She (encouragingly): Now, we could turn left here, but that would be a short cut. What do you think?
He: May as well keep going. How much further, do you think?
She: Well, I only glanced at the park map in the street directory, so I'm not really sure, but I think this road bisects the park. Anyway, this track's a closed loop, so no matter what, we're bound to end up back where we started.
He: You sure?
She: Absolutely. Trust the maths. [Frowns as she realizes her certainty is based on the assumption that Braeside Park is a two-dimensional construct embedded in a three-dimensional space ... no need to trouble her husband with this worrying detail.]
Change of Scene: Twenty minutes later. The couple have walked passed a stile over an electrified fence.
She: I can't believe there's an actual live wire there! What is this place? That cattle run back there looked in pretty good nick. They can't be keeping actual cows here, can they? It's a park, for goodness' sake! In an industrial zone!
He: I'm more worried that we're never going to make it back to the car. I wonder what direction we're heading in? [Looks at sky ; the sun is veiled by heavy cloud. Turns to his wife.] Are you sure we're heading the right way?
She: We're walking around a closed loop. The map said so. It's taking a little longer than I expected, but so long as we stay on this track, we will get back to the car. [Slight pause as she contemplates the remote possibility that the trail is, in fact, a spiral instead of a loop.] Worst case ... no, there is no worst case. Don't worry.
He: What were you going to say?
She: Well, worst case, we're walking inwards along a spiral. But even then, we'll eventually reach the centre of the spiral, and then we'll just turn around and retrace our steps.
He: Retrace our steps? For another twelve hours?
She: You're exaggerating.
He: [After a brief pause for thought] And what if we're walking outwards along this spiral?
She: [Injects a breezy confidence into her voice] Can't be the case, we'd hit one of the surrounding roads sooner or later. Look, it's a loop. At least, I'm pretty sure it's a loop. It looked like a loop.
He: And this loop is how big ...?
She: [remains silent]
Change of Scene: Twenty minutes later. A rough wooden hut has appeared around a bend in the trail. They have been laughing at the prospect of walking 'forever' through this park.
She: Look! A hut! Bet it'll have a map inside.
[They rush forward. The hut contains various yellowing notices, graffiti and signs warning of remote dangers but, mysteriously, no map.]
He: You've got to be kidding! How can there not be a map in here? What is this place?
She: Well, hopefully we're still in the same universe and haven't popped through to another n-dimensional space.
He: It's possible, with the cows, the electric fence, no map, and all ... Why would that be bad?
She: Um ... the loop might not be closed.
He: What are the chances that's happened?
She: Oh, very, very, very remote. Very remote. Hardly worth mentioning, really.
He: Except that we've been walking forever and we don't know what direction we're heading in because we can't see the sun. And there appear to be live cattle in a park in an industrial belt of a major capital city, and a hut on the designated walking trail contains no map.
She: Yes, except for all that.
Change of Scene: A further twenty minutes have passed. The couple arrive at a colourful playground populated by families picnicking with young children. Laughter fills the air. They walk through, staring at these people, perplexed.
She: Where did they come from?
He: How did they get here? More importantly, how are they going to get out of here?
She: There must be another trail to this park.
He: We must be near a car park! Perhaps we should go looking for that track.
She: No! That's the worst thing we could possibly do! If we leave the trail now, we'll never find our way back to our car.
He: Really? That's the worst thing we could do?
She: [Doggedly] Trust the maths. Trust the maths. We're walking around a closed loop on a two dimensional surface. We are going to end up back where we started.
He: Trust the maths. Right. [Faces forward.]
Change of Scene: Another ten minutes later, they are approaching a car park. It is empty except for a council ute and two men repairing the broken cable of a fence.
She: What on earth are they doing, working on a public holiday? Oh look, we're in a car park! But ... where's our car?
He: [Murmurs] Just veer over here, away from them ... this isn't our car park, but we did drive past some others on our way in.
She: Oh. Well, that's good. We must be nearly there. Trust the maths. Trust the maths.
He: [Sniffs] Council workers working on Anzac Day? Maybe we have entered another universe.
Change of Scene: Three minutes later, they see their car sitting forlorn and alone in its car park.
She: [Jubilant] There! Woo hoo! I told you to trust the maths! I told you topology would get us here in the end! [Punches air. Attempts high five.]
He: Can we go eat, now, please?
The End
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