Like its sister title Science 1001, this book takes on an enormous task: telling us ‘everything we need to know about mathematics in 1001 bite-sized explanations’.
It’s a handsome, if rather heavy book, somewhere between a typical hardback and a small coffee table book in size (though with floppy covers). Inside, it’s divided into 10 main sections – from the obvious ones like geometry and algebra, through to the exotics from statistics to game theory. Each section is split into topics – so in geometry you might get ‘Euclidian geometry’ and within each topic there may be around 12 entries.
In a sense, then, this is a mini-encyclopaedia of maths, though arranged by subject, rather than alphabetically. I had mixed feelings about the science entry in the series and those feelings are more extravagantly mixed than ever here. There is no doubt whatsoever that this is a useful book. A good marker of this is that, unlike many of the books that come into the review pile, I intend to keep this one. I think I will come back to it time and again to brush up on what some specific aspect of maths is. (As it is, really, a reference book, it would have been more helpful if the topics were alphabetic, but hey, what do you expect from a mathematician?)
However, as a popular science book to read from cover it has a number of deep flaws. Firstly it’s much too broken up into tiny segments. There is a bit of a flow, brought in by the way the topics are organized, but it’s very weak, and certainly doesn’t make for casual reading matter.
Secondly, far too much of the book is definitions. Time after time, a topic consists of defining what a mathematical term means. I feel a bit like Richard Feynman, who was told in a biology class, when explaining what the various bits of a cat were called, that everyone would be expected to memorise these. He said something to the effect of ‘no wonder this course takes so long’ – he didn’t see why people need to keep all those definitions in memory, and I rather feel the same about maths.
Then there’s the difficulty that the structure has in terms of dealing with some of the essentials of maths. Time after time, the author refers to the number e, without telling us what it is until over 200 pages after it is first mentioned. The assumption for a reader who hasn’t come across it might be that e is just a placeholder, the way j is used elsewhere – although many definitions here aren’t necessary, explaining what something like e is, and why it’s important, is pretty crucial.
As someone with a physics background, I particularly struggle to understand why there’s a whole section in here called ‘mathematical physics.’ No, it’s just physics. Newton’s laws don’t belong in a book on maths – there’s much too much to get your head around already without straying into a different subject.
And to top it all, I think the approach taken is often wrong. Popular science/maths, as opposed to textbooks, adds in explanation and context, not just the theory. By being so strong on definitions, there doesn’t seem to be room for this here. We find very little out about all the fascinating people involved. But even if you decide the format doesn’t allow for context and history, there is still far too little explanation. Two example out of literally hundreds: we are told ‘Up until the early 20th century, 1 was classed as prime, but no longer.’ Why? There are good reasons for this, but it is totally counter-intuitive. The number 1 seems like a prime. After all, it is only divisible by 1 and itself. We need explanation, not statement from authority. Another example is the topic on Bayes’ theorem. This is fascinating in its application, but the explanation is almost unreadable, being mostly equations, and there is nothing about its application in that section (a later one does make use of it, but doesn’t mention it is doing so). Highly frustrating.
Overall then, this is a very useful book if you dip into maths and need a quick reminder of what various things mean. It really is a great resource as a reference book. But it just doesn’t work as popular maths.
The Hubble space telescope has provided a massive step forward in producing images of everything from planets to distant galaxies – and this is a massive picture book, detailing Hubble’s achievements and rather a lot more. We’re talking genuinely massive here: at 37cm x 30, this isn’t so much a coffee table book as a book you could make a coffee table out of.
In a way, the title of the book is too confining for what’s actually in it. A lot of the content is from or about the Hubble telescope, but there are also images from a range of other telescopes and probes. We begin with a brief introduction to the telescope itself, then set out on a voyage across the solar system (this is where we particularly get images from other probes, such as the Mars landers). This continues to expand, taking in stars, the stunning photographs of nebulae and galaxies we have come to associate with Hubble, and finally the universe as a whole. Along the way we see how the different missions to maintain the telescope have changed things, including the first big fix to the misshaped mirror that turned images from fuzzy to crystal clear.
It’s hard to fault the photos – they are superb, and of course having that much page space means some can be presented in a truly grand fashion. The double page spread of the Crab Nebula, for example, is stunning. The text is fine, if a little summary sometimes. However, given its size and weight, I don’t think many people could be bothered to try to read this book from cover to cover. It genuinely is a popular science coffee table book, to flick through and pause in wonder at a randomly selected page – but none the worse for that.
We have a lot of books come through the office – most of them don’t stay too long, but I’ve a feeling this is one we won’t be saying goodbye to. It’s going to stay.
(Note cover has been redesigned since the one shown)
I really don’t know what’s happened to OUP – there was a time when this academic publisher had great ideas for science books, but the books themselves were practically unreadable. Now they’ve had a string of top notch titles – to which this is both a recent and an early addition, as the first edition of this book slipped under the radar back in 2002, but now it’s out in paperback and ready to wow a wider audience.
For non-UK readers, the title is a play on 1066 and All That, a humorous book on history that was very popular in the 1950s. Here, though, the topic is mathematics, and rather than mock the subject, as 1066 does, the approach here is to demonstrate the delight of maths done right. The author could just have easily gone for a 1970s appeal and called this The Joy of Maths – because a joy it truly is.
There is a slightly dated feel about the book, both in its presentation and style that, for me at least, is not a bad thing, but rather 100% nostalgia. It starts with a reference to the I-Spy books, a big part of my childhood. And then there are the illustrations. When I was young my father subscribed to a magazine called the Model Engineer. Usually full of serious articles about doing things with lathes to produce working scale models of steam engines, it was dull as ditchwater for me and I avoided it like the plague, except the Christmas edition. Here there was usually a story of the adventures of a lunatic model engineer, building the kind of contraptions that would later feature on Wallace and Grommit. The illustrations were surreal photographs that were somehow old fashioned and downright weird at the same time – and that’s exactly the same feel the illustrations here have. On one page we’ll have a cartoon, on another a photograph of a model railway, on one of the buildings of which is a poster announcing ‘Brighten your day the Geometry way!’
However, this period feel doesn’t extend to a dull approach to the topic – instead, David Acheson really does make maths – and it’s by no means all fun, recreational maths, but often the real thing – both approachable and entertaining. There are snippets of geometry and algebra, infinite series and chaos theory, trigonometry and the Indian rope trick (no, really, there is applied maths here, in a very strange way). There’s no attempt to cover any of these topics in depth – we just get a quick feel for them, plus one or two illustrations of particularly interesting, mindbending, useful, or just strange applications. I was least enthusiastic about the trigonometry, but most of it just shot past in an entertaining stream.
Popular maths is not easy to do, but David Acheson has really achieved it with this pocket-sized gem of a book. I read it in one sitting, and I think you will too.
Popular science books often seem to come in waves, and this is the second title we’ve had recently that attempts to cover all of science in one go, following the chunky Science 1001 by Paul Parsons. This is a massive undertaking and in this case the approach taken is to go for a massive format – a coffee table book 37 cm by 30 in size, and weighty enough to match at well over 2 kilos.
Inside are seven sections (Earth, climate, chemistry, biology, space, physics and cosmology), each of which consists of a series of Dorling-Kindersley style double page spreads on different topics, mixing lots of images (often including the background, which can make it a little difficult to read) with a fairly dry text. Each of these two page spreads is standalone – there is no feeling of flow from one to another, which means you don’t really get any sense of the significance of the subject or how the different aspects fit together. And given there relatively few spreads for each topic – chemistry, for instance, has 9 and physics 12) this means the coverage is patchy. Perhaps worst of all there is no feeling for the whole structure of science. Why is the most fundamental science, physics, left nearly until last? It’s a hotch-potch. If you happen to want to get a little background on one of the topics, then some of the spreads are like not-unreasonable illustrated encylopedia articles, but they could have been a lot better.
In the end, even if it were possible to give a good coverage of the whole of science in one book – something I’m personally doubtful of – the format acts against the effectiveness of this book. This format works well for what’s essentially a picture book, like the Hubble title from the same publisher, but for a book you want to actually read, this is just too big and too heavy. It’s not so much unputdownable and unpickupable. It’s not a bad attempt as an attempt at an adult version of a DK picture book, but it just doesn’t work for me.
This is such a wonderful idea for a book. No, not just wonderful, it’s absolutely brilliant. It may to some extent have been inspired by the early geologist Gideon Mantell’s book Thoughts on a Pebble – but the idea of using an in-depth exploration of single slate pebble, picked from a Welsh beach, to reveal a whole host of aspects of the formation of the universe, the Earth, early biology, chemistry, geology and more is inspired. I couldn’t help think of Blake’s lines from Auguries of Innocence:
To see a world in a grain of sand And a heaven in a wild flower, Hold infinity in the palm of your hand And eternity in an hour.
This book really is about seeing the world, if not in a grain of sand, in a pebble.
In terms of format, then, this is a top notch popular science book. What’s more, unlike many of the more academic authors, Jan Zalasiewicz has a lovely approachable writing style (if there’s any criticism, he’s a bit over-zealous in his attempt to be matey). This has all the makings of a classic. Then there are some wonderful revelations in the contents.
I couldn’t get as excited about the universe/Earth forming bits, because they are familiar from many a book on cosmology, but when it came down to all the detail that was in a single pebble, it was awe-inspiring. Apart from what seemed to be a whole chemistry cupboard full of elements, in that one pebble we have quartz crystals and zircons, fool’s gold and (in tiny quantities) the real thing. There are fossils and geologically formed structures. From these many things can be deduced about what was happening around this bit of rock as it formed, although a lot of the deductions seemed to be on the edge of what’s possible.
So with so much to love about the book – and there really is – why doesn’t it get the maximum five stars? The trouble is evident in the way the book was introduced when the author got a brief spot on the Today programme on Radio 4. Although it’s a relatively short part of the contents, the introduction talked mostly about the big bang and the Earth forming. The reality is that a good number of the chapters are about rock formations moving around and sediments, erm, sedimenting. (I know, I know.) Although what’s crammed into the pebble itself is amazing, the geological processes don’t just make paint drying look speedy – they make it rather interesting too. Zalasiewicz has an uphill struggle to make them exciting – and sometimes he fails.
Apart from the nature of this part of the material (hardly the author’s fault) the only real issues I have with book occur early on. In the chapter about the origins of matter in the big bang and stars, Zalasiewicz gets the balance of explanation wrong. There is rather too much on the details of the formation of matter post big bang, but nowhere enough basics right up front. According to a recent survey only 20 percent of Americans know what a molecule is, yet here we are told that a process ‘knocks electrons out of orbits’ without any attempt to clarify what either of these is. Someone also really should have spotted that the author is unaware that ‘enormity’ doesn’t refer to something that is very big.
Overall, a brilliant book – one of the best finds of 2010 – if only you can maintain an interest in the geology part.
Richard Cohen is a former publishing director of Hutchinson and Hodder & Stoughton. He is the author of By the Sword: a history of Gladiators, Musketeers, Samurai, Swashbucklers and Olympic Champions, has written for the Times, the Guardian, the Independent and most other leading London newspapers, and has appeared on BBC radio and television. He lives in New York City. His more recent book is Chasing the Sun.
— a question I used to ask when I was at school, which in fact I managed to get through without taking a single class in chemistry, biology, botany or zoology. I did have one year of physics, at the end of which I got 83% in the exam. My teacher, a Mr Richards, look at me suspiciously and said, ‘You were lucky. But from now on you won’t have to do any more physics. Putting you in for O level would be a waste of time.’ But eight years ago I became suddenly aware of an overwhelmingly gap in what I knew, and in writing about the Sun have had to teach myself something of physics, chemistry, biology, astronomy, cosmology, oceanography, geography, ecology…. Truth to tell, it was great fun. And I don’t ask ‘Why science?’ now.
Why this book?
Because a comprehensive study of the Sun, with all the science but also examining the star’s impact in literature, music, art, architecture, myth – even in modern politics – had never been covered in a single volume. People tend to specialize, and a trip to the New York Public Library revealed that there were nearly 6000 books about the Sun – but none was the one that I wanted to read. Luckily, I’ve been fortunate to have been given advice by a daunting number of specialist experts, and now at least there exists the book that I coveted. I also received a grant from the Sloan Foundation, which changed the range of what I was able to cover, enabling me to travel to more than 20 countries asking questions about the Sun.
I like looking at large themes that range across centuries and cut across cultures. My next book is titled ‘The History of Historians,’ and will probe into the major works of history – worldwide – written over man’s time on Earth, and what influenced their authors, from their love lives to their rivalries to their health or the cultural conditions of the day. I start with Herodotus and end with modern TV historians. Already the research is fascinating.
What’s exciting you at the moment?
I teach creative writing at the University of Kingston Upon Thames, which I greatly enjoy, and which has prompted me to start a book about how to write. I’ve also just returned from the Commonwealth Fencing Championships in Melbourne (held every four years, like the main Commonwealth Games that just ended in New Delhi, but no longer part of the main games, sadly). I represented Northern Ireland at sabre, while my 23-year-old daughter Mary fenced for England at epee. She almost got a medal, while I came 12th (but then I am 63). For the two of us to be in the same championships was a special thrill. Being on holiday in Australia was pretty cool too. Plenty of sun, only this time I wasn’t writing about it.
Richard Elwes is a writer, teacher and researcher in Mathematics and a visiting fellow at the University of Leeds. Dr Elwes is passionate about the public understanding of maths, which he promotes at talks and on the radio. His more recent book is Maths 1001.
I don’t know anything else!
I have always enjoyed the subject, and the more I have studied, the more I have realised how incredibly deep it goes, and just how much there is to know. At the same time, I am aware of the gulf between how most people see maths (a horrendous mix of tedious equations and incomprehensible jargon), and how I see it, which is as a whole other world, packed full of amazingly cool, interlocking ideas. So, as well as enjoying studying maths myself, I suppose I have a drive to try to close this gap.
Why this book?
There are two answers, both true.
The first is that I don’t think a book like this has ever been attempted before. Of course, there are plenty of excellent books discussing various mathematical topics for a general audience. But I don’t believe any have tried to be as comprehensive as this. It’s ambitious, there’s no doubt about it, and I was excited by the challenge.
At the same time, there seems to be a gap between ‘popular’ books on one hand, which take a completely equation-free, discursive approach to a mathematical subject, and ’technical’ volumes or textbooks on the other, which go fully into all the gory details. My book treads a middle path. I didn’t want to sex things up too much, I wanted the mathematics to speak for itself, and for the book to work as a reference volume. At the same time, some of the material is undoubtedly difficult and unfamiliar, and people need a way in, to understand what fundamental questions are being addressed. I wanted it to be enjoyable to read, and for people genuinely to learn from it. In some ways, I suppose I wanted to write the book that I would like to have read aged 17.
The second answer is… someone offered me money to write it.
I’m pleased to say that I have a couple of projects in the pipeline. In Spring 2011 I have a book called “How to build a brain (and 34 other really interesting uses of mathematics)” coming out, which has been a fun one to write. It covers some of the same areas as Mathematics 1001, but in a much more light-hearted and less technical style. Perhaps you could guess that from the title.
There are other things in the works too… but it is probably still too early to go into details. I can say that I am looking forward to working on them though!
What’s exciting you at the moment?
Maths 1001 is my first book, and it’s just come out. I’m quite excited about that, to be honest!
Otherwise, I find that the internet makes a wonderful blackboard, these days. There are so many people out there talking about maths, from primary school teachers discussing games kids can play to start to enjoy numbers, right up to Fields medallists presenting their latest research. I follow several mathematical and scientific blogs (I’ve got my own too, may I plug it? www.richardelwes.co.uk/blog Thank you!). It is just fun to be a part of that huge conversation.
In terms of mathematics itself, I have been thinking about recent work by the logician Harvey Friedman, which I find very exciting. It’s a sort of sequel to Kurt Gödel’s famous work. I think it will turn out to be important. I am getting quite interested in ideas from logic to do with provability, computability, and randomness, and how they relate. My background is not in exactly this type of logic, but I do find it fascinating.
It is almost impossible to rate these relentlessly hip books – they are pure marmite*. The huge Introducing … series (a vast range of books covering everything from Quantum Theory to Islam), previously known as … for Beginners, puts across the message in a style that owes as much to Terry Gilliam and pop art as it does to popular science. Pretty well every page features large graphics with speech bubbles that are supposed to emphasise the point.
Fractals are, without doubt, fun and fascinating, and this little book brings out what they are and why they are so remarkable. (Fractals are complex geometric forms produced by (often) fairly simple mathematical processes that behave rather strangely. Fractals often resemble natural forms, like trees or mountains.)
The first half of the book takes us through the origins of fractals, and really works well. In some of the books in this series the abundant illustrations get in the way of the message. Here, while they lack some of the energetic madness of some titles, they are absolutely essential to get the subject across, and do that very effectively.
I’m less happy with the second half of the book where, once we’ve got to the Mandelbrot set (a rather more complex but particularly strange fractal form), we are bombarded with hypothetical applications of fractals. After a while, the repeated message of ‘this is a fractal’ and ‘that’s fractal’ and ‘you could use fractals to do this’ becomes wearing. This is indeed the wonder of fractals – they are very common in nature. But the implication is ‘and this will do wonderful things for us’, which I’m not sure is the case. Fractals seem to be largely descriptive rather than useful.
One example I know something about – the authors get excited by Michael Barnsley’s fractal compression algorithms, which they seem to believe will transform the way we store images. I thought this too in the 1990s, when I used to use fractal compression to store photos on the limited hard discs of the day. But since then it is JPEG that has dominated the market, and fractal compression has all but disappeared. This book, written in 2000, predicts a (fractal?) trend that really hasn’t happened.
So, it’s a book of two halves. The second half is a bit of a let down. One of the key concepts of fractals is that of self similarity. If you take a bit of a fractal, it resembles the whole (think of a branch of a tree looking a bit like a tree). Unfortunately, too much of the second half is self similar. But I would say the book is worth reading for the first half alone.
*Marmite? If you are puzzled by this assessment, you probably aren’t from the UK. Marmite is a yeast-based product (originally derived from beer production waste) that is spread on bread/toast. It’s something people either love or hate, so much so that the company has run very successful TV ad campaigns showing people absolutely hating the stuff…
The tagline to this book is ‘the epic story that gives us life’ and that word epic gives pause for thought. It has good connotations (‘an epic adventure’ or just the modern adjective ‘epic!’) – but equally it can suggest a monster tome that is going to be a bit of a drag. Time will tell.
What Richard Cohen sets out to do is give a comprehensive if personal exploration of humanity’s relationship with the sun, from science to religion, sunlight to gravity. It surely is a subject that deserves this kind of treatment, and parts of this book are wonderful in the way they provide so many factoids and quite interesting (in the QI sense) deviations into all sorts of very slightly sun-related areas. I could pick out so many, but one little part that caught my fancy was a collection of early 20th century beliefs about strong sunlight, including the need to wear flannel spine pads, as the sun was thought to damage the backbone, and the requirement to wear hats indoors in buildings with metal roofs as the sun was thought to be able to penetrate iron.
From all the source books listed, this clearly is a tome that has been researched in great depth, but for me the book was too long. At 610 fairly large pages before you reach the source notes, it goes on and on. Sometimes this comes through in the examples, which can stretch out into rather long lists. Also it worries me that we get far more on the description of the other people who went to watch a solar eclipse from the Antarctic with the author, than we do about the work of Bequerel and the Curies combined, which just doesn’t seem right.
The other slight concern is that the author can be a little hand-waving about the science. There is sometimes the feeling that you are reading something written by someone who is fluent in a foreign language. He gets most of it right, but it doesn’t always feel natural. Just to pick out a couple of examples:
We hear that nuclear reactor ‘cones’ purposely imitate the lingam shape of Hindu temple domes. What cones? How do they imitate lingams? For that matter why does he say these cones are the latest tribute the Sun’s potency? What’s the connection?
He says the division of degrees (of angle) into 60 minutes and those into 60 seconds is a method ‘curiously close to that of a modern computer.’ In what way?
He tells us the neutron is ‘the most common form of particle lurking inside virtually all nuclei’ – most common how? What about neutrinos? Or all those hydrogen nuclei? What about quarks, for that matter?
Don’t take my concerns too negatively. There is plenty to enjoy in this book, both in quirky exploration of humanity’s attitude to the sun and in the author’s obvious enthusiasm. The contents are often fascinating, and I think will particularly appeal to arty types who may have previously been scared by science, but to have made a five star popular science book it would have been better at half the length with a touch more certainty about the science.
Here we go again with another collection of 114 questions (there’s a title to the next book: Why 114 Questions in these Books?) that first appeared in the ‘Last Word’ section of New Scientist magazine. The format is simple – readers write in with questions, other readers provide answers, the best of which are published. The books contain the question, selected good answers and sometimes editorial comment.
I loved the earlier Why Don’t Penguins’ Feet Freeze?, and still got a lot out of the experiment-oriented How to Fossilize your Hamster. But I did comment in the Hamster review: ‘These books have been great but they aren’t really decent popular science books as they don’t have any narrative flow. The approach has been milked to death now – let’s see something different.’ I unfortunately did get a sense of diminishing returns this time around. Enough, already.
I’m not saying that some of the questions and answers weren’t good. I quite enjoyed, for instance, the title question, which was actually significantly better than the title of the book as ‘Is it true that elephants are the only quadrupeds that cannot jump’. I liked the attempt to work out how long it would take the Earth to freeze if the Sun went out, ‘Is it possible to be too cold to light a fire?’ and ‘Do mosquitoes get malaria?’ But I still had a slight feeling that the barrel was being scraped with many of the items, and increasingly found the replies irritating in their know-it-all way.
Don’t get me wrong, this remains an excellent present for those difficult-to-buy-for people (not for me, thanks, I’ve already got one. And it’s definitely interesting if you haven’t got the previous books (though if you haven’t, I’d go for Penguins’ Feet), but I couldn’t get as excited about this title as the earlier entries in the series.