Although there are a fair number of maths books by popular science writers, like our editor’s A Brief History of Infinity, or one-off books by mathematicians there are very few popular maths writers with a sizeable output. Leader of that very small pack is the highly productive Ian Stewart, mild mannered maths professor by day, popular maths writer by night.
The premise of this book is almost one of conquest. Mathematics has had a central role in most of science throughout the ages. Galileo made it clear that maths was at the heart of science. But mostly biology has avoided it. There’s no doubt which aspect of science Rutherford most had in his sights when he came up with his famous put-down ‘All science is either physics or stamp collecting.’ The fact is that for most of its life, biology has been about collecting and classifying, with very little real science involved. But of course things have changed an awful lot now – and that includes the increasing use of mathematical techniques in the science.
Oddly, Stewart is by far at his best in his introductory chapters (and parts of other chapters) where he does a whistle stop tour of the history of biology and introduces us to all the basics of the science. This might be a bit simplistic for a real biologist, but for those among us who only have a vague memory of biology from school science it is fascinating and pitched just right. And, of course, there is plenty of biology, like the human genome project, that wasn’t around when most of us were at school. Again, Stewart incisively dissects the genome project and the reason why this hasn’t transformed medicine as was promised very effectively.
What works less well is the mathematical parts. In some of his books Stewart excels at making maths interesting to the layperson, but here it is not so good. There are aspects of mathematics here, like knot theory, that only mathematicians could get excited about. And despite Stewart’s assertion that biology has entered a new era with maths at its heart, the mathematics often seemed peripheral to the science.
This is a book that’s well worth reading, particularly for the introduction to biology, but also for some of the interesting ways that maths has been used in the field (for example in deducing the ‘wiring’ required to produce the different gaits of animals) – but it would have been even better if a non-mathematician had weeded out some of the less interesting bits.
On first inspection my paperback copy of this book had the look of a self-published title, with the small text on the back cover going right to the edge of the page and the front cover looking a little amateurish. The book is, however, published by Johns Hopkins University Press – and, luckily, once you get inside, there are no problems with the layout and no doubts about the quality.
Relativity for the Questioning Mind is a little different from most popular science titles. It is ostensibly a workbook, with the idea being that the reader gets to grips with (mainly special) relativity through problem-solving rather than passive reading alone. Each short chapter sets a variety of problems to get you thinking, having first briefly introduced the relevant ideas and concepts, with hints and answers at the back of the book. Here is one of the simpler problems, in the chapter on time dilation, to give an idea of what these problems are like (the additional information and equations you need to solve the problems are always covered beforehand):
“I trim my moustache every six weeks. If I were in a rocket ship flying past you at [four-fifths the speed of light], then how much time, in your frame, would elapse between my moustache trimmings?”
The problems get trickier as the book goes on, and whilst they’re generally fun, many end up being quite a bit more difficult than you might expect, having been told at the beginning of the book that you will be gently introduced to relativity theory – although the author believes that the mathematics in the book is all elementary, some of it will still appear fairly forbidding to non-specialists. I do still like the approach, though – Styler is absolutely right in emphasizing that exercises like these can be of great use if you want to deepen your understanding of a subject area, and the author’s philosophy – work things through for yourself and don’t take anyone’s word for it – is a good one.
If you didn’t want to work through all of the exercises, there is still plenty to get from the book. The introductions to such things as time dilation, length contraction, the relativity of simultaneity, and the equivalence principle are useful in their own right, and there are interesting detours throughout the book on, among other things, the nature of science and its limitations.
There is one other aspect that I liked a lot – incorporated into the text are regular question and answer dialogues, in which Styler imagines confused readers interjecting with requests for clarifications or objections to what’s being discussed. Styler poses and answers the questions he believes most people have when coming across ideas in relativity theory for the first time, questions which he feels are not answered in most other places, and the conversational, and often humorous, tone of these sections makes them entertaining to read.
Overall, then – informative, challenging, and fun at the same time. Perhaps not the ideal introduction to relativity, but this would complement well books on the subject that take a more standard approach.
If you decide to read this book, and you’re not a professional philosopher, you’d be advised to first find a quiet place where you won’t easily be disturbed, and proceed slowly. This is seriously difficult stuff.
Or at least I found it so in parts. This is because William Byers’s aim is nothing less than to develop the foundations of a whole new philosophy of science, based on the ideas of ambiguity and uncertainty in science, and it’s very much written along the lines of’ ‘Now I will introduce the idea of…’ etc. I’ll give a sketch of what Byers’s way of thinking about science actually is – some elements of it are familiar and easily comprehensible, some less so.
The general idea is that, whilst science has traditionally been seen as something which can provide certainty and which can give us a completely objective view of reality, there is an inherent uncertainty built into scientific ideas and a limit to what it can shed light on. Science can’t solve every problem, as we might be tempted to believe, due to its ‘blind spots’, and it’s important that we recognise this fact, Byers say. I think Byers overestimates the extent to which scientists (and the public) believe science can, in fact, solve every problem, but this is a relatively minor point.
Going a little deeper into Byers’s philosophy of science, we have talk of the self-referential nature of science, and the notion of the subjectivity of logical reasoning. We’re also invited to think of scientific concepts as ‘protoconcepts’ that are fluid and not static – they are approximations and there’s nothing concrete about them. Nothing overly challenging here – this is comprehensible stuff, and these ideas will be relatively familiar to some.
Going deeper still, though, things become quite tough. There is Byers’s idea of ‘The One’, which is a kind of unity of the universe and consciousness. This unity, it is explained, is connected to what he calls the fundamental ambiguity in science. The fundamental ambiguity is the idea that science is partly ambiguous, and partly unambiguous, with the unambiguous aspects of science also being ambiguous. Did you get that?
I wish I could say that this point becomes clearer when you read the whole book, but I’m not sure it does. I was always waiting for the point where I would go ‘Ah, yes, now I see what he means’, but this moment never came, and I was often left in a state of confusion. I was also waiting for an example of a specific scientific idea that was going to illustrate the abstract point being made – but one was never forthcoming. The idea of ambiguity in science isn’t a problem – think of an electron, for instance, which is inherently ambiguous, not being wholly a wave nor a particle. But the discussion of ‘ambiguous ambiguities’ and so on is taken to a level where it’s sometimes hard to get a real hold on what’s being talked about.
I should say a couple of things. First of all, despite the above, the general argument that we need to re-evaluate exactly what science can do for us, and what its limits are, remains clear and convincing. Secondly, what’s good is that the author is aware that parts of the book are difficult to get your head round, and is sympathetic to the fact that we’re likely to struggle with it.
It’s certainly a challenge, then (although which of us with an interest in science hasn’t come across challenging and difficult ideas before?). I would recommend that any students of philosophy of science take a look at this. As for anyone with a general interest in science and philosophy, just be aware that you’ll be encountering some pretty obscure ideas and might, at points, struggle with it.
This is a brilliant concept well executed, if occasionally missing perfection due to a bit of pretentious twaddle. Of course I am well aware that one man’s pretentious twaddle is another person’s insightful and soul-searching philosophy, so you may appreciate Brian Christian’s musings, but I’d rather he stuck to the meat of the story.
And what a wonderful story it is. Firstly, don’t be put off by the subtitle, A Defence of Humanity in the Age of the Computer – this makes it sound like a Bill McKibben style moan about how it’s time to stop with the technology and get back to nature. This isn’t what it’s about at all. Christian’s central theme is the Turing test – Alan Turing’s idea of seeing how far computers have advanced by asking a human to judge whether there is a computer or a person on the other end of a text message. In particular, Christian introduces us to the Loebner Prize which annually pits the world’s best chatbots against human beings for judges to distinguish in a 5 minute chat.
The story of this challenge, in which Christian was a human subject for the 2009 session in Brighton threads through the book. As Christian looks at ways he might distinguish himself as a human being (hoping to win the prize given for the ‘most human human’, just as one of the bots gets ‘the most human computer’), he explores what human reasoning and thought is about in terms of the development of artificial intelligence and the impact of computers, and particularly pseudo-intelligent computers have on human beings.
The book works best when Christian is dealing with technology and its implications. I first came across a chatbot when ELIZA was installed on our Dec-10 at work in the late 70s and the whole idea of interacting with a computer in conversational speech is fascinating. Similarly, when it doesn’t get too deep into the chess itself, the section where he looks at chess computers and Deep Blue’s victory over Kasparov is also delightful.
Rather less successful are the sections where he spends rather too much time on philosophy and what can come across rather too easily as intellectual waffle. So we get statements like ‘Capitalism presents an interesting gray space, where societal prosperity is more than the occasional by-product of fierce competition: it’s the point of all that competition, from the society’s viewpoint.’ Yeh, right. I also found the author’s ‘bemused with British English, funny old Brits’ tone a little condescending.
Nevertheless, it’s easy enough to skip the worst of the philosophising, which is a relatively minor part of the book anyway, and there is plenty of excellent meat in there for anyone interested in AI, what it is to be human and how one informs the other. Recommended.
This is a book with an identity crisis. When I first saw the publicity material for it I assumed it was a children’s book. After all Dino Gangs is hardly an adult title. But no, it appears it is aimed at an adult audience. And then there’s the strange case of the author. The book cover is very clear there is one author, Josh Young. And in the ‘about the author’ section of the press release, there is also just one author. Dr Phil Currie. What? At the top of the press release the book is by ‘Dr Phil Currie & Josh Young.’ Totally confused. I turn to the copyright page as the definitive source, but the copyright belongs to ‘Atlantic Productions’, whoever they are.
The reason for all this confusion is that in many ways this isn’t a book at all. Atlantic Productions is a TV production company that made a documentary about the work of palaeontologist Phil Currie for the Discovery Channel. What we have here is an attempt to turn the script of the documentary into readable form. This comes through most painfully in Phil Currie’s contributions. Despite being labelled the author and/or co-author (except on the cover), we only ever see Phil Currie as the written equivalent of a talking head in a documentary. We keep seeing things like ‘”The whole world went a little crazy for a while,” Curry says.’ That present tense is the give away. After a while the recital of ‘Phil Currie says this’ and ‘Phil Curry thinks that’ becomes a trifle nauseating, like a sort of literary hero worship.
So the presentation is weird and more than a little off-putting, which is a shame, because at the heart of it there is a really good book trying to get out. Currie has an interesting theory that tarbosaurs, a particular type of tyranosaur, hunted in packs, rather than the way they have been traditionally portrayed as lone hunters, or more recently as scavengers.
Once we get the rather childish scene setting about how ‘dino hunters’ have to be able to live rough in tents, and a truly dull chapter that is just about the background of Currie and some of his contemporaries, there is a really interesting development of the group hunter concept, taking us through various analyses from how the animals could run (comparing legs with ostriches and humans among others), modern analogues (from komodo dragon to lion) and more. It was telling how well this part of the book works, where I suspect the author has been given a little more freedom, that at the end of one chapter I was left thinking ‘Hmm, but how intelligent were these dinosaurs?’ Then the next chapter… discusses the intelligence of these dinosaurs.
Overall, I couldn’t give the book more than three stars because the format has such a deleterious effect on it – but it’s a shame, because under the fake teeth smile of the TV documentary there is a really good book trying to get out. If it had been left to the author just to write a book, it could have been so much better. We would hopefully have seen rather more of the people who pop in briefly with ideas that oppose those of Dr Phil, for example – and would have had a much better journey. Even so, I think the book as it stands is worth persevering with. It’s a quaint oddity of what happens when TV people get too much control of a different format, but the subject matter is interesting enough to make it worth reading.
This was a really refreshing book to read. We’ve been inundated lately with title after title about the latest tiny discovery in biology, or some new and complex theory in physics. Here we have a perfect scientific biography of underappreciated contributors to our understanding of the universe – William Herschel and his sister Caroline. Some of the recent scientific biographies have been overblown, but this gets the balance just right. It’s not too long because it doesn’t try to cram in every single bit of research, and it achieves a good mix of the people and the science.
Michael Hoskin leads us expertly and elegantly through the Herschels’ early life (always the hardest part because it has nothing to do with their achievements), their move to England, their musical careers and the development of astronomy from a hobby to a burning professional passion. At least for William. Just as interesting and less covered elsewhere is Caroline’s reluctant acceptance of her role as helper in William’s work on double stars and nebulae, plus discoverer of seven or eight comets in her own right. She did it, it seems, because of an intense sense of duty, but she really didn’t have William’s passion for the subject.
Everyone knows that Herschel discovered Uranus (and attempted to call it George, a name that would have caused even more giggles than the one it ended up with) – but arguably of much more importance were his systematic scans of the night sky from Slough (always the wonderful mix of exotic and down to earth here), then a tiny village on the outskirts of Windsor. And his crowning glory was his exploration of nebulae and the theories he developed that suggested they were vast collections of stars – almost island universes – and that the Milky Way was one of these, an idea that wouldn’t be accepted by the scientific community until the 20th century. It wasn’t all right – there was a lot of confusion over whether all nebulae were like this, or whether some were stars being born – but Herschel still came up with some powerful theories.
Perhaps the biggest disappointment was the book’s very summary treatment of Herschel’s son John. He really ought to have been given equal billing with his father and aunt. Not only did he repeat William’s scan of the northern skies, correcting many mistakes, he then did the same for the southern skies, making him the first and only person to singlehandedly check out the whole panorama of space. And he had many more scientific achievements – perhaps Hoskin is saving him up for a book of his own.
The other thing I disliked was the much repeated suggestion that Herschel did away with Newton’s mechanical, clockwork universe and changed the view of it to be an evolutionary one. Hoskin actually refers to it as ‘biological’. This is an analogy too far. The universe is not a biological evolutionary system. It doesn’t reproduce and select on mutations. It doesn’t rely on organic processes. In fact, Herschel’s universe was still mechanical and clockwork. It’s a mistake to suggest that mechanical clockwork structures can’t progress – ‘evolution’ is not a synonym for ‘change’. It was only with 20th century physics that we moved away from a mechanical universe to a probabilistic one. The key aspect of Newton’s clockwork was that given sufficient knowledge of the components and state of the universe you could predict what would happen step-by-step indefinitely. Herschel did nothing to take this away.
This minor irritation, though, comes through only in an admittedly much repeated, but tiny part of this book. Overall it is a hugely readable and enjoyable account of the life and work of these two remarkable individuals. William and Caroline Herschel deserve a brighter position in the stellar pantheon of astronomers, and Discoverers of the Universe puts them firmly in that place. Recommended.
Part of the massive ‘a very short introduction’ range of pocket books, this book sets you straight immediately if you thought it was going to be about mathematics – no, it’s about number, which is quite a different thing. This is both true and not true, which really sets the pattern for the whole little book. Number is a quite distinct concept from maths, yet in discussing number, Peter Higgins inevitably brings in quite a lot of mathematics.
The mixed feel continues with the presentation. The writing style is light and accessible for what can be quite an indigestible topic, but bits of the book are better than other in this respect. I wanted to keep reading, but I found myself feeling a strong urge to skip bits that seemed to be getting bogged down.
After an introduction to what numbers are we’re plunged into prime numbers in some detail. From here we go on to the various labels mathematicians have for numbers, from perfect to deficient – this is faintly interesting, but it does generate an urge to ask ‘Yes, but why does it matter?’ We go on to the likes of cryptography and the use of large primes to perform encryption/decryption, the various fractions, infinity and more. (Yes, you can have more than infinity, and you know what I mean anyway).
There seemed a couple of strange omissions. I think we could have done with significantly more on the philosophy of number – just what numbers are, why human beings use them, whether they have a real existence outside of mathematics etc. I was also surprised by the near-absence of set theory – it comes into the infinity chapter, but there is none of the use of set theory to establish the basics of number and operations, which seemed odd. I’d have expected it up front.
In the end it’s a book that falls between two stools. It isn’t consistently readable enough to be good popular science, but it isn’t detailed enough to be a textbook. I’m not really sure what it’s for. But it’s certainly not a bad addition to the series – and ‘number’ certainly deserves its place there.
There was a time when practically every review we published of an OUP popular science book had the same complaint. What we were forced to say again and again was that this was a book with a great idea, an excellent topic, and an expert writing it. But unfortunately that expert was an academic who didn’t have a clue how to write for the general public and the result was unreadable. In the last year or so, however, things have changed. OUP has come out with a good number of titles (e.g. The Many Worlds of Hugh Everett III) which have been surprisingly readable. Unfortunately, this title is a return to form. It’s a wonderful subject. It has a neat concept in the ‘seven tales’. It’s written by an expert. But it is practically impenetrable.
Things don’t start awfully well in the introduction, when Gregory L. Baker is a little condescending about producing a version of his ‘real’ book for the common herd. But he also reassures us ‘Readers may rest easy knowing that I am mindful of the warning made famous by Stephen Hawking, that every formula reduces the readership by a factor of two.’ The problem is, although it sold well, Hawking’s book has a reputation for being difficult. Yet it is vastly easier to read than this one.
This limitation is frustrating, because Baker does pack in lots of interesting stuff about pendulums. Whether it’s the basic surprise that (despite Galileo), on the whole an ordinary pendulum’s timing isn’t independent of swing size, or explorations of Foucault’s pendulum, torsion pendulums, swinging censors in cathedrals and even the Pit and the Pendulum, there is some excellent material to cover. But the writing is rarely approachable and the author simply misses the whole idea of how to write for a general audience. This is much more the sort of writing you’d find in an undergraduate physics textbook.
I opened a page at random and had a choice of at least four quotes to demonstrate this. Here’s one of them: ‘A sophisticated mathematical procedure may be used to calculate the fractal dimension for the Poincaré section of the chaotic pendulum. But our intuition can at least help demystify the result. Close examination of the Poincaré section shows that its points do not cover an area, but are really a (possibly infinite) set of closely spaced lines. Therefore the Poincaré section is more than a line and less than an area. We then expect its dimension to like between one and two. For the parameter set A(Forcing)=1.5, Q (friction)=4, ωD(forcing frequency)=0.66 the fractal dimension is found to be 1.3. In fact, it is generally true that Poincaré sections for chaotic systems have noninteger dimensions.’ That’s all right then.
The other potential quotes were more dense and impenetrable. You might excuse this because some of the terms have been explained earlier, but the problem is that the approach assumes the way to write popular science is to take a textbook and take out the maths, leaving the explanatory parts, rather than starting from scratch and putting things in terms that people will understand.
Overall, then, a useful and interesting book for physics students who want to find out more about pendulums without doing the maths, but not for the general reader.