On 30 Oct 2008, at 07:51, Kory Heath wrote:

> On Oct 28, 2008, at 12:33 AM, Bruno Marchal wrote:
>> Measure theory is the branch of math which has been invented to  
>> tackle
>> those infinities, and those similarity relations.
> I don't know much about measure theory. I understand a bit about how
> it's supposed to tackle those infinities, but I don't understand how
> it relates to similarity relations.

OK, measure theory theory does not relate directly to the similarity  
relations. This happens with the comp hyp through indiscernability  
relations. Indeed you cannot distinguish the computations which differ  
below the level of substitution, like you cannot distinguish your  
state of mind you would have if some electron has this or that  
position within the same energy level. The measure on first person  
histories has to take this equivalence into account. But we cannot  
know our level, we can only make some empirical bets. Strictly  
speaking the equivalence relation is not constructive. We don't really  
can know who we are, and the probabilities cannot be defined with  
certainty. If some probability calculus works well, empirically, it  
would give evidences (not proof) for some level, and if QM can be  
extracted from comp, this would mean that empirical quantum mechanics  
would assess the idea that, roughly speaking, our level of  
substitution is given by the position of our particles up to the  
Heisenberg uncertainiy relations. The quantum indeterminacy would, in  
that case directly results directly from the 1-person comp  
indeterminacy, but we don't yet know this. That would be nice because  
the empirical many-world (the empirical reasons for not believing in a  
collapse of the wave packet) would comfort the fact that we share  
histories (given that we can share the quantum indeterminacy). Quantum  
Mechanics would really be a non-solipsistic first person *plural*  
indeterminacy calculus, and physical reality as we know it today,  
would really be the product of dream sharing. QM would comfort that we  
belong to the same "matrix".

> What bearing does it have on the
> case when you make exactly two copies of a person, one which is exact
> and one which contains (say) roughly half of that person's memories,
> personality, or whatever?

To make a prediction on the future from the past you have to remember  
the past (or at least some relevant part of the past). If you allow  
(partial) amnesia, it could depend on many things including the type  
of computations allowing the amnesia: it makes almost no sense a  
priori. It would be like asking what is probability to get six  
(subjectively or as first person experience, like we have to do  
assuming comp) when throwing a dice knowing in advance that once you  
have thrown the dice you will forget that you have thrown the dice!
So I am not sure the question can even make sense. I said to George  
Levy a long time ago (in this list) that all first person  
probabilities in self-multiplication experiments presuppose that the  
level of substitution (of brain material) has been chosen correctly,  
and thus serendipitously given that we cannot known for sure our own  
substitution level.

Now, your question could still make sense if you accept the idea that  
there is only one person possible. We would all be the same person in  
different context. With this you can predict that amnesia would be  
lived as a remembering of your more correct identity. Unfortunately  
record of amnesia by wounded person does not confirm this, except,  
apparently for some drug induced amnesia, like the one provoked by the  
use of the plant salvia divinorum (there are many reports available on  
the net). So it looks like some type of amnesia (which belong to some  
type of computation) could confirm "we are the same person", and in  
that case, those amnesia would not change the probability rules. But  
all this is much more speculative so I conjure you to take this with a  
bit of a distance. Of course if you are lucky to belong to a country  
where the consumption of salvia divinorum is authorized, you could  
test it on yourself but read the manual before and be cautious. I have  
tested it and I do find the effect very interesting for learning  
things about identity and reality, but not to the point of having get  
any definite conclusion. It certainly opens me to be more interested  
in the amnesia phenomenon, and it makes me more open to the "only one  
person" proposition, but it is not a sort of knowledge easily  
sharable, except, well like consciousness,  through sharing identical  
brain transformation, which of course is very hazardous when they are  
produce through the use of some chemicals (but still less hazardous  
than using an hammer on your skull or getting a car accident).

The day will come (not tomorrow) where we will bet on some effective  
artificial brain, and this will lead to more systematic way to handle  
such questions in much less hazardous way. The hazardous part will be  
put entirely in the bet on our substitution level.

To sum up my comment: probability of self-multiplication with loss of  
memory depends most probably on the way such memories are deleted.
The fact that some drugs give a "remembering" feeling through amnesia  
could be an evidence that Darwinian evolution (by itself very long  
computations) has handled brain/identity recuperation mechanism, and  
that we share a personal identity. Some mystic describes similar  


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