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Archive for November, 2013

Brit GritGranite and Grit: A Walker’s Guide to the Geology of British Mountains, Ronald Turnbull (Francis Lincoln 2011)

Singh Summing SimpsonsThe Simpsons and Their Mathematical Secrets, Simon Singh (Bloomsbury 2013)

Go with the QuoStatus Quo: Still Doin’ It – The Official Updated Edition, compiled by Bob Young, edited by Francis Rossi and Rick Parfitt (Omnibus Press 2013)

Breeding BunniesThe Golden Ratio: The Story of Phi, the Extraordinary Number of Nature, Art and Beauty, Mario Livio (Headline Review 2003) (posted @ Overlord of the Über-Feral)

Brit Bot BookReader’s Digest Field Guide to the Wild Flowers of Britain, J.R. Press et al, illustrated Leonora Box et al (1981) (@ O.o.t.Ü.-F.)


Or Read a Review at Random: RaRaR

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Front cover of Granite and Grit by Ronald TurnbullGranite and Grit: A Walker’s Guide to the Geology of British Mountains, Ronald Turnbull (Francis Lincoln 2011)

For a small country, Britain has had a big influence on the world. Like a lot of other things, modern geology started here. There are several reasons for that and one is very simple: pioneering geologists had mountains of material to work with. According to the author, “Britain has the most varied geology of any country in the world.” This is an excellent introduction to the rocks of the realm, from gneiss in the Outer Hebrides to granite on Dartmoor. I like the way Turnbull discusses not only how rocks affect your eyes – their colour, texture and contours – but also how they affect your boots. He’s a hillwalker, not a professional geologist, so he conveys a strong sense of place and of how Britain’s landscape varies. But there’s more than geological variation here: Britain isn’t just rich in rocks and its landscape is shaped by more than physics and chemistry. This is the caption to one spectacular photo of a misty mountain:

Bwlch y Saethau, where according to legend King Arthur battled his nephew Mordred; behind, Y Lliwedd stands at the centre of a far greater act of violence, the Lower Rhyolite Tuff event. (ch. 10, “Redhot Flying Avalanches: Ignimbrites in Snowdonia”, pg. 98)

Britain’s varied mountains are named in Britain’s varied languages: Welsh, English and Gaelic give different flavours to the landscapes they describe, from Carnedd Dafydd to Eskdale, from Ingleborough to Stuc a’ Chroin, from Ardnamurchan to Mynydd Mawr. But English names split into Norse and Anglo-Saxon, which have different flavours too. Underlying all these languages is a common ancestor, just as some very different rocks have common ancestors too. Heat, compression and erosion change rocks; time, separation and mutation change languages. So Turnbull is writing about two kinds of history as he discusses different parts of Britain: geological history and linguistic history.

Linguistics dwarfs geology in complexity, but geology dwarfs linguistics in time. To understand why Britain looks the way it does, you have to go back billions of years and trace its movement over many thousands of kilometres. You also have to study seemingly exotic things like volcanoes, glaciers and tropical botany, all of which are central parts of Britain’s geology. Turnbull is a relaxed but knowledgeable guide to some big events and some big transformations and because he isn’t a professional he knows how to write for a general reader. He doesn’t just inform, he re-orientates: you won’t look at Britain in the same way:

Black pointy islands of volcanic ash rise above the sea, the water around them a froth of falling ash. The shores of the new islands get washed away by tsunamis as chunks of other islands fall into the sea. Lava slides down and then runs level, to form black land made of glass. The glassy ground crackles as it cools, and then quickly weathers to orange shards and gravel. Showers of sharp-edged volcanic rubble fall into the sea, forming seabed layers 300m deep which will eventually be the summit of Snowdon itself. (ch. 10, pp. 103-4)

Geology is like cuisine in reverse: from the cooked dish you have to work out the recipe. Landscapes that seem inert can have cataclysmic pasts, full of fire and thunder or flood and frost. There are centuries of ingenious deduction and painstaking observation behind the chatty text and attractive photos in this book, but there are still mysteries to solve. More maths will be needed, because matter obeys mathematical rules in all its transformations, whether geological or culinary. And those material transformations have immaterial parallels in linguistics and sociology, where maths is the key to understanding too. And science itself has metamorphosed and mutated. Geology is an important subject not just for its contemporary research but also for its influence on other fields. It made scientists realize the vast age of the earth. Charles Darwin used that idea to transform biology. Like the pioneering geologists, he was British. That isn’t a coincidence and it’s something else that increases the power of this book. The planet starts here. So does the universe.

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Front cover of The Simpsons and Their Mathematical Secrets by Simon SinghThe Simpsons and Their Mathematical Secrets, Simon Singh (Bloomsbury 2013)

I don’t like The Simpsons and I don’t think Simon Singh is a very good writer. But there is some interesting maths in this book. As the Emperor Vespasian said when criticized for taxing urinals in Rome: Pecunia non olet – “money doesn’t smell”. And simple sources can yield riches in other ways. There’s a good example of that in chapter 9 of this book, “To Infinity and Beyond”, where Singh looks at the mathematics of pancake-sorting. It was first discussed in 1975 by the geometer Jacob E. Goodman of the City College of New York. Suppose there’s a pile of pancakes of different sizes. You can insert a spatula at any point in the pile and flip the block of pancakes above it. Goodman posed this question about sorting the pancakes into order of size:

If there are n pancakes, what is the maximum number of flips (as a function of n) that I will ever have to use to rearrange them? (ch. 9, pg. 110)

It sounds simple, but isn’t. As the pile gets higher, the problem gets harder. The answer is 20 flips for 18 pancakes and 22 flips for 19. And 20 pancakes? Surprisingly, mathematicians don’t know: “nobody has been able to sidestep the brute computational approach by finding a clever equation that predicts pancake numbers”. The best mathematicians can do is find the upper limit: pancake(n) < (5n + 5)/3 flips.

This limit was proved in a paper “co-authored by William H. Gates and Christos H. Papadimitriou” in 1979 (pg. 112). The first co-author is better known now as Bill Gates of Microsoft. The Simpsons enter the story because David S. Cohen, a writer for the series, extended the problem in a mathematical paper published in 1995: the pancakes don’t just come in different sizes, they’re burnt on one side and have to be flipped both in order of size and with the burnt side down. Now the number of flips is “between 3n/2 and 2n – 2” (pg. 113). The source of the problem may seem trivial, but the maths of the solution isn’t. Pancake-flipping has important parallels with “rearranging data” in computer science.

Cohen has degrees in both computer science and physics, but his expertise isn’t unique: “the writing team of The Simpsons have equally remarkable backgrounds in mathematical subjects” (ch. 0 (sic), “The Truth about the Simpsons”, pg. 3). They have degrees and doctorates in tough subjects from colleges like Harvard, Berkeley and Princeton. And they’ve been engaged, according to Cohen, in a “decades-long conspiracy to secretly educate cartoon viewers” (back cover). They haven’t had much success with that, but they’ve succeeded in other ways: TV is no good at education, but very good at propaganda and manipulation. That’s one reason I dislike The Simpsons, which is obviously inspired by cultural Marxism, despite its occasional un-PC jokes. Another reason is that I think the characters and colours are ugly and dispiriting. Or is that cultural Marxism again? But I have to admit that the series is cleverly done. To appeal to so many people for so long takes skill, but explicit maths has been low in the mix.

It had to be, because The Simpsons wouldn’t have been successful otherwise. It has a lot of stupid fans and stupid people aren’t interested in Fermat’s Last Theorem, strategies for rock-scissors-paper or equations for pancake-numbers. That’s why you need to freeze the frame to find a lot of the explicit maths in The Simpsons. Or you did before Singh wrote this book and froze the frames for you. The implicit maths in The Simpsons is everywhere, but that’s because maths is everything, including an ugly cartoon and its science-fiction offshot. Singh discusses Futurama too and the “taxi-cab numbers” inspired by the Indian mathematician Srinivasa Ramanujan (1887-1920). I’ve never seen Futurama and I wish I could say the same of The Simpsons. I certainly hope I never see it again. But it’s an important programme and this is an interesting book.

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Front cover of Status Quo: Still Doin’ It compiled by Bob YoungStatus Quo: Still Doin’ It – The Official Updated Edition, compiled by Bob Young, edited by Francis Rossi and Rick Parfitt (Omnibus Press 2013)

Status Quo have been responsible for some good music and some bad album-covers. I can’t decide which is the worst of the covers. I don’t need to explain the appeal of the music, because Brian May does it for me, joining John Peel, Hank Marvin and H.R.H. The Prince of Wales among the big names who pay tribute to a rock institution. Queen were touring Europe at the same time as Quo and May attended one of Quo’s gigs, probably in Germany:

I manoeuvred myself behind the back line, and found myself with my ears midway between the back of Francis’s amp and the back of Rick’s. So, crouching like a true addict, I got a perfect stereo image, and at entirely suitable volume! As they launched into “Down, Down” I could hear the twin clangs of their superb rhythm guitars interacting in perfect rapport, and I thought …this is a perfect moment. A moment of sheer privilege. There is NOTHING in rock quite like these two giants at full throttle … Nothing! (pg. 57)

“Rhythm” is a key word. So is “volume”. Status Quo are very loud. And yes, despite the good songs, they can be very naff too. If they weren’t one of the inspirations for Spinal Tap, they should have been. But I think they were. Maybe even the chief inspiration. The names of both are amphimacers (dum-di-dum), both come from London and both started playing hippyish flower-power music in the 1960s before finding their true path. In early photos of Quo you can see frilly shirts, page-boy haircuts and even jumpers, cardigans and blazers. Then they put on their denim, grew their hair down and started their Piledriver. The Metallica drummer Lars Ulrich, whose first “front-row” show was Status Quo in Copenhagen when he was eleven, calls the cover of that album the “first real head-banging visual unleashed to the masses”.

Album cover of Piledriver by Status Quo

That’s in the foreword, where Ulrich goes on to describe the effects of the show and the album: “Quo were, to this snot-nosed Danish kid in the mid-1970s, KING SHIT”. But his praise may be misleading. One crucial difference between Status Quo and Spinal Tap, or Status Quo and Metallica, is that Status Quo aren’t heavy metal. They don’t write about Satan, violence or sex and they don’t use stage-props. No Stonehenge or dry ice for Quo: just massed amps and loud riffs. “Our gimmick is that we don’t have a gimmick”, as they say on page 86. So the heavy-metal side of Spinal Tap came from bands like Black Sabbath and Uriah Heep. Spinal Tap play more complex music than Quo too, but Quo don’t mind. They have their simple formula and they’re sticking to it. When they went In Search of the Fourth Chord in 2007, they were joking.

Some bad album-covers (click for larger versions)

Some bad album-covers (click for larger versions)


That’s another way they aren’t heavy metal: no pretension or pomposity. No great technical skill or musical innovation either. Very few fans of Eric Clapton think “That could have been me.” Clapton plays too well and has been too influential for fans to easily picture themselves in his shoes. But lots of Status Quo fans must think that. Quo have rocked the world, not re-written rock. This book covers six decades of two blokes in a band: Francis Rossi and Rick Parfitt have always been there, drummers and bassists have come and gone. It would have been better with an index and a discography, but it’s mostly pictures anyway. Like Quo’s songs, some pictures are good, some are bad. After all, only the mediocre are always at their best. Quo haven’t been at their best very often, but I’m glad that they’re still doing it and still enjoying it.


Elsewhere other-posted:

• More Musings on Music

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