Dan McNeil's Blog

I remember, as a child, walking up the steps of the Laxey Wheel and thinking "that is a big waterwheel". That was around 25 years ago and just this week I was back at the Laxey Wheel for the first time since. No less fascinating this time around; the sense of childlike wonder at the size of the wheel still intact, but now joined by a sense of the beauty of the 100m long rod, moved by the wheel which in turn moves a rocker, which in turn lifts a rod inside a shaft up and down which was used to pump water out of the mine. We were due to visit the Isle of Man a year ago exactly, but circumstances conspired to mean that holiday was cancelled at the last minute. So this year, to allow some time to reflect on last year and to relax, we did the same holiday we had planned. It wasn't quite the same holiday - last year we had planned to come over by plane, and stay in Central Douglas with a hire car. This time, we drove from London up to Liverpool (via a few family visits) and...

Sometimes in life, you see people struggling with things which are easy. I don't mean that you should judge someone harshly for failing to grasp the quickest way to solve a differential equation or not being able to name a Mozart symphony from the first few notes - I mean things which are really not difficult and which form part of every day life. For instance, there are times in our lives when we are faced with finding a particular seat. On a plane, in the theatre or even on a boat (which is where I am as I write this, as it happens). Usually, you're faced with a ticket which may "23 A" or "Row X, seat 76" on it. If it's really complicated then maybe it will say "STALLS ROW A SEAT 2". But in any of these cases, it's not difficult to find your seat. Though I often wonder, when sitting in the theatre waiting for the show to start or sitting in my seat on a plane waiting for others to board, whether I have some super-human ability which ...

Yesterday, I wrote a length about pigeonholes and cats . But did I get carried away? Much as I hate to presume that you've read that post - I don't think this is going to make much sense if you haven't... I'm not the kind of person who lets a blog post fester and evolve before posting; I'm the kind of person who will write a blog post and stick it up immediately. Publish and be damned. Having read back yesterday's post, I wrote the following: "Of course, given so many years, the genes of Henry IV will have spread themselves wide throughout the population and so many of us will be distantly related to him. But the only way to prove that would be to take DNA samples." I got lost in my own words when writing this and there are two distinct problems with that short assertion. The first is to suggest that DNA samples would prove relationship to Henry IV. I must put my hand up here and admit that I slipped between the idea of mathematic proof and the comm...

The pigeonhole principle is such an obvious statement that few people realise that it's actually useful. However, a few people (who should know better, given who they are) actually get a bit too overly excited and try to use the pigeonhole principle to demonstrate the truth of things which simply aren't true. Before getting into the pigeonhole principle itself, it may be interesting to muse first on the nature of truth. Mathematical truth is a strong concept. Things are not "true" in mathematics simply because we can't find couter-examples - things are only "true" in the mathematical sense when we can show via a structured and logical argument that there can be no possible exceptions to the rule. Of particular interest here is the difference between an events which has a probability of 1 and an event which has a probability of "very nearly 1". In every day life, the two things are considered the same. "99%" sure is pretty much a ...