The spider and the cleaner work in the same building, not far from each other but solitary in their worlds. The spider spins quietly, tapping and rubbing herself. When the Hoover starts up, she can hear it through her hairs, feeling the sound waves like a wind on her body.

She has eight eyes. She may not see in colour but she’s sensitive to tiny movements. There’s something stately about her panic: no noise, no head movement, simply her legs carry her suddenly into hiding. The cleaner on the other hand shouts and steps backwards: “Weird isn’t it, all those legs, very fragile and quite soft. A spider might measure an inch and a half but the mind sees something huge. I must admit, I’m a little bit unnerved by big spiders. Someone told me they bite. I might just pick them up very quickly – you know, grab them with my hand very softly and fling them out the window. I’d never kill one.”

The cleaner has only two eyes. When he’s not cleaning, he paints detailed pictures of invisible worlds. When he cleans, he keeps his eyes tuned to the task. He sees dust, mud, smears, nail clippings, spillages, hairs in plugholes, unpaid bills, kicked-off shoes, all the secret debris of a human. At a certain point he glances at the ceiling and sees cobwebs: “Ah yes, what should you do about webs? Old webs I’ll get rid of, they’re just big balls or twists of dust; and kitchen webs, the more you leave them (and I’m talking years here) the more the whole place becomes a congealment of grease. But fresh webs – I tend to take one and leave another. I make a balancing decision. I try not to get anxious about the ethics of it. There’s the issue of flies, of course. Not hygienic but I have saved flies on occasion. But those webs, when you see them outdoors they’re like cradles of jewels between the gorse – it seems so sad to damage them.”

Webs are made mostly of spaces. They break easily. They barely exist. They belong to the category of half-things: mist, smoke, shrouds, ghosts, membranes, retinas or rags; and they quickly fill up with un-things: old legs and wings and heads and hollow abdomens and body bags of wasps.

Outdoors, where their diagrams are more defined, they present themselves as dazzling displays of maths, as if the earth had spent all night noting down her rotations. In fact it takes less than an hour to make one.

Spoke to spoke

You need eight spinning glands, each capable of producing a slightly different kind of silk. First you release a floating thread, which catches on a surface. Then you spin a Y-shape from its centre and add a set of non-sticky spokes, never more than a step-width apart. As you spin the sticky cross-struts, you have to move carefully from spoke to spoke, so as not to get stuck, like a cleaner cleaning himself to the far side of a kitchen, trying not to touch the wet tiles. By the end of the day, the threads will be covered in dust. Most spiders eat and remake their webs every night.

“It’s amazing, the power of them spinning. You see that thing rotating really quickly. If I could just get a message to the spider to move off, that’s the real way to deal with them. I did it with moles once. But when I’m cleaning I just don’t have time. Sometimes I use the Hoover extension but that’s no good because it clings to the tube and you’ve only got one sucking action. I prefer feather dusters, because they’re light and easy and I just push them up and twizzle them round and it’s gone . . .”

Alice Oswald was talking to Simon Prince.