Learning to Queue

Arriving in a new country, the things you notice first are the differences.
Queuing is a peculiarly Anglo-Saxon habit, but the rugby scrum, common in most busy shops and banks here, is excessive even by Mediterranean standards and takes some getting used to.
Having the sort of bar presence that risks me dying of thirst in a pub, I got used to taking sandwiches and a couple of bottles of water just to go and pay in a cheque at the bank, but have since lowered my standards and learned to queue jump with the best.
One of the most crowded places is my local post office. Not only do we go there to send letters and parcels, it’s the place where telephone bills are paid, residency permits renewed and all manner of government forms obtained. Getting to the front needs broad shoulders (to block those coming behind), a walking stick (not for pity, but to beat others out of the way – well an old lady did it to me once), no shame and absolutely no sense of fair play.
Surprisingly then they introduced a take-a-ticket-and-wait-for-your-number-to-be-called queuing system recently. And guess what, the Beirutis took to it as if they’d been genetically programmed, just needing for the sleeping bit of DNA to be awoken by the little flashing number screen. It became a topic of conversation amongst those now waiting with what passes for patience here. Instead of the usual jostling and pushing there was chatter and even occasional smiles. OK, at one staff change over the new server didn’t understand the tickets and tried to go back to the old system, but a supervisor spoke gently to her and showed her how to press the button which advanced the aforementioned number screen, so even that little incident passed off without much of a hitch.
Queuing by numbers, pay and display on the streets of Beirut, my local pub called the Greedy Goose, after a while it’s the similarities that strike you.

Putting ignorance to work

Once upon a time, I made a complete idiot of myself. Please don’t misunderstand, I’ve done it lots of times, only this one stands out in my memory; I still let out groans of embarrassment just thinking about it.

As a young under-graduate I could be arrogant and worse - occasionally over-blown with self-importance (what’s changed did I hear from the back?). I wasn’t unique, it often comes as a free extra in the kit marked “youth”, but it being a common affliction doesn’t make it any more likeable. And it’s a trap waiting to spring.

A college after-dinner-over-coffee discussion was taking place and one of my companions used the word “bathos”. I had never heard it before and didn’t hear it properly on first meeting. “Pathos” is what my brain interpreted the sound as. And I joined the argument on that basis. What I should have done, when it was clear that I was mistaken in some way, was to shut up and/or apologize and/or make a joke of my error. I did none of those but continued to dig the hole I had started until it was so big the only choice left was to jump in and hope no-one could see me down there, but the humiliating laughter followed. And I still didn’t know what “bathos” meant.

Eventually the message of the experience hit me. If you want to learn, don’t be afraid of ignorance. Embrace what you don’t know and ask it to reveal itself. There are lots of ways to do that – “I’ve never heard that before, could you tell me more?” “That sounds really interesting, I know nothing about it, please carry on” etc. Lot’s of people like showing off what they know and even those who don’t can be persuaded with a bit of flattery. And if these don’t work, you can always Google it.

For those who want an example of bathos or descending from beauty to the ridiculous, Douglas Adams' “Hitch-hiker’s Guide to the Galaxy” provides lots of examples. One I particularly like is approximately “the alien space ships floated gracefully in the air, exactly like bricks don’t”. Thank you Google and Wikipedia.

A birthdays problem

“Hi, I phoned to wish you a Happy Birthday, how are you going to celebrate?”
“Thank you,” said my friend, “but why should I celebrate that?”
“Oh! Errrr, well, umm. I thought you Lebanese celebrated everything.”
“We do,” she said, “except getting older!”

I can understand that, having arrived at a point in life when I seem to have to go in for a service more often than the car. Problem is that a human has rather more moving parts and getting spares is pretty difficult. That means the orders of the day are to exercise, support and if necessary kick-start those aging bits you were born with, not to mention getting them checked out from time to time.

Women are supposed to be better at submitting to these check-out procedures than men, particularly those who have had children. I suppose that being able to react positively and without embarrassment to “put your legs in those stirrups so I can check how many fingers dilated you are” provides a pretty steep learning curve in juggling the warring needs of modesty, dignity and successful bodily function and having to accept that it’s the last that usually wins, at least when visiting the doctor.

Now I promised there would be no “adult content” in this blog. Here’s hoping that sharing with you which body parts just got the once over won’t breach that. Being of the male persuasion, as well as the obvious external differences, there’s a “men only” gland – the prostate – hidden from view with which I came equipped. It’s done its job quite happily down the years without let, hindrance or complaint, I even have two children to show for it. Thank you Mr. P. But some numbers on the results of a recent blood test made my doctor rather worried that I hadn’t ever had it checked. The numbers were my date of birth. So, yesterday was the day.

After close questioning about diurnal, nocturnal and urinal habits it was “OK, drop your shorts and get on the bed”: in other contexts that might have sounded inviting but not here. A trained urologist donning rubber gloves has the sort of effect I imagine is only just shy of the one produced on a Middle Ages heretic seeing the Iron Maiden trundled out for his personal benefit.

“Aaarrggh,” I gasped; “testicles all right then” said the doctor (while I had previously thought that that was so, I was glad of the reassurance that energetic palpating would leave no lasting damage). The prostate, although an internal organ, is in fact accessible for examination, so next came “turn over and face the wall” and that which I had always thought of as a one way street to the rubbish tip had traffic in the opposite direction. And then it was all over. “Well, my friend, do you want the verdict? You haven’t got a twenty year old prostate any longer, but there’s nothing wrong with it for its age”.

A few years ago I needed mild treatment from a physiotherapist for a sports injury. “I’ve played tennis for years,” I said “and never suffered from this before, why now?” Came the reply, complete with broad Aussie twang “it’s just a birthdays problem, mate”.

Maybe I should think about not celebrating mine either.

No, no, I don’t mean it, please keep the cards and chocolates and champagne coming!

Memories of a Palestinian

A friend of mine is about to have a book published and for some reason he asked me to write an introduction or forward or something. So I did. The book's title will be the same as the title of this little piece because I asked him if I could put it on my blog as a "teaser". He seemed really pleased and said "yes, go ahead" so here it is.....

"When I was growing up in post-World War II England, the schools I went to had a daily assembly for all their pupils. A good proportion of that assembly would be an Anglican service, albeit a rather cut down one. Hymns were sung, prayers were said, mainly for the good of the school and its teachers, pupils and future successes, sometimes academic but occasionally to ask the Lord for help to beat rival schools at rugby. The headmaster would say something and there would be a reading or two from the bible. The Palestinians, or Philistines, did not get a good press in those readings. Indeed the word philistine has come to mean someone not interested in culture. But did it mean much to us schoolboys? England was recovering from the ravages of war, rock ’n’ roll started up and for us just entering onto its stage, life was fun, easy, and generally safe.

"Palestine, as mentioned in those daily assemblies seemed remote, and ancient. I don’t think any one of us gave a thought to what being a modern Palestinian might have been like. But Marwan Dajani did and with good cause. He was and remains to this day a Palestinian, born and living his early life in Jerusalem, part of a family with ties to the past, a heritage, and well off – well off enough to have, amongst other things, a holiday home in neighbouring Lebanon. Marwan and his family fled to that home in Lebanon, never to return to their native Jerusalem, when he was just a boy, but a boy old enough to have memories of life in the old country.

"When I, but for very different reasons, also came to live in Lebanon, Marwan chose to make the effort to befriend me and my life is richer for that. He has a fund of stories from his double or even triple life. Now, a warm-hearted and fun-loving family man spending much time playing with and encouraging his growing collection of grand-children, he was at one time a successful executive with international companies and later business man in his own right. He never forgot his roots though, at one time being a friend and confidant of the charismatic PLO leader Yassar Arafat.

"Having cut his publishing teeth, so to speak, with a series of poems about various aspects of his life, an even larger project was envisaged, to take those stories and experiences mentioned earlier and to weave them into a book that not only relates the events and actions of a full and varied life, but adds the dimension of being seen through the eyes of a Palestinian born and bred.

"Some of them are amusing, some are hair-raising but all ring true. It’s time someone gave the Philistines a better press."

A real monster

Anybody heard of the Monster Group? Did you realize that it is the head of the happy family? Like all families not everything is perfect and the happy family has outcasts.

Now what are we talking about? A new soap or reality TV series? Another music track when numbers of celebrity pop icons get a couple of bars to sing? Well, no. These terms refer to one of the less accessible achievements of twentieth century mathematics. It is known as the enormous theorem. Enormous, because the proof is estimated to run to over fifteen thousand pages. That’s like the complete Harry Potter series about six times over.

I’d better issue a health warning at this point. Anyone looking for one of my usual faintly-humorous-with-a-whiff-of-the-ridiculous pieces is going to be disappointed. This, as they say, is something completely different and is an attempt to make something abstract understandable or at least a little more accessible. And it’s much too big for a blog really, I just can’t think of anywhere else to put it. With that out of the way, we’ll press on then.

Since the enormous theorem is so big, I think we better approach it in easy stages.

Let’s start with clock arithmetic, of the hours. When we add a couple of positive numbers together in ordinary everyday arithmetic, the answer is always bigger than either of them, but in the clock version, that is not so. Three hours after 10 o’clock is 1 o’clock. The rule is simple, if the answer is more than twelve o’clock, like forty-five o’clock, you just keep taking twelve away until you come to a proper time, so that forty-five hours after mid-day is actually nine o’clock. Are we all happy so far? Well here’s another thing, there’s no multiplication in clock arithmetic, only addition, which makes clock arithmetic particularly simple to do, there are only twelve numbers and only addition (yes, I know, but subtraction is really just a special sort of addition). A construct like clock arithmetic with a number of elements and a single way of combining them is called a (finite) Group.

We are going to construct another finite group. Imagine a square. Turn it through 90 degrees and what you get looks the same as the square you started with, flip it over, same result, rotate it 180 degrees round a diagonal, same thing. Now let’s number the corners of the square anti-clockwise from one to four and do the same things: we can flip it, rotate it, turn it, always ending up with the square landing back on itself of course, but now we have a better insight into what we did, as the numbers on each corner have changed. For example if we turn it anti-clockwise through 90 degrees, 1 is where 2 was, 2 is where 3 was and so on. Make your own square, if you like, and convince yourself that there are eight and only eight possible positions of the corners. But there’s something a bit odd. If we flip and turn 90 degrees, we don’t get the same result as when we turn 90 degrees and then flip, so the order in which these operations are done is important because different orders sometimes give different results. And this is fundamentally different from what happens when we combine numbers in everyday and in hour clock arithmetic, for then the order of doing things doesn’t matter; two plus three is the same as three plus two and any other two numbers that you can think of behave the same way. If order is not important then the operation is described as commutative.

A Group is a broad church and includes those constructs where order does not, as well as where it does, matter. A group operation can be commutative or not.

Let’s think about the clock again and this time, think about the minute hand which gives a different clock arithmetic, this time with sixty as its base. Embedded within this clock arithmetic is the idea of quarters. These happen at fifteen minutes or a quarter past the hour, half past, quarter to and on the hour. But the quarters form another group, this time with only four elements. Quarter past, plus another half (two quarters) make up quarter to, and so on. This idea of a smaller group happily existing inside a bigger group is called a sub-group. There are sub-groups inside our square changing group too, one of them consists of the rotations only. Can you see what others there are (there are in fact two)? Now our clock arithmetic sub-group is a special sort of sub-group. We can collapse the whole base sixty clock arithmetic group onto it, we can talk of up-to-quarter-past, between-quarter-past-and half-past and so on. We’ve talked about two sorts of clock arithmetic, the 12 hour clock arithmetic and the 60 minute clock arithmetic. Both have the quarters as a collapsing sub-group. For some reason, mathematicians have coined the term “normal” for such a sub-group.

We have constructed groups above which have 4, 8, 12, and 60 elements. Mathematicians began studying groups in the eighteenth century. The first question that they began addressing themselves to was “if I give you a number, is there at least one group with that number of elements?” That’s an easy question to answer and it is “yes”; just construct a new clock-like arithmetic with the given number as the base. The second question was “if I give you a number, how many different groups can you construct with that number of elements?” That, as they say, is a horse of a very different colour and eventually metamorphosed into “can we classify groups in some way to make answering that second question a bit easier”. A French mathematician by the name of Evariste Galois noticed that certain groups had sub-groups that were not normal, and indeed that some had no normal sub-groups at all. Groups of this last type, devoid of normal sub-groups, are called “simple”. If the number of elements in the simple group is a prime number, then the name is descriptive, but if not, then … wow, simple they are not. For those who want a bit of technical spice, the smallest is the group of symmetries of the dodecahedron, and it also has sixty elements.

It turns out that simple groups bear a relation to finite groups similar to the one that prime numbers do to everyday arithmetic. All groups can be decomposed into simple groups, a bit like all numbers can be factored into primes. So, if we could classify all simple groups, then we would have at least classified the building blocks of groups.

And that is what the enormous theorem does, it describes all simple groups and it does so in a constructive manner showing how to make them. It says, roughly, that there are only four (or eighteen, depending on how big you let them be) different families of simple groups, two of which were known to our friend Galois who discovered the first simple group with a non-prime number of elements – it’s the one mentioned above, the dodecahedron’s symmetries. All the families have an infinite number of members. But, and this is where we came in, there are twenty six additional simple groups, including the so-called monster group, and nineteen of the others are (non-collapsing of course) sub-groups of the monster group. This collection of twenty is known as the happy family, leaving six outcastes or pariahs. The monster group is really, really big – it has more elements than the number of atoms that make up the Sun.

Now why is this important, you may ask. Well, although they started to be looked at to help understand algebraic equations, groups crop up all over the place, for example in music, chemistry and physics, so understanding groups means that we get a better understanding of the situations where they can be applied.

But what is unusual about this endeavour is the number of people involved. Mathematics used to be a solitary occupation, but it is becoming more and more a group (sorry, no pun intended) effort, over one hundred different men and women having contributed to the final result known as the enormous theorem.

Perhaps that’s why the imagery in the name is a family one, and the monster group’s other name is “the friendly giant”.

St. George's day

That St. George fellow got about a bit.

For those of us who need to be reminded (and I am one) St. George’s day is this Friday, April 23rd. St. George is the patron saint of England, which is why you see people supporting England with a red cross painted across their faces and white clown make up on their cheeks and jaws – the red cross on a white background is the St. George’s flag. When I say supporting, I mean at soccer, rugby, tennis and oh! all the other sports we English invented and then taught the rest of the world. So they could beat us. After which, we had to go off and invent another sport. That’s the reason we invented so many. These days we’ve given up inventing new sports and just practice being good losers at the old ones. But I digress, let’s go back to St. George

I have yet to see dragons in England but perhaps they’re driving incognito up and down the M4 to go shopping in Newbury under a different name, something they couldn’t do when St. George was around, as the M4 hadn’t been invented yet. Supposedly he rescued a damsel in distress by killing a dragon but nobody knows quite where, so it could have been near Newbury. Quite a feat dragon killing, even for a Roman soldier successful enough to have become one the Empire’s most senior officials – a tribune.

My daughter told me that St. George is also the patron saint of where she now lives – Catalonia – where they make a big thing of it with pageants and days off school and gifts (flowers for the girls and books for the men according to tradition). Apparently half the people there are called “Geordie”, after St George rather than in honour of the annual vacation invasion from Newcastle - anyway it's spelt differently there - Jordi.

Rome, Catalonia and England would have been impressive enough but he is also the patron saint of the city of Beirut. Lebanon has over thirty churches named after him, not to mention a number of bays, villages and even a monastery.

Where else did he get to? Obviously, we’ll never know for sure, but he is also the patron saint of Georgia (that's where the name came from), Ethiopia, Lithuania, Aragon, Palestine (where he was born) and Russia as well as a string of cities including Moscow and Preston.

How did he visit them all? By foot and horse. While people are talking about beating the ash cloud with coaches, ferries and trains, no-one is yet planning a trip from Moscow to Preston by St. George’s favoured methods. Yes, he really got about a bit.

Don't mention the War

Beirut is going to be the featured city in the next issue of a well known airline’s in-flight magazine.

I know that because they sent me an email asking me if I’d say a few words about what it’s like doing business in Beirut. Why me? Well in another incarnation I chair an organization called the British Lebanese Business Group – catchy name eh – you can find it on facebook or google. We arranged a ’phone conversation and, when we spoke, I rambled on for a bit about how well educated the workforce is, the legendary Lebanese language skills, the importance of personal relationships and then came the question: “what do we say about the war?”

Perhaps your first reaction is the same as mine – which war? There’ve been a lot, the wacky and obscure War of Jenkins’ ear, a couple of World Wars and the romantically named, but as usual violent and bloody, Wars of the Roses. Now war is not a funny subject. There’s a line in the film “In the Loop” delivered with feeling by James Gandolfino’s wonderfully over the top three star General – “When you’ve been to war once, you never want to go back again. It’s like France” – which is perhaps as good a sound bite as you’re ever going to get on the subject. Mind you, having lived in Paris for some time, I profoundly disagree with the second part of the sentiment.

A moment’s reflection suggests two candidates in relation to Lebanon, the hostilities in 2006 with her Southern neighbour, Israel-and-the-occupied-territories, and the civil war, which began thirty-five years ago this week. Thirty-five years ago, and yet that’s the one. Why? I have a theory. It was the first war when modern communications were on hand to record every horrible moment. Yes, Pathe News was going strong during World War II, but their newsreels were shown after the fact and were heavily edited to be uplifting for the British public. The reality of the Korean War has been demolished by the fantasy of M.A.S.H. But during the Lebanese civil war, the internet began its charge to universality and CNN was founded, both media bringing direct news as it happened into your living room, with all the power of moving pictures in full colour. So, although there have been over thirty wars actively conducted in the last decade (google “wars of the 21st century” if you don’t believe me) and the Lebanese civil war doesn’t make the cut of top twenty 20th century conflicts (google again), it’s the first one we saw live on TV and so remember. There is nothing quite like your first time.

So what do we say about the war? The obvious answer is “don’t mention the war” but John Cleese destroyed that possibility with a “Fawlty Towers” episode – made nearly forty years ago as an hilariously excruciating study into the humour of embarrassment. But it wouldn’t work anyway, as, if my theory is correct, we have to accept the fact that the Lebanese civil war lives on as a kind of world group sub-conscious memory - I have heard a mum address her child thus “go and tidy your room, it looks like Beirut”. So, in the end let’s settle for something like “one thing unites the Lebanese, and that’s a desire to look forward to the future and not to dwell on events of over twenty years ago”.

I’m going to have to start reading in-flight magazines to see if that hopeful, but rather stuffy and indigestible, phrase made the cut. Somehow, I doubt it.

A day at the races

It’s time we got something straight - I’m a townie. Not an ignorant one; I understand the food chain, I know that meat comes plastic wrapped from the supermarket before it goes in the ’fridge.
Don’t get me wrong, I like the countryside, particularly in a Constable painting. And I love looking out of a ’plane’s window at all those pretty little green and yellow squarie things (the fields?) when flying across England. But you won’t catch me in it, the countryside that is. I’m comfortable on paved streets, smelling the glorious odour from a coffee shop or hearing laughter spreading through the open door of an overheated restaurant on a cold night. I am decidedly not comfortable with the dark and the haystacks and the farmyard smells and especially not with any of God’s creatures larger than a cat, unless, of course, it’s human. OK, I can tell the difference between a Great Dane and a Bengal Tiger, but only just, and certainly not from the effect on my pulse rate. Perhaps it’s something to do with having been chased by a sheep on the Derbyshire moors as a child; let’s face it, if I have problems with sheep, what chance have I got with, perish the thought, beef, pork or venison on the hoof. You’re absolutely right, none whatsoever. And I wouldn’t want to mess with a chicken either, particularly one with hooves.
Rather strange then, that I enjoy a day at the races.
Beirut has a racecourse, the hippodrome. That is a miracle in a city where so many traditional houses have been ripped down so that the land on which they stood could be pressed into service for an eight storey apartment block. The real estate value of the hippodrome must be astronomical, but it has escaped the clutches of the developers so far. There’s a decent sized track with all the trimmings, modern starting gates, photo finish equipment, winners enclosure and paddock. There’s also the stuff for us people - stands, restaurant, bar, lounges, live TV feeds from other European race meetings and, of course, betting. There’s a Tote of course, with the changing odds flashing up on TV screens, but no little men on the course waving their arms about and tapping their hats. Oh dear no, all mobiles and laptops today.
Now I wouldn’t say that gambling is big here, putting the equivalent of a tenner each way on the Tote will change the odds noticeably, but the excitement level is much the same, as are the excuses for backing the wrong horse – “Did you see what that jockey did to my nag? Trying so hard to pull him up, he was, he almost slid off down the tail!”
So there I am then, ready for the next race, in the bar, computerized betting slip in my pocket, glass of local red in one hand, binoculars in the other, focused on the closed-circuit TV on the other side of the room. Perhaps I could get used to country life after all.
Picture courtesy of Yahoo sport.

Unslipping a disk

“Agghhh” said my wife, “I can’t stand up, help, I’m in pain!”
In attempting to pick up a handbag from over the back of a chair, she’d “pulled something” in her lower back. All right, so the handbag was of the small suit-case size variety, but the combination of bending at the waist, twisting to the left and then grasping and lifting with the right hand seemed to have caused damage, and way above what might have been expected from a movement so common place.
Something similar had happened five or so years before, and a physiotherapist had taught her a series of exercises to use in the event of back strain or pain. To the untutored eye, it looks like she is rolling around on the floor on her back, but close inspection and perusal of the appropriate exercise manuals show clearly that what she is in fact doing is, well, er, rolling around on the floor on her back: but it normally does the trick. Sadly not this time.
We have, here at home, a huge pharmaceutical cupboard full of drugs that all say “only to be taken under medical supervision” (why? we can read the instructions can’t we, if we want to) and “do NOT drink alcohol while taking this drug” (I always try to wait at least five minutes). So if the floor-rolling doesn’t work, or if there is continuing pain, she reaches for a drug which is a mixture of anti-inflammatory and pain-killer, but with the unfortunate side of effect of eating the stomach lining.
Later that same day, we cancelled dinner and the cinema and booked an appointment with an orthopedic specialist, as home treatments were not being effective. Lebanon has one of the highest ratios of doctors per unit of population and all available for consultations, so no Specialist by referral only, thanks very much. The following morning a slipped disk was diagnosed.
Disks don’t actually slip, we discovered, they suffer a tear in the lining. The inner squidgy stuff, which does the shock absorbing, then leaks out. It’s the effect of the leakage on emerging nerves or the closer proximity of the disk’s surrounding vertebrae that causes the pain. And this is what everyone, inaccurately, terms a slipped disk. Treatment is a combination of ancient (hot water bottles while resting with knees bent) and modern (the above mentioned drugs).
What is horrifying about such an event is the number of things taken for granted that suddenly become difficult, making a cup of coffee, bending to smell a flower, climbing into bed and never mind driving, just getting in and out of a car.
There’s all sorts of bits of advice I could give, (avoid pot-holes when driving a sufferer, being the most obvious), but no-one is going to take them. So, I’ll just end by hoping that putting this down on electronic paper has not jinxed her recovery as, fortunately, two months down the track, the light at the end of the tunnel appears to have been switched back on – she can stand without pain again. Next week she may even pick up a handbag, but not, let’s hope, from over the back of a chair!

A new tax year dawns

April 6th is a truly significant date in the calendar of the United Kingdom; it’s the first day of a new tax year.

Once upon a time (like when my Dad did his tax return) loads of huffing and puffing over an enormous buff form, replete with boxes for numbers to be written in was the order of the day, or actually more than a day as I recall it. In those days the currency of the realm included not only the familiar pound, but shillings and pence too. There were twelve pence in each shilling and twenty shillings in each pound. Calculators were still to be invented so a facility with mental arithmetic was needed just to go shopping. My father had the trick of running three fingers, at speed, down a foolscap column of figures, one finger for the pence, one for the shillings and one for the pounds, and writing down the (always correct) total in a single flourishing movement. So if he huffed and puffed for a couple of days over a tax return, doing the sums for the inland revenue each year must have consumed a fair bit of the UK’s total production capacity. Thank heavens for the home PC and FBI (for American readers, that stands for “file by internet”).

Incidentally, next time you buy something for, oh, let’s say fifty-seven pence, hand over a pound coin, a two pence piece and a five pence piece and watch the amazement on the face of the shop assistant after they’ve wrestled with the calculator for a bit

But I digress, at least twice, from my original intent. Why April 6th? Why don’t we have a normal date for the start of the fiscal year, like the Americans and the French who pick the more memorable, if less imaginative, January 1st?

I was going to say it’s all Pope Gregory XIII’s fault, but maybe Julius Caesar should take more of the blame as he got it wrong in the first place. I refer to the correction to the calendar by some eleven days, to bring the longest day (in the Northern Hemisphere) back to June 21st (well, sort of, on average, most of the time). Britain finally adopted the Gregorian calendar in 1752, a bit late, as Pope Gregory wanted a universal changeover a hundred and seventy years earlier, but better late than never.

Well I say Britain, but it wasn’t universal. His Britannic Majesty’s tax collectors refused to change, as they thought they’d lose eleven days’ taxes, so they continued blithely on using the old calendar of Julius Caesar. A few moments thought will convince you that eleven days before April 6th is March 26th which seems about as esoteric a choice of new year as you can get. Actually another shift of a day had taken place in 1800, a leap year in the old calendar, but not in the new, which takes us to March 25th, which from 352 AD was reckoned (incorrectly) to be the start of Spring and so the beginning of Christian year and so the date from which to start reckoning tax liabilities each year. Phew!

So there you have it. Presumably April 6th is not going to change anytime soon. Makes sense that Julius Caesar would be in there somewhere, after all “render unto Caesar …” and all that.

Easter Message

Easter Sunday, the most holy day in the Christian calendar, fell on April 4th this year. Now that’s a more unusual statement than it might at first seem, for this year Easter Sunday fell on the same day for all Christians, both those of the so-called Eastern and Western varieties.
Easter day is calculated from the first full moon of Spring and, with the moon trotting saround the Earth at a crisp four thousand kilometers an hour, the timing of the full moon varies depending on where you are, as the moon is at a slightly different place in the heavens and with a slightly changed aspect as it rises in varying locations around the world.
I wondered if I’d missed something and that, after nearly a thousand years of schism, agreement had been arrived at on the timing Easter, so I checked next year and, what do you know, they’ll only be one Easter again, according to Wikipedia, on the 24th April. But when I looked up 2012 hopes were dashed, we’ll be back to same old, same old and they’ll be weeks apart. No agreement after all, something that doesn’t surprise, just disappoints.
One Lebanese friend had a different, and typically pragmatic view, though; he felt that he’d been done out of a day off, as both Easters warrant National Holidays here!
As a child, I did the Sunday school bit and still have on my desk a little booklet, written in my childish printing, of St. Paul’s revelation on the road from Jerusalem to Damascus. There’s even a map, drawn in crayon, of the Holy Land, Syria and Lebanon.
About half a kilometer from where we live is another Damascus Road, the one from Beirut to Damascus: it’s about a three hour drive. Surrounded by a fair amount of Biblical geography, it’s easier to feel a connection to events that took place all that time ago.
But there’s something incomplete, to adult eyes at least, about that childish map: there are no boundaries.
So, although I can drive to Damascus, up into the mountains of Lebanon, around the corner into Jordan and take a dip in the Dead Sea, Jerusalem is impossible. I have been driven down to the border of Israel and the Occupied Territories (the official Foreign Office nomenclature for the Holy Land that was) and walked along it. On one side of the barbed wire and no-man’s land were irrigated, green plots and pretty houses with gently sloping red-tiled roofs, built in something like Cotswold stone. On the other side were irrigated, green plots and pretty houses with gently sloping red-tiled roofs, built in something like Cotswold stone. The border fortifications had no gaps.
I broke off writing this to listen to breaking news, late on Sunday evening. Three car bombs hit targets in Baghdad, killing scores of people, so this little piece is not going to finish in the way originally planned, rather ….
What was the message behind Easter again? Oh, yes, love one another and be ready to forgive.

Do you speak Lebanese?

At first sight, “Bonjourayn, Sir” looks like a Scrabble accident: unless you live in Lebanon. It’s a collision of the three languages in use here, French (bonjour=good-day), Arabic (-ayn=two of whatever you attach this particular suffix to, it gets to be a plural when it grows up) and English (sir, addressed to a male person as a mark of respect or disdain depending on the inflection used).

It is common for an educated Lebanese to speak Arabic at home and with the family, have been to a French school or lycée and studied for business, engineering or medical degrees in English. Why French? Well Lebanon is an ex-French colony; one Charles de Gaulle used to live just up the road from where we are now. Why Arabic? Lebanon is located geographically in the Middle East and belongs to the Arab League. Why English? It’s the language of business and the Lebanese have been a trading nation since before the days of the silk route. They’re very good at both languages and business – the current head of the Forbes top 100 richest list may be claimed by Mexico, but the guy is actually Lebanese, and you’ll find a good few more on that list too. Lebanon is about as over-represented on the successful business people list as Britain’s Cambridge University is when it comes to Nobel prizes.

Trouble is, during normal daily chatter, there seems to be little attempt to stop leakage from one language to another, often in the same sentence, and sometimes in the same word, as in the example above. “Fee” - Arabic for “there is” - is also in popular and frequent use, as it’s a nice economic one syllable and not two. At first I thought I was witnessing the birth of new language, rather in the way that English must have emerged from the well stirred ingredients of French, Anglo-Saxon and Norse in the Middle Ages, but now I believe it is more likely to stem from the Lebanese respect for foreigners. They all really try to make a foreigner welcome by attempting to speak in something close to his or her native tongue; even the weather beaten and slightly Parkinson diseased beggar on the street says “thank you, sir” when I drop the local equivalent of a few bob into his hat! But when they can’t think of the right word in what they hope is your language, well, hey ho, pick one from another tongue instead, it’ll be almost as good.

This can lead to some bizarre situations. An Iranian (that’s Persian in old-speak) friend once told me he spoke European, and when I asked him what he meant he said that the words were pretty common across the Europe of the old Roman Empire, he just had to change the accent a bit! I think this was much the same attitude as that of a taxi driver who transported me recently. He’d lived in Germany and Portugal and we had a weird exchange (I was going to say conversation, but that would be an abuse of the word) with me wielding my limited kitchen Arabic and him responding and worse, asking questions, in a mixture of German and Portuguese. Not having either of these myself, you might expect the thing to have decayed rapidly into an embarrassed silence, but not a bit of it; noises were passed back and forth for a good ten minutes, with minimal comprehension on both sides, I should imagine, before arrival at my destination relieved us both from further potential ear and brain damage.

It’s time I left to go and play bridge at the local club, “fee match en une heure” as they say.

Sloth

Sloth

No
Not yet
Let’s go home
And watch TV
Maybe have a beer

Now?
Too soon
Tomorrow
Perhaps next week
Or even later

Rest
Sit down
It’s too hot
Don’t move too much
Stretch out, whatever

Pant
Respire
Move the air
Breathe in and out
Don’t battle the wind

Stay
Don’t go
There’s nothing
More important
Than chilling with friends

What?
Enough
Never stops
Time for sleeping
Where did the day go?

Taming uncertainty or why your telephone works

“There are lies, damned lies and statistics” is a remark usually attributed to Benjamin Disraeli, a nineteenth century British Prime Minister and some time novelist. It was popularized by Mark Twain who probably wished he’d said it first himself. Most of you will have heard it and maybe even used it, perhaps accompanied by a wink or a sage shake of the head in an attempt to denigrate a number that is disliked. The trouble is that statistics was not really put onto a sound basis until well after Disraeli’s death. That’s polite speak for great quote, rubbish analysis.

Elsewhere on this blog is a short piece on a few of twentieth century mathematics more accessible achievements. This is going to attempt to make accessible one of the more difficult achievements. Oh dear, I sound like a conjurer announcing his latest sawing-a-lady-in-half trick. Never mind.

Most of today’s statistical tools were either created, or at least plucked from obscure mathematical papers, during the first two decades of the twentieth century. Why? Because a number of things created a demand for them, three of these were inventions that were rapidly adopted, the telephone, the car and the punched card which in its turn had been created to fulfill a need, that of storing and using the data created by the USA’s ten year census. The punched card was to play a big part in the spread of computing many years after its conception, but I digress, that’s a story for another day.

One telephone, by itself, is not a lot of use (the person who sold the first, must have been a brilliant salesperson), but when you’ve got a lot of them you reap the rewards. Any two people can talk to one another provided there’s a line to connect their two ’phones together. That creates a problem, it is just not practical for each one to be connected to every other by a piece of wire: no problem for the first two, only one piece of wire is needed, but ten ’phones need forty five wires and a couple of thousand ’phones would need very nearly a million to join them all together. Back to the drawing board. The solution, which is still the same one used today, is to give each ’phone a label (today that’s the telephone number) and join it to a central hub. At the hub there is set of switches that allows any ’phone to be connected dynamically to any other. OK, there are multiple hubs, and the connection may be by radio, but the principle remains the same.

And now came the big question, what size does the switching mechanism need to be? Today it’s largely done by computers, but in the early days, the switchboard was operated by hand, with wires actually being connected together by plugs, a bit like those used to connect speakers to a stereo system, and at the end of the call, the plugs were removed. Whichever way it’s done, the question about the size of the switch remains, so how do we find the answer? Depends on how many calls are made and how long the calls last. Right then, how long does a telephone call last? Well it varies, it’s not certain. And how often do you make a phone call? Don’t know, it depends.

At first sight those answers do not seem terribly helpful. But please come centre stage Dr. Agner Krarup Erlang. He started by asking another question, how long is someone prepared to wait to get a connection before they give up, and then made the leap that all three questions have a statistical answer. For example there is a mean average length of time for a ’phone call and a measurement of the variation from that length, both calculable from historical data.

He then managed to combine all three questions into a formula that requires wrapping a wet towel round your head before approaching it, but which is (dare I say it) quite easy to use. Much more important, it works, is still used today and has found applications in many other fields, for example the science of epidemics.

It isn’t as catchy or as memorable, but perhaps what Disraeli might say today is “You can tell lies, damned lies over the telephone, but you need statistics to make it work”. Hmmm, I’m not certain that he would though.