Thursday, June 30, 2011

Stage six

26 kms from Gernika to Bakio, along the river, to the sea at Mundaka, which has a large area of sand and pools with birds and crabs. Then to Bermeo, another attractive fishing village where everone seemed to be in the main square- children played, old men sat in the sun, younger people drank beer.

Along the cliff road to Bakio, a beach town near Bilbao. The highlight was San Juan de Gaztelugatxe, a church on an islet just off the coast, reached by a stone stairway that links it to the mainland and climbs the rocks to the peak where the church is built.

Wednesday, June 29, 2011

Stage five

Very briefly, from Lekeitio to Elanchobe, again over the hills, passing through Itzasper, Ea and Natxitua. All but the last are little fishing villages, each with its port, its beach, and it' surprisingly large church, often of unusual design. In Lekeitio it has spectacular flying buttresses (photos in camera, sorry). Ea has a series of arched stone bridges over the last few hundred yards of river, bordered by brightly coloured houses with flowers.

Now in Gernika, famous for a symbolic tree, an abstract painting and a nasty bit of work by the Nationalists during the war. No time to tell the story, but Google is your friend.

Tuesday, June 28, 2011

Stage four

Today 24kms from Deba to Lekeitio. First over the hills to Mutriku, then along the river to Ondarroa and from there all round the old coast road through the woods to Lekeitio. Almost all of these places are old fishing villages. Much but not all of the fishing is gone but they allretain the beauty and charm of the old port with it's stone houses, the bigger, colourful houses on the overhanging cliffs and hills, the boats in the harbour, and the water cutting it all in half.

I love to approach villages of any kind on foot, to see them in their setting, silent and still, to arrive, to see the life that moves them, to be part of it for a brief moment, and to leave it behind you again, as your road goes on to somewhere else. It's how you know you're moving, when the towns go past you.

Monday, June 27, 2011

Stage three

Thirteen kms from Zarautz to Zumaia along the old coast road that never leaves th sea. A rest for the legs after two hard days in the mountains. Tomorrow we climb again. E stopped off at Getaria to see the monuments to Elcano and the peninsula in the shape of a crouchong mouse. Now we are 250 m above Deba, at a hotel by the old shrine of Itziar.

Sunday, June 26, 2011

To Zarautz

Second stage today. 22 kms from San Seb to Zarautz. Very tough kms, up and down mountains on paths that would make a goat nervous. Up here they don't call it a slope if your cow can stand on it without rolling. It's very hot, without a cloud. It good sweaty on the way towards the end.

In Zarautz there is a kind of meeting of street bands. They walk through the old town playing jazz or whatever takes them. Anything lively will do. And people dance around them as they pass. And another lovely beach, closed at each end by a rising headland.

Saturday, June 25, 2011

Donosti again, on foot

Today we began the walk. 25 kms from Hondarribia to San Sebastian, along a road through the hills parallel with the coast. The cliffs and the sea lay visible below us much of the way. We started at sea-level, at the beach on the French border, and climbed to the pass at Jaizkibel, at 450m, and down again to the sea at San Seb, through Pasajes, a particularly unprepossessing complex of industrial towns and cargo ports. We arrived at La Concha, where a triatlon was just beginning, so we swam, and ate, and swam again, and watched other people sweat for a change.

The big thing here is 'pinchos'. The bars of the old town have dishes out full of different hot and cold snacks, and you help yourself, and pay when you leave. In the old days I remember they would charge you by counting the seafood shells on the floor, but there's a lot more variety now, and we found a couple of places of a very high standard. Tonight the legs need a rest, so it'll be sth nearby.

Friday, June 24, 2011

San Sebastian and La Concha

Today San Sebastian. We start walking tomorrow, so today we just spent the morning on a train and the afternoon on the beach. La Concha is one of the most beautiful beaches in Spain, I spent a few summers her many years ago and it hasn't changed at all. It's a horseshoe, with a mountain at each end and an islet between them with it's own little mountain and hills all around and the port and the old town beside it. The beachfront apartments are worth a fortune. It used to be the place in Spain to holiday, and in a way it still is. The water was refreshing, the jellyfish didn't sting and the it wasn't so hot as down south, which becomes unbearable around mid-june.
Now fo a bit of lobster or sth. Photos later.

The rest of the year I work for a living. Honest.

Addendum: The photo is the sun going down on La Concha. Er, yes, it is my thumb. I haven't got the hang of this camera yet.

Thursday, June 23, 2011

El Retiro

In Madrid. It doesn't really count and we're going north by train, but it's the start of the journey, so an excuse to post a couple of photos.
The Retiro is a park on the centre of Madrid, where people go to do- well, just about everything you can imagine, and a lot you can't until you see it. So, skaters doing slalom and bowls played by men with half a ball.
As I have probably said before, the Retiro is Madrid at play.

Summer and the Road to Santiago

For Hickory the summer has arrived and we are off to the north, to walk the first part of the Road to Santiago, the Northern Path, which mostly follows the coast, usually along clifftop paths with the sea below you or visible off to one side. It goes through dozens of pretty fishing villages (and some not so pretty villages that are mostly factories) and is cooler and much more attractive than the more traditional route through Old Castille. We'll take about a week to do it, starting from Hondarribia, and we'll probably get just beyond Bilbao this year. We aren't in any hurry.

This post was going to be long and meandering, whimsically dwelling on the details of the trail and the reasons we have for doing it (we like the area and we like walking, to sum it up) but time has caught up with me, as usual.

Interest in, even knowledge off, the real world will be even smaller than usual for a few days. Now I have a Galaxy smartphone I can, in theory, read the papers and keep in touch with the world, even on the clifftops of Gipuzkoa, but I don't suppose I shall. I'll use it mostly as a GPS, to avoid getting lost to a philosophically unnecessary degree. I'll try to blog a little, just to report on progress and describe the places we see, and the things that happen. With photos. I love the modern world.

Thursday, June 16, 2011

Gratuitous Texan Song of the Day

Tanya Tucker, at 13, sounding like a middle-aged junkie who's almost given up on the world, with a song that won't die (not in my head, anyway). And it comes complete with a full-tone* modulation at 1:15, in case Mr Wadsworth drops by. I don't call it a gear-change because it seems to work, almost to be required*.

*I think. I'm open to correction.

And as an extra, this one, a simple but powerful story that only that young, raddled voice could tell.

Tuesday, June 14, 2011

Las Tablas de Daimiel

Another area round here worth looking at are the Tablas de Daimiel. Daimiel is a large town of no particular interest, but a few miles to the north west the river flows by and it broadens into an expanse of wetland which is full of birds (yes, we're back with the waterfowl). The best area is crossed by a network of walkways which allow you to get close to all the main breeding grounds without bothering them too much. The walkways start at an old but well prreserved bridge which manages to look shiny and fresh, rather than dusty and dilapidated, and has many several crossings, most with the arches that channelled the water from the time when there were mills along them, as there were on many of the bridges near here.

The route is perfect for the bike, about twenty miles each way through attractive country with no real hills and with birds at the end of it. Mrs Hickory still thinks it's a bit far for her, but she will allow herself to be persuaded.

Could I Have Been a Cockroach?

I was recently asked if I thought the asker could have been born a cockroach.* He seemed rather worried about the possibility that he might be looking at the world from floor level, be in proud possession of six legs and a thick black carapace, have an intellect so limited as to be barely aware of his own existence, and have to eat rotten crumbs and expect to be trodden on at any time. A disagreeable idea. Even though the danger has clearly long past, it’s a nasty thought, and I imagine we have all thought about it at some time or other.

In order to answer the question- yes, I am going to try- we need to define a few terms, and clarify some concepts. Much depends on whether you assume that the consciousness has any meaning or identity outside the body. Many, probably most, people believe that it does have some independent existence and so can be, or could have been, implanted in some other person, or some other creature.

The major religions all take something like it for granted. They all assume that what gives us identity is temporarily fused to the body in life, and is decoupled on the death of the flesh. Some believe that it will be recycled in some other container, depending on how one’s behaviour is the previous receptacle is judged. Despite my love of Indian literature I have not embraced Hinduism or Buddhism, and intellectually I reject the idea of reincarnation, but as a Catholic born and bred I don’t instinctively find the idea of an ultimate separation of body and soul to be absurd.

On the other hand, once you start thinking from a cognitive and physiological point of view, it is easy to understand that consciousness is a creation of the specific biology of a given organic structure. The thing that looks out through my eyes could not possibly have existed in any other place because it is a product of the process that brought me into existence.

This brings up the further question of what animals (and insects) are in fact conscious. Is there, somewhere, a black beetle cursing his luck that he wasn’t born a butterfly? I think not. It could not have any concept of being something other than, better than, what it was.

Then, I wonder, where does that leave the Neanderthals, the Denisovans, the Erectus, the Australopithecus, those who were almost us but not quite? Did they wish they had been us, and curse the fate that made them something else? Did they understand what they were cursing?

*Yes, people do ask me questions like that. Is it because I have a face that appears to hide infinite wisdom, or because young people have inquiring minds, or because I just happen to be there when they say what has just occurred to them? Who knows, but people do ask me improbable things. When I’m struggling with an upside down map while shooting looks in random directions with an imbecilic look on my face in some forgotten corner of a foreign city I can guarantee that a car will stop and someone will ask me if I know where Milo Terencz’s baroque hat factory is. To which the obvious answer would be, “Do I look as though I possess that particular snippet of information?” But then the answer to that is, “Yes, why do you think I asked you?”

I conclude that at least on some occasions people ask me simply because they think I have the sort of face that will at least listen to them and give some kind of response. Which is a bit like the chap who dropped his keys under a bush but was looking for them on the road because the light was better there.

Monday, June 13, 2011

On Buying Plane Tickets

While I'm busy complaining (yes, this is another rant about something which has annoyed me), I mention that I have spent hours this afternoon buying plane tickets. Every time I make a journey by air it gets worse. What with nearly being arrested the last time I'm tempted to give up the whole business but I like to travel and I have family in England so it has to be done.

Some of that time was spent comparing offers. The sites that claim to do it for you compete mostly (I advance the suggestion from my experience) by varying the way they distribute their charges. Those that lower the notional price of the flight per se, will increase the charge for a suitcase, and will charge more for paying by credit card (up to 40 pounds, I have seen, and you can't pay any other way, of course) so in the end there is little difference between them.

What they do do is give you, and the airlines themselves, information about what other airlines are doing, which has the effect of keeping prices down. This is good and if I want to waste an hour in order to save €50 it's because I think it's worth my while. Also, I can fly to England for rather less than I used to pay when I first came to Spain in 1988. In real terms, i pay a third or a quarter of the price I paid then. I love the free market.

But the rest of the time was wasted filling in forms with personal information, including email and phone numbers. The airline wants it, the booking company wants it, and the government wants it. If you don't give it, you don't travel. Some of it you could lie about, but there would still be enough to know exactly who you were and when and where you travelled.

I don't mind too much that companies want and trade with my details. The fact that they can make a living that way is what gives me cheap flights and other goods. I don't have to deal with them, if I choose not to. What i dislike is that governments will use any excuse to control what we do. It has nothing to do with security. My giving those details has not made anybody safer because I have no intention of damaging the aircraft or anyone on it. But if I had been Achmed the Sane, my pockets filled with phials of untraceable but deadly and airborne poisons, and with plastic pistols disguised among my marker pens, they would know that someone of my name was planning to board a plane. It wouldn't be my real name, of course, and it would tell them nothing, and I would plausibly explain away any little discrepancy, and despite all the security, the time-wasting, the ritual humilliation and contempt which we must suffer at airports these days, the plane would come down.

If someone could come up with a way of stopping murderers taking planes I would be delighted to see it in place. In the meantime, I would be grateful if they would just let us get on with our lives.

"Good morning, I wish to fly to London." "Yes, sir. Smoking or non-smoking?"  "Thank you, sir, you will find your plane at the end of that corridor, follow the lady with the red hair and the purple leggings." Does it really have to be any harder than that?

Sunday, June 12, 2011

This Never Would Have Happened in My Day. Harrumph!!

Watching the Gran Prix from Montreal. They have just gone off for rain. Yes, you heard that correctly. After starting behind the safety car and spending half the race that way, except for a few laps in which Hamilton discovered once again that his car will not go through a hole smaller than itself, they have now stopped and are waiting to see if it clears up. There have been no accidents of any consequence, it's purely because they're afraid of driving in the rain.

I have never seen this before and I wonder if there are new safety rules. I haven't heard of any. And if they are going to stop the races in future every time it rains, for me the show is over.


Note added: The only driver killed racing in the last 30 years was the great and lamented Ayrton Senna. In the 60's and 70's they averaged one a year. Drivers walk away from crashes that would have killed them a few years ago. Cars no longer take off when their wheels touch, they don't disintegrate on impact, the driver's head does not bounce around like a grape if he crashes, it is almost impossible for metal parts to penetrate in the river's section, and all of this is wonderful: I don't need blood on the track to enjoy the race. But rain is a different matter. Rain makes driving more difficult. You have to do things differently and pay more attention to more details. It lessens the importance of the car itself and allows the most skillful drivers to show what they can do. The complaints are that they can't control the car properly. What they mean is they have to drive differently and they don't like it. We, the spectators, do, but it seems we don't count.

Friday, June 10, 2011


Sunday will be Pentecost (or Whitsun as it's known in the land of my birth). It marks 50 days after the resurrection and is liturgically significant for a reason I can't now remember. I'm not aware that England does anything special for the occasion, although I have dim and possibly false recollections of rainy Bank Holidays and traditional games that had to be rediscovered every so often because they had fallen out of use.

Over here it's a big event in some places, because it's often when the local Virgins are commemorated. The biggest of them all is the Rocio, down in Huelva, where tens of thousands of people congregate in honour of Our Lady of that ilk. The iconic image is of gypsy caravans and long coloured dresses that swirl as they dance, and every year there are new stories and events which go down, quite literally, in legend and song.

My little city has the Virgen de Alarcos, which follows a similar pattern if not quite on the same dramatic scale. Alarcos is, or was, a mediaeval walled city guarded by a castle on a hill a few miles out of town. In the 11th C there was some continued unpleasantness with the Arabs to the south, and the Knights of the Order of Calatrava were send to guard it. One day in 1095 the Arab army turned up unannounced, overran the place and put the entire city to the sword. It was never settled again.

You can almost see the Arabs in the distance
It's been excavated and partly restored over the last 20 years. I've been up there many times. Standing on the walls, looking out over the plain, you can imagine what it was like, day after day, watching, wondering, beginning to feel safer as the days went by. Then, one day, a movement in the distance, the flash of sun on steel, dull sounds carrying in the still air, and you turn to your fellow guard and exchange a look that says something like, "You know, when I joined the army it looked like a good career. Steady job, living wage, roof over your head, food on your plate, the chance to travel, set up for life, we were. Respect, women, bit of pillage here and there, and a bit of land from the King when you retired."

When you looked back at the plain it wasn't there. It was a mass of armed men, thousands of them, moving quickly in formation with swords in their hands and murder in their eyes. You exchange another glance which just says, "Oh, fuck", and you wait.

In true mediaeval fashion the statue of Our Lady was rescued from the church and carried to safety. It is she who will be placed on a cart and taken back to her old home this weekend, accompanied along the old road by a lot of people, hundreds, and possibly thousands. Once there they will hear Mass, then set about getting completely whammed.

These events are similar in many places around the south of Spain, taking an image to a shrine out of town and setting up camp there for the weekend with the flagon and the camp stove; and the tradition involves, of course, a lot of food and drink, usually fairly simple stuff, the traditional country food. This means that when you wake up on the grass late on Monday morning wondering what you did last night, you have the added pleasure of knowing that breakfast will consist of cheap red wine and fried chorizo. Colour is added by the stalls selling food and drink, headscarves and light dresses, olives, guerkins and pickled aubergines, and the air is thick with recycled fat and the cheerful banter of aubergine salesmen discussing who has the right to the prime pitch by the band.
The Ditch by the Wall on the Left was full of Bones

We often go up there on the Monday (which is a local holiday, for obvious reasons), either on foot or by bike, and contemplate the wreckage as it slowly stirs into life and becomes human again for the last few hours of the fiesta. In case we don't get there this year, I offer this post in advance. It's always the same.

Thursday, June 9, 2011

Blogging by Galaxy Ace

Yes, I have a new toy.

Let's see if this works.
Wow. I can even upload photos. Amazing.

Blogging with a tiny keyboard, reduced funtionality and someone else's fading wifi signal when you don't really have anything to say is so much more fun, somehow.

On Truth in Socio-Biology: A Case Study

It is hard enough trying to work out what the concept of truth can mean in any given context. In fact it is almost impossible even to reach a cautious agreement on what it might, possibly, look like. It is harder still to know when you have found it, or something close to it.

We tend to think that we know truth when we see it, but this is a nonsense that we use to justify our prejudices or to convince ourselves that we understand far more about the world around us than we do. This latter is probably a necessary psychological defence against complete emotional and cognitive collapse (see Total Perspective Vortex). We don't need to know very much, but we do need to think we know.

One thing we think we know is what we are told by competent experts who have carefully conducted series of experiments, made observations, collated data, tentatively advanced an idea based strictly on the confirmed data and limited by the properly identified limits on the precision of the data itself, and had those ideas, with whatever limitations, caveats, contextual provisos may have been necessary, accepted by others equally expert and equally demanding.

There comes a point in this process where we decide that something that might be worthy of the name of truth, suitably qualified by context, has been arrived at. When this happens, those who wish to build upon it, discover new truths related to it, build an argument upon, or merely to feel that they know something about it, accept it as learned truth, and don't trry to replicate it from first princilples before using it in for any other purpose.

It would be impossible to advance in almost any field of study (mathematics is a possible exception), there would be no technological development at all. It has to be that way. But it has some consequences.

(There will now be a slight pause while I thank Blogger for swallowing the second half of this post: ME CAGO EN BLOGGER Y EN SU PUTA MADRE: thank you for your patience.)

Scientists are human, they have mental and physical weaknesses, they have ego and ambition, they have political and moral beliefs, they have intellectual and ethical blind spots, all of which can affect the way they work and how they interpret the data. In spite of this, good science gets done and truths are made known.

As one more quite unnecessary preliminary point, you should know that cranial volume is measured (still, I believe) by pouring in grain or shot or some such thing, then pouring it out again into a measuring vessel. You don't use water because it could alter the surface structure, or be absorbed or slip through cracks. You don't use one of those multi-directional lasers they have on CSI which are so intelligent they not only measure highly irregular spaces instantaneously, they even know exactly what you want to measure before you do. Despite all these advantages, these devices are not used because, I think, they don't exist.

As a case in point, and only because I happen to have read about it today, I offer you the story of Samuel Morton, professor of anatomy at the University of Pennsylvania in the mid-19thC. Professor Morton decided one day to measure the cranial volume of a large number of skulls from different tribal and racial groups, to see whether the differences in character and intellect he had observed were expressed in differences in brain size. He went to the grain store, he measured, he analysed and he concluded that there were observable differences in brain size between populations. This was the accepted position in the field for decades, helped by the fact that it corresponded closely with what other workers expected and wanted to believe.

Then, in 1978, Stephen Jay Gould reanalysed the data and came to the conclusion that Professor Morton had been rather naughty, and had, consciously or otherwise, both taken his measurements and analysed his data in a way that tended to favour the interpretation he expected to find. He explained this at great and persuasive length, and it became the accepted position in the field for decades that Prof Morton's data could not be interpreted in the way he had interpreted it. This acceptance was helped by the fact that it corresponded closely to what other workers expected and wanted to believe.

Now, Jason Lewis et al have published a paper in which they reanalyse the measurements, analysis and interpretations of both Morton and Gould, and suggest Gould has been a much naughtier boy than Morton. John Hawks discusses the arguments intelligibly and coherently, which is the only reason I've understood them, so I suggest you pop over there for further illumination.

So Lewis has shown that something  we thought we knew to be right about how something else that was once thought to be right was in fact wrong, is in fact wrong, for the very same reasons that what was once thought to be right and now may in fact be right after all, was later thought to be wrong. This sort of thing happens all the time. The world does not stop turning. We continue to believe what we want, because to believe is more important than to know. It allows us to function.

Sunday, June 5, 2011

Southern Rhythm and Idle Thoughts

In the end, no waterfowl, I fear. The weather was looking a bit dodgy, though in fact it turned out rather pleasant. But a decision had to be made on the available evidence and it was not to go too far. So we went running instead, which means we can't be 20 miles from home when the rain starts. I say running but, Mrs Hickory having short legs and your blogging hedgehog long ones, in practice she runs and I walk, and we both do satisfactory exercise and see the world a bit. The old railway line is our usual route for this, because it's flat, the ground is even and you meet a lot of people.

But, as I say, no waterfowl. Instead I offer you an observation on the limitations of political debate, and a feel-good song from the deep south; Alabama this time:

"Those who are strictly of the right tend not to recognise that some are genuinely fearful of not being able to provide for themselves and their families. Those of the left frequently forget that someone else has to pay for all their plans. When commentators of the right talk of rights (not a word they use very much, but the idea is often present) they mean freedoms, the absence of interference by government in private life. When the left speak of rights they mean other people’s money. It isn’t easy to understand each other like that, even if it’s only for the purpose of arguing. There is no common ground.

When David Cameron is asked to be, or acclaimed for being, or accused of being, brave, or responsible, or whatever, because he has approved some measure which will benefit some section of society, what he has done is simply to make a calculation as to the distribution of lost/gained votes that will result from his promising that other people will be forced to spend their money to make it possible.

By all means characterize left-wingers as being either stupid or lazy- which some of them undoubtedly are- and right-wingers as being greedy and uncaring- again, some of them are- but they both have a point, an important point essential to their ideas, which is unrecognized by those who disagree with them. We look at the world and we see different things."

Saturday, June 4, 2011

Many People May Still Know Nothing

I have a feeling that 'the wisdom of crowds' is going to be the next big thing in popular misunderstanding of difficult scientific concepts. The idea itself is simple enough- if you ask a lot of people to guess at some value, the average guess is quite likely to be somewhere close to the true value. The founding myth of the belief (the story itself is true, much of what it is taken to mean is not) is about how Francis Galton discovered that the average of the guesses made at the weight of an ox by visitors to a country fair was extremely close to the true weight of the animal.

That such an average guess would be 'quite' close to the real value, for some value of 'quite', is perhaps no great revelation, but in some cases it can be much closer than you would expect intuitively from the amount of information available to the guessers. There are two necessary conditions for this effect to work to any detectable degree- the guessers must have some information (in Galton's case they could see the ox in question and presumably had some experience of oxen in general), and the guesses must be be susceptible to linear comparison, that is, they must represent values.

Anecdotally, a TV magician last year used the idea of the wisdom of crowds to explain how he correctly  'predicted' the lottery numbers. He asked a lot of people what they thought the numbers would be. It was a diversion to hide the real trick, of course, because it fails to satisfy either condition: there is no information that the crowd could possibly have that would produce a useful 'average', and, a point too easily missed in discussions of these things, the numbers on a lottery ball are not values, they are just symbols. The 6 ball is not lower in any sense than the 12 ball. The only thing that matters is that they are different. The balls could be marked with colours from a paint catalogue, or the faces of Tiger Woods' girlfriends (I might be a bit behind with the celebrity gossip), or the shapes of random pebbles picked up on the beach. You can't take an average of something that doesn't have a spread of values.

The same applies, mutatis mutandis, to politics, in that voters are not, in fact, collectively deciding at which point on a line they want the next PM to stand, even though that is how we tend to think of parties and their policies. With markets, the problem is that, unless you are a particular kind of socialist, there is no true value to compare with the price produced by the crowd. The market price is the right price more or less by definition.

The idea is simple enough, I said, so why is it so easy to misapply it? Because to do anything with the idea you have to do understand statistics, and statistics is very tricky stuff indeed. Also, as someone on one of the comment threads linked below says, statistics is maths for boring people, so what with one thing and another we won't be seeing the press paying too much attention to the details of the concept.

Just to give an idea, here is a paper which explores some data collected from a large group of Swiss. Here is an article about it and here is a criticism of some aspects of that article. If you look at the questions the Swiss were asked, you see that their is no obvious way to estimate, even very approximately, the amount of information they could possess about the questions, so that aspect, the link between the available data and the average result, is not assessed. What we do see is the averages are wildly out, by a factor of 3 to 10 in most cases, but that the median and the geometric mean give rather closer, but still on the whole very inaccurate, answers. What this suggests is there are a number of very high guesses skewing the data, as well as the obvious fact that neither individually nor collectively did our Swiss guinea pigs have the faintest idea about any of the questions they were asked.

The paper is tough going for the non-mathematician, but the Lehrer article is readable and shows why I think we'll hear more of it. The criticism is also hard going but is worth a look for what he says about journalistic practice in these cases.

One of the difficulties is that average to most people means arithmetic mean, which is, by the way, what Galton used. But the arithmetic mean, as we said, is a very poor way of characterizing any distribution that has a number of values much higher than the concentration of most common values. And when guessing the population density of Switzerland some people are likely to be out by an order of magnitude or more. But there are other ways of finding a characteristic value. The geometric mean reduces the influence of very high values, and the harmonic mean reduces it even more, while increasing the effect of low values and of the distance between elements. You probably didn't need to know that, but there you are. There is a beauty in the harmonic mean that the other two do not possess, but, though beauty may be truth, it's not a good reason for choosing it.

There is also the median, which is the central value in a set of data points, and the mode, which is the most common value, and both have their uses in characterising data sets. You need to know which one to choose.

The point of all this is that by clicking a few links and making a small intellectual effort, you can know more about the wisdom of crowds than all the people who will shortly be talking about it as though it were the key to understanding the universe.

Tomorrow waterbirds again, I promise.