Matthew Donald wrote
>Nick Bostrom <nick.domain.name.hidden> replied
>
>> Are you saying that it is not possible in your model to define the
>> class of all points in time on all branches of the universal wave
>> function which are at a temporal distance of, say, 10 years from
>> the start of the world (assuming there was a point when the
>> world (i.e. the whole tree of branching possibilities) started?
>> (This is not a rhetorical question but a clarificationary one. And
>> I'm not asking whether we could identify those points, but
>> whether the class of such points is defined.)
>
>Yes, I am saying that.
>
>First of all, I would be unhappy with the requirement to specify a
>unique hyperplane of simultaneity.
>
>More generally, many problems arise when we try to understand the
>nature of time in modern physical theories. Prior to relativity
>theory, it seemed that there was a natual succession of
>universally-valid ``nows'' apparent simultaneously to everyone alive
>at the time. Times other than the present now had happened or
>would happen but were not currently in existence. Special
>relativity, however, taught us that simultaneity is
>frame-dependent and introduced the idea of reality as a
>four-dimensional spacetime. According to general relativity, time
>is path-dependent. In the quasi-classical cosmology of the world
>we seem to live in, time appears on all inextendible paths to have
>begun with a big bang, but on some of those paths it may come to an
>end in a black hole, while on others it may continue for ever.
>
>What will the right picture be if we ever manage to quantize
>general relativity? I suspect that we should allow for the
>possibility of black holes being formed as a result of uncertain
>``quantum events'' -- it may be harder to choose to construct a black
>hole than to kill a cat but it is not unimaginable. This suggests that
>time is not just frame dependent and path dependent, but even
>observer dependent.
>
>Now, partly in order to deal with the problem of time in special
>relativity, I have developed a many-minds interpretation of
>quantum theory which involves information being definite only
>separately for each individual observer. The information observed
>by an observer is specified by sequences of local quantum
>states associated with the life history of that observer.
>
>Applied to the EPR-Bell situation, for example, this means that
>when Alice measures a spin, her current state expresses
>a possible observed spin direction. (This is a local process.)
>When Bob measures a spin, his current state expresses a possible
>observed spin direction. (And this too is a local process.) Finally,
>another local process occurs when Alice and Bob compare their
>observations (or rather, when each separately observes the
>appearance of the other). The observed correlations which
>result are determined by the initial singlet state which was
>effectively previously observed separately by both.
>
>I believe that, in many ways, this provides a very satisfactory and
>explicit solution to the problem of what it might mean for time to
>be observer-dependent.
>
>But if time is observer-dependent, then it is hard in general to
>compare times between different observers.
I agree. With the hypothesis of computationalism, we must distinguish
first person subjective time, not sharable at all, first person plural
time sharable with clocks and relatively communicable, and then,
thanks to the Universal Dovetailer (complete by Church thesis) we can
describe an objective 'observer moment birth rank' as the minimum
number of steps of a typical UD to get the corresponding
computational state.
And that is the best notion of birth rank we get, and it is a trivial
one because time (and space) has nothing to do with it. The probabilities
are taken on the first person plural time which must be defined on all
relative computational histories going through that computational state.
>This means that I do not view the ``birth rank'' problem as being
>well-posed for my theory.
So do I, except for the trivial case mentionned below.
> Nevertheless, the broader problem of the
>extent to which we should expect to see ourselves as being
>``typical'' observers is one which I think is both absolutely crucial
>and very hard to deal with. I appreciate Bostrom's work because I
>think that he is helping to clarify some of the issues involved in
>that problem.
So do I. Bostrom's work helps me to realise I am doing
arithmetical SSA, and that I am generalising the anthropic
principle into an UTM-tropic principle.
>I also think that whether we are typical observers and whether
>time is observer-dependent are questions which are relevant for
>any ``theory of everything''.
Sure.
Then Matthew Donald quote himself
> I believe that there is no conceivable algorithm which could take
> elements of the set of observers as I define it (well-defined and
> countable although that is) and attach unambiguous birth ranks to
> each one of them.
I believe there is one! I have even got the patience to write
one in LISP and to execute it for four hours ! I mean a UD.
But any apparently physical birth rank superne on an infinite number
of birth in UD*. Physical time emerges slowly in UD-standart "time"
but we don't care, and we shouldn't. We care only on
*all* our 'observer moment birth' in UD*.
All this should be clear for those who have followed the UDA
argument. Cf.
http://www.escribe.com/science/theory/m1726.html
Bostrom replied
> Do you mean effectively computable algorithm?
> I don't see why it would make a difference if the reference could
> not be exactly computed in a finite time.
and Matthew Donald replied
>No. I just referred to an algorithm to stress that I really am
>serious when I use words like ``unambiguous'' and ``well-defined''.
Well, but this is ambiguous. Of course with UD we accept infinite
non stopping computational histories, even with random oracles and
perhaps other one.
Bostrom replied (to Matthew Donald)
> I'm not sure whether we are really disagreeing on this point,
> although I would insist that one sort of question we may
> meaningfully ask is not just what my own future will be but also
> what the world is like (and was like in the past) in general.
and Matthew Donald replied
>I am afraid that we are disagreeing here, because I do not agree that
>``the world'' exists in anything like the way that Bostrom implies.
Me too, and probably for similar reasons(*). My thesis (see the URL below)
can really be seen as a many mind interpretation of ... arithmetics.
Where mind is defined by sharable (formalise by G) and not sharable
(formalize by G* - G) first person experiences.
(G is a sound complete decidable modal propositional formalisation of
arithmetical (or set theoretical, it is the same!) godelian
provability logic. And G* is its extended truth theory, which
curiously enough is also complete, sound and decidable.
(See the book by Boolos 1993)).
(*) Your text, Matthew, is not quite easy (IMLMO).
IMLMO = In my logician-minded opinion :-)
Bruno
Bruno MARCHAL Phone : +32 (0)2 650 27 11
Brussels University Fax : +32 (0)2 650 27 15
Avenue F.D. Roosevelt, 50 IRIDIA, CP 194/6
B-1050 BRUSSELS Email : marchal.domain.name.hidden
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http://iridia.ulb.ac.be/~marchal
Received on Fri Oct 20 2000 - 05:12:38 PDT