Yes, agree and actually I said in the end of the post that “So, SIA proves that universe is infinite and stops here”.
The problem here is that after we use SIA to show that the world is infinite, we can’t use it for anything else. For example, for any world with heads in Sleeping Beauty, there is a world where all the same except that there coin is tails. What do you think about this?
Yes I saw it and I agree. I was suggesting SIA=SSA given multiverse is not surprising because their difference lies in assessing whether or not multiverse is true. If we look past that part then they behave the same.
For the sleeping beauty problem, accepting a multiverse theory does not change the conclusion for SIA supporters. It is still 1⁄3. Since there are 2 awakenings in the tails world and 1 in heads world, which all exists. Now applying an SSA type of updating would give 1⁄3.
Of course one can argue if the world is infinite then there are infinite awakenings for both heads and tails. How to do a Bayesian update in this case becomes unclear. However, I just don’t think that is a very powerful counter to SIA. Infinity is always a difficult concept, anthropics paradoxes already exist without it.
My opinion is that while SSA and SIA are both wrong, SIA does so consistently. It generates less paradox than SSA. The “free lunch” of confirming theories with more observers simply because “I exist” is the exception.
Understandable. Most if not all thinkers treat anthropic reasoning as some sort of observation selection effect. It has been the case since Nick Bostrom laid the foundation of the subject. I might be the only one thinking treating first-person concepts （like “myslef” “I” “now” and “here”）as random sample is where all the mistake is.
Yes, I know about it. In fact, it is originally purposed by Prof. Radford Neal from university of Toronto. And he is replying right below you. :)
No, it is very different from my view. In my opinion, FNC is similar to SIA and SSA. It still assumes a particular sampling procedure and considers indexical (like “I” or “now”) as the outcome of this sampling process. Though FNC is more subtle as it does not explicitly state anything in the like of “consider oneself as randomly selected from such and such”. Nonetheless, it performs probability calculations as if someone with all the specific experience of “me” (first person) is being sampled and successfully found among existing observers.
My opinion is indexicals cannot be regarded as a sampling outcome and they cannot be removed from anthropic problems. They should be treated as concepts inherently understood. e.g. I don’t need anything to differentiate myself from all people. I just inherently know who “I” is. Anthropic problems are set up using indexicals as such. They should be solved as such.
There is something lost in the discussion of the octopus example between me and Prof Neal. What I meant is that if a theory suggests there are many intelligent octopuses whose subjective experience is human-like. (maybe like matrix-style octopus-in-a-vets experiment). i.e. the octopus thinks they have are biped humans, even though they are physically not. Then no matter how crazy that sounds, as long as the theory greatly inflates the total number of observers with human-like experience, SIA will endorse it with a high degree of confidence. FNC does so too.
Yes, agree and actually I said in the end of the post that “So, SIA proves that universe is infinite and stops here”.
The problem here is that after we use SIA to show that the world is infinite, we can’t use it for anything else. For example, for any world with heads in Sleeping Beauty, there is a world where all the same except that there coin is tails. What do you think about this?
Yes I saw it and I agree. I was suggesting SIA=SSA given multiverse is not surprising because their difference lies in assessing whether or not multiverse is true. If we look past that part then they behave the same.
For the sleeping beauty problem, accepting a multiverse theory does not change the conclusion for SIA supporters. It is still 1⁄3. Since there are 2 awakenings in the tails world and 1 in heads world, which all exists. Now applying an SSA type of updating would give 1⁄3.
Of course one can argue if the world is infinite then there are infinite awakenings for both heads and tails. How to do a Bayesian update in this case becomes unclear. However, I just don’t think that is a very powerful counter to SIA. Infinity is always a difficult concept, anthropics paradoxes already exist without it.
My opinion is that while SSA and SIA are both wrong, SIA does so consistently. It generates less paradox than SSA. The “free lunch” of confirming theories with more observers simply because “I exist” is the exception.
I agree with all you said except conclusion :)
For me, both are right. SIA works by showing that all possible observers exists.
SSA works now by looking on the distribution of observables.
Understandable. Most if not all thinkers treat anthropic reasoning as some sort of observation selection effect. It has been the case since Nick Bostrom laid the foundation of the subject. I might be the only one thinking treating first-person concepts （like “myslef” “I” “now” and “here”）as random sample is where all the mistake is.
There is a theory called “full non-indexical conditioning”.
Do you know about it? Is it close to your view? I am not yet very good in it, but I saw some papers on arXiv.
Yes, I know about it. In fact, it is originally purposed by Prof. Radford Neal from university of Toronto. And he is replying right below you. :)
No, it is very different from my view. In my opinion, FNC is similar to SIA and SSA. It still assumes a particular sampling procedure and considers indexical (like “I” or “now”) as the outcome of this sampling process. Though FNC is more subtle as it does not explicitly state anything in the like of “consider oneself as randomly selected from such and such”. Nonetheless, it performs probability calculations as if someone with all the specific experience of “me” (first person) is being sampled and successfully found among existing observers.
My opinion is indexicals cannot be regarded as a sampling outcome and they cannot be removed from anthropic problems. They should be treated as concepts inherently understood. e.g. I don’t need anything to differentiate myself from all people. I just inherently know who “I” is. Anthropic problems are set up using indexicals as such. They should be solved as such.
The octopus example helped me to grok the FNC, but I still don’t have a clear example which will help me to better understand your point of view.
There is something lost in the discussion of the octopus example between me and Prof Neal. What I meant is that if a theory suggests there are many intelligent octopuses whose subjective experience is human-like. (maybe like matrix-style octopus-in-a-vets experiment). i.e. the octopus thinks they have are biped humans, even though they are physically not. Then no matter how crazy that sounds, as long as the theory greatly inflates the total number of observers with human-like experience, SIA will endorse it with a high degree of confidence. FNC does so too.
For my position, see this post for a start.
Thanks for the link.