Tag Archives: history of science

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: 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.

Book Review: The History of Astronomy – A Very Short Introduction by Michael Hoskin

I am still working my way through books I received for Christmas, and this small work was the last of those I received from my parents. The reason for putting it in on my wishlist was simply that it appealed to my joint interest in science and history. Those of you who read much of this blog can hardly have failed to notice my fondness for the subject with reviews such as this, this or this.

In this account, we focus largely on a sequence of individuals, mostly from the latter parts of the Middle Ages through the Renaissance and on into the Scientific Revolution. Before that, though, there is an obligatory look at the early history of astronomy, not least looking at the work of Aristotle and Ptolemy, though even this preceded by “astronomy in prehistory”.

In telling the story of astronomy in antiquity, our focus is largely on the planets, having been considered as stars that behaved in a peculiar way (hence the term ‘planet’ – meaning, wanderer). The puzzle, as seen from a modern perspective, is that of why the planets which are further out from the sun than earth appear to have retrograde motion.  This history that then follows is the history of the ideas put forward by means of explanation as well as a little history of the people behind their ideas. As might be expected, we come across figures such as Tycho Brahe, Nicolas Copernicus, Galileo Galilei, Johannes Kepler and Isaac Newton.

In telling this history, the book’s strongest point is in showing the detail behind the basic outline that most science students know. Our modern model of planets in elliptical orbits around the sun did not come about by a sudden eureka moment, but by a series of gradual shifts in thought.

The book ends in the early 19th century. Hoskin considers that at this point astronomy ceased to become a subject in its own right and became subsumed within physics and chemistry. So readers hoping for a history that included modern astronomy may well be disappointed. If that is the case, then I recommend following up with Peter Coles’ Cosmology VSI. I must confess that I finished this book a couple of weeks ago, so while I normally write my reviews as I read and then tidy up straight after finishing, there has been a period of gestation to mull over this work. Or maybe it was not so much gestation as a period of forgetting. For while it is interesting enough, there was nothing that grabbed me by the lapels to make me remember it.

In the other editions in the VSI series I’ve read, they have come with great lists of references and further reading. Here, though, we have little more than repeated references to Hoskin’s own work, which rather gives the impression that, though he is a subject matter expert, he hasn’t written this a standalone book, but rather that it is a concise summary of his earlier work.

Book Review: The History of Mathematics: A Very Short Introduction by Jacqueline Stedall

Having read a few of the science-based Very Short Introductions (VSIs), I have become more inclined to read those on subjects which I know little or nothing about, or where my knowledge is somewhat scatty. This volume falls squarely in the last of these. Having studied maths at university and read quite a few books about maths (for some reviews see here, here, here and here), I have picked up snippets here and there, but have never before read anything like a formal history.

Stedall opens with something of a case study: that of Fermat’s last theorem. To anyone who has a GCSE in maths, this is an understandable problem, even if the solution is still only understood by a handful of “elite” mathematicians in the world. It is through this problem that the author looks at various approaches one might take to mathematical history. At this point the unwary reader might start to get a little confused.

The reason for that is that Stedall takes her history seriously. Though the book is interspersed with the stories of some of the problems that have puzzled men and women for millennia, their friendships and rivalries, a history which is limited to dates and discoveries is one that would be superficial and misleading, as Stedall points out. An additional problem is highlighted, in that some of our sources are extremely sparse, with very little known about the likes of Pythagoras or Diophantus and even less about the development of the science outside Europe.

This begs the question: what is mathematics? It might sound like a stupid question, until you actually think about it. Much of what I did as part of my masters degree might well have been considered theoretical physics; and that was mostly studying scientific developments from the 18th up the 20th century. Most of this has been developed in western Europe. So what about the rest of history and the rest of the world? To answer that Stedall looks at a wider scope than many readers will be familiar with. Of particular note is the look at Arabic science, a topic I hope to follow up later this year with Jim Al-Khalili’s book, Pathfinders.

The next two chapters look at the spread of mathematical ideas. The first, from the perspective of the mathematician to the mathematician, the second, from the perspective of teacher to student. I must confess, I’d not really considered the dissemination of mathematical ideas from an historical perspective. The insight we get into an English Victorian education is something I probably ought to have known, but which was nonetheless a revelation to me. Less surprising, though sadly so, was the discussion on women’s mathematical education, which is a sad indictment on our education system until far too recently.

It’s only after all this that the reader who, like me, expected a more conventional story of some individual’s lives, get what they were expecting. Piecemeal, we have already had some insight but here we fill in some of the more obvious gaps, such as the lives of Euler and Lagrange. Though these are dealt with in a brief manner, that is kind of the point of this series of books.

Only towards the end do we actually see any maths. For some readers, this may come as a relief, for others, it may leave us wondering how good a history of ideas might be without the explicit statement of some of those ideas.

Stedall’s writing is perfect for the job. She is engaging, insightful and thought-provoking. As ever, we are provided with a great list for potential follow-up reading. I can’t say that I now have an encyclopaedic knowledge of the history of maths, but I have been able to glimpse some extra insights. Yet I don’t feel rushed to follow these up, but follow them up I may well do, but all in good time.

Book Review: The Scientific Revolution: A Very Short Introduction by Lawrence Principe

This was another of the books I received for my birthday. It is also a continuation of my addiction to Oxford University Press’ series of Very Short Introductions.

As can be supposed from the title, this is the telling of the story of how modern science emerged. The story of that emergence, however, must be told from something that might loosely be called a beginning. As such, much of the text is devoted to matters that we might no longer regard as being part of the scientific mainstream.

However, in telling the history of science, Principe gives the reader due warning against anachronistic thinking. In this respect, the book makes for a pleasantly refreshing change from some modern sneering of the ideas prior to the scientific revolution. An example of this might be found in how Principe looks at the origins of humanism in the first chapter, noting that its origins are complicated and shaped rather differently from its current dominant form.

Having sketched out the medieval origins of the scientific revolution (for more on this, I recommend God’s Philosophers by James Hannam), one might think Principe would simply move on, but this isn’t really possible. To understand this one period of history, Principe constantly points us to its origins. If there’s one lesson hammered home here it’s that the scientific revolution didn’t emerge out of some sort of act parthenogenesis.

An example of this is his look at how the ideas of Aristotle influenced science, not least in how things are connected, the subject of chapter 2. There’s a great little treatise on magia naturalis here which is well worth a read, as it contains a good warning about dismissing past views that are now discarded as being superstitious.

Having laid these foundations, Principe goes on to look at two major topics: the superlunar world and the sublunar world. This mostly covers what we would now know as physics and chemistry, though given the phase in history which is being looked at, chemistry wasn’t really developed yet, so Principe uses the term chymistry instead. Without recapitulating it here, these are fantastic chapters which are evident of Principe’s rigour and faithfulness to the history of the period.

Having looked at what we would recognise as these two areas, the next, naturally was biology, and indeed that is the subject of the following chapter. We get a whistle-stop tour of anatomy and microbiology, though in his brevity, there is no great loss suffered. Indeed, I could hardly praise Principe’s writing enough, as he maintains the reader’s interest from start to finish.

This could never be a comprehensive review of the period and all the developments that occurred within it. But insofar as giving the reader an excellent grounding, this is a work I would thoroughly recommend. There are, of course, references and lists of further reading on each subject. But if you have any interest whatsoever in the history of science, please do read it.

Book Review: The Age of Wonder by Richard Holmes

I freely confess that as the years count up since I left university, my favour for working through the details of science has somewhat diminished. This has been replaced by a far greater interest in the history of science and the lives of those who have been instrumental to the progress of our collective understanding of how the world and the cosmos functions. When The Age of Wonder was released a few years ago to many rave reviews, it was not long before it found its way onto my reading list. However, it was not until Christmas 2012 that I received it as a gift. Indeed, this is the last of the books I received for Christmas which I have read. As is my habit, for a particularly long book such as this (it runs for 490 pages plus appendices) I read it rather slowly. In fact, I think I started reading this towards the end of March.

So what’s it all about? In short, it’s a history of science from the late 18th century up to the mid 19th century. But it is so much more than that. Holmes has pieced together a brilliant narrative, held together with some fascinating links. The main link is the person of Joseph Banks, whose story dominates the first chapter, but who keeps cropping up at the start of the subsequent chapters, as Holmes recounts the stories of Mungo Park, William Herschel, Caroline Herschel, Humphrey Davy and Michael Faraday. There are many other characters that Holmes deals with, including those who pioneered manned balloon flights, though I think he has expanded that chapter into a whole new book subsequent to his writing The Age of Wonder.

Subtitled ‘How the romantic generation discovered the beauty and terror of science’ the book does have a distinct feel to it, for including a good discussion on the link between the arts and the sciences. This is most keenly felt in his chapter entitled ‘Dr Frankenstein and the Soul’ where the talk is a real mix of science and the lives of the romantic poets. He finishes with an epilogue in which he advocates the removal of any supposed barriers between science and other fields such as religion, art and ethics – a stance I wholeheartedly agree with.

The narrative style that Holmes chooses is executed with aplomb. I have to say the book was a pleasure to read, perfectly paced and with something interesting on just about every page. For most of the book I just wanted to keep reading, hoping it wouldn’t end; and for a long time it didn’t. It was only when we got the deaths of William Herschel and Joseph Banks that it seemed right that the book draw to a close, which it did shortly afterwards. As a piece of writing, the quality was superb. The Age of Wonder has jumped into my all-time list of best science books, and possibly the best of any books.

So who would I recommend this to? Well, just about anyone; it’s excellent. An utter joy to behold and one I may well return to. I certainly won’t be donating it to a charity shop. So you’ll have to go out and get your own copy.

Book Review: Collider by Paul Halpern

From the outset, it has to be said that the book is already a little out of date. First published in 2009, the version being reviewed was published in 2010 with a revised preface. As such, while there is much talk about the search for the Higgs boson, the book doesn’t include the detail of the research that culminated in the announcement in July 2012 of the confirmation of its existence. I do not know if the book is to be further revised or if the author intends a follow-up to include an account of the latest research.

With that forewarning, I ought to move on to what the book does contain, rather than what it doesn’t. It is the story of particle physics and the machines that have been built in order to test the theories. Since I was a teenager, I was long fascinated by the fundamental constituents of the universe. I was able to follow this through by continuing to study physics through A-levels and on into university. For someone like me, this is a great book. However, for those who aren’t interested in fundamental physics, I doubt it will be of much interest.

The scope of the book is very broad, ranging from the testing of the “plum pudding” model of the atom through to brane-world scenarios and Hawking radiation of black holes. With such breadth, it is inevitable that the technical depth is, to some extent, lost. Halpern doesn’t provide the reader with many equations, tables or technical diagrams, though a few more wouldn’t have been amiss in my opinion, especially with regard to Feynman diagrams which are described but not shown.

In telling the history of particle accelerators, there is a political history thrown in, which is unusual for a physics book but which is not an unwelcome addition. The idea of the cost of such large scale accelerators in weaker economic times is certainly worth some consideration, especially when thinking of what other things public money might be spent on. In this aspect, the author does betray a slightly jingoistic bias; the reader being left in no doubt (if they were in any beforehand) that the author is an American, though the poor spelling gives this away in a few places. 

That slight criticism aside, however, this is a very engagingly written book, accessible to most lay readers. Though some of the detail has been omitted, I don’t think this hinders its readability too much. If anyone wished to get an introductory overview of particle physics, then this would be an excellent place to start.