A stochastic process – with thanks to Charles Dickens

You, dear reader, have been even more than usually patient with me! In these last few posts I’ve been rabbiting on about things that seem at first sight to have precious little to do with walking. For example, (1) spatial patterns and processes, (2) spatialness and its importance, (3) deterministic and stochastic processes, and (4) randomness and chance. Now, at last, it’s time to draw things together. I’ll start by asking and answering a question; then I’ll get Charles Dickens to provide us with a fitting example; we’ll see later where we go from there.

The question I’ll ask is a very straightforward one. Can a walk (which is inherently a spatial process) also be a stochastic process – a process in which there is chance involved? Yes, certainly! For the example, go to The Old Curiosity Shop (https://archive.org/stream/theoldcuriositys00dickiala#page/n7/mode/2up), to the chapter in which we read about how the story’s villain, Daniel Quilp, tries unsuccessfully to escape from the burning shed at his derelict wharf on the south bank of the Thames, probably downstream of the Tower of London, perhaps in Bermondsey or Rotherhithe.

Quilp’s Wharf, with Tom Scott

London was known then for its fogs, and Dickens describes magnificently the atmosphere at Quilp’s Wharf (p. 418):

‘The day, in the highest and brightest quarters of the town, was damp, dark, cold, and gloomy. In that low and marshy spot, the fog filled every nook and corner with a thick dense cloud. Every object was obscure at one or two yards’ distance. The warning lights and fires upon the river were powerless beneath this pall, and, but for a raw and piercing chillness in the air, and now and then the cry of some bewildered boatman as he rested on his oars and tried to make out where he was, the river itself might have been miles away.’

Then he describes what happened (p. 423):

‘It was about eight o’clock; but the dead of the darkest night would have been as noon-day in comparison with the thick cloud which then rested upon the earth, and shrouded everything from view. He [Quilp] darted forward for a few paces, as if into the mouth of some dim, yawning cavern; then, thinking he had gone wrong, changed the direction of his steps; then, stood still, not knowing where to turn.’

Finally (p. 423):

‘” If I could find a wall or fence,” said the dwarf [Quilp], stretching out his arms, and walking slowly on, ” I should know which way to turn. A good, black, devil’s night this, to have my dear friend here! If I had but that wish, it might, for anything I cared, never be day again.” As the word passed his lips, he staggered and fell and next moment was fighting with the cold dark water!’

Quilp’s walk was truly a stochastic process, and with a very satisfying end.

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I can’t resist quoting here another passage from The Old Curiosity Shop (p.33). The reason is that it describes a crossing that Quilp made earlier in the story, from his dwelling on Tower Hill on the north bank of the Thames to his wharf on the south bank. My father was born on Tower Hill, albeit about 80 years later. This passage gives a hint of what the Thames might still have been like then.

‘It was flood-tide when Daniel Quilp sat himself down in the wherry to cross to the opposite shore. A fleet of barges were coming lazily on, some sideways, some head first, some stern first; all in a wrongheaded, dogged, obstinate way, bumping up against the larger craft, running under the bows of steam-boats, getting into every kind of nook and corner where they had no business, and being crunched on all sides like so many walnut-shells; while each, with its pair of long sweeps struggling and splashing in the water, looked like some lumbering fish in pain. In some of the vessels at anchor all hands were busily engaged in coiling ropes, spreading out sails to dry, taking in or discharging their cargoes; in others, no life was visible but two or three tarry boys, and perhaps a barking dog running to and fro upon the deck or scrambling up to look over the side and bark the louder for the view. Coming slowly on through the forests of masts, was a great steam-ship, beating the water in short impatient strokes with her heavy paddles, as though she wanted room to breathe, and advancing in her huge bulk like a sea monster among the minnows of the Thames. On either hand, were long black tiers of colliers; between them, vessels slowly working out of harbour with sails glistening in the sun, and creaking noise on board, re-echoed from a hundred quarters. The water and all upon it was in active motion, dancing and buoyant and bubbling up; while the old grey Tower and piles of building on the shore, with many a church-spire shooting up between, looked coldly on, and seemed to disdain their chafing neighbour.’

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