Doomsday Thereom

[eldynamite]

[ 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]

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]

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]

[ 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 [img]/images/graemlins/blush.gif[/img]

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]

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]

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]

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