wot I red on my hols by alan robson (mathemathithimuth)

x Marks the Spot

Recently all the sixteen year old school children in New Zealand have been taking their certification exams. A lot of controversy has arisen around the algebra paper. Apparently it was far too difficult for the students and many of them were reported to have left the exam room in tears. It would seem that the questions asked on the exam did not really reflect the curriculum as it had been taught during the year.

When the controversy first arose, the exam questions were published in the media so that we could all see for ourselves what the students had been struggling with. Out of curiosity I took a look at the questions and I even answered several of them. Despite the fact that I've not used algebra in any serious way for at least forty years, I found the exam to be quite straightforward and relatively simple (though some of the questions did seem oddly pointless). I must admit that I was rather surprised that the exam was aimed at sixteen year old students – I would have been dealing with these kinds of exam questions round about the age of twelve or thirteen. By the time I reached sixteen, I was well into the study of calculus and I had left this kind of elementary algebra far behind.

At this point, I could play the old curmudgeon card and grumble that the youth of today have it far too easy. The study of mathematics (and presumably of other subjects as well) has been dumbed way down. In my day we really had it hard. (Cue the Four Yorkshiremen sketch...)

Of course, every generation thinks that way. Every generation is quite contemptuous of the education that the next generation receives. I don't really believe that standards have declined to the extent that some of the curmudgeons among us seem to think. All that has happened is that the subjects are just being taught at a different pace, and perhaps with a different perspective, than once they were. If today's students ever go on to study technical subjects as part of their tertiary education, I'm sure they'll be properly introduced to the mathematical tools they need at the appropriate time. I just learned those tools earlier than they will be learning them, which is really no big deal at all in the grand scheme of things.

David Mitchell is a British mainstream writer whose books have won numerous literary awards. His novels are full of science fictional references so it is clear that he is widely read in the field, and he really doesn't care who knows it. I tend to think of him as the British equivalent of Michael Chabon (an American mainstream novelist whose books are also very science fictional and who is a proud member of the Science Fiction Writers of America). Both Chabon and Mitchell are living proof that literary novels do not have to be stultifyingly boring to make their points, and that the books can borrow freely from genre tropes without any sense of shame.

Mitchell's first novel (Ghostwritten) consists of a series of seemingly unconnected novelettes, though after a while it becomes clear that major characters from previous stories also have minor roles to play in later stories. Eventually the themes do merge and tie themselves together. Structurally the book is a little pretentious, as is often the case with literary first novels, but it's cleverly done and it certainly kept me reading all the way to the end. The book tells a series of stories that are set all around the world from Okinawa to Mongolia to New York City. There's a large cast of characters, and not all of them are human. Indeed, one of them is a disembodied intelligence that flits from mind to mind – a very science fictional concept! The novel also makes explicit references to Isaac Asimov and his laws of robotics. Science fiction fans will find themselves very much at home with David Mitchell, I think.

Black Swan Green, also by David Mitchell, is almost (but perhaps not quite) a YA novel. Some of the ideas it explores are perhaps a little subtle for a YA book – but possibly that might enhance its appeal to adult readers. The story is narrated by one Jason Taylor, a thirteen year old boy who stammers (as does Mitchell himself – there's a lot of autobiography in this book). I was at school with a boy who stammered, and I recognised much of what Jason found himself going through; from the outside at least.

The events of the story take place over a period of thirteen months. The novel has thirteen chapters, one for each month, and each tells a complete short story – Mitchell must like this kind of thing; it's a very similar structure to the one he adopted for Ghostwritten. But the whole is greater than the sum of the parts, for there is a much stronger story arc in this book than there was in his first novel. In other words, the novel is a proper fix-up, in the grand old SF tradition. And just to ram the message home, Jason reveals at one point that his favourite writers are Isaac Asimov and Ursula le Guin...

So what's it about? Well, it's a coming of age story and like all the best coming of age stories it explores themes of  love, death, beauty, war, family, politics, marriage, and prejudice. It is so easy to identify with Jason that all these deeper concerns slip down like sugar-coated medicine. At one time or another, we've all fallen in love inappropriately and seen families torn apart. We've all seen war through childish eyes (when it appears glamorous) and yet sooner or later we've also had to come to grips with the true horror of it when it has some sort of real impact on our lives. And that's what makes Black Swan Green so real. So that's what it's all about.

Oh, and did I say that it's also great fun to read? No? Well, it is!

Slow Dancing Through Time is an anthology of stories that Gardner Dozois has written in collaboration with (in various combinations) Michael Bishop, Pat Cadigan, Michael Swanwick, Jack Dann, Jack C. Haldeman II and Susan Casper. It's a broad ranging collection of surreal humour (sometimes with dinosaurs), urban fantasy with a twist and deeply thoughtful stories that nevertheless pack a punch. The stories are elegant, clever and often very wise. Sometimes, as an added bonus, they are very funny as well. It's the best anthology I've read in ages – every story worked for me. There wasn't a single dud, and it's very rare that I can say that about an anthology.

Highlights include The Gods of Mars in which Percival Lowell's Mars and Edgar Rice Burroughs' Barsoom are shown to be real – for strange values of reality, Afternoon at Schrafft's in which a cat proves to a wizard that he's not much use without his familiar, Touring which describes a concert at which Buddy Holly, Elvis Presley and Janis Joplin perform their best ever sets, Slow Dancing With Jesus in which the literal Messiah escorts Tess Kimbrough to her high school prom and Send No Money in which a lady receives junk mail that changes colour and talks back to her. You will probably have different favourites and that's exactly as it should be because your tastes are different from mine. But I guarantee that you'll have a lot of fun choosing your highlights from this superb story collection.

Traveler of Worlds is a transcription of several long conversations that Alvaro Zinos-Amaro had with Robert Silverberg over eight days in 2015. In these talks Silverberg muses about his life, his work, art in general, his own art in particular, and cats. There are no great personal revelations here. Silverberg is a very private man who keeps himself very much to himself (perhaps that comes from being an only child – as an only child myself I can certainly understand how he feels). But nevertheless we do learn some things about the inner man. He was raised as a Jew, but he himself has no religious beliefs. He consciously decided never to have children (though he does not tell us why). He is happily married and he loves gardening.

Like his good friend Isaac Asimov, Silverberg is a polymath. And, also like Asimov, he has written a huge amount of non-fiction about a vast range of subjects. So when he talks about history, travel, art, opera, archaeology, food or a myriad of other things as he does in these conversations, it pays to listen closely for he knows whereof he speaks.

But the true richness of these conversations comes from Silverberg's musing on the art of writing. He discusses the importance of sentence structure with many examples of horrible sentences from revered authors such as Thomas Hardy, who he finds almost unreadable largely because of his badly structured prose. He also talks about fitting his own style to the subject. When he expanded some of Asimov's short stories into novels, he consciously adapted his style to more closely reflect Asimov's own prose.

Silverberg is well into his eighties now and he talks candidly about how little time he feels that he has left. He has few regrets and he is, quite rightly, proud of the legacy he will leave behind him. After reading what he has to say in these conversations, I feel a definite need to dip again into my vast Silverberg collection and re-read some old favourites...

Then by Rob Hansen is subtitled Science Fiction Fandom in the UK 1930-1980 and that is exactly what it is. It's an enormous (and enormously erudite) book. Goodness knows where Hansen dug up all his information from. Somehow he even managed to track me down! I was never hugely prominent in UK fandom. I was always there on the edges but I took little part in any "real" fannish activities. Nevertheless, Hansen records, quite rightly, that I was a member of the team that won an SF quiz which was held at the Crabtree pub in Matlock, Derbyshire on 15th November 1978. I have absolutely no idea which obscure fanzine reported the details of this quiz – certainly I never saw a report of it. I do actually remember taking part in the quiz, but I really don't remember where it was held and on what date it took place... Nevertheless the indefatigable Rob Hansen (who has probably read every fanzine ever published in the UK) managed to find out about it and has now immortalised both it and me in a proper book. Clearly all of you need to own this magnificent volume. Go and buy it immediately so that you can see my name in print.

Invisible Ink is a collection of Christopher Fowler's eponymous columns for the Independent (a UK newspaper). Each column discusses a once popular author who has disappeared from sight and from print. The book collects Fowler's first one hundred columns. As far as I can tell, the columns are still going strong – a cursory bit of giggling reveals that in column 319 Christopher Fowler discusses the career of a mid-list author called Christopher Fowler! An amusing bit of cheek...

I'd heard of most of the writers mentioned in the book and I've read stories and novels by at least half of them, so perhaps they aren't as obscure as Fowler likes to pretend they are. But on the other hand, it is undeniable that these days much of their work is only to be found on the shelves of second hand bookshops. Perhaps I was just lucky to have been around in the heyday of people like Gerald Kersh and Nevil Shute (though I must confess I was surprised to find Shute on Fowler's list; I'd hardly call him an obscure author. Nevertheless, he is largely out of print these days, so perhaps there's some truth in Fowler's assertions).

It's a fascinating read and when I got to the end, I found myself wanting more. So back I went to them there interwebs where a giggle search for:

site:www.independent.co.uk "invisible ink" "christopher fowler"

gave me 222 hits, a suspiciously odd even number...

Probably the biggest scandal in Britain in the 1970s was the trial of the politician Jeremy Thorpe who was accused of conspiring to murder his homosexual lover Norman Scott. At the time, Thorpe was the leader of the Liberal party and the scandal associated with the charges against him proved to be the kiss of death for both Jeremy Thorpe's and the party's political ambitions. The Liberal party withered and died, remaining as only a pale shadow of its former self in a liberal-democrat coalition (the "lib-dems") with the Social Democrats and Jeremy Thorpe himself vanished into obscurity.

John Preston's book A Very English Scandal gives a detailed account of Thorpe's life and discusses the scandal in depth. It is a book that could only have been published after Thorpe was safely dead (he died in 2014) because even though Thorpe was acquitted of the charges against him, there seems little doubt that he really was guilty. These are words that could not safely be said (or published) while Thorpe was still alive.

Thorpe was a lifelong homosexual. For much of his life, particularly when he was most active, homosexuality was illegal in Britain. Thorpe was by no means the only gay politician in parliament and there was a gentleman's agreement with the press to keep such things from the public eye. But Thorpe's affair with Norman Scott was such that there came a time when the details could no longer remain hidden.

When the affair ended, Scott began to blackmail Thorpe. Initially Thorpe tried to placate him and buy him off. But Scott refused to go quietly and kept returning with more and more demands. He claimed to have some embarrassing letters from Thorpe and threatened to go public with them. An increasingly desperate Thorpe began to contemplate more extreme measures, and here the plot really becomes very murky...

One thing is quite clear – in October 1975, on a lonely road on the edge of Exmoor in Devon, a gunman shot and killed Scott's dog and, it seems, attempted to shoot Scott as well. Evidence emerged that Thorpe had repeatedly urged his friends to murder Scott. Eventually Thorpe and three others were charged with conspiracy to commit murder and brought to trial at the Old Bailey. But Jeremy Thorpe had friends (and probably lovers) in high places. The judge at the trial was notoriously inept and partial. He left the jury in little doubt as to where his real sympathies lay and Thorpe walked free.

Preston's book makes it clear that this was almost certainly a miscarriage of justice. There is little doubt that Norman Scott's blackmailing really had driven Thorpe to take desperate measures. The whole story is the stuff of which soap operas and cheap thrillers are made. But sometimes life really does imitate art, though for very low values of art.

There were two things about the exam controversy which worried and annoyed me.

Firstly it was reported that some of the maths teachers were also finding the exam questions difficult to answer. A photograph was published of a group of puzzled maths teachers staring at a whiteboard covered in scribbles which supposedly detailed their total failure to answer one particular question. This really is worrying. How can they possibly teach the subject effectively when they themselves are stumped by such elementary questions? What qualifications do they have to teach the subject? Are they, perhaps all English teachers who just teach maths on the side by keeping themselves the proverbial one chapter ahead of the students? Enquiring minds want to know...

The other worrying thing was the way the exam controversy was reported in the press and on radio and television. Without exception, the journalists who covered the story confessed themselves to be mathematical ignoramuses who found the whole thing quite bewildering. And what is more, one and all, they seemed to be quite proud of their ignorance.

In a particularly egregious example, one enterprising television journalist actually got a university mathematics lecturer to answer one of the questions in the studio. The lecturer launched in to a particularly lucid explanation of what he was doing and why he was doing it as he slowly worked his way through the problem. He reached a point where he noted that he had now derived one equation with two unknown values in it. In order to solve the problem, he said, he needed a second equation. At this point we cut back to the studio for the journalist to witter on about nothing very much for a while, then we returned to the lecturer who, as if by magic, now had the second equation that he needed. From that point on, the solution was trivial and he quickly reached an answer. Then we returned to the bewildered journalist who said he was sure that somebody in the audience might have understood that, but he himself had no idea what it all meant.

Obviously the decision had been made to broadcast this formal solution in small sections with linking material from the journalist, so as not to overload the attention span of the audience too much. But somewhere in the back and forth between the two, a vital step in the lecturer's argument ended up on the cutting room floor, rendering the whole explanation pointless and turning it into gibberish. But since the journalist clearly believed that the entire subject was gibberish anyway, he really couldn't see (and didn't care) that omitting a whole section, presumably for timing reasons, made a complete nonsense out of the whole business. After all, he clearly believed that no ordinary person could possibly understand such esoterica anyway, so what difference did it make?

Numeracy and literacy are two sides of exactly the same coin and without some skills in both those subjects it simply isn't possible to cope with the demands of modern society. Nobody expects the man on the Clapham omnibus to be able to apply tensor calculus to an analysis of stress in building materials or to be able to describe the significance of Anna Livia Plurabelle to the structure of James Joyce's Finnegan's Wake. These are specialist subjects which are best left to the experts. But we can legitimately expect the man to be able to perform simple calculations and to understand what he reads in a newspaper.

Illiteracy is generally felt to be shameful and people who cannot read will go to enormous lengths to conceal their lack of skill in this area. But no such stigma attaches to innumeracy and the man on the Clapham omnibus often appears to take a perverse pride in his ignorance. After all, what possible use are mathematical skills in everyday life?

Well...

When I was a child, I was very fond of the Jennings books by Anthony Buckeridge. Jennings was a pupil at an English boarding school. The books describe the scrapes and adventures that he had. They were very funny and I'd love to read them again, but they seem to have vanished from the world.

I remember one episode where Jennings has received a cake from his mother and he wants to divide it evenly among his friends. Recalling his geometry lessons, he uses his protractor to measure the appropriate angles so that everybody will have a slice of exactly the same size. Then he uses his ruler to draw the lines that define each slice. Picking up his knife, he begins to cut along the lines he has drawn. But the cake is very crumbly and the slices are very narrow. The cake disintegrates and Jennings and his friends are left with just a pile of crumbs. Jennings is disgusted and he says something along the lines of, "Huh! So much for maths. It's all very well in the classroom, but as soon as you apply it to real life everything just falls apart!"

I found this to be a delightfully satirical episode – it's at least half a century since I last read a Jennings book, but that episode has stayed with me, fresh and clear, for all that time. It perfectly illustrates both the usefulness of mathematics and the dangers of applying it too literally.

I am also reminded of the joke about a mathematician who was employed to advise dairy farmers on how to improve the efficiency of their day to day operation. He spent many months following them around and taking copious notes. Then he retired to work on his thesis. Eventually it was complete and he called a big meeting of all the dairy farmers so that he could explain his ideas to them. He strode onto the stage in the full glare of the spotlight, and marched up to the whiteboard. He drew a circle and said, "Consider a spherical cow..."

But, more seriously, yes – I do use simple mathematics in everyday life. In the supermarket I calculate unit prices so as to determine the best value for my money. In my car I calculate how long my journey will take, given the distance I have to travel and an estimate of my average speed. In the kitchen I adjust the quantities of the ingredients demanded by a recipe based on the number of people I am cooking for.

Numeracy matters and people who take pride in their lack of mathematical skills really need to take a long hard look at themselves. Maths phobia is a very real phenomenon, but it's nothing to boast about.