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

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 …

The Case Against Reality - Donald Hoffman ***

It's not exactly news that our perception of the world around us can be a misleading confection of the brain, rather than a precise picture of reality - everything from optical illusions to the apparent motion of video confirms this - but professor of cognitive science Donald Hoffman goes far beyond this. He wants us to believe that spacetime and the objects in it are not real: that they only exist when we perceive them. It's not that he believes everything to be totally illusory, but suggests that the whole framework of the physical world is a construction of our minds.

To ease us into this viewpoint, Hoffman gives the example of the Necker cube - the clever two-dimensional drawing apparently of a cube which can be seen in two totally different orientations. Calling these orientations 'Cube A and Cube B' he remarks that our changing perceptions suggest that 'neither Cube A nor Cube B is there when no one looks, and there is no objective cube that exists unobserve…

The Body - Bill Bryson ****

I am a huge fan of Bill Bryson's travel books - he is a superb storyteller, and in the best parts of his science writing, this ability to provide fascinating facts and intriguing tales shines through.

After taking on the whole of science in his first book, here he focuses in on the physiology, anatomy and diseases of the human body. Bryson does so with his usual light, approachable style, peppering the plethora of facts (and 'don't know's - it's amazing how much we still don't know about the workings of the body) with the little nuggets you can't help but share and stories of some of the odd and, frankly, horrifying goings on in the history of medicine.

So, for example, Bryson throws in 'The chin is unique to humans and no one knows why we have one.' He speculates that it might be just that we 'find a good chin dashing' and quotes a Harvard professor as saying 'Testing this last hypothesis is especially difficult, but the reader is encoura…