Each reference class has its own end

It is often claimed that the Self-Sampling assumption (SSA) is problematic, in particular, because we don’t know which reference class is a correct one. Therefore, the notorious Doomsday argument is weak. Here I will try to show that it is less a problem than seems. Central claim:* Each reference class has its own end.* Example: I am put randomly in a 2-dimensional grid of rooms. Vertically they are designated by letters from A to Z, and horizontally they are numbered from 1 to 100. So, each room has an address like E021. The Doomsday-like claim is that I am more likely to be somewhere in the middle of the grid than on its borders and thus, I am unlikely to be in the raw of 1-rooms and in A-column. Therefore, claims DA, if I learn my room number, I can estimate the total number of rooms in my raw, and the same is true for letters. (UPDATE: by "middle" I mean some region not on the borders, not exactly cell N50, but, say, between 20 and 80.) A real-world example: I assume that my height and my date of birth are two independent variables. Thus, both should be in the middle of the distribution: I am unlikely to be born on January, 1, and unlikely to have a very low height. It is actually true for me: my date of birth and my height are in the middle of the distribution. Here we use two important assumptions:

• The independence of the variables, like height and date of birth.

• Each variable is external to my cognition process, so it doesn’t affect my probability to think about anthropics. Now we could try to apply this to real-world Doomsday-like problems, that is, claims like "I am in the middle of my reference class existence in time". Let’s discuss three of my reference classes and the corresponding predictions about the end of the world:

• I am a member of the class of mammals, which existed for last 200 million years, and thus mammals may exist a few hundreds of millions of years more.

• I am Russian, and Russians have existed for around last 1000, so they can exist another millennium.

• LessWrong has existed for 13 years and thus will likely continue to exist 13 more years with 50 per cent probability. These predictions give different timing of the "end of the world". This type of inconsistency is often used to show that there is something wrong with the Doomsday argument as it depends on the choice of the reference class. However, if we ignore the idea that there should be just one "end of the world" in the Bang style, these all start to look plausible: a few hundreds of millions of years from now is a reasonable prediction about how long complex life on Earth will exist because of the Sun’s increasing luminosity. Millennium is a typical time of the existence of a nation. And a couple of decades are also a plausible prediction of the time of existence for an organization. However, there is a caveat. Assumption (2) does not work for mammals: most of the previous mammals were not able to make predictions about the end of the world. Assumption (2) is obviously true only for lesswrongers. In that case, we come to the idea of some kind of "reference class of qualified observers", which consists of the minds who do think about anthropics or at least can do it. This is bad news, as such class is new and will likely end soon if we apply DA-logic to it, and the most plausible way how it could end is a bang. One way to save reference class is to say that I am not a mammal in any relevant to my cognition sense, but I just observe mammals in a random moment of their existence. However, assumption (1) is also violated here as being a mammal and being a lesswronger are not independent variables. The lesswrongers likely exist at the end of the existence of mammals, at least according to their own world-model with x-risks.