Some time ago I wrote about an infinitesimally small moment in time by using a thought experiment involving a fly and a train.
We know from harsh experience that trains don’t run on time. Like mine this morning, which was cancelled. Or perhaps occupying an infinitesimally small spaces. Whilst watching the wheels on the…train (on the opposite platform) go round and round, I got round to thinking about the point of contact between the wheel and the rail.
Let’s assume that the train wheel is perfectly circular and incompressible, and that the train line is perfectly straight and also incompressible. How much of the wheel touches the train line?
OK, I’m no graphic designer, but I’m trying to show that no matter how much you zoom in, the point of contact between a circle and a straight line remains just that – a point.
No. I can see no other way of seeing it – the wheel is lucky to be touching the track at all! Well maybe that explains the hovering time travel train in Back to the Future III ! 😉
On a more serious note…this linking between time and space. If I can just figure out the implications on time, then maybe I’ll know if my train will turn up on time tomorrow…