Talk, Nosh and Gridlock

I paid a flying visit yesterday to the beautiful city of Edinburgh in order to give a seminar at the Institute for Astronomy, which is situated with the historic Royal Observatory. I was there not long ago, in fact, to do a PhD examination but on this occasion all I had to was stand up in a lecture room and rabbit on for an hour or so. That part of it seemed to go reasonably well, in that no more than half the audience fell asleep while I wittered away.

The morning flight from Cardiff to Edinburgh was uneventful and got me there in time to chat with various people and have lunch before the talk. I elected not to rush straight from the seminar to the airport in order to return the same day, but stayed overnight giving some of  the locals the dubious pleasure of paying for my dinner and enduring my company during it, which they did with great patience. I’d like to thank Alan, John, Alina, Stefano and Brendan for rounding off such a nice day with such a pleasant evening.

In the restaurant we ended up setting each other little geometry problems drawn on napkins, to the palpable disdain of our waiter who clearly wanted us to leave.  However, since I had to get up at 5am the following morning (i.e. this morning) to get the flight back to Cardiff, we didn’t stay out too late. I got back to the B&B where I was billeted in good time to check last night’s football results  before retiring to grab some shut-eye. Newcastle United 4 Coventry City 1 was the result, so it was good news to end the day…

I had to get up at the ungodly hour of 5am in order to catch the flight at Edinburgh airport, but the return flight was right on time. This was fortunate because, not long after the plane landed, a blizzard descended on Cardiff. Snow has fallen intermittently all day. Although I’m a bit tired after getting up so early – hence the brevity of this post –  I’m relieved I managed to get back to work without any major travel hitches.

Anyway, my contribution to the little problem-setting session that took place between the plates and wine glasses was this one, which I was asked during the interview I had to undergo to get a place to study at Cambridge:

Consider an infinite square grid made as shown above from 1Ω resistors. What is the resistance between any two adjacent nodes of this network?

If you’re really interested, a general solution for the resistance between any two (not necessarily adjacent) nodes is given here but you should be able to get the answer for adjacent nodes by a much simpler line of reasoning!