A misaddressed offer to sell wool led an English court in 1818 to decide that a deal was done the moment the "yes" went into the post, days before anyone read it. That odd idea, the postal rule, is still taught to law students.

Take a big pile of real-world numbers, such as town populations or river lengths, and about three in ten of them will start with a one. Fewer than one in twenty will start with a nine. It feels as if every digit should get an equal turn. It doesn't, and the reason is surprisingly simple.

Drive across a long bridge and you'll thump over a strip of metal teeth or a rubber seal. That's no repair job. It's a deliberate gap, there to let the bridge grow and shrink with the weather, because trying to stop it would be far more dangerous.

The swirling rainbow on a soap bubble isn't dye, and it isn't a reflection of the sky. It's light bouncing off the front and back of a film so thin that the two reflections interfere with each other. Watch a soap film drain and the colours slide downwards until the top goes black. That black patch isn't a hole. It's the thinnest part of all.

Partway through the first volume of Tristram Shandy, the words simply stop. Both sides of a leaf are printed solid black, a funeral in ink for a character who has just died. It wasn't quite as unprecedented as legend suggests, and that turns out to be the interesting part.