Skip to main content

Are Numbers Real - Brian Clegg *****

To use Brian Clegg's own words, the question as to whether numbers are real seems, at first, 'like a crazy question.'  In my mind, numbers are somewhat like natural language, in that one could argue that we don't consciously think about our native language when using it - it just happens and flows out of us.  When we have thoughts, it's interesting to ask whether one was thinking those thoughts in words, and, therefore, whether one can have a thought without having available a language in which to structure them.  

As numbers obviously don’t exist in a physical sense - you can't trip over the number ‘2’ in the street - one might conclude that, as in the language case, numbers exist only in thought.  To answer such things one might decide to conduct an experiment, to observe the reasoning process.  Sadly, to do so is like observing which slit a particle passes through in the famous double-slit experiment from quantum mechanics; when an observation is made, the effect of the observation crashes the experiment.  It would seem that the machine (the mind) cannot watch itself in operation and observe its own subtle workings.

UK edition
In the book, Clegg takes us from aspects of mathematics which seem very natural - even suggesting in an entertaining way how a basic number system could be developed as a result of lending someone your goats - to those which certainly do require conscious thought and seem very far removed from the world, though paradoxically this kind of mathematics is used to drive the way that physics currently explores reality. It's both a brief history of the human love-hate relationship with maths and a look at the way that what was once clearly a direct representation of the physical has become a language and reality of its own.

In Are Numbers Real? Clegg tackles what is a very deep question in his usual way: with clarity, wit and a wonderfully clear narrative writing style.  Not only does he tackle a wide variety of subjects to seek out the truth of the matter, he does so in an engaging and hugely accessible way.  I personally couldn’t put it down and as an active researcher in the field itself, it has provided me with some very, um, real food for thought.

Hardback (UK paperback):  
Kindle:  
Review by Peet Morris
Please note, this title is written by the editor of the Popular Science website. Our review is still an honest opinion – and we could hardly omit the book – but do want to make the connection clear.

Comments

Popular posts from this blog

Cosmology for the Curious - Delia Perlov and Alex Vilenkin ***

In the recently published The Little Book of Black Holes we saw what I thought was pretty much impossible - a good, next level, general audience science title, spanning the gap between a typical popular science book and an introductory textbook, but very much in the style of popular science. Cosmology for the Curious does something similar, but coming from the other direction. This is an introductory textbook, intended for first year physics students, with familiar textbook features like questions to answer at the end of each chapter. Yet by incorporating some history and context, plus taking a more relaxed style in the writing, it's certainly more approachable than a typical textbook.

The first main section, The Big Bang and the Observable Universe not only covers basic big bang cosmology but fills in the basics of special and general relativity, Hubble's law, dark matter, dark energy and more. We then move onto the more speculative (this is cosmology, after all) aspects, brin…

Astrophysics for People in a Hurry – Neil deGrasse Tyson *****

When I reviewed James Binney’s Astrophysics: A Very Short Introduction earlier this year, I observed that the very word ‘astrophysics’ in a book’s title is liable to deter many readers from buying it. As a former astrophysicist myself, I’ve never really understood why it’s considered such a scary word, but that’s the way it is. So I was pleasantly surprised to learn, from Wikipedia, that this new book by Neil deGrasse Tyson ‘topped The New York Times non-fiction bestseller list for four weeks in the middle of 2017’.

Like James Binney, Tyson is a professional astrophysicist with a string of research papers to his name – but he’s also one of America’s top science popularisers, and that’s the hat he’s wearing in this book. While Binney addresses an already-physics-literate audience, Tyson sets his sights on a much wider readership. It’s actually very brave – and honest – of him to give physics such prominent billing; the book could easily have been given a more reader-friendly title such …

Once upon and Algorithm - Martin Erwig ***

I've been itching to start reading this book for some time, as the premise was so intriguing - to inform the reader about computer science and algorithms using stories as analogies to understand the process.

This is exactly what Martin Erwig does, starting (as the cover suggests) with Hansel and Gretel, and then bringing in Sherlock Holmes (and particularly The Hound of the Baskervilles), Indiana Jones, the song 'Over the Rainbow' (more on that in a moment), Groundhog Day, Back to the Future and Harry Potter.

The idea is to show how some aspect of the story - in the case of Hansel and Gretel, laying a trail of stones/breadcrumbs, then attempting to follow them home - can be seen as a kind of algorithm or computation and gradually adding in computing standards, such as searching, queues and lists, loops, recursion and more.

This really would have been a brilliant book if Erwig had got himself a co-author who knew how to write for the public, but sadly the style is mostly heavy…