Published on April 22, 2025 12:34 PM GMT
TL;DR: Several experiments show that I can extract useful information just by treating myself as a random sample, and thus a view that I can't use myself as a random sample is false. But it's still not clear whether this can be used to prove the Doomsday argument.
There are two views: one view is that I can use my random location to predict the total size of the set from which I am selected – and, moreover, it is applicable to predicting future Earth population and thus the Doomsday timing and other anthropic things like the Simulation argument.
And the second view is that there will always be a person at the beginning of any large ordered set of observers who will be surprised by their early location (in the case of DA). Thus, the fact of the surprise is non-informative. Or, as a variant, it should be ignored based on Updateless Decision Theory considerations.
Here I will not argue about the theoretical validity of these two views. Instead, I will perform a series of practical experiments to test the central claim.
Let's start from a simple experiment – please check the time of the day now and use it as a random sample to try to predict the typical duration of a day in hours. When I did it the first time, I looked at my clock and it was 15:14. It gives a 50 percent probability that the total number of hours in a day is 30, which is reasonably close to 24.
The history of anthropic thought – at least in one of its lines – started from a practical experiment: R. Gott claimed jokingly in 1975 that he could predict that the Berlin Wall would exist for around 100 percent more of its current age at the time of the prediction (it was 14 years old at the time of the joke). When it fell in 1989, Gott was surprised and wrote a theoretical underpinning of such prediction method. In some sense, Laplace's Sunrise Problem also is based on experimental observation that the Sun rises every day.
Gott continued to insist that his prediction method could be experimentally tested and used it to predict the durations of Broadway shows, and it worked.
However, Gott's method is not explicitly based on some observer sampling assumption, but on the observation of the duration of the existence of external things where the observer continues to exist after they disappear. Therefore, the application of it to the future duration of humanity's existence – the Doomsday Argument – is questionable.
Here I will perform several practical experiments. I will test the central claim: that some useful information can be extracted just from my random location, that is, that I can treat myself as a random sample. This idea is often attacked from different angles (perspective-based reasoning, linear progression argument, full conditioning requirement, and the idea that future observers are not determined yet and can't be sampled).
1. How many months are in the year?
Given my date of birth, can I estimate the total number of months in a year, as if I do not know it? My birth month is September, the 9th month. This means that with 50 percent probability, according to me-as-a-random-sample logic, the total number of months in a year is 18. This is close to the real number, 12.
2. Earth size
I will try another, more difficult one. I will measure the size of the Earth, taking as input my birth location and I will take from it only the surface distance from my location to the nearest point on the equator (that is, similar to latitude, but in km). For me, it is 6190km. I then assume that it is a random sample, and will ignore anything from spherical geometry and population distribution. In that case, I assume that I was born in a random place between the equator and pole. Therefore, the surface distance to the pole, according to random sampling of me, should also be 6190 km, and the total surface distance from pole to equator will be 12380 km. The real distance is 10000 km. So here again I get a good approximation of real data by treating myself as a random sample from all observers.
However, if we apply this to time, there is a problem: future observers do not exist yet. Leslie thought that this was the real problem of DA and spent a lot of time proving determinism. If determinism is correct, there is no difference between real and future observers, and random sampling works perfectly; DA will work. In other words, DA will work in a block-time universe. But what about MWI?
One trick to escape this problem is predicting the time of the existence of a typical observer and then applying it to myself as a typical observer.
3. Predicting typical human life expectancy based on my age
For example, if I take a random alien and learn that his age is 1500 sols, I can't directly predict that this alien will live 3000 sols, but I can say that the average life expectancy of such aliens is 3000 sols, and thus this alien also has this average life expectancy as he likely is an average alien. This works for me too. My current age is 50 (at the time of writing), and this predicts that average human life expectancy is around 100. Not a bad guess, given that real human life expectancy is 70-80 years.
Here I use a trick with median life expectancy which does not change the prediction. The same trick is used in the so-called universal doomsday argument.
But can it be applied to the real Doomsday Argument?
Ape in the coat suggested that we can't think about ourselves as random samples from human history, as observers appear consequently. Any civilization discovers the Doomsday argument in its 20th-century-analogue and is surprised. But it is wrong: I am not randomly located in the history of human civilization; I am located near the date it first discovered the Doomsday Argument. In other words, thinking about DA pinpoints the specific moment in history and kills random selection. This looks like a refutation of the DA at first glance.
However, I can also say that I am randomly selected from all observers in Earth history who will ever think about DA. These observers appeared in the 1970s and the number of them has been growing at least until 2010. This suggests that such observers will disappear in a few decades from now.
Discuss
