Re: Doomsday Thereom
 

Try looking at N being the number of years humans will exist, and x being how many years we've existed so far. Using the same logic, you'll get seemingly contradictory results because the number of humans to have existed grows exponentially.

This whole exercise seems a lot like saying that, if you flip a coin, then look at it, you can confidently state there is a 50% chance it's heads. Because you'll be right 50% of the time. That's not really useful, though, since you could easily be right 100% of the time without using any logic at all.

Or you could say that at any given point in your life, there is a 50% chance that you won't live to twice your age. Because, if you guess that you won't live to twice your age at every point in your life, you'll be right 50% of the time. This is a useless result, though, as people who don't know how to do any aritmetic can get it right far more often than that.

Re: Doomsday Thereom
 

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the number of humans to have existed grows exponentially.

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This was exactly what I was going to point out. You are assuming linear growth of the total human population, or an even distrution of humans over time, this is severely flawed. Though it is not quite exponential over the complete history of man, it is definitely not linear.

Here's a really interesting website about population growth that can give you more accurate numbers to use:

http://www.prb.org/Content/Navigatio...ion_Growth.htm

Re: Doomsday Thereom
 

What I mean is, some things such this topic and many of Sklansky's god/religion/philosophy topics don't accomplish anything. If you are going to think, then select a topic that would benefit from a solution.

Your position in the world birth order, whether a meteor will wreak havoc in the near future, whether god can create some ridiculous number, etc don't bebnfit anyone. The authors of topics such as those should just read a good book instead.

Re: Doomsday Thereom
 

I don't think you can bring time into it since more people are born in some years than in others, as in it is not equal chance we were brought into this world when there was a birthrate of 10,000 people per day as there are with a rate of 100,000 people per day.

I reckon there is an equal chance of being any number though.

I think your right about the 50%, I should have used 95% for my examples, much more meaningfull, but either way my end result was 7%.

Re: Doomsday Thereom
 

I assumed now such distribution of humans over time. However I did asume a future growth rate in my calculation of 7%, and I assumed exponential growth.

Re: Doomsday Thereom
 

Doesn't benifit anyone eh? I think similarly to Sklansky here, that being able to think logically is very benificial for you throughout your enitre life, and if you view this as an excersise (as in learning to think logically) then it is beneficial, it accomplishes something.

But what do you mean by benificial anyway? We are all going to die. The entire human race will become extinct eventually. So who cares if you build a nice bridge or whatever?

Actually I can only be sure the human race will become extinct eventually if the Universe is finite with the second law of thermodynamics, and even if the Universe is infinite it is debatable.

So you tell me exactly what beneficial means.

Re: Doomsday Thereom
 

Well after a bit of thinking I think I am right and you are right (except for that last conclusion), I reckon once the guy picks 3 out of a hat, he can then correctly state:

SUM over i of P(3 given N=i)*P(N=i) from i =1 to 6 is equal to

SUM over i of P(3 given N=i)*P(N=i) from i =7 to infinity

As in he can put restrictions on the probability distribution of N just from knowing that x=3.

I reckon my theory(well it's not 'my' theory) predicts this result. My theory predicts a probability density distribution of the last person being born as {0 if y<x, x/y^2 if y>x} where y is number of number of total people. Besides the problem with continous and descreteness, I think this pretty much says that there is a x/y^2 chance that N=y, as in P(N=i)=x/i^2.

I got this from the culmulative probabity function of {0 if y<x, 1-x/y if y>x) where y is total people. This function saying that there is a 1-x/y chance that The last person born will be assigned a number less than y.

So anyway, P(N=i)=x/i^2 and P(3 given N=i)={1/i for i>=3 , 0 for i<3}

When I calulate both sums for large N, the first one is 3 times the second one and I'm not sure why. This is true for discrete or continuous calulations (for the discrete sum I think you need the Reiman Zeta function or something) I've made a mistake somewhere along the line, I'm not sure if it's a logical or mathematical mistake, I'll check it all over when I have some time.

Re: Doomsday Thereom
 

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I don't think you can bring time into it since more people are born in some years than in others

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I wasn't "bringing time into it", I was making a completely different argument using the same logic to obtain a different conclusion. That argument had nothing to do with how many people are born, just with how many years humans exist. If -you- are a random person in the order of humans born, why isn't -this year- a random year in the existence of humankind?

Re: Doomsday Thereom
 

Because we aren't born throughout time randomly. This year is not a random year through which to view the problem. There are more people alive this year to pick this year as their 'random year' then any other year in the past.

Re: Doomsday Thereom
 

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The end of the world is 2012.

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Someone's been reading a little Terrence McKenna "Timewave Zero Theory" ... no?