Wednesday 13 August 2014

Examining the birthday paradox

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Last weekend I had a birthday. One of my granddaughters celebrates her birthday on the same day.

Eleanor was fourteen, and I was %#*. My word processor has a direct link to the privacy commission and never discloses information that should not be widely disseminated among the general public. Though to be fair if my father hadn’t been so shy and retiring I’d be two years older than I am now. I’ll give you clue though. About the time I was born Winston Churchill was heard to say: “This is our finest hour” and mum and dad thought he was talking about me!

I refuse to admit I’m as ancient as I am, even though it could tend to make my children appear illegitimate. It’s a sobering thought however that when Mozart was my age he’d been dead for nearly forty years. It is now getting to the stage where a fireman may have to be in attendance when I light my birthday candles.

Suffice it to say I still have most of my hair and none of it has yet turned grey so I may be younger than you think. Despite this, every morning I get up and read the obituary column in the Dominion-Post and if I’m not in it, I shave.

If only I’d known how old I was going to get I would have taken better care of myself.

Now you may think that the chances of my granddaughter having her birthday on the same day as me stretches the bounds of common concurrence, but apparently this is not necessarily so.

Assuming for a moment that birthdays are evenly distributed throughout the year, if you’re sitting in a room with 23 people in it, what are the chances do you think of two of those people having a birthday on the same day?

Ignoring leap years, a reasonably intelligent person might conclude that the odds probably wouldn’t reach a 100 percent unless there are 366 people in the room. Such a person might therefore conclude that the likelihood of two people having a birthday among the 23 would be less than say 5 per cent. In reality, due to the convoluted reasoning behind mathematics, the odds are about 50 per cent according to numerical expert Allan Bellows. This phenomenon is apparently known as the Birthday Paradox.

If the set of people is increased to 60 the odds climb to above 90 per cent. This inconsistency can be offset somewhat because birthdays are not distributed perfectly throughout the year. Most people are born in the springtime, and also, due to the way hospitals operate, more babies are born on Mondays and Tuesdays than on weekends.

So Eleanor and I having the same birthdate is not so paradoxical at all.

So since her coincidental birth I have had to celebrate my birthdays at her parties and I always tried to be one of the gang. I resisted joining them on the trampoline, they tended to ran around the house faster than I could, there were no places big enough for me to secrete myself when it came to playing hide and seek and I always seemed to end up being the donkey they wanted to pin that tail on.


Their music was not really to my taste and I could never fathom how The Wiggles had made such an impact on the young.

We’d sit down to cheerio’s, chippies, crust-less bread and butter adorned with hundreds and thousands, chocolate cake and finally jelly and ice cream. I’d gratefully wash all this down with raspberry cordial and then I’d be ready for bed; and it would only be about four o’clock in the afternoon.

I’d stagger home bloated and exhausted and be eternally grateful that the final care of my delightful grandchildren was in the capable hands of people much younger than me.

Now that Eleanor is a teenager of course she is looking for much more sophisticated fare, amusement and friends. I suspect - though she is far too generous to let on - that grandfathers are becoming a bit of an embarrassment.

Meanwhile I’m actually looking forward to jelly and ice cream.

Yet despite the age boldly emblazoned on the birthday cards that adorn our mantelpiece you don’t feel any older than you did twenty or even thirty years ago. Frustratingly you’re the same person in an aging outer casing; glasses and hearing aids notwithstanding.

I said to my wife, “I don’t look seventy do I?”

“No,” she said, “But you did when you were.”

I don’t know whether to ignore the remark or nominate her for a comedy spot at King Street Live.

“A geriatric is a German cricketer who captures three successive wickets.” - George Coote

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