In my other life, I am constantly being told that Jazz and Science don’t sell, that if you put either word into the title of a book or CD you have limited potential sales before you even start. I assume there is sound commercial evidence behind this oft-repeated truism. Of course, you will have a ready-made audience prepared to buy the stuff simply because it has those words in the title, but it is a small, self-defined audience, the popular mass will rather fight shy of these words. In both cases, I suspect the reason is perceived difficulty.

I do not read science, because it involves hard math and concepts that strain my common sense. Anything with numbers in and my mind glazes over. And probably much the same applies to Jazz, the complex rhythms and dissonances are the audio equivalent of higher mathematics. Or, at least, such is the imagined response of the bulk of any potential audience.

In all probability, this is what lies behind C.P. Snow’s two cultures. One culture, the humanities, at least seems accessible to all. We can all read, we can all look at a picture, we can all listen to music. That we may do so with varying degrees of technical ability, that the more challenging the reading or the looking or the listening may become the fewer of us are prepared to take it on voluntarily, is beside the point. There is at least a semblance of democracy, the potential that the humanities are open to all.

But the other culture, science, starts from a position of seeming technical, starts with the appearance of needing a language (mathematics) that genuinely is not open to all. When somebody tells me a piece of writing or a painting or a musical passage is beautiful I understand what they mean, even if I do not necessarily share their standard of beauty. When a mathematician tells me that a particular equation is beautiful, I genuinely do not understand what is meant. It is not that I don’t share their particular standard of beauty, it is that I don’t understand how they are using the word in the first place. Yet I am not scientifically illiterate, I find documentaries and books about science fascinating, I am drawn to a form of the humanities (science fiction) that often makes use of the more esoteric aspects of scientific thought and I have no trouble incorporating these concepts into my worldview, I can even do simple sums (though there is something about the language of mathematics that leaves me not just illiterate but deaf and dumb). So I do understand why science may not have a broad mass appeal.

Which is why anyone choosing to write about science for a mass audience tends to make it seem as if they are writing about something else. One popular disguise is history. Yet, with rare exceptions, the history of science does not move in the same storied way that a political or a social or a military history might progress. Dead ends, false starts and failures are both more common and in a sense more productive than they tend to be in other historical narratives. So how do you write about the history of science?

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I blame Jenny Uglow. In The Metaphysical Club (2001), Louis Menand had found a way of writing about the history of ideas as a sort of group biography, a structure that allowed him to emphasise the way ideas often need to bounce around between different people, who may be allies or antagonists, before they really take a usable or familiar shape. Uglow applied that structure more directly to science in The Lunar Men (2002), and it has proved an effective way of writing about science as an historical process. Richard Holmes, for instance, did something similar in The Age of Wonder (2008) which explored the way that the romantic imagination and scientific exploration intersected during the late 18^th and early 19^th centuries.

The latest book to take this group biography approach to the history of science is The Philosophical Breakfast Club by Laura J. Snyder (2011), a work which overlaps significantly with Holmes’s book (to its detriment in many ways, Holmes is certainly a far better writer).

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The Philosophical Breakfast Club of the title is a name Snyder gives to an informal get together of natural philosophers who were students together at Cambridge in the early nineteenth century. The four are John Herschel and Charles Babbage, who feature in Holmes’s book, William Whewell who appears in Holmes’s book, and Richard Jones who isn’t even mentioned by Holmes. Other students took part in these regular breakfast meetings, and Babbage (who seems to have been a most difficult person to get along with) fell out with the other three quite early on and doesn’t seem to have worked with any of them on any of their scientific projects, so the composition of this group portrait seems questionable at least. Meanwhile Jones had considerably less impact on the history of science than his fellows, and indeed disappears from the story so often that at times Snyder seems to have to forcibly remind herself that he is supposed to be part of the story. In the end we take apart Snyder’s subtitle: ‘Four remarkable friends who transformed science and changed the world’ – they weren’t particularly remarkable, they weren’t particularly friends, if any of them transformed science it was probably Whewell, and Babbage is the one who came closest to changing the world but didn’t succeed.

Of the four, Whewell is probably Snyder’s hero, at least he is the only one of the four she follows from childhood onwards, and the other three are first seen through Whewell’s eyes. From relatively humble origins, he appears to have been a particularly brilliant student who went on to spend his entire career at Cambridge where he would become the Master of Trinity. He dabbled in many branches of science, though his greatest practical achievement was probably in the calculation of tide tables. His real impact, however, was on the administrative side. He helped establish the British Association for the Advancement of Science in opposition to the then moribund Royal Society; he wrote widely read and highly influential books on the history and philosophy of science; and he gave us the word ‘scientist’ in an apparently off-the-cuff response to Samuel Taylor Coleridge during a meeting of the BAAS.

Herschel was the pre-eminent scientist of the four. The son of William Herschel, he was rich, well-connected, did major work in astronomy and was one of the early pioneers of photography. Babbage was also rich and well-connected and supposedly a brilliant mathematician, but he gave up his Lucasian professorship at Cambridge without having ever taught anyone. He put his mathematical genius to the purpose of devising first his Difference Engine, then his Analytical Engine, neither of which he completed, and he seemed to spend most of his productive years locked in a series of arguments about funding which mostly boiled down to the fact that he wasn’t getting the recognition he felt he deserved. Jones was a country parson who had to be pushed by his friends to do anything, but somewhere along the way he did effectively invent political economy, though he did nothing further in scientific terms.

The thread that Snyder finds to bind this disparate bunch together actually dates back 300 years earlier. As students, the four set themselves the task of promoting the view of science as propounded by Francis Bacon. Bacon’s central argument was in favour of inductive reasoning: the scientist should establish a body of observation and experiment, and from those particular examples draw out general laws, which can then be tested by further observation and experiment. Bacon’s presentation of science as a communal and empirical enterprise had already led to the creation of the Royal Society, but inductive reasoning was still not the common way that science was done, and the near-medieval scholastic structures still in place in Cambridge (and, by extension, in other places of learning) still had a tendency to lean on deduction from established authority. The twin themes that follow from this are that, i) induction became the basis of everything the four did within science, and ii) they set out to change the structures of science as practiced in Britain at the time. This latter was Whewell’s enterprise in particular, and he was very successful; by the end of their lives, science had changed from being the hobby of the gentleman into a profession. This professionalization of science led in turn, of course, to the increased specialization that would in time create Snow’s other culture.

It has to be said, however, that their devotion to induction had its limits. Towards the end of their lives, both Whewell and Herschel argued vehemently against the ideas proposed by Charles Darwin in his Origin of Species. What Darwin had induced from extensive observation ran counter to the prior beliefs of these two old men of science.

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Writing about the history of science is, fairly obviously, a two-part proposition: you are writing about history, and you are writing about science. The trick is to get the balance right. What tends to happen is that writers get carried away explaining the science, and the history ends up taking a back seat. With Snyder, particularly in the early part of her book, it seems to be the other way round.

One of the things that brought the four together was the formation of the Analytical Society at Cambridge. One of the purposes of this society was to promote the use of Leibnitz’s calculus over Newton’s. The two forms of calculus were invented at the same time and independently of each other, but the Newtonian version which, for nationalistic reasons among others, still held sway in England was more convoluted. At this point in our story, therefore, you might think that some explanation of the difference between the two forms of calculus might be appropriate. I quote Snyder’s explanation in full:

Newton used a ‘dot’ to indicate differentials, while Leibnitz used the dy/dx notation. Both mean the same thing, but since the Leibnitzian notion contains explicitly the concept of a quotient, it is more effective for certain equations. (30)

Yet only a few pages earlier, she had gone on at three or four times the length to explain exactly what a guinea was. (One pound and one shilling, one of the peculiarities of the English monetary system right into the 20^th century – there, do you need to know more?)

For fully the first third of the book you get a sense of Snyder getting all excited about all this curious English history, as if she is encountering it for the first time; and, oh yes, there’s all this science stuff as well, but everyone knows that, don’t they? To be fair, she then settles down and strikes a better balance for the bulk of the book, providing far better explanations of some of the scientific notions that crop up later. (Though I could have done with more about how the Difference Engine was supposed to work, maybe with the odd diagram or two thrown in for good measure; but then, perhaps that’s just me being thick.)

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I wasn’t surprised by this book. After all, Holmes had given us a brisk canter through exactly this material in the latter part of The Age of Wonder, and the set piece with which Snyder opens – the third meeting of the BAAS in Cambridge in June 1833, at which Coleridge protested that men who dug in fossil pits or did experiments with electricity were not worthy of the name ‘natural philosophers’ and should have a different title, to which Whewell responded that ‘by analogy with artist, we may form scientist’ – is a set piece in Holmes’s book also. I was slightly surprised that the attention should be on this particular group of people, though they did seem to be the centre towards which many other distinguished figures, Faraday and Davy, Fox Talbot and Darwin, would gravitate. After all, despite Herschel’s achievements, these four were not exactly at the heart of the most significant scientific achievements of their day, they may be said to have facilitated some of them, but as I mentioned earlier they were vehemently opposed to the insights of Charles Darwin. Moreover, and I am sure that this is an accidental rather than an intentional effect of the concentration on the four, the contributions of people like Faraday and Davy do seem to be somewhat reduced, and you could come away thinking that Herschel had done far more to invent photography than Fox Talbot did.

I realized, quite quickly, that Snyder had really set out to write a biography of Whewell but, for whatever reason, had been persuaded to expand her focus. You get a sense of this even on the cover, which shows portraits of the four men arranged in a library of leather-bound books. Jones is tucked to one side, half in shadow. Babbage and Herschel are centre stage, leaning against the legs of a chair. But in pride of place, on the chair, raised above his fellows, is Whewell. This is his book, and I think it might have been a better book if Snyder had followed her instincts and concentrated more fully on him.

All that said, I don’t want you to come away with the impression that this is a bad book, far from it. There are weak moments early on, but it gets stronger as it goes. And this kind of group portrait of some of the more unsung characters in the early history of science is fascinating in its own right. I am not sure we would see science in quite the same light if not for the move to professionalise it that all four of them, in their different ways, contributed towards. It is an interesting story, it’s just that I’m not sure it’s quite as significant as Snyder thinks it is.