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Archive for December, 2012

How Many Socks Make a Pair? Surprisingly Interesting Everyday Maths, Rob Eastaway (2008)

I’ve been returning to this book with pleasure and profit for over a year now: it doesn’t just interest, it informs and enlightens too. Unlike Ian Stewart’s The Mathematics of Life (2011), which promised much and delivered little, it seems simple but points to the profound. Maths is like that: it’s a mansion with many rooms or a mountain with gentle slopes and sheer cliffs or an ocean with shallows and abysses. Infinitely many rooms, in fact, infinitely high cliffs, and infinitely deep abysses. Maths is wider than the world because it is the foundation for all actual and possible worlds and is perhaps, at the most fundamental level, the substance of all actual and possible worlds. Some of the topics introduced here, like fractals, probability, and the Fibonacci sequence, lead on to very difficult and important mathematics, but both intelligent children and amateur adults should be able to take the first steps towards the peaks, where problems wait that are still challenging and defeating professional mathematics. It’s a book that has a P, please, Rob: it discusses puzzles, paradoxes, pranks, playfulness, penney ante, Pythagoras’ theorem, and Pascal’s triangle. Plus the palindromic performativity of 196 – or rather, the non-palindromic. If you reverse and add a number like 59 or 382, you soon arrive at a palindrome, or a number that reads the same in both directions.

Despite being a lot smaller than 382, 89 takes longer, requiring 24 reversals-and-additions. 1,186,060,307,891,929,990, on the other hand, takes 281 rev-adds. And 196? It hasn’t produced a palindrome yet, despite having a lot of computer time and power thrown at it: Eastaway notes that “it is the smallest of many numbers that are now thought to be ‘unpalindromable’” (pg. 101). In base ten, anyway: in other bases, 196 quickly produces a palindrome. That’s not something noted here, but it would be a much longer book if it stopped to follow every thread. In fact, it would be infinitely long, like the book in Jorge Luis Borges’ story “The Book of Sand” (“El libro de arena”), or would take infinitely long to write. But that’s one of the things I like about this book: it doesn’t lay down the law, it leads you down the lane and then gives you the chance to explore further for yourself. You can expand and adapt the maths here to your heart’s content and for once the hyperbole on the back-cover isn’t misleading: “a witty book that provokes the imagination” is the quote from The Times, while the London Maths Society said that it “exudes a friendly charm that is hard to resist.” I agree and I wish more young males were reading books like this and looking at less porn. But porn, like everything else, is under the sway of Mathematica, the Magistra Mundi, or Mistress of the World, and if you’re like me How Many Socks…? may even make you feel guilty about neglecting the Mistress. I know that I should put more effort into understanding some of the topics it covers, like “Calculating without a calculator” in chapter 2. But maths is like a endless box of chocolates: there’s also something else to sample. To taste the magic, try this book.

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Front cover of Rock ChroniclesRock Chronicles: A Visual History of the World’s Greatest 250 Rock Acts, general editor David Roberts, foreword by Alice Cooper (2012)


Rock stars used to die of drink and drugs. Now it’s decrepitude too. Alice Cooper, who writes the foreword to this slab-like selection of sonic samurai, is in his sixties. Mick Jagger and Keith Richards are about to enter their seventies. Chuck Berry is in his eighties. They haven’t died before they got old and their tunes-for-teens are now a soundtrack to senility. Rock itself will last till the arrival of the Deus ex Machina (or DeM), I reckon, which means it probably won’t see out its century. But some of the bands in this book may already have written music for that apotheosis of the anthropic: I was both surprised and pleased to find that the big names of kraut-rock are all covered, from Kraftwerk to Can by way of Einstürzende Neubaten and Popul Vuh. Also covered are those odd and eerie avant-acousticians Magma, so you can indulge your Vander-lust and see some unusual umlauts by reading about Mekanïk Destruktïw Kommandoh and other monuments of Zeuhl. But I wonder whether the DeM – the electronically enhanced superhuman who will overthrow such concepts as individuality and personality – will find less unconventional bands more interesting. There might be more intellectual meat in Carcass than in Can, as it were. Or music might not interest him/Him at all.

Not that the Liverpudlian gore-metal pioneers Carcass find their way into this book, though they’re probably much better-known in the English-speaking world than some of the bands that do, like the Brazilians Legião Urbana, the Argentinians Soda Stereo, the Spaniards Héroes del Silencio, and the Russians B-2 (Би-2). I suspect that progressive, diversity-desirous worthiness was at work in some of the choices, but it’s good to have some unknowns in among the obvious and nowadays it’s easy to sample the music of a new band that sounds interesting. But the unknowns conform to the rules of rock: this music is overwhelmingly created by white males and white males have been its most successful and famous performers. Chuck Berry and Jimi Hendrix are big exceptions, but neither is of pure black ancestry and I don’t think blacks on their own could ever have created rock’s sonic sine qua non: the electric guitar. Or electric amplification, at least. I’m not sure the Chinese or Japanese could have either. They have the intelligence, but not necessarily the innovatory impulse. Either way, they’ve certainly taken it up enthusiastically and some Eastern bands here even play tribute to it in their names: Japan’s Loudness and Guitar Wolf, for example.

Loudness is one of the things that interest me about rock, though I prefer not to experience it for real. Electric amplification allowed man to bellow back at Mother Nature for the first time. In a controlled and sustained way, at least. We’ve been able to bang back with explosions for centuries, but the electric guitar was strum-for-thunder and put extreme volume under the control of single individuals. Camille Paglia compares rock-musicians to Dionysos Bromios, Dionysus the Thunderer, and it’s interesting to wonder whether other Dionysiac attributes, like androgyny, are reflected in the long hair traditionally associated with the loudest forms of rock. Or was it simple psychology? Loud music attracts attention and so does long hair, after all. But heavy metal is interesting, or attention-grabbing, not just for its volume: it’s one of the clearest examples of the way rock has evolved. As the book notes, the “earthy riffing” of the Kinks’ “You Really Got Me” spawned the genre in the early ’sixties. It’s gone on to mutate and morbidify in all manner of ways down the decades, but none of the metal bands here are particularly extreme, unless you want to give that label to the pretentious, po-faced, and faux-dangerous Slipknot. I don’t: I think Black Sabbath were much more interesting and original in their early days. The Sabs are one of the big names who get two pages of text and two pages of photos, which incorporate a side-column of classic album covers. The images for Paranoid (1970) and Sabotage (1975) are too small to come across as they should – which is ridiculously – but the photos of the Sabs have the c-factor in two ways: the band either look cool or make you cringe.

Covers of four Black Sabbath albums

Click for larger images

So do other big names, though some photo-sections are all cool (The Jam) or all cringe (The Scorpions). And some will make you chuckle, like Angus Young clowning in his schoolboy uniform in the entry for AC/DC. But Angus can look cool too: it’s interesting how some people photograph well and some don’t. The Californian punk-band Green Day supply one of each: the singer and guitarist Billie Joe Armstrong has camera-charisma and the bassist Mike Dirnt doesn’t. Green Day, a three-piece, raise another interesting question: why have bands usually had four members? My theory is that the instruments and personalities in a four-piece band best match the four standard forms of human personality, which were classified in the classical world as sanguine, choleric, phlegmatic, and melancholy. The labels are based on a pseudo-medical system of humours, or body fluids, but also correspond, in modern psychology, to the personality dimensions neuroticism and introversion-extraversion: sanguine people are low on neuroticism and high on extraversion; choleric are high on both; melancholic are low on extraversion and high on neuroticism; and phlegmatic are low on both. Like Green Day, Guns’n’Roses are an exception to the four-piece rule and don’t fit neatly into a tetradic personality classification. Teratic might be closer the mark for at least one Gunner. Precisely how one would classify Axl Rose’s personality remains a challenge for morbid psychiatry, but he did look good in the early days of the band, I have to admit.

Nikki Sixx of Mötley Crüe, who are also given two pages of text and two pages of photos, has managed to look good much longer, despite the heroin addiction and the near-death experiences. But da Crüe have another c-factor: they’re often more cartoonish than cool. Their priapic predecessors Led Zeppelin were coolest at their capillariest: when their locks were longest in their middle years. As the ’eighties began their hair shortened and their clothes became workaday, not flamboyant. Then Bonzo died before he got old, which I’ve always felt was a shame from a scientific point of view. Def Leppard pay obvious onomastic hommage to Zep and coagulate cool and cringe in their photos, though tending more to the latter. One of their photos puts the “cock” into rock and the “flourish” into phallic with no fewer than four guitars jutting skyward from the crotch. Stevie Nicks of Fleetwood Mac finds another way to put the cock into rock, suggestively clutching at and positioning a jutting microphone in 1979. Suggestively to the phallocentric photographer and viewer, that is: Nicks didn’t deliberately perform in that kind of way, but she is one of the rare attractive women in this book. Perhaps the most attractive is the blonde guitarist Orianthi, now performing with Alice Cooper but young enough to be his grand-daughter.

Cooper supplies another c-factor: the creepy one. I’ve never liked the look of him or felt comfortable about enjoying his music. Phil Collins has always made my flesh crawl too and Elton John is so revolting that I can’t even bring myself to look at his photos or read his biography, though I assume that, beside the creepiness, he supplies a fifth c-factor: the camp one, as evident in the photo-sections for Queen and Prince. Then there’s the cack-factor, as evident in the Scorpions, the Clash, Elvis Costello, Bruce Springsteen, and the über-egregious Iron Maiden, whose cover-art has always been more interesting than their music, though not much less adolescent. Finally, there’s the Cro-Magnon-factor: shumble forward moronic muso-Mancas Oasis. They have stiff competition from Guns’n’Roses, the Clash, and Springsteen, but I think they’re the band I hate most in this book: Liam Gallagher is Axl Rose minus the stage-presence and beauty (and Axl was beautiful, almost ethereally so, in his youth). But one photo of the Gallaghers unconsciously chimping it up for the camera does raise the question of rock genetics. What are the genetic patterns in this book? The Beatles and the Smiths look very Irish too, though in a much more positive way, and their music was obviously much more intelligent and attractive. But are Celtic genes over-represented there and elsewhere? I’d suggest they are, but how much do they contribute to musicianship and how much to the desire to perform? After all, Oasis definitely have the latter, but don’t appear to have much of the former.

The Cro-Magnon Factor: Noel and Liam Gallagher

The Cro-Magnon Factor: Noel and Liam Gallagher

I’ve also read that, beside the Cro-Magnon looks, cloddish music, and cretinous behaviour, Oasis are responsible for the curse of compression: the recording technique that reduces the difference between loud and soft sounds to give music more punch in noisy settings. If so, it would be entirely fitting: compression reduces the light and shade in music and makes it less subtle. Musically speaking, you’re painting in broader strokes with a brighter, less varied palette, as though Leonardo had created the Mona Lisa with a roller-brush and house-paint. Nice one, Cro-Mancs! Their rivals Blur, who get two pages of text but no photo-section, used to insult them with epithets like Oasis Quo and Status Quoasis, but I think that insults Status Quo rather than Oasis. I’d much rather listen to Status Quo than Oasis or Blur, but I wouldn’t like to attend one of their gigs. They don’t get a photo-section, but like Kiss, who do, I know that they like massed rows of amps and play it very loud. I prefer imagining high volume to experiencing it, because I value my hearing and don’t like insulting any of my senses with artificial stimulants. Rock-in-the-raw counts as one of those and has sometimes bellowed back too loudly and too long at Mother Nature, becoming part of modernity’s tendency to tyrannize the world with technology. Just as street-lighting drowns the stars and modern agriculture destroys subtle flavours, amplified music often drowns beautiful natural sounds or its own subtleties. Most of the bands here don’t sink to the level of dance music or rap, which has a silent-c-factor, but they haven’t always added to the beauty of the world rather than its brutality.

Or its boorishness. But those who inflict loud music on others sometimes pay the price for it. Human beings aren’t adapted to very high volume and a lot of the pale males in this book must suffer from tinnitus. Which is another interesting phenomenon: rock can be music that goes on giving, even when the recipient doesn’t want it to. Attend a Motörhead gig and your ears may remember it, or regret it, for the rest of your life. Motörhead get two pages of text but no photos and, although it’s not mentioned here, have used one of the most interesting titles I’ve ever come across: “Everything Louder than Everything Else”. It’s actually a line from Deep Purple’s Jon Lord and is a reminder than language is more interesting than music, though perhaps not more fundamental to human nature. The two may have a common origin, though music obviously evolves more easily: you can also find it, in one form or another, among birds, fish and insects. But those groups don’t have the symbolic powers of human beings: this book is all about sounds and their creators, but you can experience it in complete silence. In short, it evokes musical memories through words and pictures, all the way from AC/DC and Aerosmith to Frank Zappa and Z.Z. Top, a three-piece who are famous for their beards, of course. Except for Frank Beard, the drummer, who is clean-shaven. And when Gilette offered Billy Gibbons and Dusty Hill “a million dollars each to shave their beards for a commercial”, they turned the offer down. “We’re too ugly,” Gibbons said. The humour in this book doesn’t just come from the photos, but there are too many bands and some of them have existed too long for the text to provide detailed history or analysis. But if you like rock and want to see lots of cool, clownish, cringe-worthy, camp, crap, Cro-Magnon and creepy rock’n’rollers, it’s worth a long look. Or even two or three. But looking and listening aren’t all rock invites us to do. I wish some of the information here was easier to extract: I’d like to have a database of names, ages, and origins for some statistical analysis. There are patterns to be found in rock before the DeM drops in and humanity drops out.


Elsewhere other-posted:

• More Musings on Music

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The Reversal, Michael Connelly (2010)

As you’d expect from Michael Connelly, the chronicler of Californian crime who now lives in Florida, this book is another detailed examination of the importance of the White Heterosexual Able-Bodied Male, or WHAM. But this time you get a double-dose – in fact, a doubled double-dose. There are pairs of WHAMs on the side of both Good and Evil. The two righteous righters-of-wrong are Harry Bosch, Connelly’s LAPD murder-detective, and his half-brother, the defense attorney Micky Haller, who’s accepted an offer to appear for the prosecution in the re-trial of a child-murderer called Jason Jessup. The murderer doesn’t sound melanin-enriched, does he? But you don’t need his name to know that he isn’t: his crime is enough to ensure he can’t be anything other than a white male, in the Connelly cosmos. And it’s apparent long before the end of the book that he is guilty, although he’s been released on bail and wants to sue the state of California for a false conviction. He was found guilty in the 1980s partly on DNA evidence, when a trace of semen was discovered on the victim’s dress and shown to belong to his blood-group. But it’s turned out that it wasn’t in fact his. Twenty-first-century technology has proved the depraved deposit belonged to someone else – but still a white male, of course.

The girl’s stepfather, in fact. But he hadn’t actually been abusing the girl: she had borrowed the dress from the actual victim of abuse, her slightly older sister. Then she got snatched off the street by Jessup and strangled. Is there no limit to WHAM evil? Not in the Connelly cosmos. But the book raises a related question: Is there no limit to non-WHAM saintliness? If I didn’t know better, I’d almost start to suspect Connelly was taking the piss in one part of The Reversal, when the discoverer of the victim’s corpse testifies at the new trial. The Bosch sections of the book are written in the third person, the Haller sections in the first. Haller describes the witness being brought to the stand:

As I had gone to the lectern Bosch had left the courtroom to retrieve [William] Johnson from a witness waiting-room. He now returned with the man in tow. Johnson was small and thin with a dark mahogany complexion. He was fifty-nine but his pure white hair made him look older. Bosch walked him through the gate and then pointed him in the direction of the witness stand. (pg. 220)

The “dark mahogany complexion” and “pure white hair” are the first stages in the character’s canonization. Here are some more, as the witness identifies himself to the court and describes what he does for a living:

“…I am head of operations for the El Rey theater on Wilshire Boulevard… I make sure everything works right and runs – from the stage lights to the toilets, it’s all part of my job.”

He spoke with a slight Caribbean accent but his words were clear and understandable. (pg. 221)

So he’s Caribbean and highly competent. The saintliness is solidifying, but Connelly isn’t done. The murdered girl was callously dumped in a rubbish-bin by her WHAM killer. Haller projects a police photograph of the scene onto a screen and asks the competent Caribbean to clearly confirm that it is accurate:

“Okay, and is this what you saw when you raised the top [of the bin] and looked inside?”

Johnson didn’t answer my question at first. He just stared like everyone else in the courtroom. Then, unexpectedly, a tear rolled down his dark cheek. It was perfect. If I had been at the defense table I would have viewed it with cynicism. But I knew Johnson’s response was heartfelt and it was why I had made him my first witness.

“That’s her,” he finally said. “That’s what I saw.”

I nodded as Johnson blessed himself. (pg. 220-4)

I, on the other hand, retched. I think writing like that counts as emotional pornography, but this example has an interesting feature: the black saint who is offered for liberal self-gratification isn’t an American black but a foreign one. Is Connelly suggesting that a Caribbean is credible when weeping over the death of a white child, but a native black wouldn’t be? I don’t know, but I do know that the book, like many of Connelly’s previous books, is meant to be titillating in other ways. The details of Jessup’s known and suspected murders – he proves to have floated like a butterfly and stung like a WASP – remind me of something George Orwell said in his essay “Raffles and Miss Blandish” (1944):

It is important to note that by modern standards Raffles’s crimes are very petty ones. Four hundred pounds’ worth of jewellery seems to him an excellent haul. And though the stories are convincing in their physical detail, they contain very little sensationalism – very few corpses, hardly any blood, no sex crimes, no sadism, no perversions of any kind. It seems to be the case that the crime story, at any rate on its higher levels, has greatly increased in blood-thirstiness during the past twenty years. Some of the early detective stories do not even contain a murder. The Sherlock Holmes stories, for instance, are not all murders, and some of them do not even deal with an indictable crime. So also with the John Thorndyke stories, while of the Max Carrados stories only a minority are murders. Since 1918, however, a detective story not containing a murder has been a great rarity, and the most disgusting details of dismemberment and exhumation are commonly exploited. Some of the Peter Wimsey stories, for instance, display an extremely morbid interest in corpses.

That was written at the end of the Second World War. Plus ça change, eh? But something that has definitely changed in detective fiction is the attitude to the societies built by whites in Europe, America, and other parts of the world. Liberal writers like Connelly now attack them constantly: they’re racist, they’re oppressive, they’re evil. The Reversal re-treads a constant Connellyean theme. In several of his previous books, evil WHAMs have committed sex-crimes and hapless non-WHAMs have been unjustly accused instead. In The Reversal, an evil WHAM has committed a sex-crime and a saintly non-WHAM is weeping over the victim. That’s how it works, in the world of Bosch and Haller. But they’re WHAMs too and they’re examples of how, in liberalism, only WHAMs have free will to choose between good and evil. Bosch and Haller choose good and side with the saintly oppressed; Jessup and the stepfather choose evil and commit the oppression against the saints. But the WHAM Connelly and his WHAM fans may soon start to see that their collusion with their critics will not lead to a better world. They may even realize that sex-crimes are not always and everywhere committed by white males. But I suppose that’s what makes Connelly an imaginative writer and The Reversal a work of fiction.

Pre-previously posted (please peruse):

All Bosched-Up

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