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Careful said:I am going to knitpick here: *I am aware that I am conscious*; I thought awareness was a state of the brain which is not influenced by consciousness.
The problem is of course that you want me to give a materialistic or behaviouristic definition of something that is not materialistic, and that you then attack my tentative definition on these grounds.
However, you are right that the "I am aware that I'm conscious" was slippery. "My subjective experience" should do it. You really should read a few of the dualist objections to materialism in the link I gave you, they try to pinpoint exactly that problem ; here it was:
http://www.iep.utm.edu/c/consciou.htm
Now, I try to tell you all the time that I feel conscious too, my mother feels conscious and my brother does when I ask them (you should really do the test). The miracle is that all the humans I meet in this world guarantuee me that they are conscious, that they experience subjective experiences.
As I said, there's no problem with that, let them have their consciousness. You then simply have to accept that with one body, there go many independent subjective experiences, namely one for each state. I found that the zombie analogy would do best because I already had that idea even before studying quantum mechanics - that it was fundamentally impossible to know whether another person is or is not having subjective experiences.
I will ask you: imagine that your brain state is scanned, and written down on a (high-density :-) CD. Is that CD now conscious too ?
So are these all zombies which are cheating upon me, or do they just have the illusion they are conscious, or are they really conscious ?? So that is why you have to explain consciousness are define ``subjective experience´´ and ``I´´ as an entity.
As I said, there's no point in trying to define this for something else than yourself.
This is also why you can say you preserve unitarity, because you are not taking into account interactions with other human body states.
But that's not true: I can of course have interactions with other bodystates. There's no difficulty with that.
** I don't see where the *fundamental* difficulty comes from: this is already the case, even in a classical view, no ? **
No, the classical view is expressed in terms of binary numbers. No problems here... (there is a clear ontology to binary numbers and it is not associated to a partial consciousness state in my view)
Well, as a materialist as I would say then that you need to give me a mathematical definition of consciousness (but that is just not possible since consciousness is subjective and a materialist point of view is objective).
That, on the other hand, is not difficult to do, and I did it. It is an asteriks on a body state, which jumps from state to state according to the Born rule.
Let us take our poor cat again, and let us assume that joe and me are both conscious scientists, for a change:
|joe_scientist*> |me_scientist*> (a |live cat> + b |dead cat>) |world1>
I look at the cat:
|joe_scientist*> (a |live cat>|me_seecatalive> +
b |dead cat>|me_seecatdead>) |world1>
And, because I entangle with the cat, I have to choose a new brain state associated with my consciousness, for instance, with probability |a|^2:
|joe_scientist*> (a |live cat>|me_seecatalive*> +
b |dead cat>|me_seecatdead>) |world1>
Now let joe look at the cat:
(a |live cat>|me_seecatalive*>|joe_catalive> +
b |dead cat>|me_seecatdead>|joedeadcat>) |world1>
Joe also has to choose now, and say that he takes the dead cat with probability |b|^2:
(a |live cat>|me_seecatalive*>|joe_catalive> +
b |dead cat>|me_seecatdead>|joedeadcat*>) |world1>
Quickly this gets entangled also with the environment:
a |live cat>|me_seecatalive*>|joe_catalive>|world2>
+ b |dead cat>|me_seecatdead>|joedeadcat*> |world3>
Now, imagine I ask Joe's body about what he found about the cat on the blackboard: |joe_catalive> will write "I saw a live cat" on the board, and "joedeadcat" will write "the cat was dead"
a |live cat>|me_seecatalive*>|joe_catalive>|"Isawlivecat">|world2>
+ b |dead cat>|me_seecatdead>|joedeadcat*> |"thecatwasdead">|world3>
If I now look at the blackboard, because of the orthogonality of world2 and world3 under about all possible unitary evolutions, there will be no interference terms between the "dead" branch and the "live" branch, so I will read on the board "Isawlivecat".
So, for all practical purposes, to me, the world state looks like:
|live cat>|me_seecatalive*>|joe_catalive>|"Isawlivecat">|world2>
and it is as if an effective reduction took place. The only way for me to find out whether that "other" world exists or not, would be to show some interference with that other world. That almost never happens. It only happens in perfect EPR experiments in fact, and then I DO find (ideally) the interference I expect through the EPR correlations.
Now, nothing stops me from assigning a NEW consciousness to "joe_catalive":
|live cat>|me_seecatalive*>|joe_catalive#>|"Isawlivecat">|world2>
What difference does it make ? This new consciousness will now ALSO evolve according to the Born rule and all that. If you prefer others to be conscious, just say so, and we deliver

That is how science works, many ideas are plausible but only few survive temporarily. So, you might make advance in the game how to decide wether people in your world which claim to be conscious too are lying or not (and explain me why you are not in a real one world picture and thereby maintaining only one term in the Schroedinger wave). And this is de facto impossible in your framework. It seems much more meaningful to convert to a Penrose like scheme of objective reduction (although this might have causality problems.)
I entirely agree with you, that would make the ontology-consciousness map again much easier. We'd still be saddled up with the philosophical problems entailed with the materialist viewpoint, but we could again hold our materialist-scientist nose high and relegate them to philosopher's chat.
The problem with all the *other* speculative ideas is that they are changing the quantum formalism. I'm trying to make sense of the current formalism with unitarity and so do about all people who work on quantum gravity related areas. So touching upon unitarity should still be shown to work. In the mean time I SHOW you a way how we can make sense of the existing formalism of quantum theory.
So, I ask you : how did it get entangled to your brain at birth ? Does it die with you ??
Classically, we speak of awareness, not of consciousness.
Again, my consciousness DOES NOT GET ENTANGLED with my brain, it is ASSIGNED TO a brain state. How did it get there ? You could have a lot of speculation here, but the simplest is again: by using the Born rule !
(but this time "out of the blue", and not starting from a previous state).
|pregnant_mother> |world1> + |not_so_pregnant_mother>|world2>
evolves into:
(a|beautifulbaby> + b|uglybastard>)|mommy> |world1> + |not_so_pregnant_mother>|world2>
* BING* Assignment of consciousness, with probability |a|^2:
(a|beautifulbaby*> + b|uglybastard>)|mommy> |world1> + |not_so_pregnant_mother>|world2>

But nothing stops you from assigning also a consciousness to the uglybastard. It doesn't matter. I "happen to be" the beautifulbaby.