Philosophy

Doom For The Doomsday Argument

Heard of the Doomsday Argument, sometimes also called the Carter Catastrophe? It claims to be able to name the date, with a certain confidence, at which mankind dies off. It has been the subject of a great many discussions and scientific papers. Its disturbing results have many very concerned.

Mathematical author William Poundstone used it to say there’s a “50 percent chance that humans will become extinct within about 760 years.” Not a lot of time left.

All of us will be dead before we can check his prediction. But we still have time to see whether this calculation makes any sense.

It turns out it does not. And the reason it does not is extremely important, because the mistake made in the argument is found all too frequently in science.

The first assumption in the Doomsday Argument (DA) is that there will be N total people, adding up all the already born and those still to come, whatever this number is. That much is true.

The second assumption is that your birth was nothing special. This seems to be true, too. You were not the first person born, and, if you can read these words, it means you were not the last person to be born, either. So you are somewhere in the great middle.

That second assumption then morphs and becomes the claim you could have been born at any point among everybody ever born. Which is to say, the assumption claims it was equally likely you could be the first person born, or the second, or third, or any, up to the last.

This is clearly false on the observation you were not the first born, or even the second! But the assumption might be approximately true if N is large. For instance, if you were the 100 billionth person to be born (and several estimates put the total so far at that number), and N is 1,000 trillion, then 99.99% of all people are yet to be born. So you are close enough to be “the first” as to make no difference.

If we continue with the second approximate assumption, and say you could equally well have been born at any point in man’s history, then there is a 50% chance half of all people will come after you. If there have been n people so far, and there will be an eventual total of N, then some simple math shows that there is a 50% chance that N ≤ 2 * n.

Since there have been about 100 billion people so far, there is a 50% chance that the total ever born will be less than or equal to 2 * 100 billion = 200 billion.

This means there are 100 billion of us yet to come. If, similar to now, 150 million are born each year, then 100 billion / 150 million per year = 666 years left, which is close to Poundstone’s estimate.

Yet this can’t be right. Have you spotted the error? Many don’t.

It’s not the 50%. There is nothing special about the 50%; we could (and will) have used any percentage between 0% to 100%.

Consider the first man born. Call him Adam. For him, n = 1. He looks at the math of the DA and calculates there is a 50% chance N ≤ 2 * 1. So he will not be surprised when he comes across Eve. Adam would, though, be shocked to learn that some 100 billion more were to arrive.

Maybe Adam could have used a tighter probability than 50%. Suppose he wanted to be 99% certain instead of just 50-50. Then our equation becomes N ≤ 100 * n.

That means Adam was 99% certain that the total number of people who ever live would be less than or equal to 100—not a hundred billion, one hundred period. But there were, so far, 100 billion. Off by (as mathematician’s say) nine orders of magnitude.

Then consider man number 200 billion, who, we calculated gave a 50% chance will be born 666 years from now. He, not knowing he is the last, would calculate the DA and conclude there is a 50% chance N ≤ 400 billion! And the 400 billionth man would answer 800 billion, and so on.

It turns out when you are born, how many have come before you, makes an enormous difference. That second assumption in the DA does not hold. After reflection, it seems absurd to discard the information that 100 billion souls preceded you, and assume that you could have been born at any time from Adam to the end. You simply could not have been born before you were.

The real argument is this: we know 100 billion have lived so far; how many more are to come?

There is no way to know. Not just using your place among births. How many people there will be is a good question, but like all questions, and all probabilities, depends on what information is assumed. If you change the assumptions, the probabilities can change radically.

This small example shows how easy even sophisticated math can do wrong. There is much more to it, and for those who have a deeper interest, I have an article which lays out all the mathematics involved.

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Categories: Philosophy

14 replies »

  1. I think his estimate is wildly optimistic.

    What happens when population growth goes negative? It’s plateauing now.

    Everything that underpins human civilization will crumble.

    At least the planet will be here for another 5 billion years or so, although it’ll be really, really hot.

  2. It is no wonder the younger generation feels they won’t live as well as us boomers. Being 61, I have a 50% chance of making it past 122 years of age. My son only has a 50% chance of making 62 years.

  3. The DA argument has a fatal embedded assumption: that at t=0 we get the first human and at t=n we get the last one. Evolution says the 1st human co-existed with near humans and that the last one will similarly co-exist with some later form. The DA, in other words, suffers from a restricted view of what is, and is not, a human.

    Carry that to extremes and it is obvious that the “human” of 1823 is quite different at the molecular level (think environment and adaptive RNA, not DNA) from the current rendition – so if those people defined “human” the last one died quite some time ago.

    (And if you think the DNA was the same and defines “human” .. I know some people in the field who are convinced molecular biology has proven you wrong and is within a tenure generation of getting that widely accepted. q.v. wild speculations on my winface site. )

  4. Somehow, I’ve been spared this particular bit of pseudoscience. This DA sounds like an even dumber version of the Drake Equations: the only problem with them is that you don’t know the critical numbers. If I knew how many people would be born (or, more directly, when the human race will go extinct), then I don’t need any fancy math. But if I don’t know when humanity is going extinct, the formulas don’t tell me. It takes a lot of education to be this dumb.

  5. I’m most likely going to croak within the next twenty years or so. I know this is a harsh thing to say, but for all I care, one second after my lights go out the whole damned mess can explode in a supernova that can be seen from the next galaxy.

    Of course, that’s not going to happen.

  6. The other issue is the common assumption that current trends will always continue, ad infinitum.

    Today was warmer than yesterday, which was warmer than the day before. Therefore tomorrow will be warmer than today and the following day we all burn to death.

  7. Finally, Doomsday met its doom. At the doom-dealing hands of Doom Meister Briggs. DO NOT MESS WITH BRIGGS! You will meet your doom. Briggs wields more doom daggers than a vampire squid has tentacles. Doom is doomed. Doom at your own risk. You have been warned.

    — Doomfish Bagdoom.

  8. Population growth is not negative estimates put 2050 population at 10 billion compared to 8 billion now so if you’re around in 2050 expect a lot more neighbours. The population increase is all in countries that can’t support the populations they have now so if you think migration is high right now you’re not paying attention to what’s going to happen in the near future and beyond. Contrary to the claims of contrarians who believe there’s no such thing as overpopulation people can’t live randomly anywhere you can observe large areas of sparsely populated land. Anywhere sparsely populated in the modern world is sparsely populated for a reason. As first world cities collapse under the impact of migration destroying social capital and overloading infrastructure I expect birthrates to climb as a response to austere conditions, that what we see in the third world. In the third world the poor have children as a means of securing future resources. As resources become scarcer the impetus to have children increases, which at first seems counter-intuitive but observations don’t lie. We don’t have to have fancy models and what have you, simply look at the behaviour of populations today and adjust for larger numbers.
    I anticipate there will be a collapse of the global trade in agricultural products at some point in the foreseeable future, certainly before the end of this century. This will lead to mass starvation and global population crash. Just as well I’m old and am going to die soon anyway. It’s pretty obvious from the absurd looting of economies going on that the globalist plutocrats are as convinced of this as I am and they have much better access to genuine data and intelligence than the lies and black propaganda we’re saddled with and have to sift through and read between the lines.

  9. Are you saying that Malthus was WRONG? Not Malthus! Not population-bomb scientists! Oh, the very idea. Scientists can never be wrong and anyone who disagrees with them is anti-science!!!

    You had me worried there for a moment…

  10. @Chaeromon this on is pretty interesting…

    “how can alternatives to scientism protect against unpreventable mayhem? show empirical proofs; show empirical rewards.”

  11. John @Pate, thanks 🙂 I had to give it something to ponder, “alternatives to objectivism” was what worked (produced “understandable” output & generated from its “trained” innards –which I didn’t know in advance).

    P.S. we are saved (~promised~) with consensus:
    https://consensus.app/results/?q=does%20your%20search%20engine%20support%20physical%20world%20models?&synthesize=on
    https://consensus.app/results/?q=does%20your%20search%20engine%20support%20ontologies%20like%20SUMO%20or%20DOLCE?&synthesize=on
    P.P.S. https://github.com/f/awesome-chatgpt-prompts?tab=readme-ov-file#act-as-a-text-based-adventure-game (can also: act as lunatic …)

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