Tag Archives: science

It’s just a theory

Last week I was a watching a repeat of an edition of Horizon which was looking at the idea of what was around before the Big Bang. For UK readers, it may still be available on iPlayer and would highly recommend watching it. It features a few of my favourite scientists: the physicists Neil Turok and Lee Smolin and the mathematician Roger Penrose. Those who know me well may recall that for my master’s degree I studied Roger’s twistor theory under the supervision of one of Roger’s former students.

The programme featured a variety of views from these and other scientists about a controversial notion. I’m familiar with Roger’s view, conformal cyclic cosmology, from reading his work, Cycles of Time. The other views I had heard before (not least from when the programme was first aired) but was less acquainted with.

One post I saw on Facebook read as follows: “So watching Horizon about the Big Bang, and loving the fact that scientists clearly have not got a clue about the universe started. Mmm…

One of the comments below stated: “Most of science is all theory and guess work!

These two combined rather got my hackles up. I chose not to enter into a debate then and there but rather think about it for a few days and write something up the following weekend (which, at 9:31pm on a Saturday night, I am now doing).

The first comment

The phrase that I object to here “have not got a clue”. Cosmology may be a relatively young science with much of the universe still to explore, but the notion that there isn’t a clue simply flies in the face of the evidence.

After the discovery of galaxies and the measures of their redshifts allowed for us to realise that we live in an expanding universe. This has been backed up by numerous astronomical observations and, to the best of knowledge, no observations have been made that falsify the idea of the expanding universe.

The idea of the Big Bang (a term originally used as a derisory attempt to discredit it by the steady state advocate, Fred Hoyle) was then developed by ‘turning back the clock’ and asking: if the universe is expanding, then in the past it was smaller, but how far back does that go.

The serendipitous discovery of the cosmic microwave background radiation by Penzias and Wilson was the nail in the coffin for Hoyle’s steady state hypothesis. It also tied in neatly with the developing theory of the Big Bang.

To date, it is the best theory of how the universe came into being. It accords with the best available evidence and has been studied in great detail in papers published in peer-reviewed journals – the gold standard of scientific epistemology. (Though it should be added that it’s not foolproof, as recently attested)

That doesn’t mean our knowledge and understanding is perfect and complete. If it were, there would be no need for further analysis. A lack of understanding is not a cause for abandonment or of making presumptions, it is a cause for further study. The Big Bang theory has its limits and the Horizon programme probed at some of these limits, asking important questions. If it turns out that another theory will be needed in order to give more details into the universe’s origins then it must take into account the evidence to date.

To take an historical example, Einstein’s general relativity recast Newton’s earlier work. The formalisms look quite different, but if one starts from Einstein and make some simplifications, one can rederive Newton. But Einstein had to start with Newton. Newton’s work was necessary to begin with. It seems unlikely that the more ‘obvious’ formalism would be overlooked and that someone could have come up with the more sophisticated theory. Yet Einstein didn’t overthrow Newton. The former built upon and refined the latter.

The case may be the same with the Big Bang. If a new theory is needed it will need to incorporate the evidence gathered to date. It would likely have an element which, if simplified, would result in something that looks like the formalism of the Big Bang. It’s doubtful many  people would understand it at first. But the lack of understanding is not a good reason for rejection. It should be quite exciting.

This is why I reject the idea that “scientists clearly have not got a clue about the universe started”. We have many clues. We have a coherent and consistent model of how it came about. It’s not complete, with some aspects as yet not understood. The work of the cosmologist is to try to bridge that gap in understanding.

The second comment 

So then, with that in mind, what about the second point?

“Most of science is all theory and guess work!”

First, we have the appalling grammar to deal with. Is it all or is it most? It can be difficult to judge tone in a written text (goodness knows what you make of my tone on this blog sometimes!), especially in one so short, but I read this is a statement not made by someone well-versed in science but rather as a condemnatory statement.

One of the key words here is “theory”. It is an example of where words which have fairly precise, technical meanings are also used in colloquial English. For another example in a different context, see my take here on the use of ‘complex’.

The Oxford English Dictionary defines theory as “1. an idea or set of ideas that is intended to explain something. 2. a set of principles on which an activity is based.” A footnote adds that it is derived from the Greek theoria which is translated as ‘speculation’.

This is the more common use of the term, and represents an unscientific viewpoint. That is not to say it is an inferior viewpoint in any way. It’s just a use of the term that is not context-specific. Contrast it with this, from Encyclopaedia Britannica: “a systematic ideational structure of broad scope, conceived by the imagination of man, that encompasses a family of empirical (experiential) laws regarding regularities existing in objects and events, both observed and posited – a structure suggested by these laws and devised to explain them in a scientifically rational manner.”

I would paraphrase this as: a framework of understanding, based on observation, by which reality is modelled.

However you prefer it, the scientific theory is a lot more than speculation. For that we would generally use the term hypothesis or conjecture.

But this brings us back to the comment. We test what we want to find out, in other words, what we do not know. Science tends to come in two parts: theoretical and experimental. I’m much more of a theorist. The work of the theorist is to develop the models, usually mathematical, and develop them into a coherent system which first of all agrees with all known observed data and secondly makes new, testable predictions. Depending on what area of science one works in, one will have different standards of evidence. Mathematics is the most precise of the sciences, where the only evidence accepted is that of proof. It’s a watertight logic. In physics, such proof is hard to come by. But physics is extremely rigorous, with 5-sigma being the level of certainty required before announcing a discovery . The use of this was well documented at the Large Hadron Collider in two recent instances: 1) the discovery of the Higgs boson and 2) the possibility (later explained) that a particle had travelled faster than the speed of light.

The latter point makes for an interesting case study in the scientific method. The apparent result would, if true, have contradicted a century’s worth of physics. That was not a reason to either throw Einstein out of the window or to reject the experiment as a hoax. It demanded to be taken seriously. It was the fact that Einstein’s relativity has been tested numerous times and that the framework which is established by that theory is one that we use everyday (e.g. for satellite navigation) that made a possible falsification a prospect that was at once thrilling and threatening. Had it been wrong, how would the body of evidence that supports it be accounted for?

I could go on even more. But I hope I’ve made my point.

Yes, science is theory, but that’s how it works. In the development of our theories there are hypotheses made. These are not random guesses flung out, but are the result of disciplined work. Once those hypotheses are tested they might be rejected or incorporated into the current theory. We have a lot of clues as to how the universe began and what goes on within it. We don’t know everything, and that is why research continues.

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Book Review: Mathematics: A Very Short Introduction by Timothy Gowers

Carrying on a look at some of the books in the Very Short Introduction (VSI) series, I wanted to revisit some of the joy of university life by returning to mathematics, the subject in which I obtained a first class Masters degree. With the title as it is, one might wonder what sort of level as it’s pitched at. Here, one could be lulled into a false sense of security by mistaking it for “Arithmetic: A Very Short Introduction”. Do not expect this to be “a very simple introduction”. To anyone who has studied maths at university, this will be a very simple book. To anyone studying maths at A-level, they should find it a little challenging in places, but it should provide good food for thought, building on some familiar principles. The author says that it should be OK for anyone with a good GCSE grade, though I would express a little scepticism at that sentiment.

That said, I do think it’s a marvellous little book. One of the first things that Gowers discusses is the cumulative nature of maths. i.e. some things can be very simply stated, but only in terms of other things which need to be well-defined and understood. The danger then is how far back do you regress to be able to find ground which is widely understood?

Gowers deals with this brilliantly by having his opening chapter on mathematical modelling. In so doing, he grounds mathematics in the real, the physical, the tangible, instead of diving off into the realms of pure mathematics straight away. Though I must admit, the appeal to me comes about primarily because he enunciates the way I have thought of maths for most of the last 3 decades.

From here, he starts to ask some more fundamental questions about the nature of numbers, including complex numbers (but not quaternions) and some “proper” algebra though he cunningly avoids the use of terms such group, ring or field whilst ensuring the reader is familiar with their rules by means of definitions followed-up with examples. He also touches on some rules regarding logarithms which perplex some people, but are dealt with very well.

He then goes on to probably the most important idea in maths: proof. Though touching on a little philosophy, he tries to skirt around it and give a robust exposition of what a mathematician means when (s)he talks about proof and how it differs from the more lackadaisical use of the word in everyday (and even some other areas of scientific) usage.

Though any book on serious mathematics probably ought to contain a good amount on calculus, Gowers avoids this quite ostentatiously. Rather, he lays the groundwork for an understanding of it with a chapter on limits and infinity. In so doing, one might think he’s dodged a potential bullet of losing the interest of readers, though I think that anyone who hasn’t done calculus but who has understood this chapter will be well-placed to start studying calculus.

Moving on, we start to get a bit more geometrical. The first of these two chapters looks solely at the idea of dimensionality. One might instinctively have an idea of what a dimension is or how to count them. However, maths is rather more refined than such instinctive generalities and Gowers gives us some examples that any student would find in a 1st year linear algebra course. If anything, this is the acid test for those considering doing maths at university; if this is incomprehensible to you, then it’s best to turn away. But if, on the other hand, you can see there’s something there that can be grasped, if you don’t quite get it exactly at this stage, then you’re standing in good stead. The second of the geometrical chapters looks at much more fundamental geometry, looking at the classic issue of Euclid’s 5th postulate and the consequences of abandoning it.

The last main chapter is on one of my least favourite topics: estimates and approximations. This was a topic I did to death in my 2nd year at uni, not getting on with the lecturer (an angry Scot called Alan) and having a nightmare on the exam, barely scraping a 2:1 in it. Gowers doesn’t hide from the fact that this is not neat maths, as most of the rest of the book is, though he spares the reader from an insight into the gory detail of numerical analysis (or num anal, as we disparagingly called it). If there’s any downside to this wonderful introduction, it is this chapter. Not because it is badly written or poorly explained, it isn’t. But merely because it lacks the sexy panache that the rest of the topics have.

This is redeemed somewhat at the very end when he puts in some frequently asked questions, along with his answers. If anything, these give a far better insight into the working life of the mathematician than anything found in the rest of the book. He addresses some myths and common (mis)conceptions, giving an honest assessment on some issues where he needn’t have done so.

Overall, it’s a great book. If you hated maths at school, then this isn’t the book to get you back into it and loving it. But for anyone with a keen interest in science and how it’s done, then this is a gem. If you know any A-level students considering doing maths at uni, give them this book. Hey, they are students, so £8 for a little book is a lot of money. Go on!

Friday fun: Am I any good at playing Hearts?

As it’s Friday, I decided to take a bit of a break from the relatively serious blog posts I’ve been turning out of late and take a light look at probability and games. Games, after all, are a great arena for testing out ideas in combinatorics and statistics.

The question posed might seem to be an obvious ‘yes’ but just because something might seem obvious doesn’t always mean it’s true. I’ve had my current laptop now for a little over two years. In that time, I’ve played 345 games of Hearts on that computer. I will assume most of you have either played it, or at least know how to play. If not, here’s a quick guide.

Given that there are 4 players, if the game were entirely random, one would expect, over time, to win roughly a quarter of the games played. If your win percentage was higher, you might be justified in thinking that you’re better than the computer. If your win percentage was lower, you might think you were worse, though most people would quickly move on from that thought to trying to find an excuse.

So, how many games do you think I’ve won? Is it not 345/4 = 86.25? Obviously not, because I can only have won a discrete number. So should my expected number of wins be 86 or 87? Obvious rounding would say 86. Though since 87 is so close, that would also seem a reasonable number to have won. What about 90, though? That still seems to be within the realms of possibility. 100, perhaps? How about 120? That might seem less likely, as that would mean I’ve won over a third of the games, yet I only expect to win a quarter.

The answer is in fact 188, giving me a win percentage of just over 54%. Does that really prove that I’m good at Hearts? To try to give it some meaning, I’d like to know what the probability is of winning 188 games out 345 and compare this to the odds of winning 86 time out of 345. But there might be a snag. We would expect that the odds of winning 86 times would be the highest, but there are 345 different possible outcomes. So is one really much more likely to win 86 times than 87? Instinctively, it seems not, but we need to quantify to this to make much sense of this, and confirm or deny what “feels” right.

How do we work out the probability?

I’ll start off with a simple case, where we have only played 2 games. If it were random, we would expect to win 25% of the games. i.e. the probability of winning any given game is 0.25. Similarly, we would expect to lose 75% of the games i.e. a probability of 0.75.

As each game is independent, we need to multiply the probabilities together. So the odds of winning:

  • 0 games out of 2 would be 0.75*0.75 = 0.5625
  • 1 game out of 2 would be 0.25*0.75 = 0.1875
  • 2 games out of 2 would be 0.25*0.75 = 0.0625

But there’s a problem. Add them all up and you should achieve certainty, a probability of 1. But instead, our total is 0.8125. It falls short of 1 by 0.1875. It’s no coincidence that that matches the probability of winning 1 game out of 2. That’s because there are 2 ways we would that single game: we could win the first and lose the second, or lose the second and win the first. So we have to multiply that by the number of ways you can choose 1 ‘slot’ given 2 ‘slots’ to choose from.

How about we try it with 5 games now (to 4 decimal places):

  • 0 games out 5 would be (0.25^0)*(0.75^5) = 0.2373
  • 1 game out 5 would be (0.25^1)*(0.75^4) = 0.0791
  • 2 games out 5 would be (0.25^2)*(0.75^3) = 0.0264
  • 3 games out 5 would be (0.25^3)*(0.75^2) = 0.0088
  • 4 games out 5 would be (0.25^4)*(0.75^1) = 0.0029
  • 5 games out 5 would be (0.25^5)*(0.75^0) = 0.0010

Again, we have undercounted. With the 0 and 5 cases, there is only one arrangement each by which you can win or lose all 5 games. But to win 1 game (or to lose 1 game) there are 5 ways to do this. So we need to multiply the 1 & 4 cases by 5.

But what about 2? How many ways are there to choose 2 games to win (or to lose) from 5 opportunities? Without going into all the detail it is 5!/((5-2)!)*2!) = 120/(2*6) = 10

So to take into account the multipliers, we get the probabilities:

  • 0 out of 5 = 1*0.2373 = 0.2373
  • 1 out of 5 = 5*0.0791 = 0.3955
  • 2 out of 5 = 10*0.0264 = 0.2637
  • 3 out of 5 = 10*0.0088 = 0.0879
  • 4 out of 5 = 10*0.0029 = 0.0146
  • 5 out of 5 = 1*0.0010 = 0.0010

Adding up, we get back to our reassurance that the sum of all probabilities is 1.

What about 345 games then? Well, we just extend the pattern. The odds of winning 188 games are:

(345!/((188!)*((345-188)!)))*(0.25^188)*(0.75^(345-188)) = well, something very small indeed.

A standard calculator won’t be able to do the calculation, but with a little help from a more powerful computer (aka Excel on my laptop), the answer is roughly 0.00000000000000000000000000000012063

That seems pretty darn small. But there are a lot of options (345 to be precise) and most look pretty small. What about our expected figure of 86?

The odds for that (which I leave to you check) are 0.049574108. It is the highest probability for any number of wins, but it may surprise some that the odds of getting 25% of the wins given the odds of winning are 25% are in fact slightly worse than 1 in 20, or 19/1 against. Suddenly, the idea of a direct comparison doesn’t seem so sensible anymore.

Though our odds of winning 86 games are about 410,937,214,868,030,000,000,000,000,000 greater than winning 188 games, I’m still sceptical. What we need to do is look at some kind of spread around our two values of 86 and 188.

Let’s look at each plus or minus 20 (arbitrarily chosen, I admit, please feel free to suggest or try alternatives). So what are the odds of winning between 66 and 106 games? And what are the odds of winning between 168 and 208 games?

For that, I refer back to the working spreadsheet (which I can send you if you don’t believe me and can’t figure out how to design it yourself) and we get the former to be a quite reasonable 0.992543. In other words, if there was no skill in Hearts than you would have more than a 99% probability of winning between 66 and 108 games out of 345.

The latter turns out to be 0.00000000000000000000230188 or 1 in 434,427,345,316,048,000,000.

It is not impossible that my winning so many games is a fluke of the probabilities and that I have hit upon a streak that no one else in the history of the universe will have ever likely encountered before. It just seems very very very very very unlikely.

Maybe, then, it’s not just luck. Maybe I am more skilled at playing the game than the computer is. I’d certainly like to think so, though ‘liking to think so’ can be the downfall of anyone look at statistics…

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: The Emperor’s New Mind by Roger Penrose

This was another of my ‘books of shame’ that I felt the need to re-read. I actually got quite a long way into it first time and I can’t recall why I put it down. The aim of the book is to explore the notion of artificial intelligence (AI), whether or not machines can truly “think”. In order to get to this question, Penrose first spends a lot of time (most of the book, in fact) looking at a wide variety of seemingly unrelated topics.

After an initial discussion of AI, Penrose launches straight into what is probably the hardest chapter to get your head round. It’s all about algorithms, Turing machines and the computability of mathematical problems. He doesn’t spare the detail with pages of binary digits and computer programming languages. It takes a long time to work through, but if you can brave it, there is much easier, and more enjoyable, science in later chapters.

Once you get over the initial hump, we ease back into some gentle maths with Penrose first outlining his neo-Platonic view of notions of reality (one I admit that I share with him). He does this via some very basic complex analysis, looking at the detail of the Mandelbrot set, though without going into too much depth for the casual reader. From here he looks at the world of classical physics and then quantum physics, giving the reader a general grounding in the basics of modern physics whilst every now and then alluding back to the premise of the book, essentially asking if a machine could ever be constructed that would be capable of making the intuitive leaps that humans have managed in coming to our present understanding of the cosmos.

For the most part, this should be readily understandable with a modicum of scientific education, though to someone who didn’t do maths or physics at A-level, much of it may be new and take significantly longer to get to grips with. But even the expert reader shouldn’t get complacent. Penrose’s approach takes much which we may be familiar with and turns it sideways, giving good reason to scratch our heads and think things through anew. The 2nd half of the chapter on quantum mechanics is, admittedly, a bit tougher to get through; the section on spin was where I found my bookmark from the first time I tried to read it and gave up.

After finishing with quantum mechanics he looks at the thermodynamics of the universe, a line of thinking which led, many years later, to Cycles of Time. He ponders over some ideas of quantum gravity but not to any depth that one might be satisfied with. For other takes on that, I’d recommend The Road To Reality (also by Penrose), Brian Greene’s The Elegant Universe or The Three Roads To Quantum Gravity by Lee Smolin.

Eventually, Penrose comes back to the question of AI. In order to do this though, he needs to look at the basic physiology of the brain. Now Penrose is a mathematician and a physicist; he’s not a neurologist. As such, this section of the book doesn’t come across anywhere nearly as strong as the rest of the book. It is clear that this is a written by an educated amateur in the field rather than an expert. For much more detail on how the brain works, I would recommend John Ratey’s A User’s Guide to the Brain.

One fascinating idea that Penrose puts forth is that what may distinguish human intelligence and consciousness is not our rationality, but our irrationality. If all people behaved in accordance with a strict rationality (though even most rationalists, myself included, exhibit some irrational behaviour from time to time) then the strong AI proponents might have more of a case. But the very evidence of irrational behaviour is what Penrose finds most interesting.

Ultimately, no firm propositions are put forward in this volume. The book ends with some musings and a tentative point of view. I intend to follow up, albeit not for a while, with Penrose’s later volume, Shadows of the Mind. In the meantime, what we have is a book which is very loosely about artificial intelligence, but which is really a book about the foundation of computing, along with a tour of some of the great ideas of maths and physics.

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.

Book Review: The Man Who Changed Everything by Basil Mahon

I’m not normally a big fan of reading biographies, but I think that’s because, early on in life, I was exposed to some ghost-written autobiographies that were neither illuminating nor interesting. But my interest was re-kindled a couple of years ago when I read The Strangest Man, a biography of the physicist Paul Dirac. Though a review does not exist on this blog, I would highly recommend it to you.

Anyway, back to this book. This is a fairly recent biography of James Clerk Maxwell, another of my scientific heroes. While he is a name familiar to many (though the author labours under the impression that Maxwell is unknown to all but professional scientists) my main dealing with him was whilst I was doing my maths degree. Having done a lot of vector calculus which Maxwell had helped develop and formalise, I opted for a 3rd year module in Electromagnetism where we applied the vector calculus we had previously learned and trod in Maxwell’s footsteps, deriving the mathematical basis for electromagnetic theory.

As for the man himself, however, I would confess relative ignorance. Aside from the work which made him famous, all I knew of him was that he was a christian and that he was the driving force behind the foundation of the Cavendish laboratory in Cambridge. The latter two elements combining to explain the inscription above the door, “Magna opera Domini exquisite in omnes voluntates ejus.” (“The works of the Lord are great sought out of all them that have pleasure therein.”)

Yet Mahon’s biography is almost entirely work-based. While the account of Maxwell’s early life makes for good reading with some insights into Maxwell’s the man, the last 2/3rds of the book is little more than a list of achievements and activities. The man himself becomes just a name and the reader is not afforded an insight into his life or his thoughts. The only exception to this is when Mahon gives us little snippets of poetry that Maxwell wrote.

Possibly the most frustrating element is that Mahon doesn’t give Maxwell’s equations of electrodynamics in full. He gives a simplified form (in empty space) and then tells the reader that to include electric charges and currents they are slightly altered, without actually giving the full equations. This feels like a real let down, given that was the crowning achievement of Maxwell’s career.

The writing style is easy enough to read and should be accessible to anyone who was reasonably good at physics at school – no college or university training is required. But this has cost the reader the ability to see Maxwell in much detail. Instead of being a 3-dimensional figure we can reach out and touch, grasp or turn over in our hands, he is presented to us as a figure in a glass box. He can be admired and one may view him from a limited number of angles, yet he remains tantalisingly out of reach.