Solving the Doomsday argument

Hi Stuart. It’s a while since I’ve posted.

Here’s one way of asking the question which does lead naturally to the Doomsday answer.

Consider two universes. They’re both infinite (or if you don’t like actual infinities, are very very large, so they both have a really huge number of civilisations).

In universe 1, almost all the civilisations die off before spreading through space, so that the average population of a civilisation through time is less than a trillion.

In universe 2, a fair proportion of the civilisations survive and grow to galaxy-size or bigger, so that the average population of a civilisation through time is much more than a trillion trillion.

Now consider two more universes. Universe 3 is like Universe 1 except that the microwave background radiation 14 billion years after Big Bang is 30K rather than 3K. Universe 4 is like Universe 2 again except for the difference in microwave background radiation. Both Universe 3 and Universe 4 are so big (or infinite) that they contain civilisations that believe the background radiation has temperature 3K because every measurement they’ve ever made of it has accidentally given the same wrong answer.

Here’s the question to think about.

Is there a sensible way of doing anthropics (or indeed science in general) that would lead us to conclude we are probably in Universe 1 or 2 (rather than Universe 3 or 4) without also concluding that we are probably in Universe 1 (rather than Universe 2)?

The Doomsday argument is utter BS because one cannot reliably evaluate probabilities without fixing a probability distribution first. Without knowing more than just the number of humans existing so far, the argument devolves into arguing which probability distribution to pick out of uncountable number of possibilities. An honest attempt to address this question would start with modeling human population fluctuations including various extinction events. In such a model there are multiple free parameters, such as rate of growth, distribution of odds of various extinction-level events, distribution of odds of surviving each type of events, event clustering and so on. The the minimum number of humans does not constrain the models in any interesting way, i.e. to privilege a certain class of models over others, or a certain set of free parameters over others to the degree where we could evaluate a model-independent upper bound for the total number of humans with any degree of confidence.

If you want to productively talk about Doomsday, you have to get your hands dirty and deal with specific x-risks and their effects, not armchair-theorize based on a single number and a few so-called selection/indication principles that have nothing to do with the actual human population dynamics.

Interesting post. Could the same argument not be used against the Simulation argument?

Simplify the model into assuming there is a universe in which I, the observer, are one of many many observers in an ancestor simulation run by some future civilization, and a universe in which I am a biological human naturally created by evolution on earth, with equal probability. Again, we can imagine running the universe many, many times. But no matter how many people are in the considered universe, I can only have the experience of being one at a time. So, asking:

• What proportion of people whose experiences I have live in a simulated world?

The answer to that question converges to 1/2, as well. But if every observer reasoned like this when asked whether they are in a simulation, most would get the wrong answer (assuming there are more simulated than real observers)! How can we deal with this apparent inconsistency? Of course, as you say, different answers to different questions. But which one should we consider to be valid, when both seem intuitively to make sense?

Lets say you do not know your birth rank at first. Then someone asks you to guess whether the universe is around 200 billion or some very large number. Without any additional data you should estimate 50% for either one. Then you get to know that your birth rank is around 100 billion. Do you not then update, that smaller universe have bigger than 50% chance estimated previously?

It is probably wrong to interpret DA as "doom is imminent". DA just say that we are likely in the middle of total population of all humans (or other relevant observers) ever born.

For some emotional reasons we are not satisfied to be in the middle and interprets it as "doom" - but there are 100 billion more people in the future according to DA. It becomes look like a doom, if we account for expected population growth, as in that case, the next 100 billion people will appear in a few hundreds years.

More over, DA tells that doom very soon is very unlikely, which I call "reverse DA".