Category Archives: Science

Book reviews of the science I read

Book Review: The Blind Watchmaker by Richard Dawkins

Having read The Selfish Gene and The Extended Phenotype, I wanted to carry on reading Dawkins’ earlier works, as I have found him to be a great communicator when it comes to his specialist field of evolutionary biology. Such writing is rare and ought to be highly valued, though I fear that his later writings on religion have done his reputation more harm than good. But even though there is a sprinkling of thoughts on religion here, including in the opening premise, this is a book of science, not one of anti-religion. So let us delight in this master’s work and dive in.

The title of the book, if one weren’t aware already, is derived from William Paley’s work on natural theology, where he infers from his observations of nature that there must have been a grand designer behind it all, namely God. Dawkins’ aim is to rebuff the particular argument that Paley made. In taking this approach, Dawkins does not dismiss Paley as a fool, but in fact pays credit to him. Yet there is also an implicit understanding that Paley’s view is the peak of natural theology when it comes to biological design.

I emphasise biological design for one should be careful not to think of Dawkins’ work applying to a wider scope than is justified. For this remains a book primarily of biology. There is a bit of computer programming, along with some analogies with physics and history, but these are not what The Blind Watchmaker is primarily about. In fact, after the opening, Paley’s views seem to fade somewhat into the background, as Dawkins gets into his evolutionary stride. For while Dawkins states that he plans to counter the inferences Paley makes, the bulk of the book is stated far more positively, giving us insights into evolutionary biology, some of which Dawkins has used before in The Selfish Gene and The Extended Phenotype.

The counter to Paley is done fairly on and with some deftness. The heart of it is to dispel the idea that evolution is random. This can be used a good shibboleth to determine if anyone had reasonably understood evolution: if they insist that evolution is an entirely random process, then you can determine that they do not understand it. Rather, it is a sequential process. The image that came to my mind was a combination lock. If there are 5 cogs, each with 10 settings, then there 100,000 possible combinations. You might then argue (as Paley) that to find the right combination is phenomenally unlikely and therefore there must be another factor at play. But what Dawkins notes is that randomness only applies at any one cog, not on all 5 simultaneously. So have a 1 in 10 chance of getting the first cog right. Once that is in place, then we can look at the 2nd cog. If you work this way, then the probability against ending up at the final answer is substantially reduced from 100,000 to 1 down to 50 to 1. Dawkins makes reference to the fact that he wrote another book, Climbing Mount Improbable, at around the same time as The Blind Watchmaker and recommends it as a companion piece.

There’s a wonderful section on the varieties and evolution of echolocation. One of the reasons it stayed with me is because it coincided with a DVD I was watching at the time (David Attenborough’s ‘The Trials of Life’). From bats to dolphins, we can see a variety of different forms, some of which are better than others. As well as providing a fascinating insight into the natural world, it shows that evolution doesn’t have an end goal (and why the combination lock analogy isn’t perfect) but there are hints here of convergent evolution; an area that isn’t emphasised in this work.

The book takes a bit of a diversion away from biology and into computer programming. This is the one part of the book that hasn’t aged well. In it, Dawkins reveals his devotion to Apple computers and shows the result of a programme he used to create shapes that were randomly generated, but where he imposed conditions on them (to mimic evolutionary selective pressures) and shows how they resemble certain objects, many of them biological. What we get is what, as a maths student, I used to refer to as ‘proof by pretty pictures’. For while it is interesting, it lacks the rigour that would be necessary for a more serious scientific work, and is too far removed from the fieldwork of biological study to be of much use.

By now, Dawkins has moved a long way from his starting point of apparent design and is going through some of the finer points of evolutionary biology. He comes onto the subject of punctuated equilibrium (PE). Foremost in his crosshairs is Stephen Jay Gould, a writer who I must admit I have thus far unduly neglected; a copy of The Panda’s Thumb sits on my living room floor, waiting to be read. Gould was famously an advocate of PE. Dawkins, in his opposition to Gould, does not actually go so far as to deny the theory of PE, but instead wishes to attack the way PE advocates portray other evolutionary biologists. Dawkins comes up with an interesting analogy: that of the Israelites traipsing through the desert for 40 years. I found it interesting as it betrays his curious obsession with matters of a religious nature that were to later consume him. Dawkins states that PE advocates portray non-PE advocates as thinking the Israelites maintained a steady, but deathly slow, speed throughout their 40 year sojourn.

Yes, you did read that last sentence correctly. It all gets very accusative and, to a non biologist like me, rather pointless. To the outside observer it appears like a pointless quibbling over the finer points of language, rather than any fundamental difference in the biology. That said, I am aware how, within christianity, differences between different denominations can appear equally pointless to the casual outside observer. As an example, I might cite the infant baptism as an example where those who advocate it and those who oppose it (I am firmly in the latter camp) use it as a way of expressing their differences over what the nature of baptism is. But I digress…

The last significant section of the book goes into even more obscurantist territory where Dawkins takes on a group known as the “reformed cladists”. It’s not a term this reader was familiar with; I doubt many non-biologists would be. As I finish this review a few weeks on from having finished the book, I struggle to think back. My interest had thoroughly waned and I was more keen ‘to have finished’ the book than I was ‘to finish’ the book, if you understand my meaning.

My conclusion therefore is that what starts as a brilliant piece on evolutionary biology, defending good science against poor theology, gets a bit sidetracked by computer programming and eventually fades into denominational name-calling and put-downs. It’s a terrible shame, because it is really a rather good book. So please do absolutely read it, but if you find yourself putting it down about three-quarters of the way in, I will forgive you if you heave a deep sigh before picking it up again to finish it.

Book Review: The Spark of Life by Frances Ashcroft

While most books are those I’ve bought or requested as gifts for birthday or Christmas, this was one that was lent to me by a friend at church. Their premise was that it was recommended to them by an atheist friend of theirs who had said it was a marvelous book about reductionism, showing that there was nothing more to life than electricity. I confess I’d not heard of the book before so it seemed reasonable to look at what some others had said about it. When I read a few other reviews, the above synopsis seemed quite a long way from what the truth.

My friend asked for my thoughts on the book, and while I hold to some views on the matter of reductionism, it might well be unfair to apply them to Ashcroft’s work if that was not her aim. So the only way forward, it seems, is to press on and read the book itself.

The subtitle, ‘Electricity in the Human Body’, gives a flavour of what’s to come. Ashcroft opens by diving into the deep end by talking of K(ATP) ion channels which rather shot over my head. I think that’s the intention. Returning to the introduction after having finished the book it makes a lot more sense, so one can see how much we’ve gone through.

The heart of the book is Ashcrofts own passion: ion channels. But what are they? I’d never come across them, though you’re probably less ignorant than I. So it was for this reader a journey of discovery. In short, they are holes in the membranes of cells. i.e. they’re really really really small. They are holes that act sort of like valves, allowing the flow of ions in and out of cells. The upshot is that miniscule electrical balances (carried by the ions) are created inside and outside of the cells. This is the electricity of the human body that is referred to in the subtitle.

With this as our firm grounding, we can then go off exploring various aspects of the human body. I would imagine that everyone knows that nerves operate by electrical impulses. That much is GCSE level science. But how do these impulses operate and how do we know? These are the questions that Ashcroft sets about answering in a lively and engaging manner.

The book is full of fascinating vignettes, such as the details of how synapses operate, how a heart beats and why some goats go incredibly rigid when frightened. Possibly the most disturbing was the chapter on neurotoxins which I admit made me feel a little numb as I read it, though it hasn’t yet put me off wanting to try fugu sometime.

Yet what of this claim reductionism alluded to above? As I read, greatly enjoying the book, it simply wasn’t there. All I could find where a couple of disparate sentences towards the back of the book, which were neither justified nor expanded upon. The book would not have suffered in the least by their omission. So it is my view that the friend of my friend was perhaps engaging in an exercise in eisegesis, reading their pre-existing thoughts into a work which are not expressed by that work. Let us say no more about it, then, and get back to this wonderful work of science.

We get a brief overview of electrical activity in the brain, though as with any popular-level take on neuroscience, there is a fair admission that we simply don’t understand the details of how the mind works. This does make it a weaker chapter than the rest, though those who are interested in the workings of the brain (often worked out when things go wrong) will be pleased to see the mention of Phineas Gage. If this subject piques your interest, then I would suggest following up with The Emperor’s New Mind and in particular A User’s Guide To The Brain.

The final chapter examines the effects of electricity upon the human body, as opposed to that generated from within. Not wholly unlike the chapter on neurotoxins, this makes for uncomfortable reading in places. As someone who opposes the death penalty, it was most disturbing to read of the electric chair’s mechanism for bringing death. Yet the same chapter also tells of how a defibrillator works (hint: not how you may think if you watch a lot of fiction on tv).

With the tour over, what can we say in conclusion? It’s a captivating book, giving insight where previously this reader was blind. It is written plainly yet in such a way as to draw the reader along and infuse them with some element of the enthusiasm and passion that is evident in Frances Ashcroft. I’d thoroughly recommend it.

Book Review: Pathfinders – The Golden Age of Arabic Science by Jim Al-Khalili

It’s taken me a fair old while to get round to reading this. If you check back on this blog, you’ll see that I mentioned it back at the start of last year as one of the books I planned to read in 2014. However, my science reading has been fairly varied and this just got pushed back a bit.

Having now read it, I do rather regret the delay. The title should give you an impression of the era and geographical area which is the focus of Al-Khalili’s study. It is a time and place about which I must confess my ignorance. And not without good reason, the author supposes that such ignorance is not uncommon. His task here, then, is to give us a glimpse into a world that has largely been forgotten by the West, but where a debt of gratitude is owed.

Our story really begins with The House of Wisdom, a kind of institute or academy that was established by the Caliph al-Ma’Mun in the 8th century where the great minds of the day were gathered to study the world, which Al-Khalili notes comes not from a general curiosity, but as a command from Muhammad. As such, we also get a bit of background on the rise of Islam which serves as a useful background.

While I admit that I didn’t know much about the period and that many of the people we come across were previously unknown to me, one that was familiar was Al-Kwarizmi. Part of his story was told in Joseph Mazur’s Enlightening Symbols, but here we get a bit more flesh to the man, as well as understanding why he was so important in mathematics. For the latter, Al-Khalili relies on one of this age’s great mathematical communicators, Ian Stewart. To summarise here, what Al-Kwarizmi built upon Diophantus’ shoulders was a general way of solving problems. To Diophantus and to many who came after him, the methodology used to solve problems were specific to the problem in hand. Al-Kwarizmi’s contribution was to find a solution to sets of problems that could be widely applicable, not having to go through afresh each time. This is why his important work can rightly be seen as the origins of what we would understand to be algebra. He didn’t use symbolic means, as modern students may be familiar with, nor did he construct problems with the originality of Diophantus, but his work is the key bridge between the two.

There are plenty more besides A-Kwarizmi who are featured (and Al-Khalili does include a helpful little summary of each at the end of the book), so I will leave you to discover them for yourself. I only focus on Al-Kwarizmi because of my mathematical bent. Those of a more astronomical of chemical persuasion may find themselves drawn to other characters in the book.

Without recounting the entirety of the book, I wanted to look at one more aspect in particular, which caught my eye. It concerns the question of the decline of the golden age. What caused it? While there are myriad factors that interact in complicated ways, one that Al-Khalili highlights is the rise of the printing press. Arabic science was largely dependent on written copying and this form of communication was not readily abandoned. So it was not so much that the science in the Near and Middle East declined, but rather just got overtaken in terms of the speed of the dissemination of ideas. As a bibliophile, I will often hail the printing press as one of the greatest inventions of all time, but this puts a different, and welcome, slant on the matter. What has proved good for many may have had a detrimental effect on others.

In reviewing books of various kinds, one must always try to find some good in the worst of books and one must try to find fault in the best. Here, I find myself in the latter of the two scenarios, so this review cannot be complete without noting that Al-Khalili is very unspecific and often uncritical of his sources. Over and over again, I found myself thinking “[that’s really interesting. Where does that information come from?]” only when one searches in the text and the endnotes, there is no clear answer. Instead, the reader is invited to take Al-Khalili’s word for it, to be uncritical.

To give a specific example, there is a short discussion on the destruction of the library at Alexander. Al-Khalili cites a few hypotheses (a fire in 48 BCE, a war between the Romans and the Syrians in the late 3rd century, sacked by the Arabs in 641) but dismisses these, instead favouring the idea that it was destroyed by christians in the late 4th century. At no point, though does he say where these hypotheses came from, he doesn’t critically evaluate them and he doesn’t give his reasoning for why he thinks one is more likely than the others.

This is just one example. There are others, but I include it here to illustrate that the scepticism Al-Khalili exercises professionally as a scientist does not seem to have been well transferred as here dabbles in history. Perhaps this work is an example of why scientists aren’t always the best at writing histories of science, a point I know is echoed by Rebekah Higgitt.

As a point of curiosity, while I disagreed with one of his interpretations on this history of chemistry, I was going to cite Lawrence Principe’s The Scientific Revolution: A Very Short Introduction, though Al-Khalili cites a different work from the same author in support of his view. Overall, Al-Khalili comes across as quite critical of western science in the middle ages, buying in as he does to the metanarrative whereby christianity is the suppressor of science. For an alternative to this view, I would recommend James Hannam’s work, God’s Philosophers.

One of the added dimensions that marks this out from books on the history of science, is that Al-Khalili interweaves the story he tells with his own personal history. Having grown up in Iraq, he tells us of his connection to the places, showing us a “then and now” narrative that has a tinge of sadness to it, not least due to the history of the country in the last 40 years.

He also manages to hint at what the future of Arabic science might look like. In this respect, though the book is only 5 years old, seems sadly out of date. Only recently, the news broke that the Islamic State had burned a library to the ground.

From the pages of this work, we get a glimpse into a golden age, but it seems that another such age may be a longer way off than Al-Khalili hoped for.

Book Review: 50 Ways the World Could End by Alok Jha

This has been my coffee table book for the last couple of months. Consisting of short chapters of about 7 pages each, we get a tour of 50 possible scenarios that could result in the destruction of at least the human race. But please don’t think that this is a book of scaremongering. At the risk of judging a book by its cover, the graphics and font are all rather jovial hinting that this is a relatively light look at the matters in hand.

For some unknown reason, Jha opted not to include any kind of preface or introduction which makes his overall purpose slightly obscured when you begin by diving straight into the first scenario.

One of the early chapters is on the question of overpopulation where Jha reappraises some of Thomas Malthus’ works. Considering the reputation Malthus has, this is certainly a brave move, but not an unreasonable one.

The various scenarios are grouped by theme, though there is some overlap between the themes. There’s also some overlap between the specific scenarios. I couldn’t help but think on occasion that a few of them could have been merged, or rather that they have been artificially split into two in order to make up a predetermined quota of 50.

Some of the more technologically-focused scenarios are going to be worth visiting in years to come, given the rate of change in our collective technological abilities. These may prove to be incredibly insightful prophecies though I suspect that some may prove to be slightly wide of the mark.

The wide variety of scenarios require Jha to be a bit of a jack of all scientific trades, though the vast majority fall within the fields of physics or biology. One of the slightly misleading things about the title, though understandably so, is that it’s very anthropocentric. A more accurate, though less aesthetically pleasing title might be 50 Ways Human Civilization Might End. Some are decidedly end of the world situations, some result in the world carrying on just with the absence of humans.

In each case, there is some attempt to say how likely each is to occur. In most cases, it’s “[not very likely]” though what might have made a good addendum would be a summary. After all, anyone whose studied statistics could look at 50 fairly unlikely events and reason that the chances of at least one happening may not be insignificant. But Jha isn’t out to scare us. If you put the book down and straight away start looking bunker designs then I think you may have got the wrong end of the stick.

It’s a reasonably entertaining, well-written, informative book that is worth dipping into. I wouldn’t be in a rush to encourage any and all to read it, but if the title appeals to you then you won’t be disappointed. Just don’t expect to be overwhelmed.

Book Review: Stuff Matters by Mark Miodownik

This was the one book I received for Christmas, having acquired rather a lot in my various visits to bookshops last year. Stuff Matters was added to my reading list after it won the 2014 Royal Society Winton Prize for Science Books. Materials science is not my strongest point. I recall my A-level physics teacher trying to persuade my best friend and I to look into materials science as a degree. I also recall being rather snobbish about it as a 17 year old and dismissing it as a hybrid subject. I was more interested in the purity of maths than the mess of metallurgy.

Yet it’s precisely with metallurgy that Miodownik starts. If you’ve seen him on tv (and he’s done a few shows, most notably the Royal Institution Christmas lectures) then you may well have seen his testimony about how he first got interested in material science. He was attacked by someone with a razor blade and was absolutely fascinated about how such a small object could cut through as many layers as he had on and still cut so cleanly and sharply through his flesh. This story is told in full at the start of Stuff Matters.

The book is told as the story of a photograph. It’s a photo of Mark sat on a roof garden with various objects around him. His contention is that each of the objects are made of interesting substances that each have their own story to tell. His aim is to get us to appreciate the world around us, particularly those things which humans have manufactured or manipulated to suit their own purposes.

In this review, I shan’t cover all of the topics that Miodownik does, but I hope to give you an appreciable taste of the book.

Building on the opening salvo about steel, it is only natural that the opening chapter looks at steel, a substance that Miodownik points out is ubiquitous in the modern world, yet it goes almost unnoticed by many. An interesting point I learnt was that metals tend to be in crystalline forms and that the manipulation of steel in particular (think of a blacksmith hammering out a hot blade) is reliant on the slippage of these crystals over one another. We get a brief rundown in the history of steel, including the industrialisation of it via the Bessemer process.

From steel, we move onto paper, the latter probably having cut me more times than the former. Again we have a fascinating sort of potted history of the substance, though it’s interesting that paper doesn’t really have a single definition. For example, Miodownik includes bank notes in his analysis when many would point out that they are linen-based and not really paper. After all, linen isn’t wood-based which may be many people’s starting point of reference. One fact that I learnt was that receipt paper already has ink within it but that it only appears when treated with heat. This finally explained a feature I’ve long puzzled about whereby if I wave a receipt in front of a halogen lamp heater it appears to go black, as if burnt, yet it is never consumed.

The book is full of such little vignettes of fascination that kept me enthralled which is why I sped through the book much faster than normal. The only disappointment came in the discussion of graphene. I’ve long known what it is but have never grasped why it is has caused such a fuss in recent years. Miodownik does cover the subject but at the end of that chapter I was left none the wiser as to what it is about graphene that ensured that work on it garnered a Nobel Prize or how it could be of wider use than as a mere curio.

One of the quirks of Miodownik’s writing (and his presenting) is a passion almost verging on a fetish for concrete. While it is certainly a great construction substance that deserves to have its story told, Miodownik bemoans the fact that the concrete core of the Shard is covered up, almost as though it’s a dirty secret that is best hidden. As someone who lives not from the author in south London I cannot agree with his attempt to appeal to the aesthetics of concrete, particularly when  I pass the brutalist architecture at Elephant & Castle on my way to work. But it’s rather charming that such an offputting substance had its passionate advocates.

That passion isn’t just limited to concrete though. It permeates the whole book and is, I think, a significant factor as to why it won the Winton Prize.

There’s much more that I’ve left out of this review, but I hope I’ve given you a taste. It’s definitely a recommended read. I learnt from it and if I’ve not been effusive enough to so far, it’s made me slightly regret not looking further into materials science as a degree option.

Book Review: The Immortal Life of Henrietta Lacks by Rebecca Skloot

This was one of those books I just picked up almost at random as I was browsing round a Waterstones in Covent Garden one day. Having looked at the endorsements on the front cover, I was surprised as to why I hadn’t heard of it before. It seems to have garnered lots of praise and accolades yet I can’t recall a single reviewer ever mentioning it, nor had I seen it mentioned in the press. After buying it, it came back to mind recently when I noted it being mentioned in Adam Rutherford’s Creation.

What we have here is science told as a narrative. It is not only the narrative of the events and discoveries that were made, but also the narrative of the uncovering of the story. So while it starts out as a biography of Henrietta Lacks (prefaced by a personal story of how Skloot became interested in Henrietta) it expands its scope and becomes a part autobiography of Skloot’s battles to be able to tell Henrietta’s story, and that of her family.

Henrietta Lacks was a black American woman who died in 1954. The crux of the story is what happened shortly before she died. You see, she died young. She died of cancer. After her diagnosis a biopsy was taken from her cervix and the cells grown in culture. It is those cells that are the heart of the story. From here, we go back a short time and tell the story, as far as it is known of Henrietta’s life, growing up and getting married in the American state of Maryland.

The cells that were taken from her body were capable of being grown in a laboratory, something that scientists had been aiming for but had not been successful with. With these cells (named HeLa), it enabled labs across the world to be able to a variety of tests without doing them on living humans. After all, even though they were cancerous, they were still human cells and behaved as such. Skloot tells us the story of 20th century medicine from the cells’ point of view, both the good and the bad. Many of the greatest developments seen in the last 60 years have involved the HeLa cells in one way or another. Sometimes this was unintentional as it turns out that where other cells were grown in cultivation they were in fact contaminated by HeLa.

Coupled with this is the story of the Lacks family and their struggle to come to terms with Henrietta’s legacy. It was years before they even realised that her cells were being used for research purposes. When they did, this was around the time that details were emerging of the Tuskegee syphilis scandal where, if you’ve not heard it before (I confess I hadn’t), black people in America were deliberately infected with syphilis under the guise of free healthcare. So there was deep suspicion over what Henrietta’s cells were being used for and also who was profiting from them. Skloot’s role here was not only as someone researching a book but also of the one who helped the Lacks family, especially Henrietta’s daughter Deborah, understand what happened.

The book ranges over a number of diverse topics. One of those that I noted in particular was the development of medical ethics; not so much in theory, but the practice. For the descriptions (and yes, as a warning, they are quite graphic – particularly at the start of the book) may well strike you as particularly barbaric. The reason why this jars against a modern sensibility is that when the facts surrounding the lack of consent about what was done with Henrietta’s cells became more widely known within the medical community it spurred people into action.

As an aside, I encountered a slight confluence of issues as I read this, as I was also watching the American tv show, The Wire, during the same period of time as I was reading this (actually, I’ve been on The Wire all year; the book took about 3 weeks to read). But they are both predominantly based in the city of Baltimore and have a huge amount to say, in microcosm, of the state of racism in America in the last half a century or so.

One of the things that becomes clear, though whether this was the author’s intention, I’m not sure, was the sheer barbarism that still persists within what passes for a national healthcare service within America. One of the ongoing battles the Lacks has had, and a cause of their major gripes were that the vast leaps in scientific work as a result of Henrietta’s cells did not allow them the financial means to be able to pay for their healthcare. The USA remains a country so backwards that if you go to a hospital, they have the audacity to present you with a bill – which the rich usually pay for through insurance and the poor are made to go without. The concept of universal healthcare which is free at the point of need still hasn’t made the journey across the Atlantic.

The book has apparently become a standard text in some university courses on cell biology. That’s not because the science is overly technical, though what is there is excellently communicated, but because it is a story of one aspect of modern science that has rippled far beyond the Maryland origins of one bereaved family. C.P. Snow famously espoused the notion of the two cultures: humanities and sciences. Here, Skloot has woven the two together to make a fabric that is stronger than either and makes for a fabulous piece of writing. It is educating, enthralling and overall one of the best pieces of writing I have had the pleasure of reading. It was only because of the more immediate need to heed the words of Harry Leslie Smith that this missed out on being my top book of 2014.

Book Review: Enlightening Symbols by Joseph Mazur

Subtitled ‘A Short History of Mathematical Notation and Its Hidden Powers’ I was first made aware of this book on GrrlScientist’s blog on the Guardian website. I added it to a wishlist and was given it as a present for my birthday earlier in the autumn. Having been educated in maths to a degree further than most, I have used rather a library of symbols in my time and had cursory historical overviews of their development but I have not previously read a thorough history.

The book is split into three parts, the first focusing on the development of numerals, the second on algebra and the third on the power of symbols. All three parts are quite distinct and ought to be looked at one by one.

I must confess, I didn’t find the first part particularly coherent. That is partly a feature of the fact that the history of the representation of numbers is itself quite muddled. In reading this, I got the impression that Mazur, who I don’t ever recall coming across before, was more of a mathematician than a historian. As it turns out, this seems to be a fair characterisation, though, like me, he takes a very keen interest in history and (we’ll come to it below) into other areas as well.

The history of numerals is summed up on page 78 as follows: “There have been many scrupulous studies on the origins of our system, but even after a hundred years of scholarly wide-ranging research, we are left with only sketchy guesses of its beginning and evolution.” Perhaps this should have been an executive summary at the start of the section rather than a conclusion reached after having gone round the houses a few times. It’s not that the history is uninteresting, it is really quite captivating. It’s just that Mazur’s take on it didn’t allow this reader to get a grasp on it, so it was quite bewildering. So I must confess that I wasn’t overly enamoured with Mazur’s writing and as I finished the first part, I feared that the last 2/3rds of the book would be a bit of an unenjoyable trudge.

How glad I was to be proved wrong. For in moving from numeral to algebra, fresh life was breathed into the text and I was treated to the book that I had hoped to read.

As with the first section, the story is not straightforward, but we do get to see some of the significant historical developments in fresh light rather than the fairly dim gloom we had beforehand. The first major figure we encounter is Diophantus. His name should be familiar to most maths students, though if you haven’t come across him then this would be a good place to gain an introduction. The basic story is that problems that we think of as algebraic did not begin with symbolic representations.

If you had a good maths teacher (and I’ve been blessed by having a few) then you will have been presented with “word problems” where some question or other is asked which involves numbers and where the answer is required in the form of a number. The student is then asked to convert the word problem into a symbolic form and then manipulate that symbolic form using the methods taught to arrive at an answer. What Mazur gives us is an unpacking of this, showing that most early algebra consisted of such word problems.

We get to meet al-Khwarizmi and see some of the problems he posed in his seminal work Al-Kitab al-mukhtasar fi hi sab al-gabr wa’l-muqabala (yes, I did have to copy that carefully). We see the development of symbolic representation such as those for multiplication, powers and division. Without trying to summarise it here (I confess, this part of the review was written a couple of weeks after I finished reading the book), I would heartily recommend it to you. For those who dropped maths after their GCSEs, I will say that it might not be particularly applicable. For those who are university educated or who can still recall their A-levels then the final step will be very familiar, but it’s a fascinating story as to how we got here.

The final third of the book carried on in the same vein as the second part had, with less of a major change in tone that there was between the first and the second. As I read through the first two parts, I was struck by a quite sobering (or maybe dispiriting might be a better term) thought that in spite of having studied maths to a greater level than most people in the world, was my understanding of it merely the understanding of manipulation of symbols?

There is reassurance at the end, though. Mazur’s view is that our ability to shorthand things in symbolic frees up the mind to truly understand what is going on. This seems to coincide with how I view the abstraction in maths in general, as well as some specific aspects like Fourier transforms; here we phrase a question in a specific way, abstractify to the general case, solve the general case and then you have a template for answering the specific case. By working with symbols we may temporarily lose sight of exactly what it is we are calculating, but that lack of sight allows us to avoid getting bogged down in unnecessary detail. By all means, if we wish to come to back to an intermediate stage in the calculation and convert into word problems, we can – that is the power of symbolic maths.

The final section also deals with some other matters peripheral to our understanding of mathematics, such as the psychology and philosophy of maths. So it was little surprise to see Wittgenstein referenced at this point. Though Mazur was readily more accessible than Wittgenstein was. The breadth of this final view reveals the author to be more than just a mathematician, he is a bit of a polymath. So while the book was not hugely coherent to begin with, the last two-thirds are very creditable and I would recommend it to anyone interested in maths and the history thereof.