Monday, September 18, 2006

Reproof By Induction

A letter arrives from a neighbour asking if we are interested in clubbing together to buy the freehold of our block of flats. This sounds like a good idea, as the lease is about to fall below 80 years. In fact, the more I think about it, the more worthless leasehold properties appear. I try to explain it to my girlfriend.

“A lease of zero years is worthless, right?” I posit.


“And no one would buy a property with a lease of just one year, because in a year’s time it would be worthless, right?”


“So no one would buy a property with a lease of two years, because we’ve just said that a property with a lease of one year is worthless, so even a property with a lease of two years is only a year away from being worthless. Which we’ve just said is worthless.”

“Er, right.”

“So therefore, by induction, all leasehold properties are worthless, regardless of the length of the lease”, I say, triumphantly.

“What’s induction?”

“It’s a method of mathematical proof. Think of it like dominoes”, I explain. “You prove that you can knock the first one down, then you prove that any domino will knock the next one down. Therefore, by deductive reasoning, you’ve proved that you can knock all of them down – ie that the formula is correct for all natural numbers. So it proves that people are idiots for buying leasehold properties.”

“So why did you buy this place?”

“Well, I hadn’t yet formulated this exciting, er, formula. I suppose that people quite happily put logic aside when they’re dealing with timespans of decades. They just assume that they’ll find somebody to sell the hot potato on to. So long as nobody questions the ultimate value of it, the system works.”

“Or you can just extend the lease.”

“Yes”, I concede.

“Or buy a share of the freehold.”

“Yes. I suppose.”

She returns to the book she is reading. It doesn’t look like a very interesting book, and I don’t know why she prefers its made-up stories about people who never existed to discussing the truth of mathematics with me, her boyfriend, who does exist.

A thought occurs to me. A thought that is both brilliant and terrifying.

“In fact”, I continue, “It’s like life.”

She puts the book down, wearily, and gives me her full attention.

“When you get to the last year of life, you’re not going to achieve anything worthwhile in the next 12 months, because whatever you do, you’re about to die anyway. So the last year of your life is pointless. So therefore the penultimate year of your life is pointless as you’ve still only got 12 months to go until a point that we’ve just said is pointless. And therefore every year before that is pointless. And yet we run around like idiots when we’re young trying to achieve things, thinking that these things are worthwhile. And you can’t extend the lease of life. Or buy a share of the freehold.”

I am inordinately pleased with myself. I have just proved, by mathematical induction, that life is pointless.

My girlfriend looks at me, discomfited. I am not sure whether she is contemplating the futility of her existence, or just the futility of her existence with me.