Dear Sylvain,
Thank you for taking the time to read my essay and commenting on it so thoroughly. Also, it's remarkable that you still have the energy to comment on and rate so many essays after noticing the obvious "absurdity of community rating". I contacted the organizers to comment on this frustrating fact, but they never replied and I have been slightly discouraged from this contest since. That being said, it's still great people read and comment on the essays, the feedback definitely helps the thought process.
In answer to your questions:
1) Idealism: I don't really make any explicit comment either for or against. Personally I find it simpler to think that the mind or cognition are not needed in the description of "reality" on the fundamental level, but my essay certainly leaves room for this if you want to add it to the description. In a way, as usual, it just depends on how you want to define "reality". The note (on idealism) is there just because many assume that an observer dependent description of reality necessarily implies a form idealism, when it does not.
2) which nicely gets me to the next question "So, how can you build a coherent view describing the states of systems as relative to other systems (observers) whose status of presence or absence is itself relative to other systems ?"
In your example the cat being an observer or not depends whether or not it is alive. I see no reason for this in the framework I was using, as I said an electron can be as much an observer as a person. There is no need or relevance that cognition or awareness has in this way of speaking, I wrote "Every physical system is an equivalent observer" and I meant it. The only relevant characteristics of an observer are that it is something physical and it had interacted (or will interact) with another observer. So indeed, the dead cat is a proper observer, even though it is not cognitive (as far as we know ;) ). Of course, the dead cat 'experiences' the world hugely differently than an alive cat, but since I cut away everything related to interpretation or phenomenology (philosophically understood) there is nothing that would prefer the alive cat over the dead one.
The coherence of the descriptions of different observers is guaranteed by quantum mechanics in the sense that whenever data is compared, they match exactly. This is the only relevant or sensible coherence here, because what is real is the description of an observer relative to others, not the sum of these descriptions (see Rovelli's RQM paper for details).
3) What do you mean by "It is possible to write down a theory that is able to answer all answerable questions" ?
I mean a theory that describes all available information in the best possible, ideal, manner. For example in the case of the number of planets with life in the galaxy is definitely answerable, in principle, even without sending probes as far as there exists any interaction (however indirect or imperceptible in practice) between all of the planets in the galaxy. Of course this may change in time (btw requires you to adopt a philosophy of time) but let's say on earth there are reasonably well defined moments of interaction with the rest of the galaxy and you speak about the number in these moments. Now, what is not answerable would be the number of planets with life in a galaxy outside the observable universe. Hence, the ToE does not need to describe these even though many people prefer to think these galaxies exist equally to our own. For me the limits of the ToE in terms of what it needs to describe must run where (in principle) observable things are, i.e. hidden variables are out because they are hidden.
Importantly, a question that is not answerable is "what is the wave function of the universe?" since this information is not available to anyone inside the universe. Thus if we consider the simplest description to be made of answerable questions or obtainable information, then the wave function of the universe will be excluded. Of course, you might take the simplest to mean something else and take the wave function of the universe to be a useful concept, but you will still be physically unable to actually write it down.
4) "In my essay I argued that even assuming descriptions to be expressed as information (that can be encoded in physical objects), does not mean that the best theories to explain them are mathematical."
In some sense I am not saying this either. What I'm saying is that if the world is fully describable in terms of information given by a string of bits, then such a description is mathematical because the description of a string of bits is mathematical. Effectively, this might not be "the best" description, obviously so if "the best" is to include any form of interpretation of this information. I understood this is the direction you took in your essay, but correct me if I'm wrong.
I had a look at your website on the many-worlds, and what you call 'relative solipsism' is somewhere close to what I'm speaking about. Again though, as I do not take the mind or cognition to be important, it is not solipsism proper. Overall I should give your text a more thorough read to give it justice.
I hope I managed to lift the fog a bit!
Best wishes,
Tapio
