Niclas Thisell writes:
>I think the difference (and confusion on my part) arises from the fact
>that you are not using the measure suggested by Schmidhuber. Instead you
>are looking at all infinite computations and 'peek' into the state of
>the machine. And I agree this will probably give an additional shift
>towards 'large' numbers and concepts involving limits towards infinity,
>like the reals. And perhaps it's not a bad idea. It is, after all, a
>larger set than the set of turing machines that come to a halt - i.e.
>all halting turing-machines can be implemented by your set by simply
>adding an 'infinite loop' at the end, so to say.
I agree.
>So, how is that measure defined? One shot at a semi-formal definition
>would perhaps be something like this;
>O(p,i)=The i:th string the program p chooses to expose.
>I~(O)=An interpretation of O.
>I(p)=lim( I~(O(p,i)), i->inf )
>M(IŽ,N)=(number of programs p of length N whose I(p)=IŽ ) / 3^N
>M(IŽ)=lim( M(IŽ,N), N->inf )
>Or do you have a better suggestion? (Note that this definition gets rid
>of 'internal' UD:s since they don't have an interpretation in the limit)
I will think about it. I'm not sure it is so easy. My own way to search
a measure is based on the Godelian modal logics of self-reference.
With my UDA (Universal Dovetailer Argument, also cited as PE-omega in this
discussion) I show that comp implies that physics is a branch of
machine's psychology. Then I use the Godelian self-reference logic to
redefine notion like first person and third-person and also a notion
of observation. I conjecture that one of these logics should give the skeleton of the space of "physical" propositions, and eventually I showed that this skeleton is (quasi)-isomomorph to the Birckhoff-von Neumann
Quantum logic.
This is the way I hope to extract the Hilbert Space structure and quantum- like measure from the logic of self-reference.
I'm sorry of pointing to such a weird field which is apparantly far from physics and metaphysics, but I really think it provides, for those willing to accept the computationalist hypothesis, a formidable shortcut.
For exemple, your present little attempt is only able to define a third
person measure where I need (this is shown by the UDA) first person
notions.
>Well, that was a mistake on my part that I tried to correct in a
>followup;
I got the follow-up just a little to late. No problem I see your point.
>I didn't actually mean 'linear differential equation'.
>But I did make an assumption. And I frequently do just to see what
>happens, even though I don't even believe these assumptions to be true.
That is what I call doing science. Reasoning on assumptions.
BTW nobody in this list should infer that I believe in comp.
Of course I will not hide the fact that I am utterly fascinated by
comp's consequences. But I am still open that my or similar
works would lead to a refutation of comp.
Mmh... To be honest I begin to doubt that too :-)
I *do* find comp more and more plausible, thanks to the quantum
experimental weirdness.
>Unfortunately I don't understand a word of french :-(.
There is someone translating it. So it's a question of time ...
I am also writing two papers in English. I will also put some old
english papers in my URL, but these are very concise and
computer-science minded, and ..., well old, I say.
But I can send you copies if you want.
>> Third person physical time and first person subjective time
>> are internal
>> modalities (infered by machines entangled with deep
>> computations, ...).
>> They have nothing to do with the 'time step' of the DU. In my
>> 'ultimate
>Heh, no, I didn't think so. And I feel that I somewhat unjustly accused
>you. Perhaps I should have accused Schmidhuber instead, whose first
>assumption of his paper is "Each universe evolves on a discrete time
>scale".
Good idea, to accuse Schmidhuber instead ;-)
>I also feel that the concept of MWI splitting promotes this
>picture (and should therefore be banned :-).
Yes, but note that here Schmidhuber is rather coherent. There are
many computations and these computations differentiates.
I do not believe (with comp assumption!) that there is even one
objective universe. There is a 'phenomenology' of many universes.
In 'fact' there are only dreams (computations seen from the
machine's first person point of view). And the laws of mind, or the
machine's psychology shows that some dreams are sharable among
vast collection of machines. This makes it possible
for machines to project and believe in universes and still be
approximatively correct.
(a little like Newton's absolute time is approximatively correct
in our neighborhood).
To compare still with Schmidhuber, it seems to me that he links
our "real" universe or multiverse with one computation. Then he
try to find prior for the program generating that computation.
I give an argument (UDA) showing that, although such prior
could be (and plausibly is) necessary, our consciousness' flux
cannot be attach to a single computation. So as you say we must
take into account the collection of our infinite computational
continuations as well.
>Personally, I could just as well look at the universe as 'evolving in
>the x-direction'. Or, simply, looking at e.g. the Maxwell equation, that
>the program has a 4-dimensional array that is successively expanded and
>refined to reach an infinite extent and infinite resolution in the
>limit.
That is quite possible with comp. Nevertheless something like
"the x-direction" (in fact the notion of space) is very hard to
justify. Not to speak of Maxwell equation, nor even F=ma !
Regards,
Bruno
Received on Thu Jan 06 2000 - 07:28:38 PST
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:06 PST