Trust the Germans to make a precise estimate: dogs deposit 55 tonnes of proprietory end product on the streets of Berlin every day. The average deposit per lowering of posterior was taken to be 183.3333 grams. On that assumption, the number of spontaneous deposits per diem comes to be 300,000. Berlin’s human population was 3.45 million. So there was a canine for every 11.5 humans.

Berlin has vast forests, not to mention miles of sewers underground. But it is so well administered that a stray dog has not been sighted in recorded memory. So it is inconceivable for any dog not to belong to a human. Nor is it possible for an integral dog to belong to a fractional human. So at least 3.15 million Berliners must lack canine company; multiple ownership would raise the figure. This gives an idea of how far the 55 tonnes of posterior produce could be raised; if every Berliner, male and female, adult and juvenile, exercised his or her right to a dog, the daily deposition would increase to 632.5 tonnes. This should be perfectly acceptable in an efficiently administered city. But even the capital of Europe’s richest country cannot afford to remove the mean 106.392 kilograms deposited per square kilometre of the city. For it sweeps its streets only once a week, on days determined by rotation. When it does sweep them, it does probably remove the entire 385 tonnes of weekly canine output. But for six intervening days, the possibility of contact between such elimination products and human feet cannot be eliminated. No doubt, the contact is often between a dog’s output and his or her owner’s foot, to which no one can object, least of all the owner; a dog would not object in any case, irrespective of whether the contacted person owns him or her or not. But it is impossible to ensure a perfect correlation between pedalian contact and canine ownership; in fact, the probability of their coincidence in such a populous city could be as low as 0.289855 per trillion. These numerical considerations make human intervention essential to ensure the earliest possible removal of canine excreta from the streets.

Berlin surveyed cities that it considered its comperes in administration, and liked London’s creation of open, sand-covered canine toilets, which cleverly exploited dogs’ affinity to other dogs’ posterior creations. But whilst dog toilets were appropriate for public parks, the competition between them and pedestrian space on streets was too great. So the Berlin local authority called a conference, and on the basis of scholarly papers there presented, erected dispensers for dog poop bags in strategic locations. They were effective. But a sufficiency of bags would cost five million euros a year — a sum the municipality is reluctant to spend although it collects twice as much from dog licences. It continues to be open to bright ideas.