Doomsday Argument for Idiots

May 26, 2005 4:40 PM

Can someone explain the Doomsday Argument in a way that a math-challenged person like me can understand?

I've looked at wikipedia and several other places where this is explained, but I still can't quite get my head around it.

posted by swift to science & nature (37 answers total)

I only know what I've read on sites like the wiki. But here is a key point:

...some of the assumptions of the argument's logic [are not] acceptable; for instance, the fact that it is applied to a temporal phenomenon (how long something last) means that N's distribution simultaneously represents an "aleatory probability" (as a future event), and an "epistemic probability" (as a decided value about which we are uncertain).

In other words, it's a bunch of mathematical speculation based on dubious assumptions. I think it is just as likely that we are at the 0.05 mark of humanity as we are at the 0.95 mark. They assume there will be 60 billion humans, but there could be 600 million. It's a bunch of mathematical B.S.
posted by Doohickie at 5:31 PM on May 26, 2005

Oops.... I messed up some of my numbers, but even so, the point is that it's mathematical B.S.
posted by Doohickie at 5:36 PM on May 26, 2005

Let me try:

Let's assume you enter a lottery and each lottery ticket has a number. You know *nothing* about the lottery: it could be an office lottery or a state lottery.

You look at your lottery ticket and it says "#5". Now, given that much information and nothing else, would you say its more likely the total number of lottery tickets is closer to 80 or to 8 million?

Ok, now...when you were born you were essentially given a lottery ticket. You are the 100th billion person on the planet, ever. So, given that, and nothing else. what is more likely, that we will top out at a trillion people and then die off or that we will continue forever, going into other universes, expanding to become a population of googols and googols of people. If the latter, isnt it kind of wierd that you happened to get ticket #5?? The more likely assumptions is: we will all die off soon.

Thats the best I can explain it. And there are all sorts of reasons why I dont buy it which I wont go into.
posted by vacapinta at 5:45 PM on May 26, 2005

swift: they say: we know with 95% certainty that we're in the last 95% of humanity. therefore, some math will tell us that there's a 95% chance that the total number of humans is not larger than 20 times the current running total (all the humans that have ever lived so far). with this, we can calculate the upper limit on the number of humans (ever) and figure out how long we have until we reach this number, a.k.a. doomsday.

The problem, IMO, is that you could make the exact same argument at any point in time and come up with an entirely different upper limit. If, for instance, you had made that argument when the running total was 1000 humans, you could have said "with 95% certainty" that there would never be more than 20000 humans. In fact, you could make the same argument about any quantity whatsoever and come up with equally arbitrary results. For instance, if I have seen 100 VW.bugs, I can predict with 95% certainty that I won't see more than 2000, ever.
Quite meaningles, in my opinion.
posted by signal at 5:50 PM on May 26, 2005 [1 favorite]

signal's counterpoint (along with many others) is addressed and refuted in the book, BTW.
posted by Jairus at 6:12 PM on May 26, 2005

Yes, but the... whole point of the doomsday machine... is lost... if you keep it a secret! Why didn't you tell the world, eh?

Never heard of the doomsday argument refered to as such before, but I do believe that Paul Davies covers it in his book The Last Three Minutes.
posted by furtive at 6:29 PM on May 26, 2005

Jairus: what is the refutation? And which book?
posted by signal at 9:20 PM on May 26, 2005

The Doomsday Argument for Idiots = "You are an idiot. Trust us, we're smarter than you, and the world will end soon."

Given that the end of the world is a singular event, you simply can't predict it statistically. It's like asking what the odds are that the human race would come to exist in the first place. Well, the probability of an event that has already happened is 1, but that doesn't really tell you what you thought you were asking.
posted by kindall at 9:20 PM on May 26, 2005

cool answer vacapinta -- i read through the wiki analogies on it, and yours is a far finer one.
posted by fishfucker at 9:42 PM on May 26, 2005

signal, I'll have to dig up my copy to transcribe the refutation. The book is called 'The End of The World: The Science and Ethics of Human Extinction'.

I wish I had it handy, and I spent some time looking online to see if anyone had copied the rebuttal -- but suffice it to say that your point is one of the first (if not the first) that they bring up, and refute.
posted by Jairus at 11:33 PM on May 26, 2005

I want to publish The Future--for Dummies, comprising 365 blank pages.
posted by weapons-grade pandemonium at 11:34 PM on May 26, 2005

The good news, swift: Even if the world ends, you may not notice, thanks to Quantum Immortality.
posted by weapons-grade pandemonium at 12:06 AM on May 27, 2005

Never seen this before, but I'll have a go at explaining it :)

Suppose you are an alien who takes over a human host, at any random age you can't control. In fact you just did so right now. You don't know much about humans, and you'd really like to know how long this host-body has to live. You've examined yourself but you can't tell your own age at all. Could be the first year of its life, could be the millionth, but you know all ages are equally likely.

You know however this human will live some finite total number of years to live, let's call it lifespan. And you decide to call this year the nowth year. You have no clue what now is except it's between 0 and lifepsan obviously.

But you can state with some certainty that you're not in the first 5% of your lifespan. Not because of what you observe, but because somehow '95%' seems like a magic number to you; at 94% you suddenly lose all confidence.

So you put the nowth year sometime after the first 5% of all lifespan years, and come up with:
now > lifespan * 0.05
Which you think of as:
lifespan < 20 * now.

Later on this day you decipher some human squealgrunts and take them to mean that you are 30 years old. This leads you to conclude, with 95% confidence, that your human host-body will not live to be more than 600 years old.

Right now you might be doubting the value of your alien logic.

The Doomsday Argument makes its hay by counting people, not days in the life of a host. If the above were billions of people instead of years of life, you'd conclude that there were no more than 600 billion people ever to live. Now, that's still a lot of people, 570 billion yet to come -- but they're coming 6 billion people at a time right now, and that rate is increasing, so we're basically speeding up gobbling through the finite amount of human lives allotted.

Imagine a variation on the alien above. You've been around since the beginning of the human race, and 'ride' a host for a year, at which point you enter the body of a new host. Each time you switch you forget almost everything you know. You have no clue about your own lifespan but you know it is finite. Each time through, you wonder "how old am I?" and "how long do I have to live?". Eventually you regain enough of your faculties to figure out about how old you are, but you can never sense where you are in your lifespan, so you must deduce it.

Let's say you've been alive for 100,000 years up until right now. This time around, you conclude with 95% certainty that you will live no more than 2 million years total. Since you need humans to survive, the human race will necessarily outlive you. You expect to live no more than 1.9 million more years, therefore we can state that to propose humans will survive less than 1.9 million more years is to do so with less than 95% confidence.

Now you can say that this analysis can't be right because no such alien exists. But if the alien did exist, would that mean we suddenly gain about 1.9 million years of human existence?
posted by fleacircus at 2:11 AM on May 27, 2005

Doesn't this argument presuppose that we have entered the continuum at a *random* point?

I am not some disembodied soul that floated down from the spirit realm and landed in this body from the pool of all humans from all time.

Some particular events had to occur to bring me into existence (reaching all the way back to the beginning, I presume). Virtually no other pattern of events would duplicate this. Now is pretty much the only time I could have possibly existed.
posted by clord at 2:35 AM on May 27, 2005

Of course, the whole notion of counting all humans becomes moot of we're living in a computer simulation!
posted by abingham at 5:48 AM on May 27, 2005

but suffice it to say that your point is one of the first (if not the first) that they bring up, and refute.

I would very much like to read the refutation. And I really hope it doesn't require as many assumptions and "feelings."

This simply isn't science. It's pseudo-math/science: the application of a set of logical standards on things that have no logical standards, and coming to extremely rational conclusions based on nothing.

Let us imagine our fractional position f = n/N along the chronological list of all the humans who will ever be born, where:

n is our absolute position from the beginning of the list.

N is the total number of humans

If N equals infinity, the entire DA becomes moot. Cue dozens of assumptions as to why N couldn't possibly be infinite.
posted by Civil_Disobedient at 6:07 AM on May 27, 2005

If N were infinite, wouldn't people and their bones end up filling all the space in the universe, like clowns in a little car?
posted by swift at 6:33 AM on May 27, 2005

This whole thing reminds me of the dozens and dozens of "logical" arguments and astronomical "proofs" as to why the world was going to end during the last "Harmonic Convergence".

We're still here.
posted by aramaic at 7:58 AM on May 27, 2005

Extended MeFi discussion here. (Jairus was asking us to take his beloved book on faith back then, too: "For what it's worth, all above mentioned objections to the doomsday argument are covered in the book." Come on, Jairus, it's been almost three years -- refute the objections already. Because I agree with those who say this is obvious twaddle.)
posted by languagehat at 8:10 AM on May 27, 2005

If N were infinite, wouldn't people and their bones end up filling all the space in the universe, like clowns in a little car?

N represents all possible future human beings. Not all current or past human beings.
posted by Civil_Disobedient at 8:36 AM on May 27, 2005

but suffice it to say that your point is one of the first (if not the first) that they bring up, and refute.

n your own words, what's wrong with my argument?
posted by signal at 8:56 AM on May 27, 2005

So where does this 95% confidence come from? I see no derivation of it. It appears to be a whole bunch of made up numbers. I could use 66% or 25% and the argument is logically the same; the whole thing has no meaning for me.
posted by Doohickie at 8:56 AM on May 27, 2005

it's worth noting that this argument could have been used by anyone, at any time. and so far, for all previous generations, they've been wrong. even though they were (or logically had every justification in being) just as convinced as supporters here and now. adam and eve could have used it to argue that the human race would never grown beyond 20 people. so you might wonder exactly how long we have to keep not dying out for before people start asking why some people continue to use this argument, even though it has, for centuries, been proven wrong.

doohickie - the 95% comes from saying that we are not in the first 5%. it's explained in the wikipedia link.
posted by andrew cooke at 9:05 AM on May 27, 2005

Some particular events had to occur to bring me into existence (reaching all the way back to the beginning, I presume). Virtually no other pattern of events would duplicate this. Now is pretty much the only time I could have possibly existed.

And this is the strongest argument for a Supreme Being. Your existence appears to be anything but random. But the same is true for every creature and every object in the universe, right down to the smallest speck of dust. If you live in a universe where everything is unique, are you still special?

Years ago, I was eating lunch under one of my apricot trees, and had started with half an avocado, which left a small clear spot on an otherwise completely full plate. As I reached for a sip of beer, an apricot fell from the tree, and landed exactly on that spot. The apricot was neither ripe enough to splatter, nor hard enough to bounce, but just flattened slightly and sat perfectly centered in the spot vacated by the avocado. I still have the photo I took, which looks like I must have placed the apricot there. Had I scratched my nose first, or oriented the table or plate differently, or done anything in my life differently, this event would not have happened. What are the odds? Eventually I realized that every apricot that falls on the ground has a unique moment and trajectory, but I lump all those that don’t affect me into a general “random” category. Events that affect us seem somehow rare, special, or different, but they are not. Randomness and Perfect Order are impossible to distinguish in the big picture, but if you invent a God to explain things, why would you not pursue the mystery of His creation with the same logical fervor?
posted by weapons-grade pandemonium at 10:07 AM on May 27, 2005 [1 favorite]

I want to answer some of these objections. I think people over-complicate the Doomsday Argument; it's really just a cute little statistical trick. I have some problems with it being taken too seriously, which I'll get to at the end.

N represents all possible future human beings. Not all current or past human beings.

No it doesn't. N is the total number of human beings in the past, present, and future.

If N equals infinity, the entire DA becomes moot. Cue dozens of assumptions as to why N couldn't possibly be infinite.

Yeah, this is true. The Doomsday argument assumes that over the entire history of the human species, there will be a finite number of humans. So it's assuming that the species will become extinct, which means that it's not a good argument for the eventual extinction of the species. What the DA is trying to establish is that given that there will be a finite number of humans, there is a high probability that the date of human extinction is going to come relatively soon. This argument over the certainty of eventual extinction is separate from (though fundamental to) the DA, I think, and can go lots of places.

Doesn't this argument presuppose that we have entered the continuum at a *random* point?

The other assumption is stated technically as "our fractional position in the set of potential humans is uniformly distributed". So not only is it random, but it's drawn from a uniform distribution. I don't think there's really any argument with the "random" part of this assumption: though we are each unique in terms of the chain of events that caused us to be here, there's no reason a priori to assume that we're either closer to the beginning of the species or closer to the end of the species. We have no knowledge about when the end will be, so we have to assume that we're at a random distance from the end. As for the uniform distribution, I have a bit of a problem with that, and I'll get to it, though I suspect it might be my own weakness in statistics.

Some particular events had to occur to bring me into existence (reaching all the way back to the beginning, I presume). Virtually no other pattern of events would duplicate this. Now is pretty much the only time I could have possibly existed.

Yeah, true. But like I said, since we have no knowledge about when our species will end (the pattern of events that brought you into being gives us little insight into this), we're forced to assume that your distance from that end is drawn from a random distribution. That's pretty easy to take, I think.

In other words, it's a bunch of mathematical speculation based on dubious assumptions. I think it is just as likely that we are at the 0.05 mark of humanity as we are at the 0.95 mark.

This is true, too, but there's nothing "dubious" going on here. There's a 95% chance that we're in the last 95% of humans. There's a 5% chance we're in the last 5%. Assuming a random draw from a uniform distribution, these numbers are all consistent. And they all get you consistent results. The argument isn't asking "what's the probability we're at the .95 mark": that probability is very low. It's asking "what's the probability that we're anywhere past the 0.05 mark": that probability is 95%.

The problem, IMO, is that you could make the exact same argument at any point in time and come up with an entirely different upper limit.

This is a serious objection. While it doesn't invalidate the argument, it does make the whole exercise rather pointless. The DA tells us that N < 20n, but with every new person born, n increases, so N, the 95% confident total number of humans ever, is also constantly increasing. It's an unstable solution. If, with additional births, the number would stabilize on some finite quantity, then this whole thing would be a lot more interesting.


I also have a bit of a problem with the assumption of a uniform distribution. When you calculate a date for the end of the species, based on the population history of the earth and various estimates of population growth, death rates, and carrying capacity, aren't you also assuming a nonuniform distribution? I mean, right there, you've given the distribution a shape (level in the beginning, exponential growth, then leveling off again). It seems you could do the whole thing iteratively, first assuming a uniform distribution, getting a number for N, calculating an extinction date, figuring out the shape of your predicted distribution, and recalculating N. Am I wrong about this?
posted by mr_roboto at 11:55 AM on May 27, 2005

doohickie - the 95% comes from saying that we are not in the first 5%. it's explained in the wikipedia link.
Yeah, I know, but... well, mr_roboto captured my view of the whole argument quite nicely:

While it doesn't invalidate the argument, it does make the whole exercise rather pointless.
posted by Doohickie at 12:16 PM on May 27, 2005

DA == Mathematical Mental Masturbation.
posted by Doohickie at 12:17 PM on May 27, 2005

No it doesn't. N is the total number of human beings in the past, present, and future.

Whoops... that's actually what I meant to say.
posted by Civil_Disobedient at 4:03 PM on May 27, 2005

Some particular events had to occur to bring me into existence (reaching all the way back to the beginning, I presume). Virtually no other pattern of events would duplicate this. Now is pretty much the only time I could have possibly existed.

I need to comment on this: whoop-de-doo. So you exist. Big fucking deal.

Nothing against you personally, of course. It's just that, typical of humans, we figure our own personal existance is something special and meaningful to the universe. "Events conspired to create me" sort of thinking.

They didn't. You aren't intentional. The pattern of events that led to your existence are meaningless and random. The universe did not purposefully set about to bring you into being.

Lucky, sure. Special, no.
posted by five fresh fish at 4:16 PM on May 27, 2005

Boy, that still sounds like I'm actually addressing whomever posted the bit I quoted. I'm not, honest.
posted by five fresh fish at 6:58 PM on May 27, 2005

The universe did not purposefully set about to bring you into being.
This is one of my main gut problems with the whole argument, it assumes a priori that I am not special, nor central to this whole universe thingie, which, while certainly debatable, is not something I'm willing to grant a priori.
posted by signal at 9:11 PM on May 27, 2005

I also have a bit of a problem with the assumption of a uniform distribution. When you calculate a date for the end of the species, based on the population history of the earth and various estimates of population growth, death rates, and carrying capacity, aren't you also assuming a nonuniform distribution?

No, you're not. You're not figuring 'years' your figuring 'index numbers'. In other words I'm person number x, you're person number x, mathowie is person number z, and so on. Obviously person indexes are not distributed over time.

I think the obvious problem with this is the assumption that you yourself have an equal chance of landing on any person index.

You can only "land" at an index thats slightly greater then you're parents, and so on.
posted by delmoi at 10:46 PM on May 27, 2005

Building on what I just wrote. I now know how to show the DA is wrong.

All the math is correct, however the key assumption is wrong:

The Copernican principle suggests that we are equally likely (along with the other N-1 humans) to find ourselves at any position n, so our fractional position f is uniformly distributed on the interval (0,1] prior to learning our absolute position.

In other words, each person has a number. Bob is the 7th human ever born, and I (lets assume) am number 12,012,123,431 or whatever.

In order for this to work, that number -- 12,012,123,431 -- must have an equal probability of being assigned to me as any other number. Clearly, that's false.

My index number is based on my parents index number.

If my mom's index number is IN<sub>mom then my index number is INmom+K where K is the number of people born between the time that my mother was born, and I was born.

For all people, always, K is going to be equal average the number of people born each year times the average time after their own birth that women have children.

---

See this CS education did pay off :)</sub>
posted by delmoi at 10:57 PM on May 27, 2005

Christ I didn't close that <sub> tag. Damnit!
posted by delmoi at 10:58 PM on May 27, 2005

So much for that CS education paying off, eh, delmoi?
posted by Doohickie at 8:07 PM on May 29, 2005

Just reading AskMe for the first time in several days, so I don't know if anyone will ever see this, but I have something to add that I haven't seen addressed yet.

I think there's a subtle but crucial distinction that's being missed here. "The hypothesis that there will ever be more than 20n humans is rejected at the 95% confidence level" is not the same as "It is 95% likely that there will never be more than 20n humans." If I'm understanding it correctly, properly formulated, the Doomsday Argument says the former, but not the latter. (Alternately, if it is formulated as the latter statement, it is incorrect.)

Looking a little more critically at the example in the section of the Wikipedia article, Simplification: two possible total number of humans is instructive. The simplifying assumption is that the total number of humans ever will be either 60 billion or 6 trillion. Based on this, if I know that I am human number 59,854,695,447, I can calculate that it is more than 99% likely that the total number of humans will be 60 billion, and less than 1% likely that the total number of humans will be 6 trillion.

But this argument lies on an unstated assumption: that, without knowing anything about what number human I am, it would be 50% likely that the final number of humans would be 60 billion, and 50% likely that the final number would be 6 trillion. If we don't have this a priori assumption about the probabilities, the conclusion doesn't follow. And if we have a different a priori probabilities, we have a different conclusion. If (before knowing my birth number) there is a 99.9% chance that the number of humans will be 6 trillion, and only 0.1% that the number of humans will be 60 billion; then, learning that I am human number 59,854,695,447, I can now conclude that (if I've done my math correctly) it is 9% likely that there will only be 60 billion people, and 91% likely there will be 6 trillion.

And most importantly, if we can make no a priori assigment of probabilites at all, we can draw no conclusion at all about the likelihood of 60 billion vs. 6 trillion. Even if we knew that the total number of humans were either 60 billion or 6 trillion, we would have no reason for assigning a priori probabilities of 50% to each, and thus could draw no conclusions of the likelihood of each based on our birth number. To assign a 50% probability to each of two mutually exclusive events simply because we have absolutely no information on which to base a probability estimate is fallacious. Common, perhaps, but no less fallacious because it is common.

To illustrate the distinction I am making, suppose we flip a coin 10 times, and we get 9 heads and 1 tail. We can reject the null hypothesis (i.e., the hypothesis that the coin is fair) at a 98% confidence level, which is another way of saying that if the coin were fair, we would see such a skewed distribution only about 2% of the time. But that is not the same as saying it is 98% likely that the coin is unfair. If we drew the coin randomly from some collection of coins, and we knew that X% of the coins in that collection were unfair, and the unfair coins were skewed to come up heads Y% of the time, then we could compute a probability, based both on that initial information and on our observed distribution of results, that the coin we drew was unfair. But without that initial information about how many coins in the collection were unfair, we can say nothing about how likely it is that the coin is unfair.

Thus it is with the Doomsday Argument. If I am human number 60 billion, I can properly reject at the 95% confidence level the hypothesis that there will be 1.2 trillion or more humans. But that is not the same as saying it is 95% likely that there will not be more than 1.2 trillion humans. Without an a priori probability distribution for the various possible values of the total number of humans ever, I can draw absolutely no conclusion about the probability of various values of the total number of humans, given only the added information that I am human number 60 billion.
posted by DevilsAdvocate at 3:19 PM on May 31, 2005

They didn't. You aren't intentional. The pattern of events that led to your existence are meaningless and random. The universe did not purposefully set about to bring you into being.

That's kinda my point. I guess I should clarify a bit more. What is the unit of existence? If you call it the individual, then yes, I think the doomsday argument holds, statistically. I am the first and last Homo-Sapien-Sapien born at location x at time t, etc. Calling xt an instance of a sample space XT makes sense.

But what i was saying is that "I" am more blury than a point on XT! I have a very deterministic past. So why not include that past as part of xt?

So call xt all the people in my ancestor tree since the first person took my last name? Then my entire family group can be considered an instance xt, and the doomsday argument still makes some sense. But then where does it stop? Why stop at the first modern human? isn't THAT just as arbitrary as the set consisting of me, or the set of my immediate ancestors?

But the first modern human had an ancestor, who would be non-modern, presumably (yes, it is actually a continuum, but bear with me) and so on. Why even stop with life? lets include all of space-time which causally produced me! xt keeps on growing! and XT must be larger than xt, right? Thus 'N' in the doomsday argument is massive and meaningless.

I think the basic problem with doomsday arg is the whole 'individual is most basic unit of existence' assumption. Nope. I am attached to my past like one carbon atom to another in a diamond. The whole diamond thus is xt, not just me.

I know this argument depends on past-directed-determinism, btw ;)
posted by clord at 5:38 PM on May 31, 2005