Page 156 of Proof By Contradiction
The wallet is in my back pocket. The key in the wallet, same weight, same space it’s occupied since October.
Different everything.
Hands on the box. Not shaking.
Fallowfield behind me, Chorlton ahead.
Laurence is in the kitchen when I let myself in. Left-handed pen, marking papers, the kettle is going. A radio talking in the background, a man droning on about cod and quotas. Laurence looks up when the door opens, and his face does the thing he does when he’s letting me take part of his time: the gratitude held back, the nod minimal, the not performing a discipline he is practising.
‘All packed,’ I say.
‘The dresser is half empty. And the bathroom shelf’s empty. Left side.’
I take the box to the bathroom. The shelf is indeed empty. Laurence has wiped it. I can smell the cleaning spray, the cheap one, the one that costs £1.20 at the corner shop and which he has used for seven years because he thinks there’s no difference. There is a difference. I’ll argue it another week.
Deodorant. Toothbrush in its new slot, next to his. Paracetamol. A razor.
Mr Patterson arrives at eleven.
Seventy-three, retired civil engineer, grew up in Oldham, voted Labour in every election since 1974 except one he won’t discuss, and three weeks ago he knocked on Laurence’s doorbecause he saw the tutoring notice in the library. He’d always wanted to understand topology, but the local university wouldn’t take him as a mature student. His maths GCSE is from 1968. They couldn’t find the paperwork.
Laurence said yes. Free.Pay me in biscuits.
Mr Patterson brought custard creams.
They set up at the kitchen table. I move to the lounge with my problem set. The door stays open. They talk, and I’m not listening, exactly, I’m working on a proof, but Laurence is teaching, and it arrives whether I attend to it or not.
He’s explaining a Möbius strip.
‘Take a strip of paper. Long one, give it a half-twist. Glue the ends.’
Paper, scissors. The kettle is clicking off.
‘Now run your finger along the surface. Don’t lift. See where you end up.’
A silence that is Mr Patterson’s finger, presumably, travelling.
‘Bloody hell.’
‘Yes.’
‘Same side.’
‘Same side. One edge. The inside and the outside are the same thing. Topologically, the object has one surface.’
‘That’s not.’
‘It’s not what you’d think from looking at it. I know. The shape should have two sides because everything in ordinary experience has two sides. But topology cares about connections, not appearances. If you can get there without lifting your finger, it’s the same place.’
A long pause.
‘Dr Haldrey,’ says Mr Patterson, he uses the title even though he’s old enough to be Laurence’s father, ‘if I’d been taught this in 1965 I’d have a different life.’
‘It wasn’t on the A-Level syllabus in 1965.’
‘That’s exactly my point.’
I look up from my proof—the window. Rain is starting on the glass—the voice in the kitchen. Strip the mask, and the thing underneath is the thing itself.
