Joel:
>Bruno:
>> But don't we have a contradiction, or something like an empirical
>> contradiction here. I can certainly hope for certain futures, and
>> honestly I think (at least from past experience) that some are more
>> probable than others. For exemple I am now preparing some coffee. I
>> would have the feeling of lying to myself if I was telling you that I
>> do not believe "drinking" coffee is probable. So "something" is
>> probable. So, if we maintain comp, we must explain why, after I have
>> done coffee, drinking coffee got an higher degree of probability. We
>> must aknowledge that physicalist do have an explanation here. There
>> is coffee, there is a material machine preparing it, etc.
>
>Hmm... I think I see the problem now. But I don't understand your proposed
>solution.
I am glad you begin to see the problem. I have not proposed a
solution (yet), I have only try to give an accurate description
of the problem. Later I will point onto some strategy to search the
solution, which, btw, cannot be "proposed". The solution exists
or does not exists. If the solution does not exists (provably),
then comp is false (refuted).
>Do you want to 1) make predictions about the future based on past
>observations, or 2) make predictions about the future based on all possible
>histories, or 3) something else entirely.
Nicely formulated question: it is neither "1)", neither "2)", neither
"3)" !
What I want to do ... Well, no: what I'm *obliged* to do (keeping comp)
is to explain why "1)" seems to work giving that comp force me to
accept "2)". We must justified something like "2) => 1)".
Perhaps more precisely: why a third person "2)" implies a first person
"1)". Perhaps that will be clearer below where I will attempt
to conclude the UDA less rapidly.
>In the first case (1), I think I can see how this might be possible.
>
>For example, if every 9 out of 10 times you drink the coffee after making
>it, then you should be able to reasonably conclude that the next time you
>make coffee, you will most likely drink it.
I agree, except that this is what we need to explain.
>This seems to work in our current simulation because for the most part, our
>world appears to be mostly "predictable". But it will start to fail in
>worlds where there is little regularity. (e.g. making coffee and drinking
>coffee almost never happen)
So we must explain why, summing on all computational stories, we
stabilise on "predictable" stories. Note also that an expression like
"our world" is unavoidably ambiguous, and strictly speaking cannot
be used with comp (through the UDA).
>But in the second case (2) I can't see how we can make any meaningful
>predictions since the number of all possible histories is infinite.
Yes, even uncountable. But that is not a problem. Measure theory,
including Lebesgue integration theory has been invented for dealing
with probability on uncountable domains. This is used in elementary
(non relativistic) quantum mechanics too.
The problem is not even to find an ad hoc measure which makes the
white rabbit stories negligeable, but to show that the unique measure
forced by UDA (or arithmetical translation of UDA) is such that
rabbit stories are (relatively) negligeable in it.
In case it is not, comp is refuted.
>> Put in another way, we must derive the laws of physics from computer
>> science. And, through the role of the notion of 1-pov, we must derive
>> physical belief from coherent discourse by machines, or more simply
>> derive physics from (machine) psychology.
>>
>> Do you agree?
>
>I'm not sure. I'm still unclear about what you are proposing.
I am not proposing anything. I'm just showing that if we are machine
then next instants are defined by a (relative) measure put on
the set of consistent reconstitutions *as seen by themselves* (the
1-person psychology) generated by the UD.
>How can we derive physics from psychology?
Interesting question. Note that the UDA just show that: if we are
machine then we *must* derive physics from psychology (itself, by
comp, embedded in number (meta) theory.
Mmh... UDA shows more. It shows that your next instant is
"determined" by all computational histories (generated bu the UD)
going through your 3-state.
>Can you give some simple example, like the coffee experiment?
Excellent idea! I will make myself a cup of coffee.
>> If you follow me perhaps you can understand why, in case your MUCA
>> is *the* bottom, then we should not postulate that!!! We should prove
>> it, for exemple by showing that the measure behave well only thanks
>> to the infinite MUCAs' work generated in arithmetics (or by any DUs,
>> or in Numberland, as I like to say.
>
>No - sorry. I don't understand that either. I think you've lost me.
>
>> If you really take the comp 1-indeterminisme seriously, perhaps you
>> can guess also why our very finiteness makes us confronting some
>> continuum, and some random oracle, ...
>
>Infinite possibilities? I don't know.
Remember that you have answered "yes" to the ten first question.
Let us run the UD "again", and let us look what happens when I
am preparing a cup of coffee.
Let us consider one instantaneous (relative) description of my
state of mind S among the states I am going through during my
coffee preparation.
And look what does the UD. It generates that state S infinitely
often. Oh, at first it generates that state in 10^googol steps, and
it generates it again much (very much) later. It generates it
through different but similar computational histories. It generates
"dummy" copies also : for exemple it generate S + 0, and later S + 1,
and later S + 00, and later S + 01, and later S + 10, ... ,
and later S + 00000000100010000111, and later ..., dovetailing
on all finite initial segment of the real.
This is of course still countable when you look at the domain
from a third person point of view. But, as you aknowledge in
question 7, the delays does not count for the first person, so
the domain of 1-indeterminacy, which is of course a first person
notion, is, thanks of that delays elimination, given by the
union (which is just the set theoretical interpretation of the or)
of all portion of UD* (the execution of the UD, an infinite
three dimensional cone in case the UD is implemented in a
two dimensional cellular automaton) in which my "preparing coffee"
state appear. (Reread that sentence slowly, I have written
it slowly, and without doubts it's too long).
So UDA gives the shape of the solution. The technical problem
which remains is to isolate the "correct" proximity relation
among infinite computational histories.
Do you understand?
(But here we are near entering the second part of my thesis
where I begin to extract that topology/measure from intensional
variants of the logic of provability (godelian self reference logic),
or, as I like to say, I interview the sound universal machine
about that measure).
Believe it or not but I drank that coffee unconsciously!!!
I will try again ... :-)
Bruno
http://iridia.ulb.ac.be/~marchal
Received on Tue Jul 03 2001 - 07:43:29 PDT