There was a documentary on the string idea done by that math’s geezer. I seem to remember the piece of string being infintely as it just depended on how accurately you measure it. Something to do with fractals.
Anyway, tyres, about a year. Normally the back one will go first so if you run the same tyres it’s often worth just putting a new one on the front and the front on the rear whenever the rear wears out. Also I try and buy new ones in autumn as that way you get the new tyre grip when you need it when the trails are wet and muddy. In summer you are left with a less grippy but faster tyre for drier conditions.