To infinity and beyond

I occasionally discuss books here, and one or two people have asked me to put something about one of my own - so this is a brief dip into Infinity, one of my favourites, with a free sample of the actual thing thrown in.

We human beings have difficulty with infinity. Philosophers and mathematicians have gone mad contemplating its complexity - and yet it is a concept that is routinely used by schoolchildren. In looking at infinity, I explored the borderland between the extremely large and the ultimate, from Archimedes counting the grains of sand that would fill the universe to the possibilities of a physical reality for the infinite.

What delighted me when writing the book is that the history of infinity was a surprisingly human subject. Whether it was St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicize his vision of transfinite numbers, infinity's fascination was as much with the characters involved as the maths they were wrestling with.

Perhaps best of all, infinity is full of paradox. One of my favourite paradoxes of infinity, covered in the book, is a simple mathematical structure called Gabriel's Horn. It has the bizarre property of having a finite volume, but an infinite surface area. You can fill the whole thing up with just pi units of paint... but you can never finish painting the outside.

I've uploaded the first two chapters of the book so you can read it for free. Or if you'd like to read more you can find the book at Amazon.co.uk and at Amazon.com.

Comments

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

Why backgammon is a better game than chess

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

Search This Blog