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

The Antigravity Enigma - Andrew May ****

Antigravity - the ability to overcome the pull of gravity - has been a fantasy for thousands of years and subject to more scientific (if impractical) fictional representation since H. G. Wells came up with cavorite in The First Men in the Moon . But is it plausible scientifically? Andrew May does a good job of pulling together three ways of looking at our love affair with antigravity (and the related concept of cancelling inertia) - in science fiction, in physics and in pseudoscience and crankery. As May points out, science fiction is an important starting point as the concept was deployed there well before we had a good enough understanding of gravity to make any sensible scientific stabs at the idea (even though, for instance, Michael Faraday did unsuccessfully experiment with a possible interaction between gravity and electromagnetism). We then get onto the science itself, noting the potential impact on any ideas of antigravity that come from the move from a Newtonian view of a...

The World as We Know It - Peter Dear ***

History professor Peter Dear gives us a detailed and reasoned coverage of the development of science as a concept from its origins as natural philosophy, covering the years from the eighteenth to the twentieth century. inclusive If that sounds a little dry, frankly, it is. But if you don't mind a very academic approach, it is certainly interesting. Obviously a major theme running through is the move from largely gentleman natural philosophers (with both implications of that word 'gentleman') to professional academic scientists. What started with clubs for relatively well off men with an interest, when universities did not stray far beyond what was included in mathematics (astronomy, for instance), would become a very different beast. The main scientific subjects that Dear covers are physics and biology - we get, for instance, a lot on the gradual move away from a purely mechanical views of physics - the reason Newton's 'action at a distance' gravity caused such ...

It's On You - Nick Chater and George Loewenstein *****

Going on the cover you might think this was a political polemic - and admittedly there's an element of that - but the reason it's so good is quite different. It shows how behavioural economics and social psychology have led us astray by putting the focus way too much on individuals. A particular target is the concept of nudges which (as described in Brainjacking ) have been hugely over-rated. But overall the key problem ties to another psychological concept: framing. Huge kudos to both Nick Chater and George Loewenstein - a behavioural scientist and an economics and psychology professor - for having the guts to take on the flaws in their own earlier work and that of colleagues, because they make clear just how limited and potentially dangerous is the belief that individuals changing their behaviour can solve large-scale problems. The main thesis of the book is that there are two ways to approach the major problems we face - an 'i-frame' where we focus on the individual ...

Search This Blog