Instant strong upvote. This post changed my view as much as the risk aversion post (which was also by you!)
Does "population" in this passage and "population" in presumptuous philosopher have different meanings?
It seems here by "population difference" is kind of like density. How likely we are going to find aliens (on other planets). But in presumptuous philosopher it meant overall number. T2 does have a trillion more observers, yet it does not explain how much of that is due to higher density and how much is due to a larger universe.
I adapted the presumptuous philosopher for densities, because we'd been using densities in the rest of the post. The argument works for total population as well, moving from an average population of (for some ) to an average population of roughly .
Great post, thanks! It looks like 7 times update could be decisive in some situations. For example if initial probability that we are not alone in the visible universe is 10 per cent, and after the anthropic update it becomes 70 per cent, it changes the situation from “we are most likely” alone to “we are not alone”.
Yep. Though I've found that, in most situations, the observations "we don't see anyone" has a much stronger effect than the anthropic update. It's not always exactly comparable, as anthropic updates are "multiply by and renormalise", while observing no-one is "multiply by and renormalise" - but generally I find the second effect to be much stronger.
Ok. Another question. I have been recently interested in anthropic effects of panspermia. Naively, as panspermia creates millions habitable planets for a galaxy vs. one in non-panspermia world, anthropics should be very favourable for panspermia. But a priori probability of panspermia is low. How is your model could be applied to panspermia?
Anthropic updates do not increase the probability of life in general; they increase the probability of you existing specifically (which, since you've observed many other humans and heard about a lot more, is roughly the same as the probability of any current human existing), and this might have indirect effects on life in general.
So they does not distinguish between "simple life is very hard, but getting from that to human-level life is very easy" and "simple life is very easy, but getting from that to human-level life is very hard". So panspermia remains at its prior, relative to other theories of the same type (see here).
However, panspermia gets a boost from the universe seeming empty, as some versions of panspermia would make humans unexpectedly early (since panspermia needs more time to get going); this means that these theories avoid the penalty from the universe seeming empty, a much larger effect than the anthropic update (see here).
I am still not convinced: it seems that p(abiogenesis) is a very small constant depending on a random generation of a string of around 100 bits. The probability of life becoming intelligence p(li) is also, I assume, is a constant. The only thing we don't know is a multiplier given by panspermia, which shows how many planets will get "infected" from the Eden in a given type of universes. This multiplier, I assume, is different in different universes and depends, say, on the density of stars. We could use anthropics to suggests that we lives in the universe with the higher values of the panspermia multiplier (depending of the hare of the universes of this type).
The difference here with what you said above is that we don't make any conclusions about the average global level of the multiplier over all of the multiverse, you are right that anthropics can't help us here. Here I use anthropics to conclude about what region of the multiverse I am more likely to be located, not to deduce the global properties of the multiverse. Thus there is no SIA, as there is no "possible observers": all observers are real, but some of them are located in more crowded place.
To better understand the suggested model of small anthropic update I imagined the following thought experiment: my copies are created in 4 boxes: 1 copy in first box, 10 in second, 100 in third and 1000 in forth. Before the update, I have 0.25 chances to be in 4th box. After the update I have 0.89 chances to be in 4th box, so the chances increased only around 3.5 times. Is it a correct model?
Nope, that's not the model. Your initial expected population is . After the anthropic update, your probabilities of being in the boxes are , , and (roughly , , and ). The expected population, however is . That's an expected population update of 3.27 times.
Note that, in this instance, the expected population update and the probability update are roughly equivalent, but that need not be the case. Eg if your prior odds are about the population being , , or , then the expected population is roughly , the anthropic-updated odds are , and the updated expected population is roughly . So the probability boost to the larger population is roughly (, but the boost to the expected population is roughly .
I don't think it changes the conclusion by much, but isn't, "The q, which doesn't appear in that paper, is a constant, so has M_q = 1," incorrect? All of the valves we're looking at are constants, but we don't know what the constants are, so we have a nonzero variance, leading g to M_q > 1. We certainly don't know the exact value of q, so it shouldn't have M_q = 1.