A view of the Maramureş countryside, looking across from Breb to the Rooster's Crest (Creasta Cocoşului)

Maramureş is a county of Romania that lies within Transylvania and is in the North of the country near the border with the Ukraine. It consists of a series of river valleys and has, until now, largely resisted modern life and retained its rural traditions. It is common for both men and women to wear traditional dress and at this time of year most people are working in the fields, scything the meadows and raking up the grasses into the distinctive haystacks that scatter themselves across the undulating hills.

Change is coming: often too fast for many, such as Ramona, who loves the traditions, landscapes and architecture of the county. Hosts of young people from Maramureş have made the most of Romania’s accession to the EU and have travelled, largely to Italy and Spain, to work. As money comes back into the area the old traditional wooden homes are being replaced by new, larger and often quite garish houses.

Wooden House in Botiza

The traditional wooden churches, many of them designated as UNESCO World Heritage sites, are being supplanted in the villages by huge great churches. And it is something quite remarkable to come from Western Europe and see quite such a programme of new church building going on in the east.

For our accommodation we stopped mainly in local, independently run wooden guesthouses which sat in the same grounds as our hosts homes. Our first was Mr Pop’s house in Hoteni a village in the Iza valley. Mr Pop is in a Folk band and was touring with a theatre company and so we were looked after by his sister, Voichita and Haiduc, his dog.

Mr Pop's house

On our first day of walking we took a fairly leisurely stroll that took us in a circular route from one village to the next. First was Breb, which is one of the villages that William Blacker talks about in his book Along The Enchanted Way.  After Breb we left any idea of paths behind us and headed up the hill and across to Budeşti.

Because the Maramureşeans don’t put up fences or hedges around their fields then paths can be quite temporary affairs. Yes, you might sometimes follow relatively permanent tracks that have seen a horse and cart along them, but you can also find yourself walking along a way that barely seems to have existed until you chose it a few moments before.

This serendipitous wandering just about always leads us to our destination, eventually. The one exception was when we realized that the tracks we were following belonged to the manure cart and so we ended up not only in the wrong place but surrounded by smelly piles of shit as well. Fortunately, there are a lot of people around working in the fields and Ramona soon had instructions for a new route for us to follow.

Ramona makes a path

From Budeşti to Sarbi there isn’t much of a chance to go cross country and so even Ramona was forced to walk us along the road.  Having failed to hitch a ride with a horse and cart we were keen to leave the tarmac and so we popped into the village hatmaker’s house in Sarbi. Ramona wanted to say hello to his wife – the hatmaker died very suddenly last year and she was looking out for her a bit, I think.  His son came out with her and gave us some suitably vague instructions to get back to Hoteni.

The map above shows the two walks that we did while we were in Hoteni and includes some photos from them.

There is also a slideshow of the whole holiday that I’ve done, which includes photos from hitch-hiking a ride on a horse and cart, graves at the Merry Cemetery and the logging train from Viseu.

If you are interested in a tour of Maramureş then I can heartily recommend Ramona and her My Romania tour company. She’s an independent tour company that will run both set and tailor-made tours.

After writing about how many Panini stickers collectors should expect to buy to fill a book  I’ve had a fair few comments about it.  Greg Newman brought John Crace’s article in The Guardian to my attention where he talks about “the four-yearly great Panini conspiracy theory.”  The conspiracy being that Panini don’t distribute the stickers evenly, so you have to buy even more of them to complete your set.

As evidence, he cites Chris Taylor, whose “album is now about two-thirds full and I’ve already ended up with a whole load of Lee Young-Pyos, Hameur Bouazzas and Vince Grellas“.  He then compares the fact that he has never even seen a Thierre Henri, whereas  Chris has got six.  Which is an opening for swapsies if I ever heard one.

Anyway, what he described looked quite reasonable to me. After all, if you expect to have to buy 4505 stickers then you are going to get rather a lot of some players.  So, I decided to do a bit of mathematical modelling and wrote this little bit of Python to do it for me.

The code simulates somebody buying stickers by generating random numbers between 1 and 640, and it keeps on running until every number is picked once. It also keeps a count of how many of each sticker is bought.

When all of the stickers were bought and the album filled up I then went through and counted how many stickers had been opened just the once, how many were opened twice, three times, four times etc.

For good measure I then did it another nine times and took averages. It’s not a great sample but hey, it’ll do for the purposes of this explanation.

So, what were the result then? Well, here is the table I created

First of all, I was pleased that the average number of stickers that were bought was 4500.  Within just 10 iterations of the simulation this is already extremely close to the expected number of 4505 that Laurent et Julie corrected my earlier workings out to.  It is worth noting that the run with the fewest stickers bought was just 3306 while the most was over double that with 7244.

You can immediately see how even in a small group of friends one person could appear to be a lot luckier than the other.

Now look at the number of duplicates we get.  Even on the lowest number of duplicates out of the ten runs there were 2 players that were opened 14 times each.  And on the one run there was a player that was opened 23 times!!

Below is the averaged out graph of the 10 runs I did.

A Spread of Duplicates for the Coupon Collector problem where n=640

Which has a really interesting curve as, by the time the last sticker in the book is opened, there are duplicates for nearly every player. In fact, there are only 7 players that there aren’t swaps for.

The number of these multiples rises up to the 90 players that have 6 stickers opened and then it eventually tails off at the end where you have 20 stickers of the player who by now the poor collector must heartily hate the sight of.

And when you look at it like this you do see that the conspiracy theories are just the result of looking at the problem down the wrong end of the telescope. If anything, the examples that John writes about in the article aren’t as extreme as the ones created by the simulation.

I reckon he’s doing alright really.

There are 638 stickers to collect in total and it made me wonder how many stickers you would expect to have to buy so that you had a complete set. I was interested in how many you would need to buy without doing swapsies with anybody and on the premise that there were an equal number of each sticker and that they were randomly distributed.

Be warned, there’s some maths up ahead.

This sort of problem has been modelled as the Coupon Collector’s problem by mathematicians and I’ll walk gently through the explanation to get to the answer to the problem applied to the World Cup football stickers album.

Step 1 – Probability of getting a new sticker

Now, the first sticker you take is absolutely guaranteed to not be one you have already got. The second sticker has a 637 in 638 chance of being a new sticker. Once you have this second sticker then the probability of the next sticker being different to the first two is 636 in 638 and so on . .. . . . . .until you have all but one of the stickers in your album to fill. Then, you have a 1 in 638 chance of any sticker being that last one you want.

Step 2 – Number of stickers we expect to buy to get a new one

So, we know we can work out the probability of getting a new sticker at any point. But we don’t want to know the probability of each sticker we open being a new one. What we actually want to know is how many stickers we should expect to open each time to get a new one.

This is actually quite easy. If you know the probability, call it p, of an event happening, then the expected number of times you should have to do something to get the outcome you want is 1/p.

To make sense of this then think of throwing a die. If you want to throw a 6 then you know that you have a 1 in 6 chance of throwing one. It makes sense that you should expect, on average, to throw a die 6 times until you get a 6.

So, to get the total number of stickers you should expect to buy altogether then you just add up the number of stickers you expect to buy to get the first, the second, the third . . . . . .right through to the 638th sticker.

Still with it?

Step 3 – Adding it all up

Turning this into numbers, this means that we want to work this sum out

1 + 638/637 + 638/636 + . . . . . . 638/2 + 638/1

And that, my friends, is an harmonic series, so it is. And, to estimate the sum of an harmonic series, and skipping some of the maths, we can use the equation

S = n ln(n)

In the equation above, applied to our example, S is the total number of stickers we should expect to have to buy, n is 638, the number of unique stickers we want to get, and ln(n) is the natural log of n. So

S = 638 x ln(638)

S = 638 x 6.46

S = 4120

And so, unless you swap, then you should expect to have to buy 4120 stickers, at a total cost of £412, to fill your Panini sticker album.

Which all goes to show, that it is far better to be sociable than rich.

This means that lots of us will now have access to embed Ordnance Survey mapping into our blog posts. Just like I’ve done below, with the arrow pointing to Moseley Exchange. And to be honest it wasn’t too difficult to do.

First of all, I had to sign up for an API key. A handy hint here is to scroll down to the bottom of the sign up page to see if you can read the Captcha first. It caught me out a few times.

Secondly, I needed to find out how to produce a page that had a map centred on a point and with an arrow pointing to where I wanted it to go. To do that I went to the Open Space Developer area and copied the code from their first example.

I had to upload the resulting file into a directory on my web space in order to see it. What that meant was that I’d successfully copied the OS example and had a single web page, with their text and a map pointing to their building.

So next I wanted to change the map to point to where I wanted it. I could see that the Javascript that the OS provided included these lines

osMap.setCenter(new OpenSpace.MapPoint(407754, 287865), 10);
var markers = new OpenLayers.Layer.Markers(”Markers”);
osMap.addLayer(markers);
var pos = new OpenSpace.MapPoint(407754, 287865);

and so it seemed that the MapPoint(407754,287865) was the thing that I needed to change. Now I don’t have an OS map of Birmingham, so I was a bit stymied at this point. I asked on Twitter,

siwhitehouse

(Simon Whitehouse)

How do I convert a postcode to an OS reference?

On 8-4-2010 08:17:11 from TweetDeck

and very quickly I had a response from @pezholio, who has built this rather nifty conversion utility on his UK Postcodes website.

So, I took Moseley Exchange’s postcode of B13 8JP and plugged it into the postcode converter and I got (407621, 283112). I changed both of the MapPoint related co-ordinates in the code quoted above. The first one of these is centring the map on the point and the second one is placing the marker there.

This means that I now have a map on a page which is now centred on Moseley Exchange. All I need to do now is to embed this into my blog post. Fortunately the forum on the OS site had a thread devoted to doing just this.

I downloaded and installed the Raw HTML plug in, disabled visual editing in Wordpress – it is a user setting – and Disabled automatic paragraphs in the Raw HTML plug in settings.

And that was about it. I started a new post and copied the amended code into the Wordpress editor and then started building this post around it.

And, if you’ve got this far you might just be interested to know that I’ll be talking about the recent OS Consultation and the government’s response to it at the Exchange on Monday, 12th April at 6.30 pm. Come along, it’ll be fun.

So anyway, this is my flowchart for who I support on University Challenge each week.

Now, going from the top, we have St Andrew’s which is an absolutely unremittingly awful shite of an institution. Not satisfied with being located in the home of golf, they have also got a huge animal psychology lab, have recreated the Stanford Prison Experiment for entertainment and are responsible for the current economic shitstorm.

I’ll support anybody against those fuckers.

Next there’s Oxbridge colleges (not Ruskin). I may be more sanguine and less class warrior inclined nowadays, but the preponderance of smug public school educated Herberts is just too much to bear.

Then we come to universities that I have a proper connection with. I dropped out of Bangor when I was younger and have been saved by the marvellous Open University since I’ve grown up a bit. They both deserve a cheer for putting up with me.

Oh, and I’m from Birmingham, so I’ll happily cheer any Brummie unis on.

Next, because of University Challenge’s rule that universities can only have one team *unless* they are Oxbridge colleges then it becomes necessary sometimes to decide which one of them to support. This is a nasty, but necessary, business. So, out go the religious and the royalist and if they’ve got a women’s college then I’ll support them.

Nearly done now.

Because there are still a lot of all male teams, I’ll often support the one team that has a woman in it.

Obviously, if only one team has a mathematician on then I’ll support them.

Lastly, if one team has a better Arts/Science balance then I’ll get behind them. Medics and Vets Colleges, who up until now have been vying for my favours, often lose out here.

And that’s it, scientific rigour over, by now I’ll plump for a team based on some random criteria, like a pretty face, funny surname or an agreeable amount of face jewellery.

I’ll bet loads of other people have their own flowcharts in their head too.

The good luck of being born into the right family is profound. Two American researchers, Betty Hart and Todd Risley, show how children from professional families hear on average 2,153 words per hour compared with 616 words per hour for kids in welfare families, so that by the age of three, there is a 30 million word gap between the vocabularies of children of families on welfare and those of professional families.

A 30 million word gap in vocabulary?  Surely just reading it back would tell you that there is something wrong in that statement.  It looks as though Will has mistaken occurrence for uniqueness. 

Now what the authors state in the Major Findings of their paper is that

By age three, the observed cumulative vocabulary for children in the professional families was about 1,100 words. For children from working class families, the observed cumulative vocabulary was about 750 words and for children from welfare families it was just above 500 words.

So, either Will is making a really elementary mistake of assuming that each word is unique, or he is misusing the word “vocabulary”.

In doing so he has extrapolated a 30 million word gap in vocabulary from a report that found, at most, a 600 word gap.

I also visited one volcano where you can walk into the crater created by an eruption. I climbed up the outside and looked down into it before I realised that you could just walk in at one point where there was a gap in the crater wall.

View of crater from above

Looking down, I could see that people had created a spiral of stones in the centre of the crater.  But when I went inside I realised that this was just the most obvious sign of people making patterns with the volcanic rock

The rock spiral from closer up

If you look carefully at the photo above you will notice that there are lots of small cairns built around the spiral.  There’s one in the very front of the photo that is quite obvious, but there were many, many more.

Looking around the inside of the crater I also saw that people had created representations of the volcanic crater using the rocks scattered around.

Representing the crater using rocks found inside it

One person had decided to leave their mark by creating their initials using the stones. Two of the stones had been used to build something else so I found a couple to replace them.  This was mainly because I liked the coincidence that they are my initials.

Initials made out of stones

While I was there a German family were also looking around, and the mum and son went and walked around the spiral, moving from the outside to the centre.  I did the same afterwards, and put an additional stone on the end of it, extending it just a little bit further.

All of this fascinated me.  If you want a symbol of the chaotic power of nature then you’ll have to go a long way to beat the crater of a volcano.  And here, in its centre, the human instinct was to make some kind of order out of it, to record it and to record our presence in it.

It was also striking that at the centre people had created something, the spiral, that was like a child’s game.  When I was there I thought how this was as though we were belittling the volcano and making light of its destructive power.

It was a part of Nikki Pugh’s Uncertain Eastside project and turned out to be less of a “walk” and more of a “people clamber around a bit and take photos”. Only I don’t take photos. Sometimes I have pretensions and imagine that what I take qualify as snaps.

Anyway, ambling along Watery Lane we went by Birmingham City Mission. Here’s the view coming up to it.

Birmingham City Mission

You can see in the photo that there is also a sign for the Archway Academy, which you can get to through the gates on the left.  Archway is an independent school which specialises in

re-engaging troubled students in learning through well planned, individualised learning programmes and through high levels of adult support.

A bit further along I took this photo here

Birmingham City Mission - Front Door

And yes, I know it isn’t straight, I was standing in the middle of the road, and even though it was a Sunday I was still dicing with death. And as I said, I’m not a very good photographer.

Anyway, City Mission have been in Birmingham for 40 odd years and are a Christian group who originally handed out food to the poor and now run a number of shelters for the homeless. This isn’t one of them though, it’s their offices.  The shelters look a bit nicer than this.  I think it’s pretty safe to say that Birmingham City Mission make sure a high percentage of donations go to the people they are trying to help rather than spend them on fripperies.

Now, there’s a whole load of twaddle that I could write here about the edge of a regeneration area housing two organisations that try and rehabilitate (regenerate) people either in danger of being excluded from society or there already.  I’m not going to do that.

Instead, here’s a bit of information that I found out from Alan Cutler, who works for City Mission; he’s a lay preacher and the father of my pal, Ben, which is how I found out this :-

We (BCM) are still there in Watery Lane. We have been there for 15 years or so, I would guess, and originally occupied the whole complex – i.e. both sides of the gateway and courtyard (the Archway Academy you mention kind-of sub-let their half from us.

The property was empy for about two years before we took it on. I think it was used by a local government department before that  I seem to remember talk for 2 or 3 tenants before that. Originally it was the headquarters of Piper Construction, who still own the building. They also own, I understand a number of properties at the back of ours – I think that is Glover Street. Piper were based in Widney Lane, Solihull. It could be under the name D.W.Parkin Ltd.

So there you go.