0:00:07 > 0:00:10There are hundreds of islands along Scotland's West Coast,
0:00:10 > 0:00:13each one its own little world,
0:00:13 > 0:00:17connected to the neighbours by a great highway, the Atlantic Ocean.
0:00:24 > 0:00:29On Skye, Alice Roberts discovers a remarkable use for seaweed.
0:00:29 > 0:00:31This is brown gold.
0:00:33 > 0:00:35Newcomer to Coast, Kate Rew,
0:00:35 > 0:00:38is on the hunt for a tiny creature that eats whalebones.
0:00:38 > 0:00:42It is what some people call the bone-eating snot flower!
0:00:43 > 0:00:48And Nick Crane attempts to measure the length of the very wiggly British coastline.
0:00:48 > 0:00:5091, 92...
0:00:50 > 0:00:52Are you on the home straight now?
0:00:52 > 0:00:54I'm concentrating! 94...
0:01:20 > 0:01:24The waters of the Inner Hebrides are teeming with wildlife,
0:01:24 > 0:01:27from the smallest to the biggest creatures.
0:01:28 > 0:01:30Whales roam these seas close to the islands.
0:01:35 > 0:01:40Tobermory is the embarkation point for many a whale-watching trip...
0:01:42 > 0:01:46but wild swimmer Kate Rew is hitching a ride on an expedition like no other.
0:01:49 > 0:01:50I've always loved the idea
0:01:50 > 0:01:53that I might be swimming close to a whale in open water,
0:01:53 > 0:01:56and I'm keen to find out more about their remarkable lives,
0:01:56 > 0:01:59so it's wonderful to be here to join this expedition,
0:01:59 > 0:02:04to explore one of their mysterious secrets - what happens to whales when they die?
0:02:07 > 0:02:13Whales of all shapes and sizes swim between the islands off the West Coast of Scotland.
0:02:13 > 0:02:18These waters are a whale's super-highway - a migration route spanning the world's oceans.
0:02:20 > 0:02:23They're out there all right, just not that easy to spot.
0:02:25 > 0:02:28Very nice to meet you!
0:02:28 > 0:02:30Very nice to meet you too.
0:02:30 > 0:02:35- But today, I'm meeting marine biologists Adrian Glover and Kim Last.- Welcome on board.
0:02:35 > 0:02:39Thank you very much. They know where one whale is, or part of it anyway.
0:02:45 > 0:02:49We're heading 15 miles out to sea to recover some whalebones
0:02:49 > 0:02:52they placed on the seabed 15 months ago,
0:02:52 > 0:02:55part of an extraordinary experiment.
0:02:55 > 0:02:57It's something which is very new, really just in the last few years,
0:02:57 > 0:03:01we've started to understand what animals would eat a whale,
0:03:01 > 0:03:03and, in particular,
0:03:03 > 0:03:06whale bones, which is really what this experiment is all about.
0:03:10 > 0:03:13When whales die, they fall to the bottom of the ocean,
0:03:13 > 0:03:16becoming a hearty meal for sea life
0:03:16 > 0:03:18that strips the flesh from the bones.
0:03:22 > 0:03:24Once the flesh is completely eaten,
0:03:24 > 0:03:27you'd think the story would all be over, but it's not.
0:03:29 > 0:03:33The whale skeleton also provides a whole host of animals
0:03:33 > 0:03:34with a rich source of food.
0:03:36 > 0:03:42And it's one of these bone-eating creatures that Adrian is particularly interested in.
0:03:42 > 0:03:47We're hoping to find some of these strange animals that we call Osedax.
0:03:47 > 0:03:51We have a picture of one here, dissected out of a whalebone,
0:03:51 > 0:03:57it is what some people call the "bone-eating snot-flower", most peculiar name!
0:03:57 > 0:03:59I've got to say, it's beautiful-looking.
0:03:59 > 0:04:02When you told me we were looking for a bone-eating snot-flower,
0:04:02 > 0:04:03I wasn't expecting anything as pretty as this!
0:04:03 > 0:04:06Yeah, I think maybe we gave it the wrong name!
0:04:06 > 0:04:08It is a bit of a misnomer.
0:04:08 > 0:04:11It's actually a worm, it's a polychaete worm,
0:04:11 > 0:04:15it's highly adapted to living on this weird environment.
0:04:15 > 0:04:19So these flowers that you see, the red flowers, are actually there to get oxygen
0:04:19 > 0:04:22into this weird structure you see at the base,
0:04:22 > 0:04:26which is actually a root which is inside the whalebone.
0:04:26 > 0:04:30Would we actually see any of these with the naked eye, are we going to be seeing some?
0:04:30 > 0:04:33They stick out a centimetre or so out of the whalebone.
0:04:36 > 0:04:40What perplexes scientists is how the tiny bone-eating snot-flowers
0:04:40 > 0:04:42travel the ocean seeking whalebones to feed on.
0:04:45 > 0:04:49Adrian has a theory that they hop from whalebone to whalebone.
0:04:52 > 0:04:55If these things are concentrated along certain areas,
0:04:55 > 0:04:58they can use them as sort of stepping-stones in the deep.
0:04:58 > 0:05:02So putting down this experiment, even though it's really quite a small experiment
0:05:02 > 0:05:04that we're looking at today,
0:05:04 > 0:05:08is really important in looking at the whole dispersal of deep sea organisms.
0:05:10 > 0:05:14For over a year, 50 metres down in the cold dark Atlantic,
0:05:14 > 0:05:16the whalebone has been waiting.
0:05:16 > 0:05:20The team are hoping exotic bone-eating creatures have moved in,
0:05:20 > 0:05:24only now will the scientists find out if it's all been worth it.
0:05:26 > 0:05:28But there's a problem.
0:05:30 > 0:05:37The whalebone should be attached to a large mooring buoy, but it's nowhere to be seen.
0:05:37 > 0:05:43No buoy means no bone, over a year's work could be lost.
0:05:43 > 0:05:46We've had a lot of storms or maybe a trawler has come through
0:05:46 > 0:05:49and picked it up and dragged it away.
0:05:49 > 0:05:52So we're a little bit on tenterhooks at the moment.
0:05:52 > 0:05:54Working at sea is very unpredictable.
0:05:56 > 0:06:00Their only hope is to spot the much smaller back-up buoy or pellet.
0:06:02 > 0:06:05But there's little hope of seeing it until the tide turns.
0:06:05 > 0:06:09What happens is the current actually drags them under water,
0:06:09 > 0:06:13so they may just pop up when the tide goes slack.
0:06:16 > 0:06:20After a nail-biting wait, the pellet finally reveals itself.
0:06:24 > 0:06:27Our bone might still be recovered.
0:06:27 > 0:06:30Whenever you bring up something from the deep ocean, you always find
0:06:30 > 0:06:33interesting things, so we're guaranteed interesting things.
0:06:33 > 0:06:39I think that's one of the exciting things about this site, you never know what you're going to get.
0:06:39 > 0:06:43It's there, it's there, it's there! That's it! There's the bone.
0:06:43 > 0:06:45- Oh, my God!- They haven't fallen off.
0:06:45 > 0:06:47They haven't fallen off!
0:06:47 > 0:06:51There's one large vertebra and we've got a few smaller ones.
0:06:51 > 0:06:54A minke whale next to it, you can see.
0:06:54 > 0:06:57- That's right.- So it's like a sweet assortment, but for whales? - That's right!
0:07:00 > 0:07:04Kim and Adrian are quick off the mark to get to their bone,
0:07:04 > 0:07:08and they certainly seem excited about something.
0:07:08 > 0:07:14We've got bacterial bracts, that's the white stuff there.
0:07:14 > 0:07:19We've got gastropods, we've got sea slugs, we've got molluscs...
0:07:19 > 0:07:22- Have you found any snot-flowers? - No snot-flowers yet.
0:07:22 > 0:07:25We've found quite a few interesting animals though.
0:07:25 > 0:07:28This is something that we've been picking out.
0:07:28 > 0:07:32Oh, wow! Look at that, it's like a mini lobster.
0:07:32 > 0:07:34Squat lobsters.
0:07:34 > 0:07:36We have sea urchins...
0:07:36 > 0:07:39- You're missing out this guy! What's this strange creature?- This is a spider crab.
0:07:39 > 0:07:43All these animals are things that live on hard subspace,
0:07:43 > 0:07:46hard things in marine environment.
0:07:46 > 0:07:48So we've got quite a lot of organisms here,
0:07:48 > 0:07:52able to use the whalebone as if it was kind of a reef, really.
0:07:52 > 0:07:55I mean, no-one's done this experiment, so no-one knows.
0:07:55 > 0:07:57So whatever we get is interesting.
0:08:02 > 0:08:06Even though I haven't seen any bone-eating snot-flowers today,
0:08:06 > 0:08:09my eyes have been opened to a new world,
0:08:09 > 0:08:12that something as barren-looking as a whale skeleton
0:08:12 > 0:08:16is actually an island home to a whole community of extraordinary creatures.
0:08:18 > 0:08:22Just off our coast, deep on the seabed,
0:08:22 > 0:08:26there's a delicate eco-system at work that we know so little about.
0:08:30 > 0:08:36On their restless journey through the oceans, whales navigate their way past these islands.
0:08:36 > 0:08:38But I can't resist a stop at Canna.
0:08:46 > 0:08:53I'm always captivated by these clumps of rock and grass that seem to defy the surrounding sea.
0:08:53 > 0:08:56Each of these islands is unique, its own little world,
0:08:56 > 0:09:00a miniature eco-system where people, plants and animals
0:09:00 > 0:09:02have to learn to live together.
0:09:02 > 0:09:05But things haven't always gone smoothly.
0:09:08 > 0:09:14The sea eagles which used to soar high above these cliffs were hunted to extinction.
0:09:14 > 0:09:18By 1918, there wasn't a sea eagle to be seen on Canna.
0:09:24 > 0:09:27Since then, many people have left too.
0:09:27 > 0:09:34There's only about 20 full-time residents now, but the sea eagles have been brought back.
0:09:34 > 0:09:37It's Abbie Patterson's job to watch over them.
0:09:39 > 0:09:42Canna is a good place because it's a very wild and remote island,
0:09:42 > 0:09:44there's plenty of food here,
0:09:44 > 0:09:48plenty of rabbits for the eagles to actually feed on.
0:09:48 > 0:09:51So... and it's also a place that isn't disturbed very much,
0:09:51 > 0:09:53very few people come to this corner of the island,
0:09:53 > 0:09:58so the birds are left alone, and that's really what they need, no disturbance and plenty of food.
0:10:00 > 0:10:02The sea eagles may feel at home on Canna,
0:10:02 > 0:10:06but they had to be re-introduced from Norway.
0:10:06 > 0:10:12Back in 1975, RSPB volunteers were scaling Norway's mountains.
0:10:12 > 0:10:18As the eagles were doing well there, it was safe to remove a number of the enormous chicks.
0:10:18 > 0:10:23The chicks were then flown to Scotland and released on the island of Rumm, right next to Canna.
0:10:23 > 0:10:30At that time, no-one could have anticipated how successful the re-introduction was going to be.
0:10:30 > 0:10:35Overall in Scotland there's probably about 200 at this present time.
0:10:35 > 0:10:38And how many of those are on Canna?
0:10:38 > 0:10:39Well, we have two pair here,
0:10:39 > 0:10:42they've been here since probably the late '80s
0:10:42 > 0:10:45and probably came from Rumm and moved across to Canna.
0:10:45 > 0:10:49They've been fairly successful since then,
0:10:49 > 0:10:53one pair better than the other pair, as you always get.
0:10:53 > 0:10:57And is there anywhere here that we can see signs of Sea Eagles today?
0:10:57 > 0:11:02Yes, there is. Just on the cliff up behind me we should hopefully see some signs anyway.
0:11:02 > 0:11:05Cliff...that sounds ominous!
0:11:07 > 0:11:13In this exposed terrain, finding any sign of the Sea Eagles isn't easy.
0:11:13 > 0:11:18We're going to check a recently vacated nest to see if they're eating well enough to survive.
0:11:20 > 0:11:24What I hadn't bargained on was the nest being halfway up this cliff!
0:11:26 > 0:11:28You do a lot of this, do you?
0:11:28 > 0:11:32Occasionally, not too much these days, but in the old days I did quite a lot.
0:11:34 > 0:11:36- You know I've never done this before, don't you?- Aye, I know.
0:11:36 > 0:11:39I'd like you to know that I'm quite liking it,
0:11:39 > 0:11:41but mostly I'm hating it!
0:11:45 > 0:11:49This is not the best fun I've ever had, let me assure you!
0:11:53 > 0:11:56Oh, I'm here! I'm here!
0:11:56 > 0:12:02I'm so pleased. Right, jolly good.
0:12:05 > 0:12:08I have to say that at first sight,
0:12:08 > 0:12:12this does not look like a bird's nest as such to me.
0:12:12 > 0:12:16Is this standard issue? Just a flattened platform of debris?
0:12:16 > 0:12:17This is it, yes.
0:12:17 > 0:12:23It's... Quite often, it's built up at the beginning of the season and looks a lot better.
0:12:23 > 0:12:26You know, there's a lot of sticks and seaweed and various other things.
0:12:26 > 0:12:30And then it lines it a little bit with heather and various things like that.
0:12:30 > 0:12:34By the end of the season, of course, the birds have been here for several months,
0:12:34 > 0:12:38so by the time they're finished with this, it's as you see it now.
0:12:41 > 0:12:42What is that? It's a jawbone.
0:12:42 > 0:12:47This is a jawbone yes. It's not human, I can say, but what this is, it's herbivore.
0:12:47 > 0:12:50- And that's a small lamb. - It's a lamb? Right.- A small lamb.
0:12:50 > 0:12:52Cos that is the kind of prey, in your mind's eye,
0:12:52 > 0:12:56- that's what I think about something like a sea eagle taking. - Yes, that's right.
0:12:56 > 0:13:02There's a tendency that obviously the sea eagles are not liked by shepherds etc,
0:13:02 > 0:13:04because they are taking lamb.
0:13:04 > 0:13:11And in some of these areas, financial schemes have been set up to try and offset some of these costs.
0:13:11 > 0:13:16But here on Canna, looking at the actual dietary requirements of the eagle,
0:13:16 > 0:13:21there's only something like 0.2% of lamb amongst everything that it eats.
0:13:21 > 0:13:23Now, that's not a large amount.
0:13:27 > 0:13:30We know from the nest that the eagles are feeding well enough,
0:13:30 > 0:13:33which promises well for their future,
0:13:33 > 0:13:37but still no sign of the birds until...finally.
0:13:44 > 0:13:47It's iconic, isn't it, seeing it against the colour of the sky?
0:13:47 > 0:13:50- Absolutely.- What a backdrop.
0:13:50 > 0:13:52You couldn't get a finer backdrop.
0:13:52 > 0:13:55It's going to come right past us!
0:13:55 > 0:13:59Just to be sitting on a day's visit, to catch a sight like that is fantastic.
0:14:03 > 0:14:06So just how big is that bird that we're looking at?
0:14:06 > 0:14:10Well, it's the largest bird of prey that we've got in the UK,
0:14:10 > 0:14:13and that's an 8ft wingspan approximately, so that is huge.
0:14:13 > 0:14:15It's often described as a flying barn door!
0:14:15 > 0:14:19Well, it's about the size of a door in somebody's house, isn't it?!
0:14:19 > 0:14:23It's really big. But it's also very broad, a very, very broad wing.
0:14:23 > 0:14:27So they're absolutely massive birds and there's different sizes between male and female.
0:14:27 > 0:14:30You find a female is a much bigger bird than the male.
0:14:32 > 0:14:34- That was amazing.- That was great.
0:14:34 > 0:14:36I didn't think we'd see anything!
0:14:36 > 0:14:40Well, I was a little bit dubious myself, but I'm really happy that it's come by for us.
0:14:56 > 0:15:03The bridge reaching out to one of Scotland's most famous islands has only been here since 1995.
0:15:03 > 0:15:08It's just a thin ribbon of road, but it's a permanent connection to the mainland.
0:15:10 > 0:15:13It begs the question - is Skye an island any more?
0:15:16 > 0:15:19Members of the local community own and run a ferry
0:15:19 > 0:15:24further down the coast for those who prefer going over the sea to Skye.
0:15:24 > 0:15:27Alice Roberts is one of them.
0:15:31 > 0:15:33Well, the boats have changed over the years,
0:15:33 > 0:15:35but this journey still connects back to the
0:15:35 > 0:15:40age-old tradition of the isles, when everything - people, goods, animals -
0:15:40 > 0:15:42had to come across on the water.
0:15:45 > 0:15:48I'm meeting Donald John McLeod,
0:15:48 > 0:15:53who brought the mail across this narrow stretch of water for 50 years.
0:15:53 > 0:16:00He's witnessed first-hand how Skye has changed since the arrival of the bridge.
0:16:00 > 0:16:03When an island is connected by a causeway or a bridge,
0:16:03 > 0:16:06the island changes.
0:16:06 > 0:16:09An island community, they're dependant on each other.
0:16:09 > 0:16:13But now you can get off it 24/7,
0:16:13 > 0:16:17go to wherever in the world.
0:16:17 > 0:16:19And you used to bring the mail over to Skye?
0:16:19 > 0:16:24Yes, I did. Up to the Second World War, very few houses had telephones,
0:16:24 > 0:16:26so everything came by mail.
0:16:26 > 0:16:31- So it sounds that your boat was a bit of a lifeline for people? - Oh, yes, it was. At that time,
0:16:31 > 0:16:34absolute lifeline, yes.
0:16:34 > 0:16:37And how important are boats now, do you think?
0:16:37 > 0:16:39Tourist attractions!
0:16:41 > 0:16:46This stretch of water wasn't just a lifeline for communication,
0:16:46 > 0:16:49it was once essential for industry too.
0:16:52 > 0:16:57Running any kind of enterprise on the isles used to rely on sea trade,
0:16:57 > 0:17:02and 200 years ago, the business on the boats was booming.
0:17:02 > 0:17:05The island looks so unspoilt.
0:17:05 > 0:17:10Hard to believe that the smog of pollution once hung over these shores,
0:17:10 > 0:17:14and that an entire industry was born and died here,
0:17:14 > 0:17:17all based on the stuff under my feet.
0:17:17 > 0:17:21This is brown gold, seaweed.
0:17:21 > 0:17:25And as strange as it seems, there are chemicals in this
0:17:25 > 0:17:30that 200 years ago were crucial to the glass-making industry.
0:17:32 > 0:17:35To make glass, you need soda ash.
0:17:35 > 0:17:40Until the late 1700s, Britain's main source for that was Spain.
0:17:40 > 0:17:45But then came war with Napoleon, and all imports stopped,
0:17:45 > 0:17:48shattering news for the glass industry.
0:17:48 > 0:17:51Except, you can also get soda ash
0:17:51 > 0:17:56from burning seaweed, and that was the start of the brown gold rush.
0:17:59 > 0:18:04The beaches of the Western Isles are abundant in this seaweed or kelp.
0:18:04 > 0:18:07When burned, it produces soda ash,
0:18:07 > 0:18:13so 200 years ago, these quiet shorelines were ablaze with activity.
0:18:13 > 0:18:16The remains of the workers' cottages can still be seen.
0:18:16 > 0:18:18As the kelp industry boomed,
0:18:18 > 0:18:23they housed entire families that depended on the seaweed for their livelihood.
0:18:23 > 0:18:30Whatever the weather, they had to be outdoors - cutting, carrying and burning it.
0:18:30 > 0:18:36I want to know what life was like in the early 1800s for the people of Skye working the kelp,
0:18:36 > 0:18:41so I'm meeting historian Donald William Stewart on this desolate day.
0:18:43 > 0:18:46It was a grim task, arduous work, really.
0:18:46 > 0:18:50You'd be there knee-deep in freezing cold salt water
0:18:50 > 0:18:53for most of the summer months, sewing this stuff up.
0:18:53 > 0:18:59Then you'd have to drag it, or haul it, or carry it - backbreaking work - up to the top of the shore where
0:18:59 > 0:19:04you'd clean it, you'd dry it, then you'd put it over pits and you burnt it.
0:19:04 > 0:19:06And is this men and women working it?
0:19:06 > 0:19:09Well, the woman apparently did the burning, if you like.
0:19:09 > 0:19:11It was quite a skilled job, you couldn't burn it too fast.
0:19:11 > 0:19:16The men, well they took up kelp irons and beat this molten seaweed into blocks,
0:19:16 > 0:19:18it cooled down into blueish lumps,
0:19:18 > 0:19:23which were then broken up into chunks and taken down to the south.
0:19:26 > 0:19:33They're ruins now, but around 200 years ago these coastal houses were hives of activity.
0:19:35 > 0:19:38Piles of seaweed burning along the shore,
0:19:38 > 0:19:43covering the islands in thick smoke, visible for miles out to sea.
0:19:46 > 0:19:5120,000 people across the Western Islands were involved every summer
0:19:51 > 0:19:53in this grim, filthy, dirty work,
0:19:53 > 0:19:58just as much a product of the industrial revolution as the black coal smoke,
0:19:58 > 0:20:04which is belching out of the chimneys in Glasgow and Birmingham, and Manchester.
0:20:04 > 0:20:11Crofters and tenants along this coastline were forced into cutting kelp by landlords quick to cash in,
0:20:11 > 0:20:16rents were raised and emigration was stopped by an Act of Parliament,
0:20:16 > 0:20:20to force more and more workers into the industry.
0:20:20 > 0:20:26Tenants here in Sushnis saw little of the profits, their landlord, meanwhile,
0:20:26 > 0:20:32Lord MacDonald of Sleat, was making enough cash to turn his house into a castle.
0:20:32 > 0:20:38The landlords owned this shoreline, they owned everything that grew on the shore,
0:20:38 > 0:20:43that included seaweed and they were really raking it in off the kelp.
0:20:43 > 0:20:48At its height, he was making anything up to £20,000 a year off kelp,
0:20:48 > 0:20:51that's well over £1 million in today's money,
0:20:51 > 0:20:55just an astonishing amount of money to make off seaweed.
0:20:55 > 0:20:59Some kelp cutting continued right up to the 20th century,
0:20:59 > 0:21:03but those early boom years were short-lived.
0:21:03 > 0:21:05When the Napoleonic wars ended,
0:21:05 > 0:21:08cheap soda ash from Europe flooded into Britain again.
0:21:08 > 0:21:12The glass industry didn't need Scottish seaweed
0:21:12 > 0:21:17and so the landowners no longer needed the kelp cutters.
0:21:17 > 0:21:19Now almost nothing remains
0:21:19 > 0:21:24of the time when the brown gold rush boomed on the Western Isles.
0:21:39 > 0:21:42International disputes over territorial waters
0:21:42 > 0:21:49can depend on where a country's coastline starts and stops and how long it is.
0:21:49 > 0:21:53It's not only governments who are interested in the length of the coastline,
0:21:53 > 0:21:56it's also handy to know if you're walking around it.
0:21:56 > 0:21:59On a particularly wiggly part of Scotland's shore,
0:21:59 > 0:22:03Nick Crane is pacing out a very perplexing puzzle.
0:22:06 > 0:22:09It's a question that crops up a lot on Coast -
0:22:09 > 0:22:12just how long is the British coastline?
0:22:12 > 0:22:17A simple question and you'd think there'd be a simple answer, but you'd be wrong.
0:22:22 > 0:22:24If you just zoom out for a moment
0:22:24 > 0:22:29and really look at the coastline, especially here in the West of Scotland
0:22:29 > 0:22:35and see all those inlets and wiggles, suddenly you're faced with an intriguing problem.
0:22:35 > 0:22:41Remarkably, figuring out the precise length of our coastline has led to a whole new branch of maths,
0:22:41 > 0:22:48which affects our lives in all kinds of surprising ways, even our mobile phones.
0:22:48 > 0:22:50What's going on here, Tony?
0:22:50 > 0:22:52I think we should start by making some measurements.
0:22:52 > 0:22:54Do you want to give me one of those to carry.
0:22:54 > 0:22:56How are we going to do these measurements?
0:22:56 > 0:22:59Well, we're going to place these on the either side of two rocks...
0:22:59 > 0:23:04Dr Tony Mullholand is a mathematician from Strathclyde University.
0:23:04 > 0:23:10He's here to show me that measuring the length of the coastline all depends on the length of your ruler.
0:23:10 > 0:23:12Measuring devices...excellent.
0:23:12 > 0:23:18Having walked a good bit of our coast, I don't fancy measuring the whole thing.
0:23:18 > 0:23:24Instead we're going to concentrate on a tiny bit, but if you think that makes it easy, think again.
0:23:24 > 0:23:25OK.
0:23:25 > 0:23:32We've placed two tripods 14 metres apart, that's the direct distance between them,
0:23:32 > 0:23:35but it doesn't take into account how wiggly the actual shoreline is,
0:23:35 > 0:23:41that's what we're going to measure, firstly with a two-metre rule.
0:23:41 > 0:23:45That's one, two...
0:23:46 > 0:23:48That's 13,
0:23:50 > 0:23:5214...
0:23:52 > 0:23:54and let's call that 15.
0:23:54 > 0:23:58OK. So measuring our bit of coastline with a two-metre rule
0:23:58 > 0:24:00we get a length of 30 metres,
0:24:00 > 0:24:04so now we're going to do the same measurement with a one-metre rule.
0:24:04 > 0:24:0816, 17... I'm not very good at counting over 50.
0:24:08 > 0:24:1121, 22...
0:24:11 > 0:24:1428, 29...
0:24:14 > 0:24:1634...
0:24:16 > 0:24:1850, 51...
0:24:18 > 0:24:1951, excellent.
0:24:19 > 0:24:22Amazingly, with a smaller one-metre rule
0:24:22 > 0:24:25the coastline now measures 51 metres,
0:24:25 > 0:24:29because we're getting further into those nooks and crannies.
0:24:29 > 0:24:31The coast is getting longer!
0:24:32 > 0:24:35Now finally with a half-metre rule.
0:24:35 > 0:24:38That's if we can get there before the tide comes in.
0:24:41 > 0:24:45I never thought I'd see one of Britain's biggest mathematical brains
0:24:45 > 0:24:47measuring a coastline with a wooden ruler.
0:24:47 > 0:24:5163, 64, 65, 66, 67, 68...
0:24:51 > 0:24:54You're on the home straight now.
0:24:54 > 0:24:57I'm concentrating! 94.
0:24:57 > 0:25:00- I'm I putting you off?- Yeah. 95...
0:25:00 > 0:25:03120... Is this an amphibious ruler?
0:25:03 > 0:25:06121...
0:25:06 > 0:25:10- Judge the tide...- 123!
0:25:10 > 0:25:16So the half-metre rule gives us a reading of nearly 64 metres,
0:25:16 > 0:25:21the longest yet and much more than our original straight-line distance.
0:25:24 > 0:25:27So the difference between the straight line, which is 14,
0:25:27 > 0:25:32and the 50 centimetre ruler of 64, even I can work that out it's 50 metres, isn't it?
0:25:32 > 0:25:34It's almost four times the distance.
0:25:35 > 0:25:38This is the extraordinary result,
0:25:38 > 0:25:41as your ruler gets shorter and shorter,
0:25:41 > 0:25:44your measurement gets longer and longer.
0:25:44 > 0:25:49Mathematicians realised you could keep going like this forever
0:25:49 > 0:25:55and discovering that created a whole new branch of mathematics - fractals.
0:25:55 > 0:26:01A fractal is a pattern which reveals greater and greater complexity as you zoom in.
0:26:04 > 0:26:09It was actually the endless complexity of Britain's wiggly coastline
0:26:09 > 0:26:16that inspired Polish-born mathematician, Benoit Mendelbrot, to invent fractal mathematics.
0:26:18 > 0:26:21Mandelbrot realised that, instead of using a ruler,
0:26:21 > 0:26:25he could measure wiggliness by giving it a number,
0:26:25 > 0:26:30a number between one and two, he called this the fractal dimension.
0:26:31 > 0:26:36OK, Nick, let me see if I can try and explain this to you in more simple terms.
0:26:37 > 0:26:41Here we have a straight line and this has a fractal dimension of one.
0:26:41 > 0:26:42OK.
0:26:44 > 0:26:47Here's a more wiggly line and we give this a fractal dimension
0:26:47 > 0:26:52somewhere between one and two, this might have a fractal dimension of 1.3.
0:26:52 > 0:26:55- So a fractal dimension is a bit like a wiggliness factor.- Absolutely!
0:26:55 > 0:26:59That's just giving you a measure of how wiggly the coastline is,
0:26:59 > 0:27:02so I think we'll have a look at a map of the British Isles.
0:27:02 > 0:27:03OK.
0:27:06 > 0:27:09Now I'm from this part of Britain, I love this coastline
0:27:09 > 0:27:14and this is very wiggly and I'd give this a fractal dimension of somewhere about 1.3.
0:27:14 > 0:27:18And what about somewhere... I mean I grew up in Norfolk down here, which has got a very smooth coast.
0:27:18 > 0:27:21Absolutely and so you can see somewhere like here,
0:27:21 > 0:27:24it's got a fractal dimension nearer 1.05, almost down at one,
0:27:24 > 0:27:28almost down at one and that's borne out by the coastline.
0:27:28 > 0:27:35So, visually, I think you can see this number relates to this ruggedness of the coastline.
0:27:35 > 0:27:39Giving a number to how wiggly your shore is might seem academic,
0:27:39 > 0:27:42but the length of a country's coast
0:27:42 > 0:27:46is vital for international disputes about boundaries.
0:27:46 > 0:27:49Everybody's got to agree about how they are measured,
0:27:49 > 0:27:52so countries can't cheat using a smaller ruler
0:27:52 > 0:27:54to make their border appear longer.
0:27:54 > 0:28:01As it happens, the West Coast of Scotland is the second most wiggly coastline in the world.
0:28:01 > 0:28:04The prize for the wiggliest goes to Norway.
0:28:04 > 0:28:08I've seen the light Tony - fractal dimensions give a numerical value
0:28:08 > 0:28:13to this seemingly chaotic coast, but what has it got to do with that?
0:28:13 > 0:28:18Ah, well, you've got your car radio, or your radio at home with a long aerial,
0:28:18 > 0:28:22excellent reception, we want the same thing for the phone,
0:28:22 > 0:28:25but we don't want a long aerial, so what's the solution?
0:28:25 > 0:28:31We want to take this long aerial and cram it and squidge it and make it as wiggly as possible,
0:28:31 > 0:28:35give it as high a fractal dimension as possible and put it in the phone.
0:28:35 > 0:28:39OK, Tony, I get the maths, but the reason I've been clambering up and down rocks all day
0:28:39 > 0:28:42is to find out the length of the British coastline. How long is it?
0:28:42 > 0:28:48Well, the Ordnance Survey, they'll quote a figure of just over 11,000 miles for mainland Britain.
0:28:48 > 0:28:54It has to be borne in mind that that is measured with a ruler that's 10 centimetres long.
0:28:54 > 0:29:00- A hypothetical ruler.- A hypothetical ruler, using satellite imagery and digitised images.
0:29:00 > 0:29:02But there's no limit to how short a ruler can be.
0:29:02 > 0:29:04The length of the British coastline is infinite.
0:29:04 > 0:29:07I didn't want to hear that.
0:29:07 > 0:29:09- I'm sorry.- The coast is infinite.
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