Christmas Gift Guide

As we enter that time of year when many of us have lots of presents to buy, I thought it would be a good idea to highlight some of my titles that make useful gifts - especially for those difficult-to-buy-for people. When you consider what many presents cost these days, I honestly think you can't beat a book for value. So here's my top six, in no particular order:

Introducing Infinity: a great stocking filler (just £5.99 currently on Amazon, and pocket-sized), Introducing Infinity brings the mind-boggling subject of infinity alive with powerful illustrations in a unique graphic guide. Suitable from about 14 upwards for anyone with an inquiring mind. See at Amazon.co.uk and Amazon.com. If your gift recipient would prefer a more in-depth, though still approachable read, there is also A Brief History of Infinity.

Xenostorm: Rising: a faced-paced science fiction novel, technically for a young adult audience (12+), though it works as well for adults who like SF. (Currently £7.75 on Amazon.) Fourteen-year-old Davy comes home to discover his parents have disappeared - and then a voice in his head tells him that he will be shot if he doesn't act immediately. Davy finds himself facing a powerful underground group who have lived for hundreds of years - and want to see him dead. The future of human existence is in the balance. What that future is – only Davy can decide. See at Amazon.co.uk and Amazon.com.

The Universe Inside You: an entertaining exploration of science, using your body as a starting point to look at everything from bacteria to the scale of the universe. Bursting with eye-popping facts, and a great way to introduce science to someone who is reluctant to read about it - but equally for anyone who enjoys exploring the true sense of wonder of science. Written for adults but suitable from about 13 up. (Currently £7.19 on Amazon.) See at Amazon.co.uk and Amazon.com.

Build Your Own Time Machine: the subject I get asked to talk about most is time travel - because it's something that fascinates everyone, yet many are surprised to learn that there is nothing in the laws of physics that prevents it. This is one for the slightly more dedicated science lovers as it goes into more detail than some of the other books. But if you have a science fan, from 15 to adult, on your gift list, they will love this one. (Currently £7.61 on Amazon.) See at Amazon.co.uk and Amazon.com.

The Quantum Age: my latest book and a chance to explore the weirdest aspect of science, quantum theory. The book introduces the basics of quantum physics in a highly approachable way, but it focuses mainly on the amazing applications of quantum physics, from lasers to electronics to superconducting magnets... and even the way that strange quantum effects take place in the natural world. Despite the subject, this is not an overly-technical read, but opens up the topic they're usually too scared to teach you at school for anyone from 14 to adult. This is a hardback, so a little more expensive (currently £11.99 on Amazon), but that does make it more attractive as a present. See at Amazon.co.uk - sorry, not available on Amazon.com until February 2015.

Dice World: recently on the longlist for the Royal Society Prize, Dice World gives the reader a chance to have his or her mind boggled by the aspect of maths that we seemed designed to be fooled by: probability and randomness. Find out how to toss a head ten times in a row, how to make predictions with impossible accuracy, why people volunteer to give up thousands of pounds for no good reason, and how a game show left the woman with the world's highest IQ being reviled by a whole list of academics... until they discovered she was right. Inquisitive minds from 15 to 99 will be fascinated - and it's currently £7.19 on Amazon. See at Amazon.co.uk and Amazon.com.

... if there's nothing here that catches your fancy, take a look at my entire collection of science books, or if you want something special, I have many of my books available direct, signed and with an inscription of your choice.

Why I hate opera

If I'm honest, the title of this post is an exaggeration to make a point. I don't really hate opera. There are a couple of operas - notably Monteverdi's Incoranazione di Poppea and Purcell's Dido & Aeneas - that I quite like. But what I do find truly sickening is the reverence with which opera is treated, as if it were some particularly great art form. Nowhere was this more obvious than in ITV's 2010 gut-wrenchingly awful series Pop Star to Opera Star , where the likes of Alan Tichmarsh treated the real opera singers as if they were fragile pieces on Antiques Roadshow, and the music as if it were a gift of the gods. In my opinion - and I know not everyone agrees - opera is: Mediocre music Melodramatic plots Amateurishly hammy acting A forced and unpleasant singing style Ridiculously over-supported by public funds I won't even bother to go into any detail on the plots and the acting - this is just self-evident. But the other aspects need some exp

Is 5x3 the same as 3x5?

The Internet has gone mildly bonkers over a child in America who was marked down in a test because when asked to work out 5x3 by repeated addition he/she used 5+5+5 instead of 3+3+3+3+3. Those who support the teacher say that 5x3 means 'five lots of 3' where the complainants say that 'times' is commutative (reversible) so the distinction is meaningless as 5x3 and 3x5 are indistinguishable. It's certainly true that not all mathematical operations are commutative. I think we are all comfortable that 5-3 is not the same as 3-5. However. This not true of multiplication (of numbers). And so if there is to be any distinction, it has to be in the use of English to interpret the 'x' sign. Unfortunately, even here there is no logical way of coming up with a definitive answer. I suspect most primary school teachers would expands 'times' as 'lots of' as mentioned above. So we get 5 x 3 as '5 lots of 3'. Unfortunately that only wor

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I freely admit that chess, for those who enjoy it, is a wonderful game, but I honestly believe that as a game , backgammon is better (and this isn't just because I'm a lot better at playing backgammon than chess). Having relatively recently written a book on game theory, I have given quite a lot of thought to the nature of games, and from that I'd say that chess has two significant weaknesses compared with backgammon. One is the lack of randomness. Because backgammon includes the roll of the dice, it introduces a random factor into the play. Of course, a game that is totally random provides very little enjoyment. Tossing a coin isn't at all entertaining. But the clever thing about backgammon is that the randomness is contributory without dominating - there is still plenty of room for skill (apart from very flukey dice throws, I can always be beaten by a really good backgammon player), but the introduction of a random factor makes it more life-like, with more of a sense

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