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The Magic of Uri Geller, as revealed by the Amazing Randi (1982)

Uri Geller is a luftmensch with chutzpah. It’s no coincidence that two Yiddish words sum him up, because Jews have been as disproportionately successful at fraud as they have been in other professions requiring high intelligence and quick wits. Chutzpah, or brazen arrogance, probably won’t need defining, but a luftmensch, for those who haven’t come across the word before, is literally an “air-man”: someone who makes a living from nothing. Geller has achieved world-wide fame and made large sums of money principally by bending spoons and keys and starting “stopped” watches. Compared to the atom bomb or the moon-landings, it’s hardly the stuff of legend, but the difference is that the men behind the atom bomb and the moon-landings didn’t put a dishonest label on what they did. Geller does and that’s why he’s been successful.

Shakespeare wrote in Romeo and Juliet: “What’s in a name? That which we call a rose by any other name would smell as sweet.” In fact, it wouldn’t: it’s well-established in psychology that labels can affect emotion and sensation. The label doesn’t even have to be verbal:

The direct relationship between the quality of a product and the colour of its container is again demonstrated by an American test in which 200 women were invited to judge the flavour of a coffee served from brown, red, blue and yellow coffee pots. Although the same coffee was served in each case, almost three quarters of those tested found the coffee from the brown pot to be too strong, whereas nearly half of the women found the coffee from the red pot to be rich and full-bodied. The coffee from the blue pot was regarded as having a milder aroma, while that from the yellow pot was judged to be made from the weaker blend of bean. (The Colour Eye, Robert Cumming and Tom Porter, BBC Books, London, 1990, “Colour and Quality”, pg. 147)

Geller attributes his trivial tricks to mysterious powers, helped by a simple equation that has been at work for many thousands of years: ignorance + emotion = the supernatural. When human beings can’t understand something and are excited by it, they have always been prone to seek a supernatural explanation (or rather, non-explanation: the supernatural explains nothing, merely allows us to conceal an epistemological gap in a psychologically satisfying way). When Geller, a master of psychological manipulation, creates emotion by bending a thick key in a way his audience can’t understand, it’s easy for him to convince the gullible that he has special powers. And we are much gullible than we’d like to believe. The Amazing Randi, the author of this debunking book, reproduced Geller’s feats before an audience of scientists, having explicitly stated he was using trickery. Maurice Wilkins, who won a Nobel prize for his part in the discovery of the structure of DNA, then told him: “Mr. Randi, you’ve told us that what you did was accomplished by trickery. But I don’t know whether to believe you or believe in you!”

After all, one of the most important points this book makes is that scientists, for all their priestly prestige and status, are not the right people to investigate Geller’s claims:

Certain prominent American scientists have said, concerning the criticisms of their acceptance of Geller, that their detractors are calling them either liars or fools. (ch. 16, “Geller in England”, pg. 256)

And since prominent American scientists are obviously neither liars nor fools, Geller must be genuine. Randi points out the false logic:

Neither is correct, so far as I am personally concerned. I call them simply “unqualified” – in this particular field – to pass judgment on such matters. (pg. 256)

A clever magician can fool a clever scientist, because deception is a magician’s stock-in-trade. Geller and Randi are both masters of deception, but Randi is honest about what he is, Geller isn’t. Randi is also a master of readable prose: I enjoyed this book a great deal, and not just because it remains highly relevant, even thirty years after Geller’s heyday. Luftmenschen with chutzpah are still with us and Geller reminds me a lot of Tony Blair. Blair isn’t Jewish, isn’t as intelligent, and hasn’t lasted as long, but the mass psychology behind both men’s success seems similar. Randi quotes the Latin saying Homo vult decipi; decipiatur: “Man wishes to be deceived; let him be deceived.”

Like Blair, Geller didn’t have to do much to convince large numbers of people that he was special, but then another important point the book makes, in Geller’s case, is that failure can even be helpful. If Geller were successful all the time, he’d look more like a fraudster who uses trickery. Occasional failure not only makes him look honest but heightens the effect of his successes too, and Randi describes how magicians sometimes exploit this aspect of human psychology by deliberately failing on something small before succeeding on something big.

And not all of Geller’s genuine failures are reported. In one of the funniest anecdotes in the book, Randi describes how, on his triumphant tour of England in the mid-1970s, Geller told a pregnant journalist that she would have a girl in three days’ time:

She had the baby, all right – a boy, a month later. Determining that the lady was expectant was all that Uri had done. And just about anyone could do that, at that stage! But what if he’d been right? The press would have trumpeted it to the world. As it was, no attention was directed to the prediction. (ch. 16, “Geller in England”, pg. 253)

Yes, it would have been trumpeted to the world, even though predicting the sex of a baby, at least, is no more difficult than predicting the fall of a coin: a 50% chance of success is hardly unfavorable. But the general public’s ignorance of probability was another factor in Geller’s success. When he appeared on a television or radio show with a large audience and predicted strange happenings among his viewers or listeners, he got a a lot of people ringing in to report exactly that: strange happenings. According to Randi, so did a “psychic” called Jim Pyczynski when he appeared on a radio show in New York: lights flickered or went out; a container of milk burst; mirrors “cracked”; pictures fell off walls; cats became agitated; and a clock that had been stopped for years started working again (ch. 12, “The Old Broken Watch Trick Revealed”, pp. 191-4).

But in fact Jim Pyczynski was Randi’s “full-time assistant” and was merely proving a statistical point: “strange happenings” are inevitable when enough people look out for them, and large audiences will also contain liars and fantasists, as well as honest people who, when prompted to do so, will notice what they had previously overlooked. Did the mirrors crack during Pyczynski’s broadcast or sometime before and without being noticed?

And again, the supernatural label helps create emotion that reinforces the appearance of the supernatural. Geller’s tricks are trivial, but we can be taken in by trivial things. Part of Randi’s animus against Geller is perhaps explained by jealousy, but then Randi does seem to be a better magician who, with less honesty, could easily have achieved what Geller has achieved. It’s easy to be a psychic, because people don’t understand how easily they can be manipulated or how predictable human psychology can be. This book or Randi’s website will tell you more about how fraudsters like Geller manipulate and exploit us. For the other side of the story, see Geller’s website, where you’ll find his chutzpah as strong as ever.

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The Collected Stories of Arthur C. ClarkeThe Collected Stories, Arthur C. Clarke (Victor Gollancz 2000)

Do you want to know the difference between ingenuity and imagination? Between literary competence and literary genius? Then compare Arthur C. Clarke’s short stories with J.G. Ballard’s short stories. Reading Ballard is like exploring a jungle; reading Clarke is like touring a greenhouse. Ballard is haunting and head-expanding in a way that Clarke isn’t, much as he might have wanted to be.

You could say that the difference between them is like the difference between wizardry and engineering or poetry and prose or madness and sanity. Clark Ashton Smith and J.R.R. Tolkien are different in the same way. Ballard and Smith could conjure dreams on paper; Clarke and Tolkien could create realistic worlds. I like all four writers, but I don’t place them at the same level. There is a great gulf fixed between the wizards and the engineers. I’m reminded of it every time I read Clarke and Tolkien, so part of the value of their work is that it teaches me to appreciate Ballard and Smith more. Or to marvel more.

All the same, the engineers could do things that the wizards couldn’t. Clarke and Tolkien were better educated than Ballard and Smith, and Clarke knew more about hard science than Ballard. There are some ideas and images in this book that take realism to its limits. The life-form that Clarke invented for “Castaway” (1947) has stayed with me ever since I read the story as a child. It was thrown off its home-world by a storm – or rather, thrown out of its home-world. That’s because it was a plasma-creature living inside the sun until it was ejected by a solar storm and blown on the solar wind to the Earth:

The tenuous outer fringes of the atmosphere checked his speed, and he fell slowly towards the invisible planet. Twice he felt a strange, tearing wrench as he passed through the ionosphere; then, no faster than a falling snowflake, he was drifting down the cold, dense gas of the lower air. The descent took many hours and his strength was waning when he came to rest on a surface hard beyond anything he had ever imagined.

The unimaginably hard surface is actually the Atlantic Ocean, where the plasma-creature is detected by the radar of an overflying jet-liner. It looks like a giant amoeba to the wondering humans who are watching the radar, but they can’t see anything at all when they look at the water. The story is a very clever exercise in shifts of perspective and Clarke returned to these ideas in “Out of the Sun” (1958), in which the same kind of creature is thrown out of the sun and lands on Mercury, where it freezes to death in “seas of molten metal”. More wondering humans have watched it fly through space on radar from a solar-observation base. As it dies, the humans feel a “soundless cry of anguish, a death pang that seeped into our minds without passing through the gateways of the senses.”

There’s also alien life and clever invention in “A Meeting with Medusa” (1971), which is about a solo expedition to Jupiter that discovers giants in the clouds: browsing herbivores that defend themselves from swooping predators with electrical discharges. The explorer is called Falcon and is part-robot after an air-ship crash on earth. That enables him to survive “peaks of thirty g’s” as his air-ship, called Kon-Tiki, descends to the “upper reaches of the Jovian atmosphere” and collects gas so that it can float there and observe. The story takes you to Jupiter and teaches you a lot about Jovian physics, chemistry and meteorology: it’s realism, not reverie, and Falcon’s discovery of life is entirely plausible.

The story was probably influenced by Arthur Conan Doyle’s “The Horror of the Heights” (1913), a proto-Lovecraftian story in which an early aviator discovers similar predators high in the air above Wiltshire. Doyle’s contemporary H.G. Wells was certainly an influence on Clarke: there’s even a piece here (not a proper story) called “Herbert George Morley Roberts Wells, Esq.” (1967). Clarke also knew Lovecraft and wrote a short parody of At the Mountains of Madness (1931) called At the Mountains of Murkiness, but the parody isn’t collected here and Lovecraft’s influence isn’t very obvious. Clarke had a sunny and optimistic personality and wrote few dark or depressing stories. There is a definite Lovecraftian touch, however, in one of the mini-stories collected under the title “The Other Side of the Sky” (1957). In “Passer-By”, an astronaut describes seeing something as he travels between space-stations on a rocket scooter. First he spots it on radar, then watches as it flies past:

I suppose I had a clear view of it for perhaps half a second, and that half-second has haunted me all my life. […] Of course, it could have been a very large and oddly shaped meteor; I can never be sure that my eyes, straining to grasp the details of so swiftly moving an object, were not hopeless deceived. I may have imagined that I saw that broken, crumpled prow, and the cluster of dark spots like the sightless sockets of a skull. Of one thing only was I certain, even in that brief and fragmentary vision. If it was a ship, it was not one of ours. Its shape was utterly alien, and it was very, very old.

It’s Lovecraftian to compare the portholes of a space-ship to the eye-sockets of a skull. So is the idea of a “very, very old” wreck flying between the stars. The uncertainty and doubt are Lovecraftian too, but you could also say that they’re scientific. Clarke often emphasizes the fallibility of the senses and the uncertainty of inferences based on them. Science is a way of overcoming those sensory limitations. In Lovecraft, science is dangerous: that uncertainty would slowly give way to horror as the truth is revealed. Clarke’s protagonist experiences no horror and though he’s haunted for life by what he might have seen, he feels that way because he didn’t learn enough, not because he learnt too much.

That story may have been the seed for Rendezvous with Rama (1976), which could be seen as a more optimistic re-working of At the Mountains of Madness. Puny humans explore a titanic alien artefact in both stories, but Clarke’s humans aren’t punished for their curiosity and at the end of the novel they look forward to indulging more of it. Clarke is good at grandeur and invoking the hugeness of the universe. He wrote about galaxy-spanning empires, giant scientific discoveries and struggles to save the universe.

He wrote about the multiverse too and there’s a story that makes the multiverse seem big by portraying a very confined part of it. This is the opening paragraph of “The Wall of Darkness” (1949):

Many and strange are the universes that drift like bubbles in the foam upon the river of Time. Some – a very few – move against or athwart its current; and fewer still are those that lie forever beyond its reach, knowing nothing of the future or past. Shervane’s tiny cosmos was not one of these: its strangeness was of a different order. It held one world only – the planet of Shervane’s race – and a single star, the great sun Trilorne that brought it life and light.

Shervane is a young man who makes a very strange discovery when he tries to cross a giant wall that circles his home planet. What is on the other side? In a way, everything is. This is another story that has stayed with me from my first reading of it as a child. And it could almost have been written by Ballard: like Ballard’s “The Concentration City” (1957) or “Thirteen to Centaurus” (1962), it’s about trying to escape from confinement and making an unexpected or ironic discovery about the true nature of things. Unlike Ballard, Clarke didn’t spend the Second World War locked in a prison camp, but he could get big ideas from a wall and the limit it imposed.

Neither he nor Ballard always wrote about big and serious ideas, however. Many stories here are deliberately small and silly, or big in a ludicrous way. P.G. Wodehouse seems to be an influence on the stories that come under the heading of Tales from the White Hart, in which Harry Purvis spins fanciful yarns for an audience of scientists and science-fiction writers in a pub in London. One story has an exploding moonshine still, another a giant squid that’s angry about its brain being manipulated, another a fall of twenty feet during which an unfortunate scientist doesn’t merely break the sound-barrier, but travels so fast that he’s burnt alive by air-friction.

It’s a horizontal fall too, although the story is called “What Goes Up” (1956). Clarke was playing with science there; elsewhere, in stories like “Green Fingers”, part of “Venture to the Moon” (1956), he’s making serious suggestions. The story is about a botanist on the moon who is killed by his own ingenuity, but it’s not a gloomy, Lovecraftian doom. Risks are part of exploration and adventure and Clarke presented space-travel as a new form of sea-faring. He loved both the sea and the sky and his love shines brightly here. So do “The Shining Ones” (1962), the intelligent cephalopods who end the life of another of his protagonists.

The premature death of adventurous young men is a theme he shared with A.E. Housman, whose poetry he greatly admired, but Clarke could also write about the rescue of adventurous young men, as in “Hide-and-Seek” (1949), “Summertime on Icarus” (1960) and “Take a Deep Breath” (1957). And deaths in his work aren’t futile or proof that man is always ultimately defeated. If Clarke had written pessimistically like that, he wouldn’t have been so popular among working scientists or inspired so many children to enter science. But he could appeal to children partly because he never properly grew up himself. Unlike Ballard, he never married or had any children of his own and his decision to live on Sri Lanka was probably inspired in part by paederasty, not just by his interest in scuba-diving.

My final judgment would be that he was an important writer, not a great one. I’ve enjoyed re-reading the stories here – even the numerous typos were fun – but that’s partly because they’ve sharpened my appreciation of J.G. Ballard. Clarke had no spark of divine madness: he was Voltaire to Ballard’s Nietzsche. His work does sparkle with intellect and ideas, but he made more out of science than he ever did out of fiction.


Previously pre-posted on Papyrocentric Performativity:

Clarke’s Arks – reviews of Imperial Earth (1976) and Rendezvous with Rama (1972)

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19186368.jpgA Buzz in the Meadow, Dave Goulson (Jonathan Cape 2014)

A book that is both a rhapsody and a threnody: Dave Goulson celebrates nature and laments what we’re losing of it. This is what he says in the preface:

In 2003 I bought a derelict farm deep in the heart of rural France, together with thirteen hectares of surrounding meadow. My aim was to create a wildlife sanctuary, a place where butterflies, dragonflies, voles and newts could thrive, free from the pressures of modern agriculture. In particular I was keen to create a space for my beloved bumblebees, creatures I have spent the last twenty years studying and attempting to conserve. (pg. ix)

Bumblebees were the subject of his previous book, A Sting in the Tale (2013). I haven’t read that, but if it’s half as good as this I will certainly enjoy it. Perhaps it’s better: Goulson is a biologist who can both educate and entertain. Expect the unexpected here: he writes about bumblebees and wild-flowers with the same enthusiasm as he writes about cheese and wine.

He’s also good at using the particular to illustrate the general. You’ll learn a lot about science and the scientific method here, from the “robotic beetle drum” he used to study death-watch beetles to the creation of “mathematical models” for predicting outbreaks of flies at a landfill site. Biology is full of puzzles and solving one often creates another. Not that they are always easy to solve: failure and frustration are part of science too and Goulson is happy to admit his own.

But he isn’t happy about the loss of wild habitats and the quickening pace of extinctions. Homo sapiens could also be called Homo exterminans:

New Zealand was colonised much more recently, about 1,000 years ago. As there were no mammals apart from bats, giant birds evolved there, including at least eleven species of moa, the largest of which stood 3.6 metres high, the tallest bird ever to live. They must have been terribly easy to track and kill, for carbon-dating of Maori middens suggests that all eleven species were driven to extinction within just 100 years of man’s arrival. (ch. 15, pg. 242; his emphasis)

It’s a long way from French meadows to Maori middens, as the crow flies, but similar themes apply: humans have exercised power over nature without proper thought for the consequences. Science is giving us more power all the time, but will it kill us or cure us? Dave Goulson is a scientist who increases my hope of the latter.

He also links apparently disparate parts of biology: parasites are part of both botany and entomology. Yellow rattle is a hemi-parasitic plant that exploits grasses and the bumblebees that visit it are parasitized by mites. The world is a web in more ways than one and many aspects of the web are described in this happy, hopeful and highly enjoyable book.

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The Million Death Quake by Roger MussonThe Million Death Quake: The Science of Predicting Earth’s Deadliest Natural Disaster, Roger Musson (Palgrave Macmillan 2012)

“As solid as the earth,” we say. That’s why even mild earthquakes are often frightening and always memorable. Suddenly you can’t rely on the earth any more: it’s not rock-steady, it’s dancing. And it might be about to dance you to death.

But Robert Musson, author of this excellent guide to the history and future of seismology, points out that even in a big earthquake you’ll usually be safe in the open away from buildings. The problem is that few people spend much time like that. Cities are getting bigger and more crowded, which is why he suggests that one day an earthquake could kill a million people or more. Tehran is one candidate. So is this:

The case of Istanbul is unnerving for another reason. The North Anatolian Fault, the great strike-slip fault that starts in eastern Turkey and dies out in the middle of the Aegean, has an interesting property. Earthquakes along it tend to occur in sequences, starting in the east and moving progressively west. Each quake, as it occurs, throws more stress on the next section of fault to the west, which then fails a few years to a decade or so later. it’s like a series of dominoes toppling. […] The current sequence began with a 7.8 magnitude event near Erzincan, at the eastern end of the fault line, in 1939. This was followed by quakes progressively further west in 1942, 1943, 1944, 1957 and 1967. Then, after a lull, the next most westerly stretch of fault broke in 1999 with the Izmit earthquake. The next stretch of fault to the west goes straight through the Sea of Marmara, just south of Istanbul. This is the next domino to fall, and it could happen at any time. (ch. 12, “Stay Safe”, pp. 233-4)

Or there could be another lull. That is one of the interesting things about earthquakes: their unpredictability. The subtitle of this book is misleading, because there is no reliable science of prediction for earthquakes. Seismologists can say in great detail why and how they occur, but they can’t say where or when or what size. We are far better at predicting the behaviour of the sky above our heads than we are at predicting the behaviour of the earth beneath our feet. Meteorologists are refining and extending their forecasts further all the time. Astronomers have been accurately predicting eclipses and planetary orbits for thousands of years.

Seismologists would like to make their discipline predictive rather than reactive, but it’s proving very difficult. Masson discusses one team of Greek seismologists who claimed to be able to predict quakes using “seismic electrical signals, or SES for short” released by “rocks once they are stressed beyond a certain degree” (ch. 8, “Next Year’s Earthquakes”, pg. 172). But the team, led by Professor Panayotis Varotsos, made their predictions by sending telegrams to each other rather than informing an official body. When the earthquake occurred, they would produce the telegram and its date-stamp: “The question that was whispered in the corridors at conference sessions was this: How many telegrams were quietly burned when the prediction failed?”

Then a “moderate earthquake” hit Athens in 1999 and although the team claimed to have predicted it, they hadn’t said so in public. Apparently stung by the criticism that followed, Professor Varotsos issued a public prediction of a larger earthquake on its way in central Greece. But it never happened and the team were no longer taken seriously.

It’s not difficult to understand why earthquake prediction is so difficult: rocks aren’t transparent and gathering data from the depths of the earth is much harder than gathering data from the sky. Seismologists would be delighted if they could realize the suggestion made by Arthur C. Clarke in his short story “The Fires Within” (1949):

Sonar, as you will know, is the acoustic equivalent of radar, and although less familiar is older by some millions of years, since bats use it very effectively to detect insects and obstacles at night. Professor Hancock intended to send high-powered supersonic pulses into the ground and to build up from the returning echoes an image of what lay beneath. The picture would be displayed on a cathode ray tube and the whole system would be exactly analogous to the type of radar used in aircraft to show the ground through cloud.

Nearly seventy years on, we’re still waiting for a geoscope like that. Seismology is still a hobbled science and earthquakes are still mysterious and frightening things. As Sherlock Holmes says in “The Adventure of the Copper Beeches” (1892): “Data! data! Data! … I can’t make bricks without clay.” But seismologists have done a lot with the limited data they’ve got, as you’ll learn here. Writing clearly and colloquially, Masson traces the history of mankind’s attempts to understand earthquakes, describes their effects on history, discusses related phenomena like volcanoes and tsunamis, and explains why seismologists don’t use the “Richter scale”. The Million Death Quake has a hyperbolic title and a misleading subtitle, but it’s one of the best popular science books I’ve come across.

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The World of Visual Illusions by Sarcone and WaeberThe World of Visual Illusions: Optical Tricks That Defy Belief!, Gianni A. Sarcone and Marie-Jo Waeber (Arcturus 2012)

A bigger, better and brain-bendy-er version of Eye Bogglers by the same authors, The World of Visual Illusions has nine chapters of old and new illusions. The illusions aren’t just entertaining: they raise some very profound philosophical and scientific questions and teach you some important lessons. For example, on page 97 there’s a simple arrangement of multi-coloured blocks and thick black lines. But Sarcone and Waeber ask this: “Do you perceive bright ‘ghost’ blobs or smudges at the intersection of the lines?”

I do and so will almost everyone else. But when I look directly at a blob or smudge, it disappears. Why? What’s going on? No-one knows for sure: “there are many explanations and counter-explanations regarding this illusion, which is related to the Hermann grid illusion.” So this illusion is multum in parvo: much in little. It’s very simple, but it baffles modern science. And, like many other illusions here, it teaches you that your senses aren’t reliable. They can be subverted and you aren’t in control of what your eyes tell you. Even when you know that the lines on page 109 are “perfectly straight and parallel”, it’s impossible to see them like that because of the background they’re set against.

That kind of trickery can also be applied to words and ideas, and although Sarcone and Waeber don’t talk about advertising or politics, the implications are obvious. Appearances can be deceptive and simple things may have hidden depths. So may complicated things: Holbein’s The Ambassadors (1533) would be a rich and detailed painting even without the anamorphic skull that hovers between the feet of its two subjects. Sarcone and Waeber give the painting a page and a handful of words, but there’s enough there for a long book (John Carroll analyses the painting in a chapter of The Wreck of Western Culture).

There’s enough in the other illusions here for a library, but you don’t have to puzzle over how they work if you don’t want to. We aren’t all equal in intellect or education, but vision is much more egalitarian and this book will entertain all ages and all levels of intelligence. What you experience in an instant can take decades or even centuries for scientists to understand:

It looks like this cat has green eyes. Actually, only one eye is green – the other one is shown in black and white but seems tinted because of the purple context. Thanks to a mechanism of colour adaptation, the brain desensitizes itself to the purple veil which covers the right side of the cat’s face and by doing that it subtracts a bit of purple from the gray eye, which then become yellowish-green. (pg. 120)

I’d like to see Sarcone and Waeber look at other senses. Sight is the most important and powerful sense for human beings, but the ears, nose, mouth and skin can also be illuded. And what about the role of illusions in biological competition and evolution? It’s a big field, often fun, always fascinating.

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Infinitesimal by Alexander AmirInfinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, Amir Alexander (Oneworld 2014)

Infinitesimal is an entertaining read on a fascinating topic: the pioneers of a new form of mathematics and those who opposed them. Amir Alexander claims that “the ultimate victory of the infinitely small helped open the way to a new and dynamic science, to religious toleration, and to political freedoms unknown in human history” (Introduction, pg. 14).

It’s an extraordinary claim and I don’t think he manages to provide extraordinary proof for it. In fact, he probably gets cause-and-effect reversed. Is it likelier that new mathematics opened minds, dynamized science and transformed politics or that open minds created new forms of mathematics, science and politics? I’d suggest that support for the new mathematics was a symptom, not a cause, of a new psychology. But Alexander makes a good case for his thesis and there is no doubt that the world was changed by the willingness of mathematicians to use infinitesimals. Calculus was one result, after all. The book begins in Italy and ends in England, because the pioneers lost in Italy:

For nearly two centuries, Italy had been home to perhaps the liveliest mathematical community in Europe. … But when the Jesuits triumphed over the advocates of the infinitely small, this brilliant tradition died a quick death. With Angeli silenced, and Viviani and Ricci keeping their mathematical views to themselves, there was no mathematician left in Italy to carry on the torch. The Jesuits, now in charge, insisted on adhering close to the methods of antiquity, so that the leadership in mathematical innovation now shifted decisively, moving beyond the Alps, to Germany, England, France and Switzerland. (ch. 5, “The Battle of the Mathematicians”, pg. 178)

Why were the Jesuits involved in an esoteric mathematical dispute? You might say that de minimis curat Loyola – Ignatius Loyola (1491-1556), founder of the Jesuits, cared about anything, no matter how small, that might undermine the authority of the Church. In the view of his successors, the doctrine of indivisibles did precisely that: “in its simplest form, the doctrine states that every line is composed of a string of points, or ‘indivisibles’, which are the line’s building blocks, and which cannot themselves be divided” (Introduction, pg. 9).

Indivisibles must be infinitesimally small, or they wouldn’t be indivisible, but then how does an infinitesimal point differ from nothing at all? And if it isn’t nothing, why can’t it be divided? These paradoxes were familiar to the ancient Greeks, which is why they rejected infinitesimals and laid the foundations of mathematics on what seemed to them to be solider ground. In the fourth century before Christ, Euclid used axioms and rigorous logic to create a mathematical temple for the ages. He proved things about infinity, like the inexhaustibility of the primes, but he didn’t use infinitesimals. When Archimedes broke with Greek tradition and used infinitesimals to make new discoveries, “he went back and proved every one of them by conventional geometrical means, avoiding any use of the infinitely small” (Introduction, pg. 11).

So even Archimedes regarded them as dubious. Aristotle rejected them altogether and Aristotle became the most important pre-Christian influence on Thomas Aquinas and Catholic philosophy. Accordingly, when mathematicians began to look at infinitesimals again, the strictest Catholics opposed the new development. Revolutionaries like Galileo were opposed by reactionaries like Urban VIII.

But the story is complicated: Urban had been friendly to Galileo until “the publication of Galileo’s Dialogue on the Copernican system and some unfavourable political developments” (pg. 301). So I don’t think the mathematics was driving events in the way that Alexander suggests. Copernicus didn’t use them and the implications of his heliocentrism were much more obvious to many more people than the implications of infinitesimals could ever have been. That’s why Copernicus was frightened of publishing his ideas and why Galileo faced the Inquisition for his astronomy, not his mathematics.

But Amir’s thesis makes an even more interesting story: the tiniest possible things had the largest possible consequences, creating a new world of science, politics and art. In Italy, two of the chief antagonists were Galileo and Urban; in England, two were the mathematician John Wallis (1616-1703) and the philosopher Thomas Hobbes (1588-1679). Alexander discusses Wallis and Hobbes in Part II of the book, “Leviathan and the Infinitesimal”. Hobbes thought that de minimis curat rex – “the king cares about tiny things”. Unless authority was absolute and the foundations of knowledge certain, life would be “nasty, brutish and short”.

However, there was a big problem with his reasoning: he thought he’d achieved certainty when he hadn’t. Hobbes repeatedly claimed to have solved the ancient problem of the “quadrature of the circle” – that is, creating a square equal in size to a given circle using only a compass and an unmarked ruler. Wallis demolished his claims, made Hobbes look foolish, and strengthened the case for religious toleration and political freedom. But I don’t think this new liberalism depended on new mathematics. Instead, both were products of a new psychology. Genetics will shed more light on the Jesuits and their opponents than polemics and geometry textbooks from the period. Alexander’s theory is fun but flawed.

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Discovering the UniverseDiscovering the Universe: The Story of Astronomy, Paul Murdin (Andre Deutsch 2014)

First published in 2011 as Mapping the Universe, this is a well-written, well-illustrated history of astronomy that begins in the Stone Age and ends with the Hubble Space Telescope and Large Hadron Collider. The photographs will stimulate your eyes as the text stimulates your mind. The universe is a big place and big things happen there, like gamma-ray bursts (GRBs):

Until 1997, astronomers didn’t know whether GRBs originated in some sort of explosions on the edge of our solar system, around our Galaxy, or far away. Two examples proved that the explosions occur the edge of the observable Universe. For their duration of a few seconds, the bursts had been over a million times brighter than their parent galaxy, the biggest bangs since the Big Bang. (ch. 17, “Exploding Stars”, pg. 87)

Ptolemy, Galileo and Newton would all be astonished by the technology that allows modern astronomers to study phenomena like gamma-ray bursts, but one thing has remained constant: the importance of mathematics and measurement in studying the sky. The story of astronomy is not just about seeing further and clearer, but also of measuring better and mathematizing more powerfully. Ptolemy’s geocentric universe entailed the arbitrary complexity of epicycles on epicycles, to explain how the planets sometimes seemed to move backwards against the stars. Then Copernicus resurrected the ancient Greek hypothesis of a heliocentric universe.

Back cover

Back cover


Planetary retrogression became easier to explain. Other hypotheses, like the steady state universe and Kepler’s planetary Platonic solids, haven’t proved successful, but data don’t explain themselves and astronomers have to be adventurous in mind, if not usually in body. This book contains the big names, the big sights and the big mysteries that are still awaiting explanation. More big names, sights and mysteries are on their way.

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Philosophy 100 Essential Thinkers by Philip StokesPhilosophy: 100 Essential Thinkers: The Ideas That Have Shaped Our World, Philip Stokes (Arcturus Publishing 2012)

Caricatures are compelling because they simplify and exaggerate. A good artist can create one in a few strokes. In fact, a good artist has to caricature if he can use only a few strokes. The image won’t be recognizable otherwise.

This also applies to philosophical ideas. If you have to describe them in relatively few words, you’ll inevitably caricature, making them distinct but losing detail and complexity. So this book is a series of caricatures. With only 382 pages of standard print, what else could it be? In each case, Philip Stokes uses a few strokes to portray “100 Essential Thinkers” from Thales of Miletus, born c. 620 B.C., to William Quine (1908-2000), with all the big names in between: Plato, Aristotle, Descartes, Pascal, Hume, Kant, Leibniz, Schopenhauer, Nietzsche, Russell, Wittgenstein and so on. The philosophical portraits are recognizable but not detailed. But that’s why they’re fun, like a caricature.

It’s also fun to move so quickly through time. There are nearly three millennia of Western philosophy here, but the schools and the civilizations stream by, from the Pre-Socratics and Atomists to the Scholastics and Rationalists; from pagan Greece and Rome to Christianity and communism. Bertrand Russell’s History of Western Philosophy, which inevitably comes to mind when you look at an over-view like this, moves much more slowly, but it’s a longer and more detailed book.

It’s also funnier and less inclusive. This book discusses men who are more usually seen as scientists or mathematicians, like Galileo and Gödel. But in a sense any historic figure could be included in an over-view of philosophy, because everyone has one. You can’t escape it. Rejecting philosophy is a philosophy too. Science and mathematics have philosophical foundations, but in some ways they’re much easier subjects. They’re much more straightforward, like scratching your right elbow with your left hand.

Philosophy can seem like trying to scratch your right elbow with your right hand. The fundamentals of existence are difficult to describe, let alone understand, and investigating language using language can tie the mind in knots. That’s why there’s a lot of room for charlatans and nonsense in philosophy. It’s easier to pretend profundity than to be profound. It’s also easy to mistake profundity for pseudery.

And, unlike great scientists or mathematicians, great philosophers should be read in the original. Reading Nietzsche in English is like looking at a sun-blasted jungle through tinted glass or listening to Wagner wearing earplugs. Or so I imagine: I can’t read him in German. But some philosophers suffer less by translation than others, because some philosophical ideas are universal. Logic, for example. But how important is logic? Is it really universal? And is mathematics just logic or is it something more?

You can ask, but you may get more answers than you can handle. Philosophy is a fascinating, infuriating subject that gets everywhere and questions everything. You can’t escape it and this book is a good place to learn why.

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Scented Flora of the World by Roy GendersScented Flora of the World: An Encyclopedia, Roy Genders (Robert Hale 1977)

It’s hard to believe that even a horticulturalist as expert and dedicated as Roy Genders (1913-85) was personally acquainted with every flower, tree, and shrub in this large and detailed book. But the back cover claims that it was “a thirty-year labour of love”, so perhaps he was. Either way, he was a lucky man. There is a Chinese saying that runs: “If you want to be happy for a day, get drunk; happy for a year, get married; happy for a lifetime, get a garden.”

Plants and flowers are endlessly rewarding and in a way the absence of pictures here intensifies the romance and sensuality of its subject. Even the appendices, running from “A” to “T”, are good to read: “Night-Scented Flowering Plants” combines the mystery of night with the strangeness of scientific names (Heliotropicum convolvulacaeum), the evocation of scent (vanilla, honey, lily), and the enchantment of distance (Mexico, Brazil, South Africa).

Then there are “Scented Aquatic Plants” and “Scented Cacti and Succulents” — and that is only the appendices. In the first part of the book Genders discusses the history, chemistry, culture and psychology of scented flora, then plunges head-and-heart-long into the encyclopedia of the book’s title. There’s everything from Abelia chinensis, with its “rose-tinted flowers, like miniature fox-gloves”, to Zylopa glabra, whose seeds, “much sought after by wild pigeons… impart their particular odour to the birds’ flesh”. In between there are plants like Illicium religiosum, an omnifragrant Japanese tree used for incense and for strewing at funerals. Genders says that it’s known in China as “Mang-thsao, ‘the mad herb’, for it is said to cause frenzy in humans”.

Scent can do that, either by attracting or by repelling. And Genders doesn’t neglect the repellent side of his subject: he describes the pongy and pungent with the sweet and soporific. The final appendix draws up a “Phew’s-Who” of “Plants bearing Flowers or Leaves of Unpleasant Smell”. It’s like a remainder of the death and decay that await us all, but those are what nourish the plants that are beautiful and sweetly-scented, as well as those that are only one of those or neither.

So Scented Flora is big both in bulk and in its themes. According to the Oxford English Dictionary, “encyclopedia” is spurious Greek for “all-round education”. Despite its focus on one aspect of one subject, that’s what Genders reveals and provides here. He knew a lot not just about horticulture and science, but about literature and culture too. We call Filipendula ulmaria “meadow-sweet” nowadays, but Ben Johnson knew it as “Meadow’s Queen”, perhaps after the French reine-des-prés, “queen of the meadows”. The herbalist Gerard said that its scent “makes the heart merry and delighteth the senses”. It does exactly that, but there are thousands more scented plants to explore and anticipate here.

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Mapping the World by Beau RiffenburghMapping the World: The Story of Cartography, Beau Riffenburgh (Carlton Books 2011, 2014)

A good map is like a swan on a river. Beneath the elegance there is a lot of effort. This book is about that effort: all the millennia of research and refinement that have gone into perfecting maps. Not that any map can be perfect. As Beau Riffenburgh explains here, there are always choices to be made: what do you put in, what do you leave out? And how do you represent spherical geometry on flat paper?

The Flemish cartographer Gerardus Mercator came up with one famous answer to that question:

Mercartor’s major achievement came in 1569 with a new projection that represented a breakthrough in nautical cartography. Since known as the Mercator projection, it is cylindrical-like, with the meridians as equally spaced parallel lines and the lines of latitude as parallel, horizontal lines, which are spaced further apart as their distance from the equator increases. This projection is uniquely suited to navigation because a line of constant true bearing allows a navigator to plot a straight-line course. However, this projection grossly distorts geographical regions in high latitudes – thus Greenland is shown larger than South America, although it is actually less than one-eighth of the size. (“Cosmographies and the Development of Projection”, pg. 51)

So the map looks wrong, but leads right. So does the famous map of the London Underground, which ignores true distances and bearings: the designer Harry Beck made it look like an “electrical circuit, with straight lines and the inclusion of only one feature above ground – the Thames” (“Mapping for the Masses”, pg. 143). Maps are about abstraction: they condense and confine what people find interesting or important about the real world.

So minds mould maps and in writing about maps, Riffenburgh is also writing about culture and politics. About art too, because maps can be very beautiful things, sometimes deliberately, sometimes incidentally. Above all, however, he’s writing about mathematics. What was implicit from the beginning – the importance of maths in mapping – became more and more explicit, as he describes in the chapter “Men, Measurements and Mechanisms” (pp. 70-3). The men are drawn from the world’s most evil and energetic group: white Europeans. Galileo, Newton and Huygens are three of them: as they contributed to maths and science, they contributed to cartography.

Another man is the Yorkshire watchmaker John Harrison (1693-1776), the hero of Dava Sobel’s Longitude (1995). He was a remarkable personality and looks it in the portrait here: proud, determined and self-possessed. He needed all those qualities to get his due. He invented a chronometer that kept accurate time on long voyages and enabled navigators to determine longitude, but British officialdom “made him wait years for all of his prize-money” (pg. 73).

Elsewhere the names are obscurer and the stories sometimes sadder:

In the history of cartography, few individuals stand out for their work in so many geographical regions and aspects of science as James Rennell. Born in Devon in 1742, Rennell went to sea at the age of 14, learned maritime surveying and then, at the end of the Seven Years’ War, received a commission in the Bengal Army as an engineer. … Equipped with quadrant, compass and chain, Rennell began a thorough and scientific survey of [Bengal’s] major river systems, roads, plains, jungles, mangrove forests and mountains. (“James Rennell: Mapping India, Africa and Ocean Currents”, pg. 86)

However, he “never fully recovered from a severe wound received in an ambush” and retired to London to produce his “masterpiece – A Map of Hindoostan, or the Mogul Empire” (1782/1788). But en route to England, he had an “extended stay in Southern Africa” and developed an interest in ocean currents. So he became a pioneering hydrographer too: his posthumous An Investigation of Currents of the Atlantic Ocean (1832) “is often considered to form the historical basis of the study of currents” (pg. 89).

Later in the century, the German August Petermann worked for the Royal Geographical Society and was appointed “Physical Geographer Royal” by Queen Victoria. His assistant John Bartholomew said “no one has done more than he to advance modern cartography”, but Petermann committed suicide in 1878 after returning to Germany (“Maps reach a wider audience”, pg. 132).

Nietzsche would not have approved. But I think he would have applauded this:

Perhaps the most remarkable nautical drawings of all, considering the conditions under which they were produced, were those of William Bligh, captain of the British ship HMAV [His Majesty’s Armed Vessel] Bounty in 1789. Following the infamous mutiny, Bligh and 18 loyal seamen were set adrift in the ship’s launch. During the next 47 days, Bligh navigated approximately 3,600 nautical miles (6,660 km) to Timor, with only one stop. Throughout the journey, which is considered one of the most remarkable accomplishments in the history of open-boat travel, Bligh kept a detailed log and made sketches of his course. (“Mapping Australia and the Pacific”, pg. 77)

His chart is reproduced here. Using anecdotes like that with serious analysis and intellectual history, Riffenburgh tells the story of cartography from Mesopotamia and before to the moon and beyond. The story of maps is the story of man: even pre-literate societies like the ancient Polynesians have used maps to record the sea and its currents. In Europe, maps have reflected every advance in technology, like printing and photography. But as they’ve responded to technology, they’ve altered the way we see and interact with reality. When you look at a map, there’s a whole world of exploration, endeavour and ingenuity just beyond its margins. Mapping the World is about that world: the margins of mapness without which the maps themselves would not exist. It’s a book to stimulate the mind and delight the eye.

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