Hooptedoodle #84a - The Big Drop

Our resident artist's impression of the alternative Lottery Rainfall system 

Further Mathematical Rambles with a 10-year-old

The only connection with the previous post is that this one also is prompted by conversations with my son. For a while we have chatted idly about the idea of the rain falling as a single drop – which is potentially amusing and environmentally catastrophic at the same time, but doesn’t actually convey very much unless you try to put some numbers on it.

Numbers would also involve defining some boundaries. It seems unlikely that Nature would distribute rainwater to match municipal or parliamentary dividing lines, but we can well imagine what, say, an inch of rain looks like, in the measuring glass, in the puddle on the lawn, in our garden, in our county...

We spend a significant amount of time watching, or being aware of, rain falling outside the windows. Our own county seems a reasonable area to consider – we know it pretty well, can envisage it. An inch of rain is a reasonable concept, too – it is not uncommon to get an inch on a particularly wet afternoon. I am confident that I have taken part in many picnics, hill walks, barbecues, football matches and so on which involved an inch of rain. I have also, I am reminded, visited the odd battlefield in such weather.

OK – to specifics. We had a go yesterday. The results are the sort of thing that prompts reactions such as:

1) Wow

2) Imagine that

3) What shall we play now?

4) I wonder what’s for tea?

This is an honest effort here, but we make no guarantees about the decimal point always being exactly in the right place – decimal places are not a strong part of my act. East Lothian is a small county on the East coast of Scotland. It seems it has a land area of 679 sq Km, which is certainly not large. If we take 1 inch as 2.5-something centimetres, an inch of rain all over the county (imagine, if you will, a rain cloud the same shape) gives a volume of almost exactly 17 million cubic metres – that’s 17 million metric tonnes of water. Two tangential thoughts – firstly, that represents 867 metric tonnes for each resident in the county, and – secondly – intuitively it seems astonishing that such a delivery doesn’t batter us to our knees and flatten everything in sight. And remember, an inch is not an exceptional amount of rain for a single day.

Obviously this all works because the stuff is sprinkled gently over the area, trickles into ditches and streams and drains, then into rivers and eventually into the North Sea, apart from any bits we choose to keep for later use. Our original idea, though, was to examine the effect of applying a National Lottery principle to rainfall, and dumping a single, giant drop on some poor fellow at some random point in the county [tee-hee]. One inch for East Lothian, we calculate, would require a spherical drop of water 318 metres in diameter – i.e. a bit larger than the average football stadium.

That’s big, isn’t it?

For later use - Hopes Reservoir, Lammermuir Hills, East Lothian

I wonder what is for tea?

If you realise that we’ve messed up the arithmetic, and the required droplet is disappointingly smaller than this, there’s probably no point in letting us know, since our attention span has now been exceeded. We are bored with this now, and are moving on to consider other sources of wonder, like how much does the moon weigh, and why wood-pigeons always say exactly the same thing.   

Hooptedoodle #84 - Fun with the Recycling

With the completion of the ECW infantry, I was once again encouraged to look at the rate of increase in my collection of painting bottle-tops, and also the likely trend in the sizes of my future figure-painting batches. The two curves do not meet, my friends. I have reached a situation where I cannot throw out a bottle-top of the two proscribed types (Tesco’s fizzy mineral water for infantry and Tesco’s semi-skimmed milk containers for cavalry); the collection is continuing to grow without purpose, simply because it has been doing so for a while and it is hard to break a habit.

So I have decided to keep 40 of the little ones and 30 of the big ones, and throw the rest out. Sorry -  that should read “put the rest in the recycling bin”.

My son (who is 10) is a real maths enthusiast, so we spent a little while piling them up before they went away, and did some messing around with tetrahedral pyramids, and a touch of gentle finite difference theory to see if we could construct a formula for the number of bottletops in a tetrahedron of side n (and so on). Oh what fun....

We had enough of the smaller tops to make a tetrahedron with a side of 11 tops, it turns out, which our formula tells us contains 286 bottletops. It did occur to me that if I have the spare time to fiddle around with this stuff (it was for the boy, really...) then someone else might have the time to look at a photograph of the event.

The eleventh tetrahedral number is 286

Good, eh?

We have subsequently thrown them out (though it was a struggle to part with them in the end), together with the other surplus tops which didn’t fit into the construction. Now then, at 500ml a bottle, let’s ponder how much water that represents, and where it has all gone now. And then there’s the gas... 

Hmmm.

ECW - Finished the Foot

A small landmark today - still maintaining strict parity (8 units of foot for each side), I've now completed the infantry target for the first phase (you mean there will be a second?) for my ECW project.

Here are the Royalist greencoats of Broughton and Gibson, on the left, and the Parliamentarian units of Brereton and Mainwaring. Dragoons and artillery are coming along, and recruitment of cavalry will continue for a while.

The odd lighting in the photos is the result of a strange luminous object appearing in the sky over South-East Scotland today. I feel an inexplicable urge to rush out and sacrifice a lamb, or a maiden or something.

I was listening earlier to a discussion on the radio - some people were complaining that a ceremonial funeral for Lady Thatcher seemed a bit of an extravagance in the current economic situation. I think it is an excellent idea - in fact, I think they should break with tradition and hold the procession in Leeds, or maybe Glasgow, so that her loyal former subjects can take the opportunity to show their gratitude and affection.

I'll see you there? Looking forward to it.

Bamburgh Castle

Since we have the school holidays upon us, and since my health is (infuriatingly slowly) getting back to normal, the lad and I took a trip down to Bamburgh Castle yesterday. It’s only an hour and a bit down the road from here, and I haven’t been there for years and years.

We managed to take the wet, wintry weather with us, so anyone in Northumberland who was enjoying the onset of Spring should have been warned of our coming, to be strictly fair. We loaded up our German refresher course on the car stereo and donned our arctic service underwear and off we went.

It was a good day out – I’m not going to attempt any sort of serious tourist review of Bamburgh – it was too cold for us to see everything on offer (we swerved the walk down to the sandhills – we can die of hypothermia doing that sort of thing at home).

There has been a fortification on this site for thousands of years, and it really is a terrific looking place, but somehow it doesn’t quite feel right for an ancient monument. It is a real place, with real history, but it has been destroyed a number of times – most notably by Edward the Kingmaker – and much of the rebuilding that has taken place has been aimed at making it a nice place to live. People still live there, for goodness sake, and the state rooms are in excellent condition. There was a hefty amount of refurbishment done in the 18^th Century, and the Earls of Armstrong (that’s the engineering Armstrongs) made it an elegant and comfortable home from the 1880s onwards.

Don’t get me wrong – it’s an excellent place to visit, but it doesn’t give you the immediate step-back into history you might expect. It’s all very well maintained and very obviously has buildings from all sorts of periods. They have an interesting little museum for the Armstrongs – mostly of aviation and marine specimens – and the state rooms hold a wealth of examples of armour and weapons.

I believe that in the village church there is a monumental window for a young cavalry officer killed at Waterloo, but we didn’t get that far. Too cold. Nick liked the tea-room and the dungeons best (he took the photos) – I think I liked the artillery pieces on the walls, which included a splendid 6-inch Georgian mortar and a carronade. Apparently the whole lot are about to get sand-blasted and refinished, so this will remove 200 years of paint in short order.

Nice castle – I liked it. It looks like a proper, kid’s idea of a castle, and it’s mostly in very good shape, which is why it has been used for so many films.    

ECW "BattleFinder" - alternative map cards for the North West

After some previous mention here of my intention to produce some tweaked map cards for the BattleFinder battlefield generation system, with place names which are more appropriate to an ECW campaign in the North West of England, a couple of people kindly emailed to express their interest in such cards. I've produced the first of an intended three sets of add-on cards, and they are here. If they are any use to you, please feel free to download them.

To put this into context, BattleFinder is available (free) from the website of The Perfect Captain, along with their Tinker Fox ECW campaign game and a few other goodies. These cards are not a corruption or rip-off of BattleFinder - you will still need to download the official rules and the playing board - my map cards use the original artwork and are merely re-named to suit a mythical area stretching from the old Lonsdale Hundred of Lancashire to the West Riding of Yorkshire - the idea is that the place names should sound reasonable rather than be real places.

As I sit here, I believe it is unlikely that I will use The Perfect Captain's Very Civil Actions or Spanish Fury tabletop rules, but the campaign stuff is definitely intriguing. My thanks to my son Nick for his skill with PaintshopPro and the magic copy-&-paste touch.

ECW Horse - another 2 units

Another two units of horse arrived for my ECW armies - usual lovely job by Lee. Here you see the first of what will be two units for the Earl of Newcastle's Northern Horse [R] - this lot might be Sir Edward Widdrington's regiment - and the more sedate chaps below them are John Lambert's RoH [P].

We are very close to a White Easter - two inches of snow this morning, though it appears to be melting now. I really am very tired of this. I need to understand - this is Global Warming, right? During this last week I was reminded that it is just a year since I went to visit Old John in North Wales, and to collect the first instalment of my ECW lead mountain. Two things about this:

(1) it doesn't seem a year ago

(2) on the 27th March last year, it was sunny and hot - rather too hot for a comfortable motor trip

Same world, different planet.

Boom in Very Old Property Continues

I've been pretty much out of things for a fortnight with the accursed flu, which, as ever, has hit harder and lasted longer than my own patience or the available sympathy window allows.

Better today - going into Edinburgh to see a concert tonight, armed with sucky sweeties to avoid my coughing the acts into silence. On the hobby front I've done a few lightweight organisation chores - fitting out more A4 box files with steel paper - stuff like that - and I've continued to work away at my supply of 15mm buildings for the ECW. Steady progress continues, though I may eventually convince myself to do a little re-work to tone down a couple of my paler thatch roofs. These little Hovels castings are really nice to work with, though I'm finding the finished buildings are a bit of a nuisance to store safely.

As I've progressed through the stock of unpainted resin over recent weeks, I did a lot of checking with the painted examples on Hovels' website, to see how they are intended to look, and as my confidence has grown I have found that I am frequently setting about doing something different. In particular, since my intended theatre for the ECW is the North West, I've had a go at producing some buildings which are a bit less obviously Cotswold Stone than standard. I am pleased with the little brick smithy shown here, and especially with the Bunter Sandstone mansion house, though it does bother me a bit that it looks like a childhood memory of Rathbone Road school in Liverpool - if it had bright green railings it would be the complete thing.

I'm going to have a go at a dark sandstone church next. And a timber windmill, though the mill is a real construction kit job with cast metal sails and everything.

I've been reading David Johnson's Adwalton Moor of late. It is written in heavily correct "thesis" style, and took a little getting into, but I have been won over. Great little book. The detective work involved in unscrambling old references and old maps, to get a picture of the battlefield as it was in 1643, is especially fascinating. I have also been very impressed by the accepted de facto form of classification of events in the ECW into "of general interest" and "of interest only to local study groups" - a whole pile of stuff I have suspected but never seen written down before. Recommended book for any ECW enthusiasts.

For anyone who is interested in the funny way us northern folk speak, Adwalton appears to have been pronounced "Adderton" or even "Atherton" in 1643. By 'eck.