There can be no doubt about it.
A quick circuit of the park and sure enough, there they are, the old man and his fat dog.
As an exercise in mathematics you could plot the timings and sightings on a graph, you would not be short of data to input.
Jim decides to ramp things up a bit and take four walks a day to see what might happen.
Despite quadrupling the walks, again at entirely random times, he bumps into bandana man and his seafaring dog who has somehow washed up on dry land.
After a few months of this they all begin to get familiar with each other. Being a civil kind of chap Jim doesn't feel comfortable with passing this man without some kind of acknowledgement. It’s one thing blanking a purple banana but the old man and his dog were meeting him with such regularity that it was becoming, for Jim at least, faintly embarrassing.
To get round the problem he resorts to the slightly desperate tactic of dodging the old man before getting too close. This was okay for a while although the tactic relied upon having somewhere convenient to dodge too. You wouldn’t, for example, want to barge through bushes and join an impromptu Lidl lager party would you now? Or suddenly appear like a wildlife explorer out of the bushes to trigger a nervous breakdown in a purple banana.
Worse still, the old man and the fat dog might start to notice that you were deliberately trying to avoid them.
Jim can only draw one conclusion: the man must spend his entire waking life walking his dog around the same park in perpetuity.
Jim returns to his desk, looks around the office and wonders.