Caution - deduction from infinity can lead to madness

I'm currently reading for review Max Tegmark's intriguing newish (well, new in paperback) book, Our Mathematical Universe. It's generally rather good, though it's a bit infuriating that they clearly haven't updated the text to reflect this edition, as Tegmark keeps referring to the image on the front of the book as showing the Cosmic Microwave Background - if the CMB really looks like that, cosmology truly has got exciting again.

However, that wasn't my point. Having set the stage with an explanation of the hot big bang with inflation theory, Tegmark begins launching off into the possibilities for multiverses, and there's a lot of deduction from infinity. (If this doesn't mean anything to you, I'll get there in a moment.) Georg Cantor, the great mathematician of infinity, ended up in a mental hospital - you play with this stuff at your peril.

What I mean by deduction from infinity is arguing along these lines. If eternal inflation holds, there are an infinite set of big bangs producing universes (of which ours is one). Each will be subtly different due to quantum fluctuations. So as they are infinite, every possible outcome will happen in one of these universes - for example, one where you read this blog and sneer, rather smile at its cleverness as you currently are doing. (Hopefully.)

The problem is that infinity can't be used like this to deduce things. Let's look at some simpler infinite sets to see why. First, bear in mind that every member of an infinite set does not have to be different. So, for instance, you can have the set 1, 0, 0, 0... where all the members are zero except the first. If 1 represents our universe, all the others could be devoid of life. (I do remember those quantum fluctuations, but that doesn't mean that you couldn't end up with all but one devoid of life.)

Here's another one that's a little more interesting: 1, 4, 9, 16... - the infinite set of the squares. One for every universe that has life in it. But what if the actual infinite set of universes only corresponded to the numbers that aren't squares with a different value to its square root: 1, 2, 3, 5, 6, 7, 8... - there's an infinite set of those, none of which has life, apart from no 1 - us.

Or again, think of the infinite set of positive integers: 1, 2, 3, 4, 5, 6... If one of these could be part of an infinite set but also demonstrably unique, that could like the condition for life. And guess what - 1 is unique. It's the only positive integer that is its own square and that when something else is multiplied by it, that something else doesn't change. So despite there being an infinite set of subtly varying possibilities only one is in the 'life' state.

My examples here don't prove that there aren't all those different variations of you in parallel universes, but rather they demonstrate that you can establish pretty well anything you like if you try to deduce things from an infinite set - and my suspicion is that the deductions made by cosmologists are equally suspect.

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...

Murder by Candlelight - Ed. Cecily Gayford ***

Nothing seems to suit Christmas reading better than either ghost stories or Christmas-set novels. For some this means a fluffy romance in the snow, but for those of us with darker preferences, it's hard to beat a good Christmas murder. An annual event for me over the last few years has been getting the excellent series of classic murderous Christmas short stories pulled together by Cecily Gayford, starting with the 2016 Murder under the Christmas Tree . This featured seasonal output from the likes of Margery Allingham, Arthur Conan Doyle, Ellis Peters and Dorothy L. Sayers, laced with a few more modern authors such as Ian Rankin and Val McDermid, in some shiny Christmassy twisty tales. I actually thought while purchasing this year's addition 'Surely she is going to run out of classic stories soon' - and sadly, to a degree, Gayford has. The first half of Murder by Candlelight is up to the usual standard with some good seasonal tales from the likes of Catherine Aird, Car...

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...

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