PDA

View Full Version : Doomsday Thereom


jimdmcevoy
10-24-2004, 04:49 PM
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.

A_C_Slater
10-24-2004, 09:03 PM
Maybe you can help answer my doomsday meteor question. I
however, cannot help you. No one can. We're all doomed!

DOOMED!

Mike Haven
10-24-2004, 10:01 PM
OK.

I'll bite.

It's "theorem".

Piers
10-25-2004, 12:12 PM
[ 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.

jimdmcevoy
10-26-2004, 12:28 AM
"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.

BruceZ
10-26-2004, 12:51 AM
[ 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 (http://www.iespell.com) That will put a spell checker right in your browser, assuming you use Internet Explorer. It works great.

Piers
10-26-2004, 01:29 AM
[ 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 *

jimdmcevoy
10-26-2004, 02:04 AM
cool

jimdmcevoy
10-26-2004, 02:09 AM
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.

Mason Malmuth
10-26-2004, 04:36 AM
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

aces961
10-26-2004, 10:58 AM
Well your logic is equivilent to the following. X is a uniform random variable on (0,1). A specific value of X, call it a, is chosen. a happens to be .25. Since a was .25 there is a 50 percent chance that a uniform random variable chosen on (0, 1) will be greater than .25.

jimdmcevoy
10-26-2004, 12:07 PM
Yeah I think so, from the perspective of the person who recieved a that is. He doesn't know that he recieved a random number between 0 and 1, he just knows he recieved a random number between 0 and a number greater than or equal to .25

aces961
10-26-2004, 01:42 PM
[ QUOTE ]
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.

[/ QUOTE ]


This last line is not necessarily correct unless you know the probality that N equals any given number. Thus in your original problem you are assuming the distribution of N to be something specific already, so any conclusions you make are based on themselves.

jimdmcevoy
10-26-2004, 04:42 PM
I reckon the last stametment is necessarily correct. I don't see why you need to know the probability that N equals any given number, I think that once you know the probability that N equals a given number then the theory has to be changed.

Put another way, suppose you chose N to be whatever. If you put a person in all possible situations (put him in N situations where you give him the number 1, then another situation where you give him 2, etc.) And then in each situation ask what he thinks N is greater than 70% of the time, he will state a number and 70% of the time he will be right. So no matter what you choose N to be this will be true. This won't change if you choose N=6 60% of the time and N=1,000,000 40% of the time or whatever distribution.

I'm not sure I have made any sense here, so if you don't follow I will work out that last example.

N=6 60% of the time
N=1,000,000 the other 40% of the time

so if you give a person a number with this system, there is a 10.00004 % chance he will get 1,2,3,4,5, or 6 and a .00004% chance he will get a 7,8,9....1,000,000

Then you ask him, "There is a 70% chance N is greater than what?"

If he is given the number 1, 2, 3, or 4 he will say a number less than 6 and his 70% guess will be right. This will happen 40.00016% of the time.

If he is given the number 5 or 6, his guess will only be right if N=1,000,000, this will happen .00008% of the time.

If he is given the number 7,8,9...700,000 his guess will be right, this will happen 27.99972% of the time.

So over all his guess will be right 68.0014% of the time. This is not exactly 70% because I have not taken into account that N has to be an integer, but this effect is negligable if N is large anyway.

So what I'm trying to say is given any distribution if he says "I think N>(whatever) and I am x% sure" he will be right x% of the time. Now, if he knows the distribution of N, he can make even more accurate guesses, but I don't want to make any more guesses or asumptions.

aces961
10-26-2004, 05:33 PM
When you added these probabilities up to get 68 this was for all values he picked out of the hat. The application you are using in the doomsday scenario is only 1 specific value. When you make the statement if he picks 3 out of the hat there is a 50 percent chance that N<6. This is stating that SUM(P(3 given N = 1 to 6)) is .5. evaluating this sum is competely depenendent on the distribution of N, so for it to be .5 you have to be assuming some distribution of N.

jimdmcevoy
10-26-2004, 06:24 PM
I'm not sure what you mean when you say

SUM(P(3 given N = 1 to 6))

aces961
10-26-2004, 06:47 PM
oops, I realized I didn't type all I meant to before, I need to sleep more, I'll clarify the notation as well.
that sentence should read.
"When you make the statement if he picks 3 out of the hat there is a 50 percent chance that N<6. This is stating that 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"


P(3 given N=i) is the probability 3 is chosen given N=i. In your example this is 1/N for n 3 or greater.

These sums being are equal are completely dependent on what the distrubution of P(N=i) is for each i. Also I changed this to <=6 but you can easily change the sums to 1 to 5 and 6 to infinity it doesn't change any of my arguement.

tek
10-26-2004, 10:56 PM
You really, really have too much time on your hands /images/graemlins/confused.gif

jimdmcevoy
10-27-2004, 12:58 AM
Very interesting remark. I actually have way too little time on my hands and I am procrastinating, but this is not why I find your remark interesting.

How better do you reckon I spend my free time? I enjoy thinking. I also enjoy mindless tv, mindless work(sometimes), mindless sex, mindless eating, mindless drug taking (alcohol and every now and again the odd joint), mindless shooting the [censored] with friends, etc. but thinking is the only thing that gives me any kind of lasting substantial satisfaction in life.

In my mind I just can't grasp how most people in this world go through life eating, sleeping, [censored], killing, and then dieing. It seems all people do their whole life if fullfill there primitave urges. Of course I may be wrong, but this is my impression of the majority of people in the world.

I can't say that thinking, fullfilling 'higher', or 'more complex' urges is any better or worse that fullfing primitive ones, but it just ain't my cup of tea, and I don't get how this is most peoples' cup of tea. What's your cup of tea?

Piz0wn0reD!!!!!!
10-27-2004, 03:09 AM
The end of the world is 2012.

reubenf
10-27-2004, 11:47 AM
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.

sexypanda
10-27-2004, 03:48 PM
[ QUOTE ]
the number of humans to have existed grows exponentially.

[/ QUOTE ]

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/NavigationMenu/PRB/Educators/Human_Population/Population_Growth/Population_Growth.htm

tek
10-27-2004, 04:19 PM
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.

jimdmcevoy
10-27-2004, 11:43 PM
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%.

jimdmcevoy
10-27-2004, 11:46 PM
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.

jimdmcevoy
10-27-2004, 11:54 PM
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.

jimdmcevoy
10-28-2004, 01:33 AM
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.

reubenf
10-28-2004, 03:33 AM
[ QUOTE ]
I don't think you can bring time into it since more people are born in some years than in others

[/ QUOTE ]

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?

jimdmcevoy
10-28-2004, 03:35 AM
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.

RiverTheNuts
10-28-2004, 06:45 AM
[ QUOTE ]
The end of the world is 2012.

[/ QUOTE ]

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

tek
10-28-2004, 10:08 AM
What if people like Edison sat around musing about the same crap you do?

Perfecting the lightbulb was beneficial. Your topic is not. Edison was able to work on inventions as an excersise (as in learning to think logically).

You say "We are all going to die. The entire human race will become extinct eventually." I agree, but does that mean we should waste our abilities in the meantime? If you answer yes, then you have proven yourself to be a fool not worthy of further consideration.

jimdmcevoy
10-28-2004, 10:16 AM
You still have not fully defined what you mean by beneficial, and why my example is not.

And I don't disagree with you about how we shouldn't waste our time in the meantime. I mentioned human extinction because I had a feeling that your definition of beneficial would not make sense in light of this, so I went ahead and said it just in case my feeling was right.

Sephus
10-29-2004, 01:31 AM
this post is just terrible. there are so many things wrong with it. when i read it i was hoping it was a joke.

[ QUOTE ]
When you think about it, if we were just as likely to be an ant as a human,

[/ QUOTE ]

what the hell? you think there's a chance that there are quintillions of souls floating around in the ether and then "zap," they become ants, aardvarks, arthropods, by random assignment? like god is picking souls "ok you trillion get to be plankton, and you over there get to be floyd johnson of plano, texas."

you don't seem to believe in god/the supernatural, yet you believe that "you" have an existence apart from your body. you couldnt have been an ant because you are YOU, and the reason you're YOU is that you were born a fricking human being! if you're not born a human, there IS no "you."

that's so [censored] stupid, it sounds like something a five-year old would wonder about, not a college student. "i wish i were born a bird."

[ QUOTE ]
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.

[/ QUOTE ]

so you're saying intelligence is proportional to combined weight of an ESSENTAILLY ARBITRARY GROUPING (the reason the concept of "insects" exists is because biologists find such a grouping useful)! dude, you know what, those insects have a ton of combined weight, but bacteria have a combined weight that is SO much greater! bacteria must be SMART. but you know who's even smarter than bacteria? plants, humans, and spotted eels! when you combine the weights of plants, humans, and spotted eels, its MUCH greater than the combined weight of either insects or bacteria, therefore THAT group has more intelligence than the others.

i'd go on, but i've wasted enough time. get a clue.

jimdmcevoy
10-29-2004, 12:54 PM
"this post is just terrible. there are so many things wrong with it. when i read it i was hoping it was a joke."

I am facinated by the way some people like to tell other people they are stupid one way or another (very common among americans). I would really like to know, what are you trying to acomplish from this? Do you really think that I'll think "Well, he called me stupid, therefore I must be." I'm sure you're aware that for most people if you call them stupid and then argue with them they are much much less likely to agree with you, and even if they do agree with you they will still argue against you out of spite. So the question remains, what's the purpose?

It reminds me of say someone going all in with pocket kings in NL holdem preflop, they get called by J9 and the J9 makes two pair and wins, the guy with pocket kings goes nuts and then berates the other guy for bad play. I just don't see the point, I for one would like those calls against me.

Anyway it is my opinion that you don't understand what I am saying, and given the tone in your post, there is zero chance that you will change your mind, so I won't even bother explaining your misunderstandings.

But I am curious as to why you posted what you did, I can see no logical reason for it(actually I can take a guess, but I want to hear what you have to say)

rdu $teve
11-01-2004, 12:39 PM
Interesting post, interesting logic. When I say interesting, I mean that you need to get some serious help, and you have far to much time on your hands, that could be used more efficiently playing poker. Im no math wiz, or anything like that, so I'll stay out of that part of it.

However, aside from religious beliefs, who is to say what will cause the end of the world. I really dont see how this can be figured mathmatically based on the number of humans, or other life forms, that have lived throughout history.

just my 2Ę


PS you forgot to include all the aliens living on other planets! What were you thinking? [/sarcasm]

Grisgra
11-01-2004, 05:24 PM
Probably someone already posted this, but just in case they haven't:

http://www.anthropic-principle.com/preprints/lit/

eldynamite
11-01-2004, 07:58 PM
[ QUOTE ]
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.


[/ QUOTE ]

In my opinion, this is where the fallacy lies. It simply isn't possible to choose a positive integer 'randomly'. You must specify a range. If the range is infinite, as is the case with positive integers, then any integer that purports to be random will be larger than a finite number of integers, and smaller than an infinite number of integers. So, the candidate 'random' integer is guaranteed to have a magnitude that is infinitesimal compared to range from which it was chosen -- an obvious contradiction.

In the Doomsday argument, it is assumed that a particular human has been chosen at random, but this is patent nonsense because we have no idea what the range is. It is even possible in principle that there will be an infinite number of human beings. (We might need to revise Big Bang theory to accommodate this, however.)

Mike Caro, the "Mad Genius of Poker", describes a paradox related to this one. See:


Mike Caro Article (http://www.poker1.com/newsmanager/templates/mculib_articles.asp?articleid=95&zoneid=6)


Tim

irchans
11-01-2004, 08:48 PM
I notice that many very smart people call each other stupid during political campaigns.

Piers
11-02-2004, 02:01 AM
[ QUOTE ]
[ QUOTE ]
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.


[/ QUOTE ]

In my opinion, this is where the fallacy lies. It simply isn't possible to choose a positive integer 'randomly'. You must specify a range.


[/ QUOTE ]

You are right about not it making much sense to choose an integer randomly without specifying a particular probability distribution.

However you are wrong about that being the fallacy in his doomsday argument.

N is the total number of humans to ever exist, which is assumed by one of the axioms to be finite. So there is no problem in choosing a random number between 1 and N.

[ QUOTE ]
It is even possible in principle that there will be an infinite number of human beings.


[/ QUOTE ]

Well of course, however we will never know. So it is OK to make ether assumption.

Apart from being presented badly there is no particular fallacy in his argument. To get his absurd conclusion he had to claim that the random number assigned to him was a specific value, 50 billion in fact. That is the problem he had no right to do this.

If N is the total number of Humans to ever exist. Choose a number between 1 and N. 90% of the time it will be between 0.1*N and N. Or to turn this on its head, if you know that a random number between 1 and N is say 72. This makes it very likely that N is less than 200 say. Certainly it would be very very unlikely to large say 2000000 billion.

In effect he said lets consider a random number between 1 and another number that I donít know but is quite big. Then he magics up the statement that this number has to be around 50 million with no further assumptions, then goes on to show that this leads to an absurd conclusion.

jimdmcevoy
11-02-2004, 09:01 AM
I actually only used 50 billion for an example, but wouldn't you say it's within an order of magnitude anyway?

I didn't discuss my "magics up" because I thought it would make my argument even more boring. If you really really want I will discuss my magics up-ing.

eldynamite
11-02-2004, 09:08 AM
[ QUOTE ]
Apart from being presented badly there is no particular fallacy in his argument. To get his absurd conclusion he had to claim that the random number assigned to him was a specific value, 50 billion in fact. That is the problem he had no right to do this.


[/ QUOTE ]

No particular fallacy? Surely, it cannot be seriously maintained that the argument is sound. Common sense should tell you that an abstract mathematical argument cannot make valid predictions about the fate of humanity.

Let's suppose that this Doomsday Argument (DA) had been advanced by somebody every hundred years since the first humans emerged perhaps a hundred thousand years ago. We cannot tell if the DA is valid today, but it has failed 999 times in a row, so by historical standards it doesn't have much going for it.

Getting back to the point that our hero has no right assign a particular number to himself (50 billion), isn't it possible in principle to determine how many people were born before you? I'm not sure why the practical difficulty in doing so has much bearing on the argument.

Let me try to explain my point a bit more clearly. I'll concede that N is almost assuredly finite, and that it is possible to choose an integer at random between 1 and N. However, asserting that 50,294,771,302 (or whatever) is a random integer is simply wrong, because there is no way to generate a number at random without knowing what N is. In the vernacular, "random" is frequently used to describe something undistinguished. Now, 50,294,771,302 looks pretty undistinguished (maybe not -- remember 1729?) but that doesn't make it random in the mathematical sense. The DA as described by jimdmcevoy is based on the assumption that one's place in the line-up of all humans is random, but since there is no way to generate a random integer between 1 and N, where N is unknown, this assumption is simply false. By assuming that 50,294,771,302 is random, he assumes something about the likely value of N. The DA is a circular argument.


Tim

jimdmcevoy
11-02-2004, 09:18 AM
Iv'e responded to most people so far, and in truth I am a little dissapointed. Anyway if you wish to post about anything relating to this theory I probably won't reply, I'm a bit too busy. If you wish to post about how I have too much time on my hands don't bother, it's aready been said. The only interesting responses I have gotten are from Aces, and when I have some time I will continue our tangent, since he has brought to my attention that somewhere I have made a mistake and am out in a calculation by a factor of 3.

I've been told how poorly I presented my argument, maybe it is poor, but thanks to Grisgra there is a link to someone else who discussed this more clearly

http://www.anthropic-principle.com/preprints/lit/

jimdmcevoy
11-02-2004, 09:22 AM
I'll let you two work this out, in my opinion each of you is right about one thing and wrong about another. I decided today to give up on this thread.

http://www.anthropic-principle.com/preprints/lit/

MortalWombatDotCom
12-04-2004, 05:52 AM
[ QUOTE ]
What if people like Edison sat around musing about the same crap you do?

Perfecting the lightbulb was beneficial. Your topic is not. Edison was able to work on inventions as an excersise (as in learning to think logically).

You say "We are all going to die. The entire human race will become extinct eventually." I agree, but does that mean we should waste our abilities in the meantime? If you answer yes, then you have proven yourself to be a fool not worthy of further consideration.

[/ QUOTE ]

That's what i thought too... then i went back, and found an error in the proof /images/graemlins/blush.gif

For those who are wondering, line 337 of the proof assumes that the cardinality of the set of smoothings of the unit circle over 4-space is smaller than that of smoothings of the unit circle over 5-space; however, both sets have cardinality Aleph_two. I can't believe i missed that the first time.

Sephus
12-04-2004, 01:51 PM
i didnt say you were stupid. i said your post was stupid. and i also said why i thought your post was stupid. if you aren't going to read my post and think "maybe he has a point" about one thing or another, that's your choice.

i posted my response because i was bored and was entertaining myself.

magic_man
12-04-2004, 05:05 PM
I don't look at this forum very often, so I just found this thread and realize that it pretty much died a month ago, but I'd like to try to explain why I think you are confused. A very very similar theorem appears in the book "Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time" by J. Richard Gott. It's a good book - find it at amazon.com. What jimdmcevoy was trying to say was the following:

The number of people to ever exist will be some finite number, N. (Looks like we all agree that this might be a reasonable assumption).

Take each person and number them from 1 to N IN THE ORDER of their birth. I think we all understand this part too.

Now, the part that's confusing some people. Call YOUR number 'x'. EVERYONE who is currently alive will have a number close to 'x', and thus x will be close to the total number of people who have been alive up to the present. Jimdmcevoy says this number is approximately 50 billion, which is probably within an order of magnitude of the correct number. Thus x ~= 50 billion.

HOWEVER: You are just as likely to have been born at any time. There is no reason that you should have been born at the present, when x = 50 billion. You could just as easily have been born when x = 10 billion. x is therefore a random variable distributed from 1 to N. You may not agree that x is distributed randomly (since there are a higher number of births when x is larger), but THIS is what the original argument was saying. He didn't "magic" anything out of thin air. All he said was "I was born randomly, at any time between the beginning of human existence and the end. As it happens, I was the 50 billionth person born. This means that there is a 50% chance that only 100 billion people will ever be born."

Again, this theorem (or a very similar one) is explained in detail at the end of the book above. In the book, Gott uses the theorem to correctly predict the dates of the fall of the Berlin wall, as well as the death of several famous people from history.

~Magic_Man

magic_man
12-04-2004, 05:12 PM
Actually, in my post above I cite a book where the author uses a very similar theorem to predict the dates of many historical events. This is not just useless mathematical banter.

~Magic_Man