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.


Hardback 

Kindle 
Review by Brian Clegg

Comments

Popular posts from this blog

Lost in Math - Sabine Hossenfelder *****

One of my favourite illustrations from a science title was in Fred Hoyle's book on his quasi-steady state theory. It shows a large flock of geese all following each other, which he likened to the state of theoretical physics. In the very readable Lost in Math, physicist Sabine Hossenfelder exposes the way that in certain areas of physics, this is all too realistic a picture. (Hossenfelder gives Hoyle's cosmological theory short shrift, incidentally, though, to be fair, it wasn't given anywhere near as many opportunities to be patched up to match observations as the current version of big bang with inflation.)

Lost in Math is a very powerful analysis of what has gone wrong in the way that some aspects of physics are undertaken. Until the twentieth century, scientists made observations and experiments and theoreticians looked for theories which explained them, which could then be tested against further experiments and observations. Now, particularly in particle physics, it…

Gravity! - Pierre Binétruy ****

I had to really restrain myself from adopting the approach taken by The Register in referring to Yahoo! by putting an exclamation mark after every word in the text when faced with reviewing Gravity! One thing to be said about the punctuation, though, is it makes it easier to search for amongst a whole lot of books on gravity and gravitational waves (the subtitle is 'the quest for gravitational waves') since their discovery in 2015.

Despite the subtitle, Pierre Binétruy gives us far more - in fact, gravitational waves don't come into it until page 160, which makes it really more of a book about gravity with a bit on gravitational waves tacked on than a true exploration of the quest. 

However, those early pages aren't wasted - Binétruy gives us plenty of detail on all kinds of background, for example plunging in to tell us about element synthesis, something you wouldn't expect in a book on gravitational waves. I also really liked a little section on experiments you can…

Brain Based Enterprises - Peter Cook ****

A quick flag on this one: it's a management/business book, and the four star rating is with that in mind. Brain Based Enterprises does contain a surprising amount of science, considering this, which is why it's here, but don't expect it to be like a four star pure science book.

This is an eclectic attack on the status quo of our ideas about business. Peter Cook suggest that much of current business simply isn't oriented to the realities of a modern, technological world, and that we need to handle things very differently in a knowledge-based economy.

The book is divided into three sections. For me, the most interesting was the first 'brainy people' part, as my own business doesn't have teams and such - but for those who do there are also 'brainy teams' and 'brainy enterprises' sections. Cook stirs together a heady mix of science - from psychology to economics - music (a passion of his and a significant part of the way he works) and business the…