Shape - Jordan Ellenberg ***

I really enjoyed Jordan Ellenberg’s earlier book How Not to be Wrong, so looked forward to Shape with some anticipation. In principle what we have here is a book about geometry - but not seen from the direction of the (dare I say it) rather boring, Euclid-based geometry textbooks some of us suffered at school. Instead Ellenberg sets out to show how geometry underlies pretty much everything.

Along the way, we are given some nice turns of phrase. I enjoyed, for example, Ellenberg’s remark on the philosopher Thomas Hobbes, where Ellenberg remarks Hobbes was ‘a man whose confidence in his own mental powers is not fully captured by the prefix “over”’. Whether or not what we read about here is really all geometry is a matter of labelling (as is the ‘number of holes in a straw’ question that Ellenberg entertainingly covers). Arguably, for example, there is some material that is probability that can be looked at in a geometric fashion, rather than geometry that produces probabilistic results - I find the probability viewpoint a lot simpler and more interesting. In the end, despite his efforts, unless you are a mathematician, some aspects of geometry (and maths in general) feel laboured and uninteresting. But the marvel of this book is that he does make a surprising amount of it quite the opposite.

Unfortunately, Ellenberg can go into far too much detail sometimes (which may be why the book is a bit of a doorstop at 463 pages) - for example, a story that starts with the mosquito’s random walk seems to go on and on for ever and I rather lost the will to continue, in a topic that interests me a lot more than geometry does. In a different way, I struggled to get my head around the lengthy section on US electoral district gerrymandering which seemed only of interest to someone with in-depth enthusiasm for US politics, while some of the final meandering final chapter should certainly have been lost in the edit.

I do wonder if the success of the earlier book meant this one was not given the editorial scrutiny it needed. Although Ellenberg failed to convince me that geometry is the foundation of many of the topics he discusses, there is material to interest the reader here - and it’s certainly a far cry from those laborious proofs and QEDs.

Hardback:

Bookshop.org

Kindle:

Using these links earns us commission at no cost to you

Review by Brian Clegg

Comments

Luna: Moon Rising (SF) - Ian McDonald ****

I'm not the natural audience for this book. Game of Thrones l eaves me cold - and it's hard not to feel the influence of GoT (and a whole lot of Dune ) underneath a veneer of science fiction and the trappings of a South American drug cartel in the cod-medieval family power battles and chivalric details. There are even dragons (of a sort). I'd be really sad if the future did involve this sort of throwback feudalism. However, remarkably, despite this I found Luna: Moon Rising kept me engaged. The fact is that Ian McDonald can put together a good plot with intricate machinations, which is enough to carry the reader through what can be a bewildering collection of characters. The two page scene-setter saying who did what to whom at the start was useful, but I could have done with family trees for the main family as I was constantly forgetting who was who - especially easy as McDonald endows many families with characters with the same first initial (e.g. Ariel and Al...

Adventures of a Computational Explorer - Stephen Wolfram ***

Stephen Wolfram, the man behind the scientist's mathematical tool of choice, Mathematica, plus a whole host of other software products, including the uncanny Wolfram Alpha knowledge engine, is undoubtedly a genius of the first order. In this book, we get an uncensored excursion into the mind of genius - which is, without doubt, a fascinating prospect. The book consists of a collection of essays and speeches that Wolfram has produced over the last ten to fifteen years, covering an eclectic range of topics. Like all such collections, the result is something that lacks the coherence of a book with a narrative that runs through it, inevitably introducing a degree of repetition and a mix of interesting and not-so-interesting topics - but there's likely to be something to catch the attention anyone who is into computing or mathematics. One of the most interesting pieces is the opening one, where Wolfram describes being a consultant on the SF movie Arrival. He seems to hav...

The AI Paradox - Virginia Dignum ****

This is a really important book in the way that Virginia Dignum highlights various ways we can misunderstand AI and its abilities using a series of paradoxes. However, I need to say up front that I'm giving it four stars for the ideas: unfortunately the writing is not great. It reads more like a government report than anything vaguely readable - it really should have co-authored with a professional writer to make it accessible. Even so, I'm recommending it: like some government reports it's significant enough to make it necessary to wade through the bureaucrat speak. Why paradoxes? Dignum identifies two ways we can think about paradoxes (oddly I wrote about paradoxes recently , but with three definitions): a logical paradox such as 'this statement is false', or a paradoxical truth such as 'less is more' - the second of which seems a better to fit to the use here. We are then presented with eight paradoxes, each of which gives some insights into aspects of t...

Search This Blog