On Thu, Jan 03, 2002 at 05:55:32PM +0100, Marchal wrote:
> Wei Dai wrote:
> >I have a problem with trying to quantify 1-indetermincy. I'm not sure it's
> >a useful exercise, useful in the sense that a decision theory will involve
> >1-indetermincy.
> It depends about what the decision theory is for. If the decision theory
> is used by a subject for maximalising some gain, only that subject can
> decide what is a gain for him, and this (as Kant realised) can only be
> based on first person experiences, lived and expected.

I don't agree with this, because as I said earlier people expend effort to
obtain results that they'll never see, for example by writing wills.
Clearly what is a gain for a subject is not only based on first person
experiences. Suppose someone offered you $1000, but if you accepted Earth
would be destroyed and everyone on it killed as soon as you die. Would you
take that offer? Even if you did I'm sure most people wouldn't.

While it's true that evolution has programmed us to make decisions mostly
on the basis of first person experiences, I think this is really because
we haven't had access to mind duplication or quantum suicide technology.
If you consider those techonologies, it should be clear that there are
some valid goals that can't be expressed in terms of expected first person
experiences.

I admit the decision theory approach I gave in the last post has problems,
some of which you've pointed out. But what's the alternative? I've been
thinking about this issue for several years, starting with the
expected-first-person-experiences approach (if you read the earlier
archives you'll see many posts from me on this). I gave up on those when I
realized that some reasonable goals can't be expressed in terms of
expected first person experiences.

> I'm not sure what you mean by the GTM (Great Turing Machine?).

GTM means general Turing machine. It's defined in Jürgen
Schmidhuber's paper at http://www.idsia.ch/~juergen/toesv2/. Please read
it if you haven't already.

> I partially agree with you in the sense that I know there is a Universal
> Dovetailer capable of simulating all "universes" in parallel (+ all    
> dream of universes, etc...) and capable of generating all version of
> "me-now", but I stop here, because no Turing machine can keep track
> of the "me-now", and besides, even if such machine could exist (and
> it cannot by a theorem of RICE) then for any UD you can build another
> UD which will, on any finite portion of its execution, give
> different ratio between the me-now and their continuations (only in the
> infinite will the "ratio" be the same).

Wait, even in the infinite the ratios will not be the same in general. Why
do you think they will be?

> >From this position it appears that there is no need or room for an
> >objective measure.
> 
> ??? This is exactly what I don't understand (and where I agree with
> Finney's reply). 
> 
> Once such or such person has some (subjective and personal) goals,
> and has decided to put much weight on that goal, it seems to me that
> it is better for him/her to take into account the most objective 
> measure she/he can calculate or bet on his/her continuations.
> Exemple: 1) my goal is to drink a hot coffee. I put a recipient of
> water onto the stove (or cooker?). I use some implicite high measure
> on the probable boiling water phenomenon.
> 2) I use teletransport everyday because I got a job on Mars.
> Now the channel has been made secure (thanks to some quantum
> protocol). My goal here is to make as little as possible the
> probability of being duplicate without my consent by some sadical
> channel-pirate in need of flesh (not chair!). So I decide to pay
> the bill for the quantum protocol.

If you read Schmidhuber's paper, you'll see that he offers several
measures for consideration. He believes that the Speed Prior is the
correct objective measure, but I think it's a matter of subjective
preference. Adopting the Speed Prior basicly means you care more about
universes that are fast to compute then universes that are slow to
compute. Here's an example to illustrate what I mean. This is really key
so please let me know if you don't understand it.

Suppose you want to crack a bank's encryption key, which is worth $4
million to you, and there are two ways to do it. You can spend $2 million
to build a quantum computer to crack the key, or you can spend $3 million
to build a classical computer to do this. Now if you believe the Speed
Prior is the correct measure, then you'll think that the quantum computer
will very likely fail, and therefore you should go with the classical
computer instead. But if you believe the Universal Prior is the correct
measure, then you'll think that both computers will work and you'll go
with the quantum computer because it's cheaper.

However, there's another way to think about this situation that doesn't
involve an objective measure. The fast-to-compute and the slow-to-compute
universes both exist. (The fast-to-compute universes are the ones where
quantum computers fail.) So when you adopt the Speed Prior you're really
saying "I know the slow-to-compute universes exist (and my actions affect
what happens in them), but I just don't care very much about those
universe." 

To me the attraction of think about it the second way is that it allows us
to just say that all universes exist. We don't have to say that
objectively one universe has a higher measure than another. What does that
mean anyway? If all universes exist, how is it that some universes have
more of an existence than others? We don't have to answer those questions.

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