Page 30 of Proof By Contradiction
He caps the pen. Gives me his full attention.
‘Go on.’
I hesitate. Not because I don’t know what I want to ask. Because I do.
‘When you talk about detachment in the Cauchy framework,’ I say, ‘you frame it as a tool. Something you pick up.’
His head tilts. Interested.
‘In most analytical contexts, it is.’
‘And if it isn’t?’
A pause. Not long. Long enough.
Haldrey leans against the desk. Folds his arms. The sleeves rolled to their usual precise midpoint, forearms exposed. Six inches from the wrist. Consistent across every lecture.
‘Then it’s usually misidentified,’ he says. ‘People frame avoidance as something imposed on them. In my experience,it rarely is. The mechanism feels external, but the function is almost always protective. The system detaches because detachment is cheaper than engagement.’
Clean. Structured. Every step is visible. A proof with its logic sound and its conclusion airtight.
‘Cheaper,’ I say. ‘Cheaper how?’
He tilts his head a fraction. Weighing whether I’m arguing.
I’m not arguing. I’m asking him to keep going because he doesn’t know I’m asking him to keep going.
‘Cheaper in the sense of predictable,’ he says. ‘A system that detaches pays a small, fixed cost for every interaction. A system that engages pays a variable one. Sometimes nothing. Sometimes ruin. Most agents optimise against variance, not towards reward. Usually they’re right to. Detachment only looks irrational if you assume the reward is symmetric. It almost never is.’
He’s forgotten, for two sentences, that I’m a first-year.
He’s talking to a peer.
I was asking about the thing that happens everytime I walk out of this room, and the distance between this desk and the door feels like a unit of measurement I don’t have notation for.
Is this a choice? Am I choosing this? Or is this happening to me?
And he answered me like a textbook.
‘Right,’ I say.He watches me for a second longer. Expecting the push-back I always give him. The friction that makes his attention sharpen.
I don’t give him one.
‘Thanks.’
I turn before he can recalibrate. Pack the rest of my things with movements that have nothing wrong with them. The zip of my bag is louder than the room needs.
‘Mr Carrick.’
I stop. Not fully. Enough.
‘If the reading’s giving you trouble,’ he says, ‘I can point you towards a couple of supplementary texts that might help with the?—’
‘It’s not.’
Too fast. Clipped.
He pauses. Adjusts.
