While you didn’t make any assumption like this in the post, it’s a bit weird to talk about “Doomsday Argument” and “Solutions”, as if we know in principle that the argument is wrong and we just have to find out why.
In other words, whether it is right or wrong, there isn’t any special reason for the argument to be wrong just because people would like it to be wrong. Trying to get rid of the argument by looking for “solutions” is kind of like going out of your way to look for proofs for the existence of God, just because you want that to be true.
Solution are not only about research if DA is wrong, but about how we should live if it is true.
Personally I think that it is true and the doom is almost inevitable.
We should make some research to prove or disprove DA. The main line of such research would be to try similar to DA logic in other domains, starting from most mundane, like human age, and up to most complex and civilizational level ones.
For example, it is possible to measure size of the Earth using only Copernican mediocracy principle. All we need to know is distance from my birth place to equator, and assumption that human birth places are distributed on randomly distances from equator. I was born 6000 km from equator, and it may be used to conclusion that Earth’s radius is around 7000 km which is almost true (real radius is near 6300) Exact calculations here should be more complex, as it must take in account spherical distribution of the observers and will result in bigger (edited) radius.
I think it is an excellent idea to try DA logic in other domains.
Example: A a biologist prepares a petri dish with some nutrients, and implants a small colony of bacteria. The question is: will this colony grow exponentially under these conditions? According to DA logic (with a reference class of all bacteria that will ever live in that petri dish), the biologist does not need to bother doing the experiment, since it is very unlikely that the colony will grow exponentially, because then the current bacteria would be atypical.
To the best of my knowledge, this sort of DA logic is never used by scientists to analyze experiments of this sort (or to decide which experiments to perform). I believe this casts severe doubt on the validity of DA.
Your example is not DA-style, because observer is not self-sampled here. Observer is not bacteria in this experiment.
(By the way, most from all existing bacteria is not starters of exponential colonies)
I may suggest another experiment: you tell me your age and I will tell your life expectancy based on DA-logic.
I claim that self-sampling plays no essential role in DA logic.
If you think that self-sampling is essential, then you still must allow one of the bacteria in the petri dish to use DA logic about its own future. If you do not allow the biologist to use DA logic, then the bacterium and the biologist will make different predictions about the likely future. One of them must be more accurate than the other (as revealed by future events). If it is the bacterium that is more accurate, what prevents the biologist from adopting the bacterium’s reasoning? I argue that nothing prevents it. And since, in the real world, biologists (and scientists of all fields) do not adopt DA logic, I claim that the most compelling reason for this is the invalidity of DA logic from the get-go.
Look, we could replace “self sampling” with “random”. Random bacteria (from all existing bacteria on Earth) will not start exponential growth. Infinitely small subset of all bacteria will start it. There is no difference between prediction of statistic and biologist in this case.
DA is statistical argument. It just say that most of random bacteria will not start exponential growth. The same may be true for young civilizations: most of them will not start exponential growth in the universe. But some may be.
So do you agree with me that, in the experiment I described (a biologist sets up a petri dish with a specific set of initial conditions, and wants to find out if a small bacteria colony will grow exponentially under those conditions), DA logic cannot be applied (by either the biologist or the bacterium) to judge the probable outcome?
DA should be applied to the situation where we know our position in the set, but do not know any other evidence. Of course if we have another source of information about the set size it could overweight DA-logic. If in this experiment the substrate is designed to support bacterial growth, it have is very strong posteriory evidence for future exponential growth.
But if you put random bacteria on random substrate it most likely will not grow. In this case DA works.
DA here says that 1 bacteria most likely will have only several off springs, and it is true for most random bacteria on random substrates.
So, will DA works here or not depends of details of the experiment with you did not provide.
The biologist has never heard of DA. He sets up the initial conditions in such a way that his expectation (based on all his prior knowledge of biology) is that the probability of exponential growth is 50%.
Now the biologist is informed of DA. Should his probability estimate change?
Probably, not, as he has a lot of information about the subject. DA is helpful in case if you don’t have any other information about the subject. Also DA is statistical argument thereby it could not be disproved by counterexample. It is always possible to construct a situation where it will not work. Like some molecules in the air are not moving, despite the fact that median velocity is very high.
It may be used in such problems as bus waiting problem (variant of Laplace sunrise problem). If last bus was 5 minutes ago, want is the probability that it will come in next 1 millisecond, next 5 minutes? next 1 year?
At least some DA proponents claim that there should always be a change in the probability estimate, so I am pleased to see that you agree that there are situations where DA conveys no new information.
The situation would change, if I were Adam, first man in the world, and a priory will be able to start exponential human growth with P= 50 per cent probability (or think so). After finding that I am Adam, I would have to update this probability to lower. The way I update depends of sampling method—SSA or SIA but both result in early doom.
SSA says that I am in short world.
SSI said that my apriory estimation of universal distribution of short and long civilization may be wrong. It would be especially clear if apriory P would not 50 percent, but say 90 per cent.
It’s clear that this assumption may be refined in two ways: accounting for spherical geometry and accounting for agriculture conditions, both of which will result in higher density near equator and thus larger Earth radius in this calculation. But if we are interesting to estimate Earth’s radius just up to order of magnitude, it will still work.
The main idea was to present another DA-style calculation and check if DA-logic works. It works.
Before accounting for agricultural conditions you probably should account for the distribution of land masses… But anyway, how is this a “DA-style calculation”?
DA-style here means that my position is some set is used to estimate total size of the set, assuming that I random observer from this set.
DA-style is also means that we ignore other available information about me, Earth etc, but use only my position in the set to get very rough estimate of total size of the set.
The study of such DA-style predictions in known domains could help us estimate validity of DA in unknown domains.
While you didn’t make any assumption like this in the post, it’s a bit weird to talk about “Doomsday Argument” and “Solutions”, as if we know in principle that the argument is wrong and we just have to find out why.
In other words, whether it is right or wrong, there isn’t any special reason for the argument to be wrong just because people would like it to be wrong. Trying to get rid of the argument by looking for “solutions” is kind of like going out of your way to look for proofs for the existence of God, just because you want that to be true.
Solution are not only about research if DA is wrong, but about how we should live if it is true.
Personally I think that it is true and the doom is almost inevitable.
We should make some research to prove or disprove DA. The main line of such research would be to try similar to DA logic in other domains, starting from most mundane, like human age, and up to most complex and civilizational level ones.
For example, it is possible to measure size of the Earth using only Copernican mediocracy principle. All we need to know is distance from my birth place to equator, and assumption that human birth places are distributed on randomly distances from equator. I was born 6000 km from equator, and it may be used to conclusion that Earth’s radius is around 7000 km which is almost true (real radius is near 6300) Exact calculations here should be more complex, as it must take in account spherical distribution of the observers and will result in bigger (edited) radius.
I think it is an excellent idea to try DA logic in other domains.
Example: A a biologist prepares a petri dish with some nutrients, and implants a small colony of bacteria. The question is: will this colony grow exponentially under these conditions? According to DA logic (with a reference class of all bacteria that will ever live in that petri dish), the biologist does not need to bother doing the experiment, since it is very unlikely that the colony will grow exponentially, because then the current bacteria would be atypical.
To the best of my knowledge, this sort of DA logic is never used by scientists to analyze experiments of this sort (or to decide which experiments to perform). I believe this casts severe doubt on the validity of DA.
Your example is not DA-style, because observer is not self-sampled here. Observer is not bacteria in this experiment. (By the way, most from all existing bacteria is not starters of exponential colonies)
I may suggest another experiment: you tell me your age and I will tell your life expectancy based on DA-logic.
I claim that self-sampling plays no essential role in DA logic.
If you think that self-sampling is essential, then you still must allow one of the bacteria in the petri dish to use DA logic about its own future. If you do not allow the biologist to use DA logic, then the bacterium and the biologist will make different predictions about the likely future. One of them must be more accurate than the other (as revealed by future events). If it is the bacterium that is more accurate, what prevents the biologist from adopting the bacterium’s reasoning? I argue that nothing prevents it. And since, in the real world, biologists (and scientists of all fields) do not adopt DA logic, I claim that the most compelling reason for this is the invalidity of DA logic from the get-go.
(I did not downvote you)
Look, we could replace “self sampling” with “random”. Random bacteria (from all existing bacteria on Earth) will not start exponential growth. Infinitely small subset of all bacteria will start it. There is no difference between prediction of statistic and biologist in this case. DA is statistical argument. It just say that most of random bacteria will not start exponential growth. The same may be true for young civilizations: most of them will not start exponential growth in the universe. But some may be.
So do you agree with me that, in the experiment I described (a biologist sets up a petri dish with a specific set of initial conditions, and wants to find out if a small bacteria colony will grow exponentially under those conditions), DA logic cannot be applied (by either the biologist or the bacterium) to judge the probable outcome?
DA should be applied to the situation where we know our position in the set, but do not know any other evidence. Of course if we have another source of information about the set size it could overweight DA-logic. If in this experiment the substrate is designed to support bacterial growth, it have is very strong posteriory evidence for future exponential growth.
But if you put random bacteria on random substrate it most likely will not grow. In this case DA works. DA here says that 1 bacteria most likely will have only several off springs, and it is true for most random bacteria on random substrates.
So, will DA works here or not depends of details of the experiment with you did not provide.
OK, let me rephrase the question.
The biologist has never heard of DA. He sets up the initial conditions in such a way that his expectation (based on all his prior knowledge of biology) is that the probability of exponential growth is 50%.
Now the biologist is informed of DA. Should his probability estimate change?
Probably, not, as he has a lot of information about the subject. DA is helpful in case if you don’t have any other information about the subject. Also DA is statistical argument thereby it could not be disproved by counterexample. It is always possible to construct a situation where it will not work. Like some molecules in the air are not moving, despite the fact that median velocity is very high.
It may be used in such problems as bus waiting problem (variant of Laplace sunrise problem). If last bus was 5 minutes ago, want is the probability that it will come in next 1 millisecond, next 5 minutes? next 1 year?
At least some DA proponents claim that there should always be a change in the probability estimate, so I am pleased to see that you agree that there are situations where DA conveys no new information.
The situation would change, if I were Adam, first man in the world, and a priory will be able to start exponential human growth with P= 50 per cent probability (or think so). After finding that I am Adam, I would have to update this probability to lower. The way I update depends of sampling method—SSA or SIA but both result in early doom. SSA says that I am in short world. SSI said that my apriory estimation of universal distribution of short and long civilization may be wrong. It would be especially clear if apriory P would not 50 percent, but say 90 per cent.
Which is a pretty silly assumption that happens to be not true in real life.
It’s clear that this assumption may be refined in two ways: accounting for spherical geometry and accounting for agriculture conditions, both of which will result in higher density near equator and thus larger Earth radius in this calculation. But if we are interesting to estimate Earth’s radius just up to order of magnitude, it will still work.
The main idea was to present another DA-style calculation and check if DA-logic works. It works.
Before accounting for agricultural conditions you probably should account for the distribution of land masses… But anyway, how is this a “DA-style calculation”?
DA-style here means that my position is some set is used to estimate total size of the set, assuming that I random observer from this set. DA-style is also means that we ignore other available information about me, Earth etc, but use only my position in the set to get very rough estimate of total size of the set. The study of such DA-style predictions in known domains could help us estimate validity of DA in unknown domains.
Isn’t this approach better known as “generalising from one example”?
No, it is evidence, but very vague.