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

God: the Science, the Evidence - Michel-Yves Bolloré and Olivier Bonnassies ***

This is, to say the least, an oddity, but a fascinating one. A translation of a French bestseller, it aims to put forward an examination of the scientific evidence for the existence of a deity… and various other things, as this is a very oddly structured book (more on that in a moment). In The God Delusion , Richard Dawkins suggested that we should treat the existence of God as a scientific claim, which is exactly what the authors do reasonably well in the main part of the book. They argue that three pieces of scientific evidence in particular are supportive of the existence of a (generic) creator of the universe. These are that the universe had a beginning, the fine tuning of natural constants and the unlikeliness of life. To support their evidence, Bolloré and Bonnassies give a reasonable introduction to thermodynamics and cosmology. They suggest that the expected heat death of the universe implies a beginning (for good thermodynamic reasons), and rightly give the impression tha...

Humble Pi - Matt Parker ****

Matt Parker had me thoroughly enjoying this collection of situations where maths and numbers go wrong in everyday life. I think the book's title is a little weak - 'Humble Pi' doesn't really convey what it's about, but that subtitle 'a comedy of maths errors' is far more informative. With his delightful conversational style, honed in his stand-up maths shows, it feels as if Parker is a friend down the pub, relating the story of some technical disaster driven by maths and computing, or regaling us with a numerical cock-up. These range from the spectacular - wobbling and collapsing bridges, for example - to the small but beautifully formed, such as Excel's rounding errors. Sometimes it's Parker's little asides that are particularly attractive. I loved his rant on why phone numbers aren't numbers at all (would it be meaningful for someone to ask you what half your phone number is?). We discover the trials and tribulations of getting cal...

Quantum 2.0 - Paul Davies ****

Unlike the general theory of relativity or cosmology, quantum physics is an aspect of physics that has had a huge impact on everyday lives, particularly through the deployment of electronics, but also, for example, where superconductivity has led to practical applications. But when Paul Davies is talking about version 2.0, he is specifically describing quantum information, where quantum particles and systems are used in information technology. This obviously includes quantum computers, but Davies also brings in, for example, the potential for quantum AI technology. Quantum computers have been discussed for decades - algorithms had already been written for them as early as the 1990s - but it's only now that they are starting to become usable devices, not at the personal level but in servers. In his usual approachable style, Davies gives us four chapters bringing us up to speed on quantum basics, but then brings in quantum computing. After this we don't get solid quantum informat...

Search This Blog