John Fremlin's blog: All the way home

After more than two months of travelling back to England from Japan, covering more than 10 000 km without flying, crossing South Korea, China, Kazakhstan, Uzbekistan, Azerbaijan, Georgia, Armenia, Turkey, Bulgarian, Macedonia, Albania, Montenegro, Croatia, Austria, Germany, Luxembourg, Belgium and France, using three overnight ferries and countless trains and buses, I am now back in front of the Internet with a great deal to update on this blog and a financial compulsion to contribute to society by working.

One problem that kept me perplexed on this often bizarre journey, was how best to respond to a delay in the arrival of some mode of transport. In most cultures, honesty and reliability are not highly prized, and consequently it is not unusual for buses and trains, etc. to arrive and set off much later (though sometimes earlier) than their scheduled times (if there are scheduled times at all). To muddy the waters, numerous greedy people will lie to travellers by claiming that these forms of transport are unavailable.

Given that the ferry, bus or train is likely to be late, how much should one hurry to meet its supposed departure time? And how long should one wait before giving up on it?

Walk versus Wait: The Lazy Mathematician Wins suggests that one should generally wait, but it assumes that the probability of the bus arriving is known. However, the frequency of buses is generally not known, and you could model that as a random variable in its own right. You could say that the longer you wait, the higher the estimate of the period between buses becomes. Alternatively, you could suppose that the commercial incentive for someone to ply the route increases, as the number of passengers has increased.

The situation is riddled with uncertainty, and it would be useful to have some sort of model to apply to the questions (1) of how early one should make one's way to the train station, (2) how long a break from waiting one can reasonably take, and (3) how long before one should give up entirely. I can't find anywhere where these things are addressed in a systematic way. At least with a system in hand, there would be something to do.

Just as a point of reference for my stick-to-it-ed-ness, the longest I waited for land transport was thirteen hours in Bokhara. Night fell, my fellow passengers started camping out at the bus stop, and I practised a little Russian at the communal fire.

I am open to any sort of offer for work. My email address is on my CV.