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Wed 19th May 2010

Posted on May 20, 2010 at 1:55 AM

birds : Nothing much to report, despite the conditions this morning that looked pretty good for migrants, I only had a single Yellow Wagtail at Fort Hommet and even less on Lihou Headland. Below are some nice photos of a Stonechat that I've got round to processing from the weekend. At this time of year the plumage of Stonechat gets very dark, and the brown back feathers are overlayed by black, creating an appealing burgandy colouration.

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male Stonechat, Pleinmont

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the strange stance of this second bird was because it was watching a GBB Gull overhead.

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nonsense : I was reading on the internet the other day about mathematical probability (as I'm sure everyone does on a regular basis) and came across something which I found pretty amazing called the "Birthday Paradox". I'm sure it's a well-known problem amongst mathematicians, but it asks "how many people need to be in a room before, more often than not, two of them have the same birthday?" Instinctively we think that it must be quite a high number as there is 365 days in a year and each persons birthday is only 1 in 365, but the actual answer is just 23 !

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When you first hear this figure you think that it can't be right, it can't be so low surely. So I checked the registers of the first 8 form groups in our school, since pupils in a form are not at all chosen by birthday so it is quite (but not perfectly) random. There are between 22 and 27 pupils in these forms so according to the birthday paradox, four of these forms should have a pair of pupils with the same birthday. In fact 5 out of 8 classes had a birthday match - so it works!

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The mathematics of this are actually quite complex but it can easily be proved to be true. To simplify a lot, if you meet someone in the street there is 1 in 365 chance they have the same birthday, very low. But if you consider this problem as comparing pairs of people, in a room of 23, there are actually 253 pairs. This is well over half of 365, so there is a reasonable chance that there will be a match in these pairs. Of course this is not a true paradox but an "intuitive" paradox, because it is so unexpected that the answer is so low.

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My favourite paradox is what will happen when Pinnochio says "my nose will grow now!"?

Categories: 2010 Spring