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 
Using these links earns us commission at no cost to you
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

Artificial Intelligence - Melanie Mitchell *****

As Melanie Mitchell makes plain, humans have limitations in their visual abilities, typified by optical illusions, but artificial intelligence (AI) struggles at a much deeper level with recognising what's going on in images. Similarly in some ways, the visual appearance of this book misleads. It's worryingly fat and bears the ascetic light blue cover of the Pelican series, which since my childhood have been markers of books that were worthy but have rarely been readable. This, however, is an excellent book, giving a clear picture of how many AI systems go about their business and the huge problems designers of such systems face.

Not only does Mitchell explain the main approaches clearly, her account is readable and engaging. I read a lot of popular science books, and it's rare that I keep wanting to go back to one when I'm not scheduled to be reading it - this is one of those rare examples.

We discover how AI researchers have achieved the apparently remarkable abiliti…

The Art of Statistics - David Spiegelhalter *****

Statistics have a huge impact on us - we are bombarded with them in the news, they are essential to medical trials, fundamental science, some court cases and far more. Yet statistics is also a subject than many struggle to deal with (especially when the coupled subject of probability rears its head). Most of us just aren't equipped to understand what we're being told, or to question it when the statistics are dodgy. What David Spiegelhalter does here is provide a very thorough introductory grounding in statistics without making use of mathematical formulae*. And it's remarkable.

What will probably surprise some who have some training in statistics, particularly if (like mine) it's on the old side, is that probability doesn't come into the book until page 205. Spiegelhalter argues that as probability is the hardest aspect for us to get an intuitive feel for, this makes a lot of sense - and I think he's right. That doesn't mean that he doesn't cover all …

Colin Stuart - Four Way Interview

Colin Stuart is an astronomy journalist, author and science communicator. He has written fourteen science books to date, which have been translated into nineteen languages, including 13 Journeys Through Space and Time: Christmas Lectures From the Royal Institution and The Universe in Bite-sized Chunks both published by Michael O’Mara Books. He also has written for the Guardian, the European Space Agency and New Scientist and has spoken on Sky News, BBC News and Radio 5 Live. He is a fellow of the Royal Astronomical Society and even has an asteroid named after him. His latest title is Rebel Star: our quest to solve the great mysteries of the Sun.

Why science? 

For me the stories that you can tell with modern science rival the most imaginative leaps in fiction. The secret, invisible kingdoms of bacteria and sub-atomic particles. The logic defying realms of black holes and Big Bangs. That excites me more than Hogwarts or Mordor. The universe is an amazing place and we’ve only just scratche…