Canine Math

I. Pythagoras

The dog starts out as a black dot in a faraway field, like a bird of prey might, at first, seem like a dot in the sky to a mouse. He’s not barking, not making a sound. As he closes the distance and proves himself to be a much larger animal than I’d first thought, I point him out to Jerry – just behind me – and we start moving faster. This dog can run. At first, he’s easily going twice as fast as we are. But we start pedaling madly, really putting some weight into it. I try to resurrect the Pythagorean Theorem from some foggy back corner of my brain. Will this distance squared plus that distance squared save us or condemn us? I feel like a mechanical rabbit. But even as I’m panicking, I’m impressed by the dog’s ability to close the gap, at his innate knowledge of where to go to intersect our path. Ultimately, we beat him, but only because he respects his own property line. If he’d gone through the woods, he’d have had us. 

II. Length Of An Arc

The dog who is tied is sometimes a placid creature, happy to hang in her little house. Or she stands and follows our progress along her street, proud body immobile, only her head moving from left to right as we pass. Sadly, most often she is attached to a post or a pole or a sapling in the yard, with little shade and no toys, nothing to do all day but wait for any entertainment. Two bikes more than qualify, and she’s frantic with the desire to break free of her chain and pursue us. She runs back and forth, back and forth, refreshing the deep arc she’s already worn into her sandy patch of ground, to no avail. We leave her behind, and I imagine her disappointment as her street returns to the calm, inert landscape it once was. 

III. Length of A Radio Wave

He’s a small dog – a terrier – with a high-pitched yippy howl that we can hear from a quarter mile away. He stands so close to the road, I’m afraid I’ll end up steering too far into the lane to get away from him and be hit by a car. At the last minute, I see the reassuring black box at his neck, attached to the collar. Invisible fencing. He’ll avoid the vibration and the inevitable shock. I tell him he’s a good boy. Discontented, he’s left with nothing but his voice: a way to protest our existence in his territory. 

Infinity 

He appears just after we enter the town where we’re hoping to take a break. But it turns out there’s no restaurant, no diner, no gas station even. A hound mix: pretty and in his prime. I don’t notice him at first. We’re riding in 41 degree weather. It’s raining and there’s a 20 mph wind coming straight at us. So I’m not noticing much. Our ride is due to be thankfully short: 32 miles. But we’re less than halfway, the wind is wearing on me, and I could really use a coffee break. Jerry lets me know he’s there: “Ride a little faster, we have company.” When I look in my little rearview mirror, I see him trotting along behind Jerry. He’s not barking, he’s not charging. He’s joining in. We ride a little faster, he runs a little faster. We shout “No!” and “Go home, now.” These exclamations deter him briefly, but he soon picks up his pace and joins us again. As we move through the town with no coffee, we come upon other dogs. But OUR dog becomes the magnet for their attention, rather than us. Each dog that barks at us or charges us turns their gaze upon him, and this slows him down, but every time, he comes back again. We really need a rest from the wind and rain, and we finally decide to take one, with or without him. We pull our bikes off the road, and take refuge from the wind behind a couple of large shipping containers in a field. 

“How long’s he been following us now?” I ask Jerry. Five miles. After we finish our stretch and eat our snack, we get back on the bikes. Our friend seems distracted by some small creature in the woods. “Let’s wait til he goes into the woods,” Jerry says. But he turns back then and looks at us. We give up, climb onto our bikes, begin to ride. Two miles later, I’m starting to wonder if we’ll have to name him. I’m picturing us making reservations at dog-friendly motels from now on, when a muscular lab mix comes barreling out at us from a side yard. She is barking ferociously; she is your basic biking nightmare. But our dog again takes the brunt of her focus, once she notices him. And this time, he falls back. Because she is SCARY. We ride fast because she has no collar, no fence or chain. She’d come right out into the road, and would have been right on us if it weren’t for him. But she leaves us alone, satisfies herself with bullying him back in the other direction. I see him retreating in my rear view mirror. The nasty lab mix makes her way back into her own yard. I consider our seven-mile companion, and wonder how often he does this. For a time there, it did feel like he’d be with us forever.