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The Great Mathematical Problems by Ian StewartThe Great Mathematical Problems: Marvels and Mysteries of Mathematics, Ian Stewart (Profile Books 2013)

If you asked me what the Riemann hypothesis was, I would be able to say that it was a very important mathematical problem that had something to do with prime numbers and zeros on a line. And that would be it. There’s an entire chapter in this book about the hypothesis, but with me as a reader Stewart might as well have been “teaching Urdu to a marmoset” (as Laurence Olivier said about trying to teach Marilyn Monroe to act). Stewart is a great popularizer of advanced mathematics, but he faces a big problem: if you understand the profundity, you’ll understand the popularization of it. If you don’t, you won’t.

So I don’t understand what the Riemann hypothesis is about. Or the Poincaré conjecture. Or the Hodge conjecture. Or the Birch–Swinnerton-Dyer conjecture (note long hyphen: it’s named after two mathematicians, not three). So more than half of the chapters in this book lost me almost immediately. The other chapters lost me later, because it’s easy to understand the questions behind the Goldbach conjecture, the four-colour problem and the three-body problem. Is every even integer greater than 2 equal to the sum of two primes? Can we colour all flat two-dimensional maps with four colours or fewer? Can we write an equation to predict the gravitational interaction of three celestial bodies?

The questions are easy to understand, but the answers are very difficult. In fact, only the four-colour problem has been solved. The mathematicians who solved it famously used computers to do so, and their solution can’t be held in or followed by a single human mind. That was something new and it raised interesting questions about the nature of mathematical proof. Stewart discusses them here and supports the idea that computer proofs are legitimate. He ends the book with a list of newer, less famous but perhaps, in some cases, even more important problems. Again, some of them are easy to understand, some aren’t.

So you can get a good sense of the size, scope and complexity of mathematics from this book. And the difficulty. I found a lot of it incomprehensible, but if Ian Stewart can’t explain it to me, no-one else could. And there’s fun amidst the befuddlement:

According to a time-honoured joke, you can tell how advanced a physical theory is by the number of interacting bodies it can’t handle. Newton’s law of gravity runs into problems with three bodies. General relativity has difficulty dealing with two bodies. Quantum theory is over-extended for one body and quantum field theory runs into trouble with no bodies – the vacuum. (ch. 8, “Orbital Chaos: Three-Body Problem”, pg. 136)

There are also ideas to explore for yourself, like Langton’s ant, because maths is like a mountain range. Even if you can’t get to the peaks, you can enjoy climbing some of the way. There are gentle slopes before the sheer, ice-sheened cliffs. Ian Stewart doesn’t get to the cliffs, but there’s some tough climbing here and I quickly fell off. A lot of amateurs will do much better and this book is worth trying anyway. Being baffled teaches you something both about a subject and about yourself.

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The Riddle of the Labyrinth by Margalit FoxThe Riddle of the Labyrinth: The Quest to Crack an Ancient Code and the Uncovering of a Lost Civilisation, Margalit Fox (Profile Books 2013)

I remember starting an Agatha Christie book and being delighted by the simplicity of her style. But I’d got bored long before the end. The Riddle of the Labyrinth was the opposite. I found it dull at the beginning, but was delighted by the end. I look forward to reading it again. Margalit Fox weaves a compelling story out of three complex people: the English archaeologist Sir Arthur Evans (1851-1941), the American classical scholar Alice Kober (1906-50) and the English architect Michael Ventris (1922-56); and the complex problem they all worked on: the decipherment of a forgotten script found on the island of Crete.

It’s a story of clay in two ways. There’s the literal clay on which the script was recorded:

It took fire to give us Linear B. In about 1400 B.C., the final conflagration at Knossos destroyed most of the palace [of Minos] and its contents, marking the end of the great civilization that had been rooted there for centuries. But the blaze had one completely beneficial effect: It preserved for future generations the clay tablets that recorded the palace’s final year. (Book One, “The Digger”, ch. 3, “Love Among the Ruins”, pg. 67)

There’s also the metaphorical clay of humanity and its frailties, physical and psychological. Sir Arthur Evans died at ninety, laden with honours, but Alice Kober died at forty-three, probably of cancer, and Michael Ventris at thirty-four, possibly by suicide. Evans and Ventris have long been famous in the Linear B story, but I’d never heard of Kober until I picked up this book. According to Fox, she was central to the decipherment and made the critical breakthrough: explaining the relationship between two known facts about the unknown script and unknown language of Linear B:

Kober had shown that the Minoans spoke an inflected language. Now came the real payoff from that demonstration: In a discovery that would have enormous implications for the decipherment, she now homed in on precisely what happens when an inflected language is written in a syllabic script. (Book 2, “The Detective”, ch. 6, “Splitting the Baby”, pg. 134 (emphasis in original))

The language of Linear B was infected because it added suffixes to stems, as English still does a little and Latin does a lot. Where English says “I love, you love, he loves”, Latin says “amo, amas, amat”. It’s easy to spot stems and inflexions like am-, -o, -as, and -at in an alphabetic script, which uses single signs for single sounds (generally speaking). But Linear B was syllabic, using single signs for single syllables. For example, ka, ke, ki, ko, ku were all written using entirely different signs, as was every other combination of consonant and vowel. Inflectional patterns are harder to spot in a syllabic script.

But syllabicity itself isn’t hard to spot: the number of signs used by a script is a good indication of whether it’s an alphabet, a syllabary or an ideography. You might say that the decipherment of Linear B rested on three C’s: counting, comparison and compulsion. Counting and comparing the signs established the relationships between them, but it took compulsive people to do that, because it was hard work. And “work” is the word:

Because she [Alice Kober] was under pressure to copy as many inscriptions as possible in her brief time in Oxford, she spent the weeks before her departure training for the task like an athlete preparing for the Olympics. Using the inscriptions in [the Finnish scholar Johannes] Sandwall’s new book as test material, she put herself through rigorous time trials at the dining table. “I’ve timed myself,” she wrote Myres in February 1947, “and think I can copy between 100-125 inscriptions in a single day.” (ch. 6, pg. 133)

“Myres” was the archaeologist John Linton Myres, a former assistant to Sir Arthur Evans who both helped and hindered Kober in her work. He gave her access to a lot of material, but he also made unreasonable demands on her time by asking her to help with his own writing on Minoan archaeology. Kober put up with a lot in her short time on earth, facing obstacles that would have daunted or deflected a less determined woman. But “The Detective”, as Fox calls her, forged on, straining both brain and body in her pursuit of the decipherment. It’s hard in 2014 to imagine having to copy inscriptions by hand, for example. And having to analyze them by hand. Kober used “cigarette-carton card files” and “index cards”:

What she had created, in pure analog form, was a database, with the punched cards marking the parameters on which the data could be sorted. But for all their rigor and precision, the file boxes also “reveal a gentler side to Alice Kober,” as Thomas Palaima and his colleague Susan Trombley have written. On one occasion, they note, Kober “took extra care in cutting a greeting card used as a tabbed divider, perfectly centering a fawn lying in a bed of flowers.” (Book Two, ch. 4, “American Champollion”, pg. 108)

Kober might have had a gentler side, but it’s no surprise that she also had a broad, masculine face and wore her hair short. Her task was a masculine one: systematizing and implicitly using mathematics. In fact, her hand-copying and “analog database” remind me of the enormous labours expended by nineteenth-century mathematicians on calculating the digits of pi or hunting for primes. What then took months and years can be performed in an instant by a computer. The same, I’d guess, is now true of Linear B. If it were discovered today and the necessary data were computerized – unknown signs, known neighbouring languages – its mask would probably be lifted very quickly.

Kober spent years on the task and died without completing it. Would she have beaten Michael Ventris if she’d lived? It’s easy to think so. But work on Linear B was, in effect, her hobby: she had a full-time job as a lecturer in classics at Brooklyn College. With more time, more help, fewer distractions, perhaps she would have solved Linear B in the 1940s.

As it was, the labyrinth was mastered by someone else: “The Architect” after whom the third and final section of this book is named. Unlike Evans or Kober, Michael Ventris wasn’t a professional classicist. And he went astray in a way the more cautious Kober didn’t, because he hypothesized for a long time that Etruscan was the language behind Linear B. It was a “position … to which he would hold fast until only weeks before his decipherment” (Book Three, ch. 10, “A Leap of Faith”, pg. 225).

If he’d been more cautious, might he have made faster progress? Probably, but he still beat all the professionals and deciphered Linear B, which turned out to be not Etruscan but a dialect of classical Greek. Ventris lifted the linguistic veil, but he found no literary treasure beneath:

There are no grand narratives lurking in Linear B – no epic poems, no romances, no tales of gods and their derring-do. Arthur Evans knew as much from the start, as did every serious investigator after him. They were all aware, as Alice Kober reminded her Hunter College audience that June evening in 1946, that “we may only find out that Mr. X delivered a hundred cattle to Mr. Y on the tenth of June, 1400 B.C.” And that, of course, is precisely what they did find: records of crops harvested, goods produced, animals tended, and gifts offered up to the gods. (“Epilogue: Mr. X and Mr. Y”, pg. 269)

But there’s a kind of poetry in the prosaic, especially when the prosaic is many centuries old. And it’s not just the gifts that are named: so are the gods. This means that if Kober had achieved her ambition, she would discovered an appropriate title waiting for her on the tablets. The names of familiar Greek gods and goddesses appear

with more curious ones, many of them pre-Greek, long-forgotten by Classical times. Among them are various female names – most likely those of local deities – beginning with the word potnia, “mistress”: Mistress of Wild Beasts, Mistress of Horses, Mistress of Grain, Mistress of Asia, Mistress of the Labyrinth. (Ibid., pg. 282-3)

Kober would have been “Mistress of the Labyrinth”, the one who solved Linear B. As it was, the Labyrinth had a master instead. So this book tells the story of three: the master, the mistress manquée and the man who supplied the materia of their obsession. That was Sir Arthur Evans, who discovered the tablets and began the work of deciphering them. His story contains one of the briefest but most memorable images in The Riddle of the Labyrinth. The story of Linear B isn’t all about concentrated effort and mental toil: there are moments of spontaneity too:

Over years of excavation, the palace emerged as a vast, increasingly complex organism. As each section was revealed, Evans gave it a name. Beside the Throne Room, these included the Queen’s Megaron, or great hall, with its elaborate bathroom and graceful mural of leaping dolphins; the Domestic Quarter, with artisans’ workshops in which traces of the goldsmith, the lapidary, and the ceramicist could still be still be discerned; and the Grand Staircase, down which, in 1910, a visiting Isadora Duncan danced an impromptu dance to the horror of Evans’s straitlaced Scottish assistant, Duncan Mackenzie. (Book One, “The Digger”, ch. 2, “Love among the Ruins”, pg. 77)

Dancing Duncan, dour Duncan and dogged decipherment. I like the contrast and it’s another reason to like this book. But will it ever be matched by one about the decipherment of Linear A, another lost language found on Crete and written in a related script? Perhaps not, because the language of Linear A seems to be an isolate, without living or ancient relatives. Barring some big scientific or linguistic breakthrough, Linear A may remain a labyrinth no-one ever masters. But perhaps Margalit Fox will be telling the story of its decipherers one day too. I hope so.

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Lost Stolen or Shredded by Rick GekoskiLost, Stolen or Shredded: Stories of Missing Works of Art and Literature, Rick Gekoski (Profile Books 2013/2014)

In her hilarious hatchet-job on her departed idol Susan Sontag, the lesbian academic Terry Castle describes the “relentless quizzing” she underwent in the “early days” of their friendship:

I almost came a cropper when I confessed I had never listened to Janáček’s The Excursions of Mr Broucek. She gave me a surprised look, then explained, somewhat loftily, that I owed it to myself, as a ‘cultivated person’, to become acquainted with it. (‘I adore Janáček’s sound world.’) A recording of the opera appeared soon after in the mail – so I knew I’d been forgiven – but after listening to it once I couldn’t really get anywhere with it. (It tends to go on a bit – in the same somewhat exhausting Eastern European way I now associate with Sontag herself.) (“Desperately Seeking Susan”, London Review of Books, 17th March 2005)

In other words: Sontag was a gasbag. And is there a sulphurous whiff of antisemitism in the phrase “Eastern European”? I fear so. I also fear that this book tends to go on a bit à la Janáček and Sontag. Which was a disappointment. I would like to have read it properly, but I couldn’t: like The Hitch, Rick Gekoski, who has a D.Phil. on Joseph Conrad, doesn’t use English as though it is his mother-tongue. Which is a pity. There are some interesting topics here, from the “carbonized” but still legible papyri in an ancient library at Herculaneum, which were bequeathed to posterity by the eruption of Vesuvius, to the richly jewelled cover of a “bookbinding executed in 1911” for Fitzgerald’s Rubaiyat of Omar Khayyam, which was lost with the Titanic. Plus the alleged “wanking fantasies” in Philip Larkin’s diaries, which were destroyed on Larkin’s own instructions after his death.

There are also some Guardianista topics: the book is based on a series on BBC Radio 4, like Gekoski’s earlier (and better) Tolkien’s Gown and Other Stories of Great Authors and Rare Books (2005). And so there are constant references to the Holocaust and to white man’s inhumanity to non-white man, like African blacks and the Māori. There is also a lot about giants of European culture whom I don’t like: Joyce, Mahler, Kafka, Conrad and so on. True, I agree with Gekoski when he says, in the chapter about the looting of Iraqi antiquities, that Donald Rumsfeld was “indefatigably loathsome”, but I’m rather worried that I do. And I don’t like that way of putting it. Christopher Hitchens might have put it like that, though not, in his later days, about Rumsfeld. Gekoski is a successful book-dealer and knows a lot about art and literature. I just wish he could convey what he knows more elegantly and concisely.

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