Solve for X / Mathematical Physics

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12 Jun 2019 / Physics World

Taken from the June 2019 issue of Physics World. Members of the Institute of Physics can enjoy the full issue via the Physics World app.

Ian Randall reviews All of Physics (Almost) in 15 Equations by Bruno Mansoulié

“For the average journalist,” particle physicist Bruno Mansoulié notes astutely, “equations just mean a vanishing audience.” Being one of those mathematics-adverse science writers myself, the task of reviewing Mansoulié’s book, All of Physics (Almost) in 15 Equations – which has recently been translated into English from its original French – offered the promise of a brilliant redemption narrative, for me at least. In the ultimate in immersion therapy, I imagined reluctantly allowing Mansoulié to expose me to the wonder of once-dreaded equations. My hope was that I should emerge, transformed and enlightened by the book. Unfortunately, that wasn’t the case, and Mansoulié has not quite cracked the formula for success.

The premise of this short volume is certainly sound. Each chapter introduces a fundamental equation from across the history of physics (or, in a couple of exceptions, a set of linked equations, or the concept of Feynman diagrams). The equation is then explained, and its importance contextualized. As one progresses through the book, the chosen equations become inherently more complex. The opening chapter, for example, contemplates Ancient Greek mathematician Euclid’s law of light reflection. Having explained the basics of how mirrors function, Mansoulié uses this as a launchpad to explore how we see – and the disconnect between the intuitive concept of actively “watching” and the passive receipt of light rays.

Later chapters ramp up the complexity, addressing such cornerstones as the ideal gas law, the Dirac equation and the matter–energy equivalence. I especially enjoyed a humorous aside in a chapter concerning Maxwell’s equations, in which Mansoulié joyfully imagines a secret society of special scientists lurking unknown among the physics community, all of whom have unbelievably managed to complete all the final exercises at the end of a particularly vexing textbook – Jackson’s Classical Electrodynamics. This joking sidebar is entirely frivolous, and yet delightful for how it blasts the stereotype of the humourless, perfectionist scientist clean out of the water.

But when it comes to the core body of the volume, All of Physics (Almost) in 15 Equationswould have benefited from spending a little more time demonstrating its workings. While the slim chapters have a definite appeal in their bite-sized length, the exploration of each equation left me wanting more detail on the context and application of each concept. More time could have been employed explaining to the uninitiated how to read each chapter’s equation(s) – and, for those similarly unfamiliar with the manifold players in the history of physics, more care in introducing the names of important scientists would have been welcome. The average reader cannot be assumed to already know who, for example, Snell van Royen was, and context would have made for a more accessible and humanized narrative.

Similarly, it seems unreasonable to expect that anyone apart from a particle physicist would have the necessary background to understand the nature and importance of the Z0 particle, which becomes relevant to the latter half of the chapter on Maxwell’s equations. Yet, the text does little to explain this. The recurrence of esoteric knowledge and terminology from outside the realms of physics, in addition, hints at a more fundamental confusion as to the volume’s target audience, which the back cover claims to be “the interested general public”. Case in point: “appoggiatura”. This is “a grace note which delays the next note of the melody, taking half or more of its written time value”, according to the dictionary. The word may be a good target for one’s new word-of-the-day, but the average person might, unlike Mansoulié, struggle to squeeze it into natural prose twice within as many brief chapters.

Invitation to the LASER World of PHOTONICS

In a work intended to induct a likely reluctant population into the wonders of physical equations, it is odd that Mansoulié so often pauses to interject that the equation being discussed is not a favourite of his. “I like most the equations which change my way of seeing the world, but this is not the case here,” he writes of the Navier–Stokes equation. “Despite its high-level appearance, its Greek letters and the ‘nabla’ operator with its esoteric look, the underlying physics is simple – nothing more than Newton.” The application might be beautiful, as he goes on to concede, but as a reader I would rather be introduced to those equations that the expert views as the crème de la crème.

As a reader I would rather be introduced to those equations that the expert views as the crème de la crème

Furthermore, the volume’s content seems beset by a few curious editorial decisions that left me with the impression of a work in need of further polish. A section on Newton’s second law makes the fundamental mistake of telling rather than showing, as Mansoulié describes a fascinating-sounding physical misunderstanding in a Renaissance draftsman’s depiction of a cannonball’s path through the air – wherein it took a straight trajectory before dropping straight downwards. How much better it would have been for the illustration itself to accompany the text (or at least a reference provided).

While perhaps intended poetically, Mansoulié’s prose has a shade of the purple about it – and repeated comparisons between physics and Buddhism are too easily read as being rather reductionist towards the latter. Singularly disconcerting is the decision to succeed the headline “The physics of the industrial revolution” with a not-inconsiderable summary of core aspects of particle physics, deferring any mention of said technological shifts until two pages later.

Special mention and unblemished praise must be given, however, to the enchanting illustrations of Lison Bernet, the presence of which graces the opening of each chapter. Full of whimsy, Bernet delightfully illustrates the context of each equation; painting, for example, Alice’s encounter with Schrödinger’s Cheshire cat in the forking forest path of a quantum wonderland; and a mash-up of Einstein’s equations with a melting clock in the style of Salvador Dali.

Perhaps I am overlooking the hidden value of All of Physics (Almost) in 15 Equations. Despite its superficial premise, the volume may be better viewed as an autobiographical character study; one of a scientist who, if not the best pedagogue, nevertheless cannot help but telegraph both his unabashed and poetic love for physics and the extent to which his relationship with the titular equations has intersected with every facet of his character. Such a frame would make far better use of Mansoulié’s anecdotes from across his physics education.

Taken in this adjusted context, the work is compelling and worthy of being perused – regardless of whether one sees in certain equations total personal revulsion or such aspects as, in the words of Mansoulié, “the sensuous curve of a ∂”.

  • 2019 World Scientific £25pb 156pp

Ian Randall is a science writer based in the UK