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If Wales was flattened out...

Take fractals seriously in mapping and statistics
  [vote for,

This is about a map projection that maps all surfaces as if flat, measuring distances down to those between atoms on solid and liquid materials exposed to the atmosphere. It has some interesting consequences, reminiscent of the Hitch-Hiker's Guide To The Galaxy:
All well-known places on the map are far apart, and unless the map is very small scale it would usually be blank. Surfaces fluctuate in size, water more than land. Surfaces made discrete particles vary quite dramatically so their area changes with the weather. Windblown sand and soil particles mean dry surfaces alter in area. Flooding involves the shrinkage of the submerged area rather than its growth. Tides and waves cause unpredictable fluctuation in the length of strands and coastlines.
Other consequences:
Any area bounded partly by coastline, lake or river has a very long border, but any artificial borders are relatively very short, for instance most of the border between the US and Canada.
Arid areas have relatively larger and more easily determined areas than humid ones.
Hilly areas are relatively larger than flat ones, so for all we know, Andorra is bigger than the Netherlands.
The size and roughness of the particles composing the surface strongly influences its area, so a dried up delta is bigger than a pebbly beach of the "same" size, but a wet delta is much smaller.
Vegetation is also important. Deforestation, along with mowing the lawn, drastically changes the area of a region. Therefore, it may be that countries chopping down rainforests reduce the size of their territories, and leaving an area to go to scrubland enlarges it.
Annexing a country can reduce the length of its border while increasing its area.
The population density of any territory is close to zero persons per square kilometre. Its rainfall is also very low considered in those terms. Certain places are deserts even in the middle of a rainforest. In temperate regions, time of year has a stronger influence on hours of sunlight per unit area because of the length of shadows, and sunny dusk is relatively less significant than sunny noon.
Landlocked powers invading island nations hugely increase their border length.
Distances between two officially named points on a map are very large. The only imaginable distances are between almost entirely unknown points, such as two soil particles in one's back garden. Other distances are inconceivably huge.
Rivers are very long.
Latitudes and longitudes tend to change irregularly, so the location of any point on the map is unpredictable, both in general and through time.
The highest and lowest points vary, as do altitudes generally. Mining and building tend to increase the area of a region unpredictably. Opening and closing windows and doors alter the sizes of built-up areas. Hence suburbs get bigger in summer and smaller in winter, but business areas vary less in size.
Finally, on a slightly different note, since the territories extend to the centre of the Earth, every administrative unit has a border with every other there at a point. The volume of these wedges gives a more realistic estimate of the size of the region than their true area.
nineteenthly, Aug 30 2009

Size of Wales http://www.simonkel...uk/sizeofwales.html
This is wrong [nineteenthly, Aug 30 2009]

Shooting the Welsh http://www.chesterw...Shooting_the_Welsh!
The "truth" (haven't read it yet) [nineteenthly, Sep 01 2009]


       We're waiting for the bit where we get to flatten Wales. Our steamroller is ready ....
8th of 7, Aug 30 2009

       [ of ], it could happen if the monkeys' typewriters were replaced with irons and they were relocated to Snowdonia.
nineteenthly, Aug 30 2009

       It would, however, be new and also, given that it'd need more room, also south of where it is now.
nineteenthly, Aug 30 2009

       Fruity beer? The Atomium? The fact that it isn't France?
nineteenthly, Aug 30 2009

       Don't forget Tintin, James Ensor, and the Smurfs.
DrWorm, Aug 30 2009

       And, as a good friend once said "If all the nurses in King's College Hospital were laid end-on-end...
No-one would be the least bit surprised."
Dub, Aug 30 2009

       if Wales was flattened out it wouldn't be Wales!
po, Aug 30 2009

       Arg. Overuse of the word "smurf". What's Flemish for "smurf"?
[po], were Wales flattened out, it would be a much larger country susceptible to flooding, where Flemish was more widely spoken than it currently is there. It would be a sort of "counter-Belgium" with more cheese on toast and cawl, and possibly a cycle-based version of rugby.
nineteenthly, Aug 30 2009

       This would play havoc with the Peltier.
MaxwellBuchanan, Aug 30 2009

       po, - you're saying "save the Wales"?
Ian Tindale, Aug 30 2009

blissmiss, Aug 30 2009

       how would pebbled areas, or indeed any area not covered in igneous rock or water be counted? In the detailed view you are proposing, a pebble as well as a sand particle would not actually be part of the surface, just lying around, on the real surface (which might be far beneath)
loonquawl, Aug 30 2009

       what I mean by *not* Wales is that the whole of its history and culture is shaped by the valleys.   

       one of the most beautiful countries in the world imho.
po, Aug 30 2009

       I agree, [po], and i have nothing against Wales, a principality whence half of my significant others hailed. The phrase "If Wales was flattened out, it'd be bigger than England" is of Walian origin. I wouldn't presume to impose that concept on them - they chose it themselves.
[Loonquawl], it's actually worse than that. If you entertain, for a moment, the Atomium-style model of atoms and molecules, you could say i'm drawing the line at mapping out the balls and sticks which supposedly represent the atoms and bonds concerned. However, we both know that's not really how things are because of the quantum thing, and in any case the topology of such a surface makes it impossible to project onto a plane without drastically distorting distances.
Given that, i want to modify the idea thus: i draw the line at the point where the surface i want to map ceases to be topologically of genus zero. Therefore, i wouldn't map an archway, a shed with two open doors or the Atomium, and i use that as the limit.
nineteenthly, Aug 30 2009

       so much for "as the crow flies" [+]
FlyingToaster, Aug 30 2009

       Ah well, whereas crows move at the velocity concerned, terrestrial animals move extremely fast on this map, even snails. Oddly though, snails shrink the distance behind them as they travel.
nineteenthly, Aug 30 2009

       Do they travel through wormholes?
Ian Tindale, Aug 30 2009

       Can't we just put Wales on eBay?
MaxwellBuchanan, Aug 30 2009

       If it was sold per unit area maybe.
I can see there's a topological problem with this idea which i haven't worked out how to fix yet.
nineteenthly, Aug 30 2009

       // how would pebbled areas, ....... be counted? //   

       Easy. Sweep up all the lose stuff and put it in bags. Flatten out Wales. Then lift the edge and sweep all the loose stuff underneath.   

       There's a precedent. It's called the Welsh Assembly.   

       // put Wales on eBay? //   

       But in what category ? "Collectables" ?
8th of 7, Aug 30 2009

Seven maids with seven mops could provide a solution.
On a slightly serious note, i need to solve the topological problem of the likes of wormholes and open windows. This is probably quite crude, but i suppose one answer might be to divide the Earth's surface into contiguous triangles of the minimum area needed to consider the surface they're on to be homeomorphic to a triangle. That is, as soon as you get a triangle one of whose sides or corners disappears down a hole, you make it slightly bigger, so the surface would be considered to be an aperiodic tiling of mainly scalene triangles, each of which contains at least one hole, which is ignored. Some of these holes would be gaps between atoms, some would be rabbit burrows, gratings on air conditioners or drainhole covers, and others would be archways and bridges. I have a sneaking suspicion that hasn't solved the problem but i can't quite get why.
The other problem is [loonquawl]'s one of the underside of objects on the surface. I suppose each object could have its own map, which would have to include pebbles buried deep in the shingle of Aberystwyth beach. However, the tesselating network of scalene triangles could also solve this problem, since as soon as a gap appears, the details are no longer considered, which would include the underside of rocks and crevices between grains of sand.
nineteenthly, Aug 31 2009

       No, i was thinking minimum size. Triangles just big enough to contain the holes.
nineteenthly, Aug 31 2009

       It's an algorithm or a thought experiment, but i would hold out for it being an actual map projection. Some of it is unfeasible, but not all. For instance, if you assume a sandy or woody area is fairly homogenous in its roughness, you would just need to sample a small part of that area, look at it under an electron microscope or otherwise calculate its surface to volume ratio, and you'd have an estimate of the ratio of the "true" area to the projected area. Similarly, you could do a LIDAR scan of a beach from above at low tide and you'd have a relatively accurate idea of its variability in length. You could then extrapolate to a rule concerning the length of a rocky beach (not much), shingle (a bit more), sand (a lot more) and a muddy one (absolutely huge). It might even have a use, though i don't know what that would be. At the very least, it would be a source of regional or national pride for an apparently small but craggy or dusty country or province to be able to say they were larger than a rival place which was apparently larger. For instance, an area covered in volcanic glass or maybe a salt flat would have an apparent size quite close to its "real" size, but one with quite serious soil erosion would be much bigger. For all i know, there might be a relationship between evaporation or the "wetability" of soil and its productivity or its ability to support particular kinds of ecosystem, or meteorological significance. It isn't completely trivial.
nineteenthly, Aug 31 2009

       how often would you have to repeat the process - whichever process you decide on?
po, Aug 31 2009

       You could do it experimentally. Take a "small" area and monitor its properties according to season, weather, planning, building, human activity and so forth until you have something like a set of laws, then apply them to a mathematical model which produces a map. The thing is, i have a hunch that this relationship would be chaotic. That exercise would in itself be interesting.
nineteenthly, Aug 31 2009

       Yes i think it probably would, but in the end, given the irregular nature of surfaces on different scales, aren't all estimates of lengths and areas rough guesses?
nineteenthly, Aug 31 2009

       rough guess = UB's experience of Wales
po, Aug 31 2009

       Don't forget New South Wales, [po], though for all i know he's never been there either. Unlike him, we don't live on a huge landmass and i'm probably underestimating the distances, which is sort of the point of this idea come to think of it.
nineteenthly, Aug 31 2009

       Sorry to hear that, [UB]. My honest opinion of Wales is that it isn't foreign enough to be interesting as a holiday destination and it lacks the feature of being home, which both England and Scotland have to me. Earth, air, fire and water in most places in the world tend to be discrete. In this archipelago, this is seldom so, and that's particularly true north west of the Tees-Exe Line.
nineteenthly, Aug 31 2009

       // My experience of Wales was a number of fun-filled days //   

       Careful, the irony is nearly at head height and there may be non-swimmers in the HB ....   

       // trying to get any sort of customer service from surly natives //   

       Otherwise known as "Stuffing runny butter up a Porcupine's arse with a red hot needle", although that's not exactly fair, as it's considerably easier than getting served in a shop in Wales. And that's during the week Sundays are worse.....   

       // dodging homicidal drivers on narrow, winding sheep tracks recently sealed with asphalt //   

       You have no idea how recent. Fire and the knowledge of the use of tools has still not reached many area.   

       // (bloody near died when a postal van rounded a blind corner near Garth, on our side of the road and two wheels. //   

       That would be Garth near Llangollen, on the hill above the Pontycsyllte aqueduct ? Many natives from the wilder areas still worship it as some sort of Deity.   

       // Can only assume the driver's ewe was feeling frisky and had called him); //   

       Could be. Or he was late for the Eisteddfod.   

       // trying to find cover from the wind //   

       Why do you think that Wales has a tradition of mining ? it's the only place to get away from the wind and the rain ...   

       // in a place where all of the trees were stolen and burned for warmth in the first millennium AD, //   

       No, they were eaten raw.   

       // and struggling to read road signs bearing supposed place names spelled using only the letters C, D, F, G, L & W. //   

       They have been trying to introduce vowels, but without much success. That's why there are all those castles around the place. The English used to go out into Wales to spread Civilization, or, falling that, flint-knapping, which would be a start. But they would put up signs with vowels in the words, then have to run back to the castles for safety -the Great "E" Riots of 1286 were particularly unpleasant.   

       Eventually the English gave up and went home, and the castles were largely eaten by the natives who could not grasp that stones were not edible.
8th of 7, Aug 31 2009

       If England was flattened out, it'd be bigger than England.
Spacecoyote, Sep 01 2009

       [UB], in that case i would have to take into account the upper and lower surfaces of the underscores as well as the ends.
See link about the Welsh in Chester. It seems the law about decapitating Welsh people was imposed by the English to prevent the Cestrians allying with the Welsh.
nineteenthly, Sep 01 2009

       // Is it still legal to shoot a Welshman on sight, //   

       Not really, but people do it anyway ....   

       // If England was flattened out, it would look like this //   

       If Australia was flattened out, it would look .... pretty much the same as it does now.
8th of 7, Sep 01 2009

       But it would be shinier.
nineteenthly, Sep 01 2009

       <through gritted teeth> If Wales /were/ flattened out. </tgt>
coprocephalous, Sep 01 2009

       "Was", "Were" .... yes, you're right, but don't argue, just be thankful they have vowels in them.
8th of 7, Sep 01 2009

       The actual quote does use the indicative, [shitfer]. What you've now made me wonder, though, is about how Welsh verbs work.
nineteenthly, Sep 01 2009

       In a way that's true because like other Celtic languages they do that weird periphrastic thing.
nineteenthly, Sep 01 2009

       [shovels more coal into the boiler of 8th's steamroller and sounds the steam whistle]

"Come on 8th! Stop nattering with your friends and let's get on with it!"
DrBob, Sep 01 2009

       There are vitrified hill forts, but i think they're in Scotland. The risk there would be scratching the surface. As soon as there was even the slightest erosion or irregularity, the map would be out of date.
nineteenthly, Sep 01 2009

       If you made a fullsize model of Wales and stuck it on top, no-one would be any the wiser.
nineteenthly, Sep 01 2009

       Ooh yes, that'd be good. Then it could be made out of glass and be an exact replica except in colour, including caterpillars, except for one tiny detail which would remain secret. If you found out what it was, you could claim a prize, say the Isle of Man or something.
nineteenthly, Sep 02 2009

       This is a bespoke sort of thing, i think. I would suggest turning the Moon into a really long fibre, cutting it up and weaving it into a huge tarpaulin.
nineteenthly, Sep 02 2009

       // and struggling to read road signs bearing supposed place names spelled using only the letters C, D, F, G, L & W. //
Don't forget the letter Y (as in the old town of Pant y Girdl) - we all know that this letter was invented by the someone French and gifted to Wales when it set sail from Brittany at the turn of the last millennium but one.
gnomethang, Sep 03 2009

       when we are finished with wales, lets gets started messing with that coral thingy around that island down under where we send our crims.
po, Sep 03 2009


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