Le 10-août-06, à 14:16, Stathis Papaioannou wrote :
>> Bruno: I am not sure I understand. All real number exist, for
>> example, and it
>> is the reason why we can put a measure on it. All computations exist
>> (this is equivalent with arithmetical realism) yet some are or at
>> could be relatively more frequent than others.
> Stathis: Sure, but it's the details that are mind-boggling. Why do
> bark and cat-computations meow? If there is a definite mathematical
> how do we even begin to fathom it?
I think there is a "definite (but necessarily partial) " mathematical
answer once we assume the comp hyp. It seems to me that the UD argument
explains informally what shape this "mathematical answer" could have: a
measure problem. Now I am not sure I understand why you don't see it.
This is because I can infer by most of your posts that you handle well
the relevant thought experiments. You certainly convince me I should
explain more about the UDA in the roadmap-summary, before explaining
the lobian interview.
> Or would you go the reductionist route
> of starting with basic physical laws, on which chemistry, biology,
> etc. are built, the more basic sciences supporting the less basic?
Except that the UDA is supposed to help to understand that the
basic-ness of science could be the other way round: psychology/theology
being more fundamental than physics. I hope I will be clear on that.
I have put a first version of the "roadmap" in the trash, because it
was too long and at the same time it was not even addressing some
difficulties which I am guessing many people have through your post. It
is hard because I try to write a short text, and simultaneously I try
to anticipate the sort of objections I find reasonable through my
reading of the current many posts on the notion of persons.
>> I know it looks counterintuitive, but an AI can know which computer is
>> running and how many they are. It is a consequence of comp, and the
>> shows why. The answer is:
>> the computer which is running are the relative universal number which
>> exist in arithmetical platonia (arithmetical truth is already a
>> universal video game, if you want, and it is the simplest). How many
>> are they? 2^aleph_zero.
>> I have already explain it here:
>> It is a key point and we can come back on it if you have some
> Well now I'm confused! I thought the whole point of the earlier part
> of the UDA
> as discussed in the cited post (and many others of yours) is that you
> know the details of your implementation, such as what type of computer
> you are
> being run on, how fast it is running, if there are arbitrary delays in
> the program,
> and so on. Are you now saying that if I am being run on the 3rd of 100
> PC's in
> the basement of the local university computer science department, but
> is keeping this a secret from me, there is a way I can figure out
> what's going on
> all by myself?!
Did you read my old post to Brett Hall:
Perhaps you could comment it and tell me what does not convince you. It
is indeed correct that the earlier parts of the UD Argument show that a
machine cannot know about comp-delays, or about the real/virtual nature
of a computer which would support the machine's computation until ...
you realize that for exactly those reasons the machine first person
expectations can only be computed (exactly and in principle) through a
measure on all possible computations (reducing physics to searching
such a measure). But then the first person can no more be associated
with *any* particular computations. Read the Brett Hall post where I
explain more, again in a "steppy" fashion (but the point is different
from the UDA).
To sum up that point:
1) comp shows we cannot know which computations supported us.
2) digging deeper in comp, this means eventually we are supported by
*all* (relative) computations (relative to some actual state; the
"actuality" itself is handled in the traditional indexical way, and
eventually "indexicality" is treated through the logic of
self-reference (G and G*).
>>> Yes, I think what you mean by "relative probabilities" is that if
>>> there were
>>> several possible versions of "me next moment", then I would be more
>>> to experience the one with higher measure. It is only relative to the
>>> possibilities that measure makes a subjective difference.
>> Ah but you get the point now!
> So, as long as this *relative* measure does not come into play, the
> measure makes no difference?
But physics arise (or should arise, with the comp hyp.) from the
*relative* measure, and physics will be what makes possible for
consciousness to be able to manifest itself. George asked me to explain
this like if I was talking to some grandmother, but it is tricky to do
that. The reason is that either what I say is understandable, but then
it is unbelievable. And that is why I have never published the UDA
alone, I always publish the UDA together with its arithmetical
translation. The reason is that only the math translation can help to
understand how this "paradox" is resolved by distinguishing truth and
provability, but also provability and true-provability, etc.
Another difficulty with the UDA is that the consequences contradicts
some supplementary hypotheses which start the reasoning. Those
supplementary hypotheses are implicit in the 8-step version and
explicit in the longer 15-step version (which explains then how those
supplementary hypotheses are eliminated). For a logician this is not so
difficult: the formula "(~p -> p)" is not a contradiction: proving it
gave just a proof of ~p, which explains why I don't need to go through
those supplementary hypotheses at all, except, well, that non logician
eventually discovered them, and feel then something is wrong ...
Perhaps it is related to your difficulties, in which case I take the
opportunity of Peter D. Jones' post who kindly recall the 15-steps
version of the UDA to suggest to read it, perhaps that could help.
I hope this does not discourage you. Obviously we are tackling very
difficult questions. And I am still searching some better pedagogy
(besides I can be wrong too of course).
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