Skip to main content

Infinitesimal - Amir Alexander ***

While some books have obscure titles, a combination of the title and the subtitle will usually make it plain what the book is about. But I can pretty much guarantee that most readers, seeing Infinitesimal - how a dangerous mathematical theory shaped the modern world would leap to an incorrect conclusion as I did. The dangerous aspect of infinitesimals was surely going to be related in some way to calculus, but I expected it to be about the great priority debate between Newton and Leibniz, where in fact the book concentrates on the precursors to their work that would make the use of infinitesimals - quantities that are vanishingly close to zero - acceptable in mathematics.

The book is in two distinct sections. The first focuses on the history of the Jesuits, from their founding to their weighing into the mathematical debate against those who wanted to use infinitesimals in maths. For the Jesuits, everything was cut and dried, and where Aristotle's view and the geometry of Euclid had an unchanging nature that made them acceptable, the use of infinitesimals was far too redolent of change and rebellion. This was interesting, particularly in the way that the history gave background on Galileo's rise and fall seen from a different viewpoint (as he was in the ascendancy, the Jesuits were temporarily losing power, and vice versa). However, this part goes on far too long and says the same thing pretty much over and over again. This is, I can't help but feel, a fairly small book, trying to look bigger and more important than it is by being padded.

The second section I found considerably more interesting, though this was mostly as a pure history text. I was fairly ignorant about the origins of the civil war and the impact of its outcome, and Amir Alexander lays this out well. He also portrays the mental battle between philosopher Thomas Hobbes and mathematician John Wallis in a very interesting fashion. I knew, for example, that Wallis had been the first to use the lemniscate, the symbol for infinity used in calculus, but wasn't aware how much he was a self-taught mathematician who took an approach to maths that would horrify any modern maths professional, treating it more as an experimental science where induction was key, than a pure discipline where everything has to be proved.

Hobbes, I only really knew as a name, associated with that horrible frontispiece of his 'masterpiece' Leviathan, which seems to the modern eye a work of madness, envisaging a state where the monarch's word is so supreme that the people are more like automata, cells in a body or bees in a hive rather than individual, thinking humans. What I hadn't realised is that Hobbes was also an enthusiastic mathematician who believed it was possible to derive all his philosophy from geometry - and geometry alone, with none of Wallis' cheating little infinitesimals. The pair attacked each other in print for many years, though Hobbes' campaign foundered to some extent on his inability to see that geometry was not capable of everything (he regularly claimed he had worked out how to square the circle, a geometrically impossible task).

Although I enjoyed finding out more about the historical context it's perhaps unfortunate that Alexander is a historian, rather than someone with an eye to modern science, as I felt the first two sections, which effectively described the winning of the war by induction and experimentation over a view that expected mathematics to be a pure predictor of reality, would have benefited hugely from being contrasted with modern physics, where some would argue that far too much depends on starting with mathematics and predicting outcomes, rather than starting with observation and experiment. An interesting book without doubt, but not quite what it could have been.


Review by Brian Clegg


Popular posts from this blog

Beyond Weird - Philip Ball *****

It would be easy to think 'Surely we don't need another book on quantum physics.' There are loads of them. Anyone should be happy with The Quantum Age on applications and the basics, Cracking Quantum Physics for an illustrated introduction or In Search of Schrödinger's Cat for classic history of science coverage. Don't be fooled, though - because in Beyond Weird, Philip Ball has done something rare in my experience until Quantum Sense and Nonsense came along. It makes an attempt not to describe quantum physics, but to explain why it is the way it is.

Historically this has rarely happened. It's true that physicists have come up with various interpretations of quantum physics, but these are designed as technical mechanisms to bridge the gap between theory and the world as we see it, rather than explanations that would make sense to the ordinary reader.

Ball does not ignore the interpretations, though he clearly isn't happy with any of them. He seems to come clo…

Jim Baggott - Four Way Interview

Jim Baggott is a freelance science writer. He trained as a scientist, completing a doctorate in physical chemistry at Oxford in the early 80s, before embarking on post-doctoral research studies at Oxford and at Stanford University in California. He gave up a tenured lectureship at the University of Reading after five years in order to gain experience in the commercial world. He worked for Shell International Petroleum for 11 years before leaving to establish his own business consultancy and training practice. He writes about science, science history and philosophy in what spare time he can find. His books include Atomic: The First War of Physics and the Secret History of the Atom Bomb (2009), Higgs: The Invention and Discovery of the ‘God Particle’ (2012), Mass: The Quest to Understand Matter from Greek Atoms to Quantum Fields (2017), and, most recently, Quantum Space: Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe (2018). For more info see: www…

Quantum Space: Jim Baggott *****

There's no doubt that Jim Baggott is one of the best popular science writers currently active. He specialises in taking really difficult topics and giving a more in-depth look at them than most of his peers. The majority of the time he achieves with a fluid writing style that remains easily readable, though inevitably there are some aspects that are difficult for the readers to get their heads around - and this is certainly true of his latest title Quantum Space, which takes on loop quantum gravity.

As Baggott points out, you could easily think that string theory was the only game in town when it comes to the ultimate challenge in physics, finding a way to unify the currently incompatible general theory of relativity and quantum theory. Between them, these two behemoths of twentieth century physics underlie the vast bulk of physics very well - but they simply can't be put together. String theory (and its big brother M-theory, which as Baggott points out, is not actually a the…