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Old 10-24-2004, 04:49 PM
jimdmcevoy jimdmcevoy is offline
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Default Doomsday Thereom

I have been studying physics and maths at university for four years and I am not sure I have spelled 'thereom' correctly, oh dear. Please don't hold it agaisnt me if it is wrong.

Anyway, this is an interesting thereom I read about one day and thought a little more about it, first off I'll give you some assumptions, if you don't like these assumptions please don't argue them on this thread, another thread another time.

1. There is a finite number of humans ever to live in this Universe. Call this number N.

2. If you give each human to ever exist a number from 1 to N in order of when they were born, the number we and every one else has recieved (around 50 billion for us I am guessing) was random, it could have just as easily been 1 or N or 50 or 51 etc.

Please note this does not necessarily depend on whether or not you believe in god, so please don't bring god into it unless you think you really have to.

Okay, so I did a quick search one day and guestimated my number, which should be relativly close to everyone else's number who is currently alive, is about 50 billion. I am 95% certain that I am no more than an order of magnitude off with this (As in N<500 billion).

But for now lets just call my number x.

Now, given that x (me) has an equal chance to be any integer between and including 1 and N, it is just as likely that x<N/2 than x>N/2. As in it is just as likely I am in the first half of all people then in the second half. This can be genaralised as there is a probablity p that x<N*p. Convince yourself this is true with a few examples if need be before you go on.

Now, if there is a probability p that x<N*p, then there is a probability p that N>x/p. This implies there is a probability 1-p that N<x/p, which with further algebra implies there is a probability p that N<x/(1-p).

Now this is interesting, try plugging in a specific p, say .5

There is a 50% probability N<x/(.5)

And if x=50 billion then there is a 50% probability that N<100 billion.

Anyone scared yet?

I actually figured out my best estimate of being alive when the last person to ever be born would be born, as in the person assigned the number N. Some could interpret this as the end of the world, as what else would cause humans to stop having kids? (Certainly people will always be trying to have sex)

Anyway I looked up the statistics of the death rates of a normal male like myself from 22 years old onwards, I guessed how many people will be born over the next 80 years (I actually estimated an infinite number of ways the population will grow and weighted them to what I thought was reasonable), and then using the previously derived equation and some maths that most people would find boring I think I got the figure of 7%.

7% chance I will be alive when the last person to ever be born will be born.

That's low but not that low, after all, we've all seen AK beat AA all in preflop haven't we? Well I have anyway.

Should I re-evaluate my 7% if someone rigged a computer up to nuclear bombs place evenly all over Earth, and using a decent random number generater the Computer executed a program where 95% of the time it will blow up the world?

I would, but others argue maybe it is still 7%.

Another interesting thought, suppose you are Adam (you know, Adam and Eve) and you are number 1 and Eve is number 2, and this was before you had any children. Suppose Adam is hunting one day and is lazy. Suppose he thinks "I am going to sit on this rock, and I will wait for a wounded deer to walk right in front of me, if this happens I will have many children with Eve, if this doesn't I will not have any children." Will this change the possibility of a wounded deer walking near Adam?

I don't think so, but I'd like to hear what other people think about this.

Now there are actually a few problems here, which in my opinion only make the theory more interesting.

I said N is the number of humans to ever to be born, what do I mean by humans? For those who believe in evolution (I would bet heavily on it) where along the line is the 'first' human? Does a smart chimpanzee not count while a less intelligent human count?

When is the human officially born? From conception, or at what stage through pregnancy or at what age, or when? Does it happen in an instant (Is someone assigned their number instantly) or is this continuous?

Is everyone weighted equally? I don't know how to communicate my thoughts on this one, if half of all humans were very simple and dumb and not even self aware and the other half are smart and intelligent, are you equally likely to be a smart or dumb person?

When you think about it, if we were just as likely to be an ant as a human, don't you think it's highly unlikely that we are the species who is the most intelligent on Earth? If you just compare the weight of all insects to the weight of all humans, I think the insects would weigh about million times more. This is a pretty wild guess, anyone out there with a more accurate number?

You can take this even further, if you think you are an extremely smart person, do you think it was chance you are much smarter than most other people to on Earth? I read somewhere that Mike Caro said there was a 30% chance he was god. I don't know if he actually thinks this or not, but if he does is his logic similar to this?

Anyways, I have actually applies this theory once in my life. I was walking to my lab one day, and wasn't allowed in because of an alarm that was triggered by who knows what. I asked around and found out the alarm had been going off for half an hour. So I thought, well if I came to the building at a random time this alarm went off, there is a 50% chance this alarm will still be on in half and hour, so I left to get a slushy at the gas station, came back, and it ended 45 minutes after I first tried to get in the building. Take that experiment for what it's worth.
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  #2  
Old 10-24-2004, 09:03 PM
A_C_Slater A_C_Slater is offline
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Default Re: Doomsday Thereom

Maybe you can help answer my doomsday meteor question. I
however, cannot help you. No one can. We're all doomed!

DOOMED!
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  #3  
Old 10-24-2004, 10:01 PM
Mike Haven Mike Haven is offline
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Default Re: Doomsday Thereom

OK.

I'll bite.

It's "theorem".
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  #4  
Old 10-25-2004, 12:12 PM
Piers Piers is offline
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Default Re: Doomsday Thereom

[ QUOTE ]
I am not sure I have spelled 'thereom' correctly, oh dear. Please don't hold it agaisnt me if it is wrong. I am not sure I have spelled 'thereom' correctly, oh dear. Please don't hold it agaisnt me if it is wrong.

[/ QUOTE ]

I know what you mean, when I was writing my Maths Phd, I never could spell theorem right and had to always correct with a spelling checker afterwards. 2+2 really should incorporate a spelling checker into the forum to help people like us. Alternately you could get hold of a word processor with a spelling checker in (should not be too expensive) and write your posts there before copying them into a 2+2 post, thatís what I do anyway. Hope Iíve helped.

[ QUOTE ]
There is a 50% probability N<x/(.5)

[/ QUOTE ]

This is obvious if you think about it.

[ QUOTE ]
And if x=50 billion then there is a 50% probability that N<100 billion.

[/ QUOTE ]

Yes, of course thatís true. Its also just as true that if x=7 then there is a 50% probability that N <14. Of course this is academic as there is no way you can know what your x is.

[ QUOTE ]
7% chance I will be alive when the last person to ever be born will be born.

[/ QUOTE ]

To get this conclusion you have assumed that your personally number is 50 billion. It is this assumption that produces your conlusion that the end of the human race is close. To make it clearer you have said.

[ QUOTE ]
1. There is a finite number of humans ever to live in this Universe. Call this number N.

2. If you give each human to ever exist a number from 1 to N in order of when they were born, the number we and every one else has recieved (around 50 billion for us I am guessing) was random, it could have just as easily been 1 or N or 50 or 51 etc.

3 My number is 50 million

1,2 and 3 imply 7% chance I will be alive when the last person to ever be born will be born



[/ QUOTE ]

This is perfectly reasonable. Most peopleís number will be within an order of magnitude of N. so if N=100 millioin 90% of people will have a number greater than 10 million. If N = 10000000000000 million, then 90 % of peoples number will be greater than 1000000000000 million.

As I do not believe you number is 50 million I do not think what you say is particularly relevant.

[ QUOTE ]
Another interesting thought, suppose you are Adam (you know, Adam and Eve) you are number 1 and Eve is number 2,


[/ QUOTE ]
I donít know Adam and Eve. However I will just remind you that you assumed that your 'numbers' were random not ordered.

[ QUOTE ]
Does a smart chimpanzee not count while a less intelligent human count? Ö lost of other similar stuff.


[/ QUOTE ]

You defined the axioms. You can make whatever restrictions you like, which of course will be reflected in how relevant your results are to the real world.

Why do I feel I have just wasted half an hour of my life.
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  #5  
Old 10-26-2004, 12:28 AM
jimdmcevoy jimdmcevoy is offline
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Default Re: Doomsday Thereom

"As I do not believe you number is 50 million I do not think what you say is particularly relevant."

For the record I said 50 billion, and I'm curious why don't you think I'm close on this?

"I donít know Adam and Eve. However I will just remind you that you assumed that your 'numbers' were random not ordered."

I may not have made this clear, I was trying to imagine an alternate universe where some how you know you are the only person alive, or one of two more like.
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  #6  
Old 10-26-2004, 12:51 AM
BruceZ BruceZ is offline
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Default Re: Doomsday Thereom

[ QUOTE ]
2+2 really should incorporate a spelling checker into the forum to help people like us.

[/ QUOTE ]

No they should not. The forum runs far too slowly as it is. Try www.iespell.com That will put a spell checker right in your browser, assuming you use Internet Explorer. It works great.
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  #7  
Old 10-26-2004, 01:29 AM
Piers Piers is offline
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Default Re: Doomsday Thereom

[ QUOTE ]

For the record I said 50 billion, and I'm curious why don't you think I'm close on this?

[/ QUOTE ]

I think you main confusion is here.

[ QUOTE ]

If you give each human to ever exist a number from 1 to N in order of when they were born , the number we and every one else has recieved (around 50 billion for us I am guessing) was random

[/ QUOTE ]

The numbers cannot be both random and ordered.

Your argument that ends in the ď7% chance I will be alive when the last person to ever be born will be born.Ē Assumes that the numbers are random. In particular this bit

[ QUOTE ]
Now, given that x (me) has an equal chance to be any integer between and including 1 and N,

[/ QUOTE ]

However your assumption that your number x=50 billion is based on the assumption that the numbers are ordered. If they are instead are random then there is absolutely no reason why it should be anywhere near 50 billion.

If you choose a series of random numbers between 1 and 1000, There is absolutely no reason why the 123 rd random number should be anywhere near 123.

[ QUOTE ]

I may not have made this clear, I was trying to imagine an alternate universe where some how you know you are the only person alive, or one of two more like.


[/ QUOTE ]

* bangs head against wall *
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  #8  
Old 10-26-2004, 02:04 AM
jimdmcevoy jimdmcevoy is offline
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Default Re: Doomsday Thereom

cool
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  #9  
Old 10-26-2004, 02:09 AM
jimdmcevoy jimdmcevoy is offline
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Default Re: Doomsday Thereom

Let me make a simpler analougy for this.

I get N people, give them all a number between 1 and N randomly, as in put the numbers 1 to N in a big hat and let them draw from it.

This will give each person a random number between 1 and N, and it will be ordered as you put it.

Suppose I chose N randomly to begin with.

If a person drew the number 3 from the hat, there is a 50% chance that N<6.
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  #10  
Old 10-26-2004, 04:36 AM
Mason Malmuth Mason Malmuth is offline
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Default Re: Doomsday Thereom

Hi Bruce:

My understanding is that the software did not come with a spell checker and we can't incorporate one even if we wanted to.

best wishes,
Mason
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