The Okavango Delta

 Earlier in the year, Leighton wrote about the incredible pantanal area of Brazil and surrounding countries – a vast wetland unlike anything else.  This week I want to tell you about an area of Botswana that is also a jewel.  It is my favorite place in southern Africa.

The Okavango Delta lies in the northwest of Botswana bordering Namibia.  It is formed by the Okavango River, which rises in the heart of Angola to the north and west, then flows over 1200 kilometres south, then east away from the Atlantic Ocean through Namibia into Botswana.  There it fans out into a huge delta approximately 15000 sq. kms in size and appears to disappear abruptly into the Kalahari Desert.  It is indeed a remarkable sight to see the waters of the Delta on one side of a road and the desert on the other.

The 15000 sq. kms of the Delta comprise very low islands, few more than a two or three metres high, channels of water, and areas that are covered with water in the flood season (June to August) and are water-free much of the rest of the time.  Consequently, the Delta is a maze of islands and beautiful, crystal-clear water.  Access to the islands is by boat (powered on the main channels), mokoros on the smaller channels, and small plane.  There are a few roads on the larger islands, but access from outside is usually impossible.

Sausage tree

Mokoro

One of the greatest pleasures I have ever experienced is to wander along the waterways on a mokoro, which is a dug-out canoe, often made from a sausage tree (Kigelia africana).  The passengers, two at most, sit almost at water level, while the boat is poled by a poler standing at the back (like a punt).  The shallow draft allows the mokoro to go almost anywhere in the Delta.  It is magical to slide silently between the papyrus watching and listening to the birds and spotting wildlife, some of which – the lechwe and sitatunga - are found only in this type of  habitat.

Flying lechwe

Of course you have to be careful, because the larger channels are home to many a hippo (‘kubu’ in Setswana), which, when disturbed, can turn in a flash from a sleepy, tranquil lump of lard into Africa’s most dangerous mammal.  It gets one attention when nearly 3 tonnes of hippo surfaces next to you, jaws open.  Of course, having a hippo surface next to the mokoro is infinitely better than under the mokoro.  If that happens the impact can be so great that the boat may break.  Even if it doesn’t, the poor occupants will be flung into the water.  This too is not a good place to be because although vegetarian, hippos are not reluctant to bite.  A glance at the accompanying photo of a hippo mouth shows how dangerous a bite can be.

Open wide!

In addition, the Delta is inhabited by thousands of Nile crocodiles.  I believe a cooperative agreement exists between hippos and crocs with respect to knocking people into the water, but I haven’t figured out what’s in it for the hippo. 

Actually, such incidents are few and far between because the polers are experienced and know what to do.  In general, when on a boat in hippo territory, the strategy is to bang the side of the boat periodically.  The noise piques the hippos’ curiosity, and they pop their heads above water to see what the kerfuffle is all about.  All you have to do then is NOT to get between them and deep water, which is their haven.

African Fish Eagle

The Okavango is, of course, a magnet to wildlife, particularly when the water is high.  Not only are there dozens of different species of mammals and reptiles (over 120,000 elephant are thought to be in Botswana alone), but the birdlife is spectacular, with the Delta boasting around 450 species, from the rare (the huge Pels Fishing Owl, for example) to the abundant –the Red-Billed Quelea can form flocks so large (millions and millions) that they black out the sun and destroy crops like locusts. 

Red-billed quelea

Quelea flock

Pell's Fishing owl

Michael and I are avid birders and love being in the Delta.  About fifteen years ago, I flew up to a small town called Shakawe with some friends.  Shakawe is on the Okavango River just as it spreads out to form the Delta.  There, in the only time of our lives, we suffered from bird overload.  There were so many species in such abundance that we were overwhelmed.  A dozen African Fish Eagles in a tree; hundreds of Slaty and other egrets; dozens of different types of kingfishers; lily-trotting Jacanas; cliffs full of Carmine Bee-eaters; and on and on.  We just couldn’t keep up with the recording of what we had seen, let alone the photography.  Astonishing!


 

Our Detective Kubu is not a bird-watcher and hasn’t visited the Okavango, although he was in prime bird habitat at Jackalberry Camp in the Linyanti.  Unfortunately his situation is true of most Batswana.  Although I agree with the government policy of low-impact, high income – that is few visitors at a high price  - it means that many locals can’t afford to visit the Delta and enjoy what it has to offer.  It is probably up to Michael and me to find a pretext for Kubu to make it to the Delta and enjoy what we have always enjoyed.

CarmineBee-Eater

But it is so difficult to conceive of a murder in the Delta’s tranquility!

Malachite Kingfisher

African Jacana

But I’m sure Michael will find a way.

Stan - Thursday

Engineering Ethics

Are you still there reader? Probably not. And I don‘t blame you.

But why then did I select this awful heading which must constitute the bluntest hook available? To cut a long story short, these past few days I have spent most of my free time reading up on ethics in order to prepare for a lecture on „the Virtuous Engineer“. This had nothing to do with crime fiction but everything to do with a new ethics code being hammered out for Icelandic engineers and a conference held to promote the issue. So, having had to delve into philosophical texts I understand the dizziness and the haze that accompanies anything and everything philosophers put into writing. At one point I had begun to suspect my IQ was only half of what I believed it to be as I numerously had to re-read sentences in order to understand their meaning. And even then I did not. My mind began to drift....and drift....and drift....and then....bleep. All contact was lost.

But thankfully the conference had more on offer than people with dulled bulbs in place of heads like myself. One of the speakers was a bright light, one that has none its like in Iceland, namely our former president Vigdís Finnboga-dóttir. Vigdís was elected to office in 1980, the fourth person to become president following Iceland's independence in 1944. At the time she was not only the first female president in our country but also the first democratically elected female head of state in the world. If that is not achievement enough please note that she was at the time a single mother. This family staus, although somewhat frowned upon, probably ended up being in her favor in some sense since at the time there was much discussion amongst elder voters that it would be too embarrassing for a man to be known as the president‘s husband and hence women could not take office. So her not being married meant this ridiculously biased over-sensitivity did not pose a problem. All of the previous presidents had wives that no one worried about being offended oddly enough.

Vigdís was our president for 16 years, leaving office in 1996. She earned a place in all of our hearts with her grace, intelligence and exceptional morals. She is still, at 80, the belle of the ball wherever she goes, her gracious presence alone rekindling our admiration and respect for a beloved statesman. At present, Vigdís acts as a UNESCO Goodwill Ambassador and is a member of the Club of Madrid, an organization which promotes democracy in the world. This club is pretty darn exclusive and money cannot grease membership applications as the prerequisite is having been a head of state which sort of puts a damper on any of the club's efforts to increase membership. But since even this condition opens the door a bit too wide – so you also need also to have proven yourself as a catalyst for positive change in a global sense. Enoguh already, we get it. We're not getting in.

Vigdís' speech was great. The rest of us? Not so much. The only thing in my speech that might be of interest to anyone outside the engineering society was that in 1955 the public tariff for engineering services in Iceland was set up in a highly unusual way. As an example, to design a beam the charge was 25 krona times the square root of the length of the beam. I don’t think any profession other than mine could have some up with something like this. But aside from this bit of trivia I will spare you the rest, i.e. the virtue and ethics angle. You might drift and finally go: …bleep.

But every cloud has a silver lining, standing outside during the break I had a philosophical epiphany.

I smoke, therefore I am.

Yrsa - Wednesday

All Over the Map

The folks who contribute posts to this blog have access to a cool feature: Down at the very bottom of this page there’s a little oblong box surrounding the word “sitemeter”.

If you, as a visitor, click on it, all you’ll get is an ad for the service.

But when I, and the other registered administrators of this blog click on it, we get information about our readers.

We don’t get email addresses, or anything confidential like that.

We get general information.

Information like how you got here.  (Did you have us bookmarked? Did you find us through Google? Did you access us via a link from someone else’s site?)

Like how many visits we got in the past hour, past day, past week, past year.

Like which of our posts were most popular, most read, most stood the test of time.

But coolest of all, I think, is the map feature.

When I click on that one, I get a world map.

I can zoom in on a particular area, or I can choose to look at it by continent.

I can choose the last ten visits, twenty, or fifty, or a hundred.

And every visit is indicated by a little dot on the map.

For the last three days, I’ve been doing regular checks to see where you, our readers, dropped in from.

Turns out, it’s all over the map.

You’re on every continent and a lot of islands in between.

Just in the last seventy-two hours you’ve been checking-in from Korea, Thailand, India, Sri Lanka, Pakistan, Malaysia, Singapore, The Philippines, Australia, New Zealand, Brazil, Chile, Argentina, Mexico, Colombia, Peru, The United States, Canada, Puerto Rico, Anguilla, Antigua, Hungary, Norway, Denmark, Sweden, Finland, Russia, Iceland, Greece, Turkey, Israel, Italy, Spain, Portugal, the UK, France (including one visitor from Corsica), Switzerland, the Czech Republic, Tunisia, Cyprus, The United Arab Emirates, South Africa, Jamaica, The Netherlands Antilles and Vanuatu.

Vanuatu?

Yeah,  Vanuatu.

Honest.

Murder is Everywhere is…well…truly everywhere.

Our books, alas, are not.

The two great impediments to that are language (translations) and availability.

If you’re reading this, you obviously don’t have much of a problem with English.

But, if you’re our reader on Vanuatu (I’d find it hard to believe there’s more than one) you might find it difficult to get your hooks into a copy of Yrsa’s latest, even in English.

That’s changing.

And what’s changing it is ebooks.

Ebooks are exploding.

I just got a royalty statement from my publisher and discovered that my ebook sales doubled in 2009 over 2008, and, to date, have more than tripled in 2010 over 2009.

These days, it doesn’t matter where you live – as long as you own an ebook reading device, you can get Yrsa’s latest.

Last week, I did something I should have done earlier.

I digitalized my first book, Blood of the Wicked, and put it up on Amazon everywhere in the world where Kindle Books are sold, and where I hadn’t already sold the rights to a local publisher.

And I’m going to do the same with my other books at the rate of one book a month.

The cover image, because of copyright restrictions, is very different from the versions sold in places where the book has already been available. Here's what it looks like:

And, if you’re a reader of this blog, you can get it for free.

Not forever, but absolutely free until the end of this month.

Own an ebook reader?

Haven’t yet read Blood of the Wicked?

Live outside of North America, the U.S. Possessions and the Philippines?

If the answer to all three of those questions is “Yes”, then all you have to do is contact me.

Write to me through my website (you can get there by clicking on my photo over there on the right).

In your email, simply specify whether you’d like to have the book in Kindle or epub format.

And I’ll write back, attaching a free ebook.

Again, because of copyright restrictions, the deal isn't available to residents of the United States, Canada, the U.S. possessions and the Philippines - and it expries at the end of the month.

Write now.

Wherever you are in the world, it'll take you less than a minute to ask for it.

And only seconds to download it once you receive my reply.

 Leighton - Monday

Constabulary Notes

From the "Police Blotter" of the Phnom Penh Post:
Cops nab ‘gangster’ wielding two cleavers
Battambang provincial police on Monday arrested one of eight “gangsters” accused of injuring two people from a rival gang with meat cleavers. Police said the two gangs fought outside a dance party in Moang Russey district, but so far were unsure of the reasoning behind the scuffle. They arrested one suspect, 30, and confiscated two long cleavers used to injure two rivals, aged 42 and 16. The suspect denied involvement in the fight, despite having the cleavers.


In a country  -- in this case Cambodia -- where the outcome of criminal trials is usually determined by the relative sizes of the bribes being offered and by which side the local power structure favors, newspapers have to be careful about what they report and how they report it.  Generally speaking, the only reason a story like the one above ever appears in print is that the events were witnessed by dozens and dozens of people, and it would look peculiar for no public notice to be taken.  


But since there's no way to know -- no matter what happened -- how the judge will ultimately rule, the language in which these stories are written degenerates into a kind of journalistic "cloud-speak" that raises more questions than it answers.  "The suspect denied involvement" although the altercation happened in front of the whole party and in spite of having the weapons in his possession.  And was one person wielding two long cleavers?  Is he ambidextrous?  Did he singlehandledly injure two people?  Or did the other guy or guys bribe the cops on the spot?  If there were "eight gangsters" did seven of them evaporate?  Was one person designated to take the hit?  And (as the paper obviously anticipates), will even he ultimately be found innocent?


Then there's this kind of story - Suong Sophorn, a man evidently beaten by police (in front of a crowd) at a demonstration against, of all things, the government's attempt to stonewall a UN probe into police brutality and torture.


“They hit me in the head with a walkie-talkie, punched me in the face several times, hit me with an electric baton and then pulled me into the car by the throat,” Suong Sophorn said yesterday. 


Daun Penh deputy governor Sok Penhvuth denied that police had used force against the protesters.

“Suong Sophorn pushed the authorities and then hit his head repeatedly against the police car door,” Sok Penhvuth said. “No one hit or arrested him – the police just helped him get treatment.”


Aren't you glad you're not a reporter in Cambodia?  The man just beat himself up with the door of a police car, and this claim -- by a very high-ranking official -- has to be soberly reported.  


And finally, you have a story from the simply incomprehensible category, in which all the words form sentences and the sentences form paragraphs, but when you've finished reading it, you know to the bottom of your soul that you have no idea what happened.  


Man warned against walking, not hanging
A 26-year-old man hanged himself in Phnom Penh’s Meanchey district on Wednesday because his parents warned him against walking. Police claimed the man committed suicide by hanging himself with a scarf after his parents warned him not to go walking very often. Instead, they wanted him to concentrate on the family business, and his constant walking was preventing that. Police concluded that the suicide was caused by the warning.


This is the kind of thing you'd get if Salvador Dali had been a writer, not a painter.

Mani Get Your Gun

Vathia, a Mani fortified settlement

 If Mystras (see last Saturday’s post) was the heart of Peloponnese history, Mani was its fist.  It is the mountain-spine middle peninsula on the trident tip of Greece’s most southern mainland part, on the same latitude as Sicily and pointing across the Mediterranean at Libya.  It is where ancient Spartans are said to have settled, and if you’re wise, do not quarrel with a Maniot who makes that claim.

Unlike much of the Peloponnese, Mani has no grand, established sites such as Mystras or Epidauros, but nor did ancient Sparta, whose inhabitants lived a warrior life disinterested in the great edifices so important to their northern neighbors and Athenians.  Besides, much of what Spartans built disappeared amid the region’s earthquakes and millennia of scavengers for building materials.

A Maniot fighter

What Mani does offer is a present day spiritual presence giving life to a history far grander than most legends.  Say “Mani” to a Greek and the usual response is “tough, proud, enduring people.”  Greece’s war of independence against the Turks began there in 1821, and though the history of the Peloponnese (and Greece as a whole) is largely one of occupation by foreign powers, the story goes that Mani was never occupied (essentially true), never paid taxes (at least not that much), was a refuge for the politically persecuted (willing to fight, I assume), and in some parts has not seen a piece of land sold to foreigners (tough to verify, though proudly claimed). 

Mesa Mani landscape

A few weeks ago I was in the southwestern part of Mani, called Mesa (inner) Mani doing “inspirational” research for a new book.  Mesa Mani runs inland from the Ionian Sea, across arid, rugged land, onto the majestic, north-south Taygetos mountain range.   This is where ancient stone towers loom practically everywhere above the land, an ever-present reminder of a violent past. 

Mani tower

The generally four to five story tall towers (each a pyrgos in Greek), offered defensive positions to families against bandits, pirates, and foreign invaders.  But far more often they served to protect families from their neighbors, for Mani was a land where the concept of family vendetta was so deeply engrained in its culture that rules existed on how, whom, and when not to reek vengeance against an offending family.  For example, those lucky enough to be a doctor or a priest were considered too valuable to the community to serve as a permissible target for vengeance by another family.

There are said to be 800 ancient towers still standing in Mani, some with roots back to the 13th Century.  That might explain why many find Maniots among the friendliest and most courteous people in Greece.  It’s probably a serendipitous, positive result of living in a society where to offend likely led to something far worse than a nasty letter to your boss.

Gerolimenas harbor with Hotel Kyrimai at point

Road to spiritual experience

I stayed in Gerolimenas, a picture-postcard harbor village of less than sixty inhabitants, at a world-class inn once a seafront warehouse for agricultural commerce between Peloponnese and the outside world.  The same family that built and ran the warehouse in the early 19^th Century created and now runs the inn.  On the morning of my departure to Athens, the owner suggested I travel south a bit more, toward Cape Tenaro at the very tip of the peninsula, where the Ionian and Aegean seas meet.  “It is a spiritual experience that will take you back in time,” he said.  And so I did, toward I knew not what. 

Vathia

The photograph at the top of this post is not a painting, nor is the one to the left.  They are of the hillside village of Vathia.  It exists exactly as you see it.  As I stood there, contemplating a Harry Potter scenic against the region’s Mad Max-like history, a funeral procession passed out of Vathia directly behind me.  Mani has mesmerizing landscapes, charming places, and friendly people, yet I could not help but wonder if that funeral bore some relation to its fierce history.  I’m just cursed with such thoughts: I think murder is everywhere.

Pause for groaning to subside.

A final resting place

I never made it to the southern tip, for on the way there I passed the funeral procession.  Cars were parked along the side of the road, at the top of a steep, rocky incline.  Men below were carrying the coffin toward a mountain church along the edge of a cliff overlooking the sea.  I saw no cemetery, just the church.  The only other visible sign of life was up ahead, an isolated, distant taverna on a tiny beach.  I stopped there, but didn’t get out, just sat for a while.  I turned around and drove back toward Athens. I had no need to go further, I’d found my inspiration.  Besides, I’d be back; there were too many mysteries here to ignore—past, present, and future.  

Distant Cape Tenaro where the Ionian meets the Aegean

If you’re interested in more about this fascinating part of the world, I came across Mani: A Guide and History, on a website created by John Chapman.  He seems to have spent a large part of his life immersed in Mani’s history and ways.  Though I cannot vouch for the accuracy of his observations, nor do I dare challenge them, for in describing how vendetta vengeance could be taken against any family member of the perpetrator, he writes, “The only exception to this 'collective' form of vengeance was in the case of slander where vengeance had to be meted out on the perpetrator.” 

I’d prefer not to test that sort of thinking.

Jeff — Saturday

Urban Legend has it

 I'm a sucker for an urban legend. I've even been know to adopt a few for my fiction. I have my favourite ones too, mainly involving the London Underground, whose subterranean mystery generates more than its fair share of myths (underground spaces do generally - alligators in the sewers of New York anyone?): the guy who wakes up on a stopped tube train late at night and thinks it's his station and so gets off, only to reach the surface and find it bricked up - turns out he's in a disused station, lit for the purpose of maintenance, and he's going to be in there overnight bwahahaahaa etc); the stories of secret tunnels that pass Buckingham Palace and/or Downing Street to whisk away the Royal Family and cabinet in times of national emergency; another (which I even tried once) that said if you you encounter an emergency on the tube network, where there is no mobile phone signal, you could still dial 112 and reach emergency services via satellite. It wasn't true.

So I was delighted to be told one the other day by a friend. It goes like this: a young woman gets on the tube late at night. The carriage is empty save for a young man. Three other people embark; two men and a woman, all looking the worse for wear and rather seedy. They sit, the woman between the two men. The young woman, like all good city dwellers, does the right thing when faced with undesirables and avoids any eye contact whatsoever.

While the young woman is reading an advert for throat pastilles or wondering how to pronounce Plaistow, anything to avoid looking at the others, the man in his thirties sits beside her and whispers in her ear: 'Get off at the next stop.' She is obviously taken back by this, not one for trusting orders given by strange men, but something in the man's eyes and the urgency of his voice tells her she should obey, and she doesn't want to be left alone with the other three. So off they get. As the train starts to pull away the man points to the three still on the train, their backs to the window. The woman clearly sees a pair of scissors sticking out of the back of the skull of the woman on the train. As it departs the young man tells her she was dead and he saw them drag her on to the train.

Very creepy. So much so that I had to Google it. It turns out that it is an urban legend par excellence. The story is told relocated to Sydney, Australia, though this time featuring three girls, with the one in the middle staring out at the subject of the story. Later she discovers the girl was dead, strangled by the other two. Then there was another tale where a doctor is involved and recognises the woman opposite is dead.

It doesn't stop there. Variations on the story date back to the 1980s, pre-Internet and the rocket boosters it puts on rumours and conspiraces. One emanates from Manchester, with two girls observing and the later realising the girl with the intense stare is dead. There's a New York version too, dating back before the tube. This time a husband and wife travelling by stagecoach, when three ruffians board, one seeming insensible with drink. The two others get off leaving him there and when the couple try to rouse the last they discover his throat has been cut.

There is even an Italian version, told this time from the point of view those smuggling the corpse on board. The father dies and to save the cost of a coffin to take him home for burial, his two sons take him in the carriage and prop him up either side. So the story has it, they leave the body unattended, but when they return he is gone and a family are sat there instead. Under questioning the terrified family reveal that the train jolted unexpectedly, their heavy suitcase fell on the elderly gentleman below, and when they checked to see if he was ok they found he was dead. Thinking it was their suitcase which killed him, they threw his body from the train. More darkly comic than creepy, but cut from a similar cloth.

It was an instructive exercise, revealing how the stories evolve and are adapted over time. My theory is that like most  of these legends, this story contains a kernel of truth - that an event happened somewhere in which a body was found on a train, or a stagecoach, which other people initially thought to be alive, and because it resonates so much - perhaps due to the impersonality of public transport, where strangers are crammed together in a confined space and rarely speak or even look at each other - it has mutated into myth. There are countless urban legends of bodies riding around and around on the tube for hours on end, dead as doornail, but everyone is too preoccupied to care.

One article even took me to a recent story in which two German women attempted to smuggle the body of a dead relative on to a plane. I learned there is a phrase to describe the phenomenon where real life shares a parallel with urban legend - 'ostension of folklore.' Which then set me to thinking about how much ostension of folklore takes place in crime fiction, and vice versa. I have spoken before how I wrote a scene for my latest book in which someone is poisoned eating a curry, and only a few days later a woman stood trial accused of doing exactly that to her husband. Of course, she had not read my draft, but the reports of her being arrested and charged might have appeared a few months before and seeped into my subconscious.

That or I'm blessed with psychic abilities. Come to think of it, I do remember walking to a sports shop in my home town when I was a kid humming Pinball Wizard by The Who, only to arrive at the shop and hear it playing on the radio. Spooky.

cheers

Dan - Friday

nb. Scary footnote. Just paid a quick visit to the BBC website and read that Circle Line trains are returning to normal after being delayed when the body of a young man was found in a tunnel near Bayswater (cue Twilight Zone music.)

Mathematical Problems Solved, or Maybe Not.

Conventional wisdom is that mathematics is the one area of certainty in the world. 2+2 is always four. Set theory is consistent. Well, maybe not. Let me describe two iconic mathematical problems.

The most famous and intriguing problems in mathematics tend to be the ones that share two features. First they have been around for a really long time - which means that many people have tried to solve them and failed - and second they must be easy to explain. Curiously, they often lead to controversy - have they been solved or not? I want to describe two mathematical chestnuts that, on balance, mathematicians agree are solved. But...

Pierre de Fermat

The first problem is known as Fermat's Last Theorem. Pierre de Fermat was a brilliant self-taught seventeenth century mathematician who solved a variety of deep number theory problems in his spare time for his own amusement the way you or I might attack an 'extreme' Sudoku. The most famous of these is his so-called Last Theorem.  He explained his ideas and mathematics by writing them up in notebooks. After his death these notebooks proved a treasure trove to mathematicians. In one of them he wrote a theorem in the margin and commented: "I have a truly remarkable proof of this theorem, but it is too long to fit here". Mathematicians worked on it flat out for the next 358 years. The consensus is that, despite being a great genius, he actually didn't have a correct proof. (But maybe that's not true after all, because Lisbeth Salander solves it in her head - while being shot at - in The Girl who Played with Fire, so maybe Fermat managed it too!)

Here is the problem:

There are many triples of positive whole numbers x,y,z so that the equation x² + y² = z² is true.  For example x=3, y=4, z=5. Or x=5, y=12, z=13. Fermat’s last theorem says that this cannot be done for any higher order equation.  That means x³ + y³ = z³ has no solutions using positive whole numbers. Neither does the equation where we use the power 4 or 5 or... In general xⁿ + yⁿ = zⁿ has no solution in whole numbers for ANY whole number n greater than 2.

Andrew Wiles

The problem was finally solved by Andrew Wiles in 1995. Or was it? Mathematicians fell upon his proof like hyenas, gulping down the exciting ideas and the new areas of mathematics it opened up. (By the way it took him years and he created whole new fields of mathematics in the process, but he's not really smart like Salander!) And one of them found a mistake. It took another year to fix the mistake. Are there others? Probably not. But it's possible. Most mathematicians don't come close to understanding his proof. I certainly don't. Could the ones who do have a blind spot? It's really easy to fool yourself when you want something to be true. When I was a graduate student, one of my professors produced an incredibly slick proof of the four color map problem. We were all in awe. Here was a man on his way to a Fields Medal. (The Fields Medal is the Nobel Prize for mathematicians. The story goes that Nobel's wife had an affair with a mathematician. He never forgave the profession and excluded it from his largesse.)  Our professor always illustrated his proof with a key diagram when he explained it. The first expert who read the proof without the author there to describe it, drew it differently and realized at once that it was wrong. None of us had spotted that alternative way of drawing it.

Here's the problem:



Kenneth Appel & Wolfganh Haken



If you want to color a map in such a way that no two countries with a common border have the same color, then you only need four different colors. The problem was posed in 1852. Ten minutes playing around will convince you that this is so reasonable, it's obviously true. It took mathematicians until 1976 to come up with a proof, and even then...

Four colors is enough for the US

Of course the problem has no practical interest. Every real map is colored to distinguish the countries using plenty of colors. After all there is no shortage of them! And no one has ever come across a map requiring more than four colors anyway. In fact proving that five colors is enough is easy - usually included in undergraduate mathematics graph theory courses. But four? 

Well, the proof was curious. The authors reduced the problem to a large number of different cases which required checking. A very large number. A number so large that it could only be checked by computer. They wrote the program, ran it, and the results were that all the cases checked correctly. So what's the problem? Well, a recent article in the Chronicle of Higher education suggests that only 20% of scientific programs are completely correct. So if you're checking millions of cases...well.

The proof has been replicated in other ways since then. But do we know if the original proof was correct? Maybe. Maybe not.

Michael - Thursday.