Saturday, June 24, 2006

Posing the 100 Year Question: The Mathematical Answer

Brandon Carter.This image is licensed under the Creative Commons Attribution ShareAlike License v. 1.0:
It's possible to argue, mathematically, that there is a 95% chance of mankind's extinction within 9120 years. This calculation is derived from the Carter Prediction.

I first came across the "Carter Prediction" in Stephen's Baxter's SF novel "Manifold: Time". It's a real proposition by a real eminent physicist, Brandon Carter.

Wikipedia calls it the Doomsday Argument, and I recommend you to read their article on this.

So what is this prediction? It's about how many humans will ever be born. Suppose you are shown a magic records office which contains a special birth certificate for every human that will ever be born, either in the past, the present or the future. The certificates are all numbered, starting at 1. There's been about 40 billion people born so far. If we die out in the next century, the total that will ever be born is about 46 billion. However, if we go on to exist as a species for a million years, the total number could be 50000 billion or more.

Suppose you ask for one of the birth certificates, completely at random. Suppose the certificate you are given is number 41 billion. - that is - it belongs to somebody alive now. So what's more likely - that there are 46 billion certificates in there- or 50000 billion or more? It's much more likely that there are only 46 billion or so.

Now, let's think about people instead of birth certificates . You are about the 41st billion person born. If mankind was going to last one million years, it's amazingly unlikely , isn't it, that you were one of the first 0.008 percent to be born.

This argument, to say the least, is disputed. I don't believe it myself - because if the "first" human had considered it, he or she would have deduced that the total number of humans to be born would be about 5, and that the species would die out in a generation.

However, despite attempts to shoot it down , the Carter Prediction still has it's supporters. Maybe the mathematical answer to the 100 year questiion is "Yes, humanity will survive, but statistically the odd are against us lasting much longer".

Ah well, I'll be getting to the politics side of this soon...


Cllr David Morton said...

Just to say i been reading your "100 years" posts and have really enjoyed them and the links as well. Very thought provoking.

Trevor said...

The maths may be OK Chris but I'm a bit skeptical on the useflulness of this approach. We could probably spend the rest of our lives trying to define 'human' and what is truly 'random'. May I suggest another Stehen Baxter book "Evolution" as a more fruitful source of speculation - will nature abandon its experiment of 'intelligent' life and revert to other mechanisms so that life survives?

Joe Otten said...

This argument illustrates a defect in what statisticians call the "maximum likelihood estimate".

A simple but equivalent example is this. The enemy have conveniently numbered all their tanks 1,... N.

You want to know how many tanks they have, and you have seen some tanks, numbers: 4, 101, 40.

What is your estimate based on this information of how many tanks they have altogether? It turns out the maximum likelihood is 101 - just the largest number seen.

Similarly, the maximum likelihood single number estimate of the number of humans who will ever live is the number that have ever lived right now.

But there is an infinite number of possible answers, and although individually each is less likely than the lowest, there are a great many more really big numbers than relatively small numbers among the possibles. If that makes any sense.

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