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I have taken the liberty of a major rewrite to the page. I think I've presented the basic argument in the most straight-forward way possible. A more formal version of the argument would have to be made using a bit of Bayesian analysis. I've taken the current cumulative human population to be 50 billion which is a compromise between Gott's 70 billion and the previous page's 20 billion figure. If people really don't think my version of the argument is any good then of course they're free to discard it (and replace it with a previous version if they want).
User:John Eastmond 4 Oct 2004
Taken out Singularity section
The only two things Heinz von Foerster's argument has in common with Brandon Carter's Doomsday Argument are the words "Doomsday" and "Population" and nothing else. The Doomsday Argument is a probabilistic argument based on cumulative population whereas von Foerster's argument is based on an extrapolation of a particular model of population growth.
User:John Eastmond 30 Nov 2004
The Onion extrapolated the survival of human culture a couple of years ago. They calculated that the earliest date pop-culture is nostalgic about is 9.5 years ago, and that every passing year reduces that by about 4 months, so that the "world will run out of past" circa 2030. The Onion's 'singularity' is probably a lot more credible than von Foerster's, and a better comparison to the probabilistic DA. My comments in the next section (on grouping the von Foerster singularity with this in a category) were meant as a reply to John Eastmond's point here. Wragge 00:56, 2005 Apr 29 (UTC)
Special Relativity and the Reference Problem
I've been thinking of putting the following paragraph in but I'm not sure about it. I'd be interested in any comments about it:-
There has always been the problem of which observers to include in the definition of "humans": the so-called Reference problem. Should we include just homo sapiens or should our definition include all "intelligent" observers together with any artificial intelligences we might create in the future?
Actually there is a more fundamental constraint on the definition of the class of observers arising from considerations of Special Relativity. The Doomsday argument asks us to consider our position within the chronologically ordered list of all human births. However the set of human births comprise a set of distinct "events" in spacetime. The order of these events along a "timeline" actually depends on the velocity of a particular observer's frame of reference. Thus different observers will have conflicting ideas about the chronological order of the birth events.
Perhaps the Doomsday argument can only be pursued in terms of the lifetime of the individual observer whose physical states form one continuous worldline of events. Such a worldline does have an invariant "proper" time associated with it. As each event is causally connected to the next in a chain of events there is no ambiguity about their chronological order.
Thus it seems that the only reference class that can be used is the set of days (say) that comprise the lifetime of the individual. When we wake in the morning our experience of "today" selects it from the set of N days that will comprise our life. As each morning awakening is equivalent to any other (apart from arbitrary details) then each day has the same prior probability. Thus the prior probability of "today" is always 1/N. One thus deduces that N must be finite in order that the prior probability of today is non-zero. Have we proved that an individual's immortality is impossible? :)
User:John Eastmond 20 Jan 2005
Well maybe. Assuming that the argument is correct, N cannot be infinite but it can still be boundless (in the sense that whichever finite value you choose for N, I can choose a bigger one and we can repeat the process without limit). You might say that the argument would allow us to rule out the possibility of immortality but not the possibility of living forever, one day at a time. If that makes sense, <grin>. -- Derek Ross | Talk 15:43, 2005 Jan 20 (UTC)
What do you think about the special relativity objection to applying the argument to the human race? Apparently a set of birth events in spacetime can only be said to have a time-order if it is possible in principle to send a slower-than-light signal from each event to the next. But this is an unnatural constraint which need not be realised at all. One could imagine the human race colonizing the galaxy. It could easily be the case that a birth event on one side of the galaxy cannot be linked by a slower-than-light signal to a birth event on the other side of the galaxy (in other words each is outside the "light-cone" of the other). If the Doomsday argument is applicable to populations of observers then surely it should be applicable to all populations regardless of the spacetime positions of the individuals' birth events? The fact that it isn't seems to show that it can only be applied to an individual's set of life-events (that are naturally causally connected and thus time-ordered).
User:John Eastmond 21 Jan 2005
- I'll need to think about that, John. However note that this sounds suspiciously like original research and may therefore be irrelevant to this Wikipedia article. -- Derek Ross | Talk 05:46, 2005 Jan 24 (UTC)
You're right - these are original ideas and therefore should be published elsewhere.
User:John Eastmond 2 Feb 2005
New "Other Versions" sub-section
Henrygb suggested that I make the choice of sampling variable point more explicit, so I've added a new sub-section: "Sampling from observer-moments" under "Other Versions" that details an alternative f distribution, by a uniform sampling over (life-span * n). This includes the earlier reference I made to Bertrand's paradox (probability), but I now directly link to the definition.
Unfortunately, some of the Anthropic subjects I refer to in this section aren't defined yet as Wikipedia pages. Rather than make red links I've added cross-references to discussions of these topics in other articles. Is this better style than adding red-links if those red-links already exist (on Anthropic bias)?
I am concerned that this section might be too long, but I wanted to give a full description of this argument. Is it too wordy, or still not explicit enough?
I added the sub-section to "Other Versions" partly because that only had a single subsection. Is this the appropriate place?
Anyway, it should act as a stub for extension of the function-form side of the definition. Talk:Doomsday_argument#Why_is_N.3D.23_of_humans.3F relates to this.
Wragge 18:40, 2005 Apr 8 (UTC)
Exactly, it is not a hoax, but its name and the way of its presentation are very unfortunate, especially the calculation of the doomsday date. The fact that we have lived here for 3 billions years (counting whole evolutionary line from microbes) does not mean that we have a recipe for survival for another 3 billions years, which is counterintuitive. In real world, if a stone has been lying somwhere for 10 years, we can infer that the stone is in a stable place and expect it to lie there another 10 years in our reality. But in case of unique stuff, such as physical constants or existence of our race for time T in past, anthropic principle says that we do not know which alternative reality we are in, apart from the trivial fact that it is one of those we that has allowed our existence for certain time. The method of multiplying 60 billion by a constant, such as 2, to get expectation of total number of human beings assumes that alternative realities are "normal" in some way, e.g. they do not usually have half life of 1 second until totally blowing up.
the main point of the argument is NOT that the human species may become extinct. (section Numerical estimate of Doomsday9
Hello, in the "Numerical estimate of Doomsday" (the first section), it says:
"N is the total number of humans who will ever be born"
and at the end of the section, it says:
"The argument predicts, with 95% "confidence", that humanity will disappear within 9120 years. Depending on the projection of world population in the forthcoming centuries, estimates may vary, but the main point of the argument is that the human species may become extinct."
However, the main point of the argument cannot be that the human species will become extinct, because this has been assumed at the beginning ("N is the total number of humans who will ever be born"). The main point of this particular section is the actual numerical estimate, I think.