of these bare patches vary in size from 5cm in diameter to around 15cm, with the larger examples in this distribution being disproportionately disruptive of a pleasant dining experience.
Other important parameters are the mean height of blades of grass, taken here to be 5cm, and the height above ground of an average person's eyes, taken to be 160cm. Figure 1 schematically represents the scenario facing a picnicker during the site-hunting stage.
The situation depicted is the limiting case, where an unsightly patch of bare earth just remains hidden from view by blades of grass. If the observer advances any closer then the patch will no longer be completely occluded by grass, and will become apparent to the prospective picnicker as an ugly spot of mud in an otherwise blemish-free area of grass.
Figure 1. The limiting case for seeing a patch in the grass, illustrating the despair horizon.The geometry of this limiti