Last Night's Television: Vampires: Why They Bite, BBC3
Horizon, BBC2

My relationship with Horizon has been a bit rocky of late. We were pretty much inseparable back in the Eighties, but recently it's been nothing but bickering and rows. I've often thought about cutting my losses entirely and going for a clean break, perhaps even dating other science strands less obsessed with cosmetics and celebrities. The only problem is that there aren't any out there, and certainly none that can match the memories I have with Horizon. Also, every now and then, something clicks and I remember what made me fall in love in the first place. It happened last night, with Stephen Cooter's "To Infinity and Beyond", a dizzyingly enjoyably attempt to net the ineffable. It won't, I think, have been one for the real puritans, those for whom a Seventies Open University physics module remains the apogee of science broadcasting. But I thought it was close to exemplary in its quiet wit and patience and relish for paradox.

It had one following wind. Infinity is a concept so simple that a four-year-old can grasp the basics and yet so complex and challenging that it has driven geniuses mad. And nobody is immune to the vertigo of a limitless sequence. So it made a lovely sense to begin with primary-school children counting upwards and segue by steps into advanced mathematicians doing the same thing. The children did the little numbers and the mathematicians did the big ones: "Googolplex-plex-plex five, googolplex-plex-plex-plex six," intoned one, making it plain that things get pretty tedious in the upper reaches. And there some dazzlingly large numbers out there. A googolplex, incidentally, is 10 to the power of googol, which is itself a one followed by 100 zeros, a number larger than all the atoms in the universe. And both of those are dwarfed by Graham's number, formulated (or discovered, if you can discover a number) by Ron Graham, wonderfully introduced here as a "former circus performer and mathematician". Graham's number is so big that nobody knows what it is, though after a lot of work with a pencil, Ron was able to assure us that its last digit is seven.

A five-year-old child can think of a number bigger than Graham's number, of course. Just add one. The problem being that infinity does very odd things when you think about it rationally like that. So much so that some mathematicians get nauseous. Another merit of Cooter's film was that it put dissidence about these ideas right at its centre, in this case in the shape of a Professor Doron Zeilberger, who thinks that numbers are finite and that you would eventually reach a point when you'd add one and get back to zero again. "If you think that this is ridiculous look at the alternative," he said, sensing a mental flinch from his interviewer. The same split – between supporters of infinity and supporters of the finite – turned out to be replicated in cosmology, though by then we were deep into complexities of multiple worlds and cosmic doppelgängers.

I wasn't always convinced that the film needed Steven Berkoff to add numinous enigma to it, looming out of the dark now and then like an furious boiled egg. But even his little vignettes strengthened the sense of the thing as a magus's tale, its gothic speculations pinned down by the slightly eerie matter of factness of the professors and theoreticians and their pleasure in cosmic flippancy. "I think the universe is infinite on Mondays, Wednesdays and Fridays," one said, "and I think it's finite the rest of the week. I'm having a really hard time making my mind up." By the time it had finished – and we had calculated precisely how unlikely it was that a monkey would type the works of Shakespeare (same odds as one person winning the lottery every week for 29,000 years and infinity makes it a dead cert) – my head was aching. But it was a good ache, as though someone had tried to jam the universe in there. Mostly Horizon drives me up the wall, but programmes like this make it difficult to think of divorce just yet.

I don't understand, given the existence of such real-world enigmas, why anyone could get worked up by synthetic mysteries such as vampires, but I know a lot of people do, and in Vampires: Why They Bite, Lisa Hilton set out to explain the fascination. "I'm going on a journey," she told us (can someone put a wooden stake through the heart of that cliché, please?) "to find the truth behind the V-factor." Interesting enough if you're interested, I guess, but I found Hilton's advocacy of the undead counterproductive. "Like most teenagers, I desperately wanted to be cool," she confessed, explaining an adolescent interest in the pallid goths that were the prevailing type of vampire in the Eighties. That's the problem, I thought. Vampires are just eternal teenagers, self-absorbed and moody and liable to bite those they love. Why bother with the fictional version?

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