Bruno Marchal wrote:
> Le 21-août-06, à 19:48, Tom Caylor a écrit :
> > I'd rather go with Pascal. ;)
> Comp has its own "Pascal wag", when the doctor said that either you
> will die soon or you accept an artificial brain. Some people will
> believe an artificial brain could be a last chance to ... see their
> grand grand children married, or to follow the next soccer
> championship, or whatever.
> >> As I remember it, my interpretation/expansion of the "Yes Doctor"
> >> assumption is that 1) there is a (finite of course) level of (digital)
> >> substitution (called the "correct level of substitution") that is
> >> sufficient to represent "all that I am", and "all that I could be if I
> >> hadn't undergone a substitution", and 2) we (including the doctor)
> >> cannot know what the correct level of substitution is, therefore we
> >> have to gamble that the doctor will get it right when we say "Yes
> >> Doctor".
> >> Suppose that the level of substitution actually *performed* by the
> >> Doctor is S_p. Denote the *correct* level of substitution S_c. S_p
> >> can be expressed by a finite number, since the substitution itself can
> >> be expressed by a finite number (whatever is written on the tape/CD or
> >> other storage/transmitting device). We know what S_p is and it is a
> >> *fixed* finite number. But since S_c (*correct* level) is totally
> >> unknowable, all we "know" about it is our assumption that it is
> >> finite.
> >> The next *obvious* step in the logical process is that the
> >> probability
> >> that S_p >= S_c is infinitesimal.
> >> I.e. the probability that the doctor
> >> got it right is zilch. This is because most numbers are bigger than
> >> any fixed finite number S_p.
> Why? If the level is high it could be that even a drunk doctor will
> always choose it correctly. Your inference does not seem valid.
I think your and my "levels" are inversely proportional to each other,
hence the confusion. My "level of substitution" is directly
proportional to the number of digits/bits/whatever needed to encode the
substitution. So a finer substitution I am calling "high", like using
a high number of subintervals in a numerical integration to get a
better approximation. I image the Doctor having a dial that he cranks
up to "HIGH" if you pay him more money. You need to (temporarily) use
this definition to follow through my argument above, even though your
use of the term "low level" is probably more sophisticated.
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