The Number Devil by Hans Magnus Enzensberger

It’s been a while since I’ve written anything really meaty on my blog and an entire year since I last wrote a post that reviewed a book on mathematics.

But what I really like about this particular post is that it renders the near to the global. This arose from a Christmas drink that I had with my neighbour across the road, Sarah, who lent me a book, that she never lends, on the proviso I write it up on my blog. So from my neighbour, who literally lives directly opposite me with her 2 sons, Andre and Emelio, to the blogosphere.

Over a bottle of Aussie red (Barossa Valley Shiraz 2008) – yes that’s worth mentioning because we both agreed that it was a bloody good drop (literally and figuratively) – we somehow got into a discussion on mathematics and the teaching of mathematics in particular, which led us to swapping books the next day.

On Christmas Day 2009, I published a post on The Bedside Book of Algebra (Michael Willers), which is the book I swapped with Sarah. The Number Devil; A Mathematical Adventure covers some of the same material but it’s aimed at a younger audience and it has a different approach. The whole purpose of this book it to reveal to young people that mathematics is a world worth exploring and not just a sadistic intellectual exercise designed by teachers to torment young developing minds. Sarah’s book has 2 bookmarks in it: one for her and one for her 7 year-old son; and her son’s bookmark is further advanced than hers.

It is written in novel-form and the premise of the narrative is very simple: the protagonist, Robert, is having tormenting dreams when he is visited by a devil, who calls himself the ‘Number Devil’ and begins to give him lessons in mathematics. It’s extremely clever, because it’s engaging and contains entertaining and informative illustrations, as well as providing exposition on some of the more esoteric mathematical concepts like infinity, transfinite numbers, combinations and permutations, Pascal’s triangle, Fibonacci numbers, prime numbers and Goldbach’s conjecture.

Whilst Enzensberger reveals the relationship between Pascal’s triangle and Fibonacci numbers, he doesn’t explain the relationship between Pascal’s triangle and the binomial theorem, which I learned in high school. He also explains the relationship between Pascal’s triangle and the combination algorithm, but not the way I learned it, which I think is more intuitive and useful. He uses diagonals (within Pascal’s triangle) whereas I learned it by using the rows.

The cleverness is that he provides these expositions without revealing to the reader how advanced these mathematical ‘lessons’ are. In fact, the reader is introduced to the ‘mysteries’ that have fascinated ‘ancients’ from many cultures across the world. Enzensberger’s inspired approach is to reveal the appeal of mathematics (that most mathematicians only find in adulthood) to young people before they are turned off it forever. He demonstrates that esoteric concepts can be taught without emphasising their esoterica.

Even the idea of a ‘number devil’ is inspired because mathematics is considered to be so devilish, and, in some cultures, mathematicians were considered to be devil’s apprentices (refer my recent post on Hypatia). In the second chapter (chapters are sequential nights of dreaming) Robert finds himself in a cave with the Number Devil, and the illustration is an obvious allusion to Plato’s cave, though no mention is made of this in the text.

At the end, the Number Devil takes Robert to ‘Number Heaven’ and ‘Number Hell’, though they appear to be the same place, where he meets some of the ‘masters’ like Russell, Fibonacci, Archimedes and a Chinese man whose name we don’t learn. We don’t meet Pythagoras who lives in a higher realm altogether, up in the clouds.

I’d recommend this book to any parent whose children show the slightest mathematical inclination and also adults who want an introduction to this esoteric world. As Sarah said, it’s like a mathematical version of Jostein Gaarder’s Sophie’s World, which is a high enough recommendation in itself.

Oh, I should mention that the illustrations are by Rotraut Susanne Berner; they augment the text perfectly.

Ayaan Hirsi Ali

This woman should need no introduction, she’s been in the media in most Western countries I’m sure. I thought this was a really good interview (Tue. 21 Dec. 2010) because it gives an insight into her background as well as a candid exposition of her political and philosophical views.

I haven’t read either of her biographies, but I’ve read second-hand criticism which led me to believe she was anti-Islamic. This is not entirely true, depending on how one defines Islam. To quote her own words: “I have no problem with the religious dimension of Islam.” She’s not the first Muslim I’ve come across to differentiate between religious and political Islam. Most Westerners, especially since 9/11, believe that any such distinction is artificial. I beg to differ.

She makes it very clear that she’s against the imposition of Sharia law, the subjugation of women and any form of totalitarianism premised on religious-based scripture (irrespective of the religion). In short, she’s a feminist. She decries the trivial arguments over dress when there are other issues of far greater import, like arranged marriages, so-called circumcision of women and honour killings. (For an intelligent debate on whether the burqua should be ‘outlawed’ I refer you to this.)

What I found remarkable, and almost unimaginable, was how violent her childhood and upbringing were. There was violence in the school, violence in the home, violence in politics. As she points out it was so pervasive that a peaceful environment was considered unthinkable. One of the most poignant stories she tells was when she went to Holland to seek asylum, and on going to a Police Station to register, the policeman asked her if she would like a cup of coffee or tea. This was a revelation to her: that a man in uniform should offer a woman, a stranger and a foreigner, a cup of coffee or tea was simply mind-blowing.

It is beyond most of us to imagine a childhood where violence is the principal form of interrogation and negotiation between people in all walks of life: home, education and work; yet that was her life. That she can now talk of falling in love and of writing a letter to her unborn child for a hopeful future is close to miraculous.

What resonated with me was her argument that it doesn’t take 600 years to reconcile Islam with the modern secular world, but only 4 generations. I have Muslim friends, both in America and in Australia, and they belie the belief, held by many in Western societies, that Muslims can’t assimilate and yet keep their cultural and spiritual beliefs. They demonstrate to me that Ayaan Hirsi Ali is correct in her fundamental assumptions and philosophical approach.

On-line interview for Elvene

This is a blatant promotion. Obviously the interview is totally contrived by the publisher, and if you press TOP at the end of my piece, you will get an overview of the current state of play in Oz publishing and distribution, from the perspective of one of the (minor) players.

Having said that, the questions were not vetted by me and the answers are all my own.

The term 'jack-of-all-trades' is a complete misnomer. Anyone who actually knows me, knows that I'm totally useless at all trades involving genuine dexterous skill. The rest is mostly true, though I've only written one screenplay and one novel that I'm willing to own up to.

The interview contains some of my philosophy on writing in 'nutshell' form, with the added relevance of referencing something that I've written.

Hypatia

Last week I saw a movie by Alejandro Amenabar called Agora, which is effectively the story of Hypatia and her death at the hands of Christian zealots in Alexandria towards the end of the Roman Empire in AD 414. So the film is based on a real event and a real person, though it is a fictional account.

Amenabar also made the excellent film, The Sea Inside, starring Javier Bardem, which was also based on a real person’s life. In this case, a fictionalised account of a quadriplegic’s battle with the Church and government in Spain to take his own life through euthanasia.

I first came across Hypatia in Clifford A. Pickover’s encyclopedic tome, The Math Book, subtitled, From Pythagoras to the 57^th Dimension, 250 Milestones in the History of Mathematics.  He allots one double page (a page of brief exposition juxtaposed with a graphic or a photo) to each milestone he’s selected. He presents Hypatia as the first historically recognised woman mathematician. In fact she was a philosopher and teacher at the famous Library of Alexandria, even though she was a Greek, and like her father, practiced philosophy, science, mathematics and astronomy in the tradition of Plato and Aristotle. By accounts, she was attractive, but never married, and, according to Pickover, once said she was ‘wedded to the truth’. The film gives a plausible account of her celibacy, when her father explains to a suitor that, in order to marry, she would have to give up her pursuit of knowledge and that would be like a slow death for her.

The film stars Rachel Weisz in the role of Hypatia and it’s a convincing portrayal of an independent, highly intelligent woman, respected by men of political power and persuasion. The complex political scene is also well depicted with the rise of Christianity creating an escalating conflict with Jews that the waning Roman military government seems incapable of controlling.

It’s a time when the Christians are beginning to exert their newly-found political power, and their Biblical-derived authority justifies their intention to convert everyone to their cause or destroy those who oppose them. There is a scene where they drive all the Jews out of Alexandria, which they justify by citing Biblical text. The film, of course, resonates with 20^th Century examples of ‘ethnic cleansing’ and the role of religious fundamentalism in justifying human atrocities. Hypatia’s own slave (a fictionalised character, no doubt) is persuaded to join the Christians where he can turn his built-up resentment into justified slaughter.

Hypatia would have been influenced by Pythagoras’s quadrivium, upon which Plato’s Academy was based: arithmetic, geometry, astronomy and music. In the movie she is depicted as a ‘truth-seeker’, who questions Ptolemy’s version of the solar system and performs an experiment to prove to herself, if no one else, that the Earth could move without us being aware of its motion. I suspect this is poetic licence on the part of Amenabar, along with the inference that she may have foreseen that the Earth’s orbit is elliptical rather than circular. What matters, though, is that she took her philosophy very seriously, and she appreciated the role of mathematics in discerning truth in the natural world. There is a scene where she rejects Christianity on the basis that she can’t accept knowledge without questioning it. It would have gone against her very being.

There is also a scene in which the Church’s hierarchy reads the well-known text from Timothy: “I suffer not a woman to teach or to control a man”, which is directed at the Roman Prefect, who holds Hypatia in high regard. The priest claims this is the word of God, when, in fact, it’s the word of Paul. Paul, arguably, influenced the direction of Christianity even more than Jesus. After all, Jesus never wrote anything down, yet Paul’s ‘letters’ are predominant in the New Testament.

Hypatia’s death, in the film, is sanitised, but history records it as brutal in the extreme. One account is that she was dragged through the streets behind a chariot and the other is that she had her flesh scraped from her by shards of pottery or sharp shells. History also records that the Bishop, Cyril, held responsible for her death, was canonised as a saint. The film gives a credible political reason for her death: that she had too much influence over the Prefect, and while they couldn’t touch him in such a malicious way, they could her.

But I can’t help but wonder at the extent of their hatred, to so mutilate her body and exact such a brutal end to an educated woman. I can only conclude that she represented such a threat to their power for two reasons: one, she was a woman who refused to acknowledge their superiority both in terms of gender and in terms of religious authority; and two, she represented a search for knowledge beyond the scriptures that could ultimately challenge their authority. I think it was this last reason that motivated their hatred so strongly. As a philosopher, whose role it was to seek knowledge and question dogma, she represented a real threat, especially when she taught ‘disciples’, some of whom became political leaders. A woman who thinks was the most dangerous enemy they knew.


Addendum: I've since read a book called Hypatia of Alexandria by Michael Deakin, Honorary Research Fellow at the School of Mathematical Sciences of Monash University (Melbourne, Australia). In the appendix, Deakin includes letters written to Hypatia by another Bishop, Synesius of Cyrene, who clearly respected, even adored her, as a former student.

We have to win the war against stupidity first

In Oz, we have a paper called The Australian, which was created by Rupert Murdoch when he was still a young bloke. Overseas visitors, therefore, may find it anomalous that in last weekend’s The Weekend Australian Magazine there was an article by Johann Hari that was critical of US policy in Afghanistan and Pakistan. Specifically, the use of drones in the so-called war on terror. The same magazine, by the way, runs a weekly column by one of Australia’s leading left-wing commentators, Phillip Adams, and has done so for decades. In his country of origin, it appears, Murdoch is something of a softie. Having said that, the article cannot be found on the magazine’s web page. Murdoch wouldn’t want to dilute his overseas persona apparently.

If I could provide a link, I obviously would, because I can’t relate this story any more eloquently than the journalist does. He starts off by asking the reader to imagine the street, where they live, being bombed by a robotic plane controlled by pilots on the other side of the world in a ‘rogue state’ called the USA. A bit of poetic licence on my part, because Hari does not use the term ‘rogue state’ and he asks you to imagine that the drone is controlled from Pakistan, not America. Significantly, the ‘pilots’ are sitting at a console with a joy stick as if they’re playing a video game. But this ‘game’ has both fatal and global consequences.

The gist of Hari’s article is that this policy, endorsed by Obama’s administration and “the only show in town” according to some back-room analysts, is that it actually enlists more jihadists than it destroys.

David Kilcullen, an Australian expert on Afghanistan and once advisor to the American State Department ‘…has shown that two percent of the people killed by the robot-planes in Pakistan are jihadis. The remaining 98 percent are as innocent as the victims of 9/11. He says: “It’s not moral.” And it gets worse: “Every one of these dead non-combatants represents an alienated family, and more recruits for a militant movement that has grown exponentially as drone strikes have increased.”’

David Kilcullen, who was once advisor to Condoleezza Rice during Bush’s administration, once said in an ABC (Oz BC) radio interview, that ‘…we need to get out of the business of invading other people’s countries because we believe they may harbour terrorists.’

‘Juan Cole, Professor of Middle Eastern History at the University of Michigan, puts it more bluntly: “When you bomb people and kill their family, it pisses them off. They form lifelong grudges… This is not rocket science. If they were not sympathetic to the Taliban and al-Qa’ida before, after you bomb the shit out of them they will be.”’

According to Hari, drones were originally developed by Israel and are routinely deployed to bomb the Gaza Strip. Not surprisingly, the US government won’t even officially acknowledge that their programme exists. Having said that, Bob Woodward, in his book, Obama’s Wars, claims that ‘the US has an immediate plan to bomb 150 targets in Pakistan if there is a jihadi attack inside America.’ In other words, the people who promote this strategy see it as a deterrent, when all evidence points to the opposite outcome. As Hari points out, in 2004, a ‘report commissioned by Donald Rumsfeld said that “American direct intervention in the Muslim world” was the primary reason for jihadism'.

I could fill this entire post with pertinent quotes, but the message is clear to anyone who engages their brain over their emotions: you don’t stop people building bombs to kill innocent civilians in your country by doing it to them in their country.

ELVENE, the 2nd edition

My one and only novel, ELVENE, has been published as an e-book by IP (Interactive Publications) and also POD at Glasshouse Books, a Queensland based company. The cover is by Aaron Pocock, so it’s an all-Aussie affair, though I believe Dr. David Reiter, who founded IP, is an ex-pat American.

I haven’t met David or Aaron, or even spoken to them, such is the facility of the internet. Even though IP engaged Aaron (I paid for the artwork), we corresponded via an intermediary, and I’m very pleased with the results. I believe he captured both the atmosphere and the right degree of sensuality that is reflected in the text itself. I’ve always been a strong believer that the cover should reflect the content of the book, both contextually and emotionally.

If you read the blurb on the web site (written by me) you may be mistaken in the belief that this is a variation on James Cameron’s Avatar. Nothing against Avatar, but I need to point out that ELVENE was written in 2001/2, about 8 years before Avatar was released, but I suspect we have been influenced by the same predecessors, in particular, Frank Herbert’s 1965 classic, DUNE. If any of you have seen Miyazaki’s anime, Nausicaa of the Valley of the Wind (refer my recent post, 5 Oct.10) you may also see some similarities. I did when I saw it in 2006, even though it was first released in 1984. Obviously I can’t be influenced by something I didn’t even know existed, but I’m happy to be compared with Miyazaki anytime.

The book contains oblique references to Clarke, Kubrick, Coleridge, Kipling and even Barbarella (her ship was called Alfie for you train-spotters). So, whilst Avatar could be best described as Dune meets Dances with Wolves, Elvene is Dune meets Dances with Wolves, meets Ursula Le Guin, meets Ian Fleming, meets Barbarella, meets Edgar Rice Burroughs. So my influences began with the comic books I read in the 1960’s, not to mention the radio serials I listened to before TV (yes, I’m that old). At the age of 9, I started writing my own Tarzan scripts, and I started drawing my own superheroes about the same time, possibly a bit older.

I once described ELVENE as a graphic novel without the graphics, and more than one person has told me that it’s ‘a very visual story’. An interesting achievement, considering I believe description to be the most boring form of prose (refer my August post on Creative Writing).

Most people who’ve read it ask: where’s the next one? Well, the truth is that I have started a sequel but I find it hard to believe I will ever write anything as good as ELVENE again. It really feels like an aberration to me. I’m not a writer as a profession, more a hobbyist, nevertheless I’m proud of my achievement. It’s not for everyone, but I’ve found that women like it in particular, including those who have never read a Sci-Fi book before. Maybe it’s a Sci-Fi book for people who don’t read Sci-Fi. I can only let others be the judge.

Two unsolicited reviews can be found at YABooksCentral: one by a teenager and one by a retired schoolteacher (both women).

More reviews can be found here. (Note: the top review contains spoilers)

Also available on Amazon, iBookstore, Lightning Source (Ingram) and ContentReserve.com.