Hi Nick,
On 07 Jan 2010, at 01:39, Nick Prince wrote:
Hi Bruno
OK so there is a good deal of the technical stuff that I've got to
catch up on yet before I can interpret what you are saying (although
I think I can understand why the everettian imperative based on comp +
UDA is there).
Nice. It is already a big part.
However if I could for the moment get an intuitive
understanding of what you mean by a consistent extension then perhaps
that would help with what Brent brought up. From what I gather you
are saying our next observer moment is based not on the laws of
physics but on what possibilities the UD brings up in UD*.
Our "next" first person observer moment. This comes simply from the
fact that the UD generates my current state (at the doctor
substitution level or below) an infinity of times. In each computation
I have a well defined third person next state, but my next 1-state is
defined olny statistically on all my next 3-states in all computations
going through my current state.
As an
analogy, in conways game of life, the next screen output display (=OM
for the little inhabitants) depends on the rules put into the cellular
automata (I know this only accounts for a single little universe here
and there would be an infinity of universal numbers for the real
universe etc, but lets try to keep it simple for the sake of clarity).
OK, but the distinction between 1-state and 3-state forces us to NOT
make that simplification. You will encounter a problem.
So in this game any (little) laws of physics (regularities in the
game) are emergent and would become evident to a conscious entity that
arose in the game.
Only if you implement the game in an already "self-multiplying"
computations. If not, then, from the first person points of view of
the little entities appearing in your game, they will survive
somewhere else in the UD*. They will survive "here" (in your game)
only from *your* point of view. But "your reality" is a white rabbit
universe from *their* point of view.
Of course, if you do it concretely, what you will build is most
probably a quantum object implementing the game of life, and as such,
it could gives the right measure. But this is "accidental" in the
reasoning, and based on the fact that we know already our
neighborhoods are quantum (and/or comp) multiplied.
So here is a case where physics (regularities in
the little world) arise from "a program". Is there any simple way
this analogy or example can be adapted to demonstrate how the
consistent extensions we experience come about. Does it have
something to do with the prescription of the UD. If not then how does
my existence pick its next consistent extension.
It is really the consciousness which picks the consistent extension.
It is your consciousness in Moscow which will pick up the consistent
extension "Nick + "I am in Moscow"". Similarly, your consciousness in
Washington will pick the Washington consistent extension. All the
consistent extension are picked, that is why we have to isolate a
measure on those extensions.
It's all to do with
what makes extensions "consistent".
Not really. A non consistent extension does not exist, simply. Unless
0 = 1. In auda, we can see that some extension lead to a belief into
inconsistency: those are the cul-de-sac worlds. They are consistent
("0 = 1" does not belong to them, but "provable ("0 = 1")" belongs to
them, and they are dead end, they have no consistent extensions.
This is subtle and related to the second incompleteness theorem (and
Löb theorem). Consistency entails the consistency of inconsistency.
Provable(false) does not entails false, because we cannot prove our
consistency (if we are consistent).
If we are inconsistent we can prove everything (including the false, 0
= 1).
But if we prove our inconsistency, we still cannot prove everything.
We may prove only that we can prove everything, and that is
different, and that difference eventually plays a key role.
You may think to buy the Davis Dover book "The undecidable". It
contains the original paper by Gödel, Turing, Church, Rosser and
Kleene, and also the formidable paper by Post (which initiate the
whole recursion theory), and also its incredible 1920-24 anticipation
(up to my thesis!). And it is cheap.
http://www.amazon.com/Undecidable-Propositions-Unsolvable-Computable-Functions/dp/0486432289
His little other Dover book "computability and unsolvability" is
rather nice too, but you don't need it if you have the Mendelson or
the Cutland book.
If it's not physics then it must
be something
It is arithmetic.
and is there a simple analogy that can help me to grasp
it? I find I can always work out the technicalities better if I have
a "road map" or analogy to help.
Arithmetic defined all the lawful sequences of states. But from inside
"1-persons" do not belong to any precise computations, but to an
infinity of them, and their relative next 1-state is defined
statistically on all computations. This comes from the global 1-
indeterminacy (cf step 7).
But if we believe that our next 1-state is related to the physical
laws (as we have good reason to do, indeed physics comes from that
observation, really), we have to justify the "stable physical laws"
from the statistic on all computations (or to abandon comp!).
A simple consequence of this, is that our physical reality has to be
described in term of a sum/statistics on infinity of computations, and
this, very startling and shocking fact, is confirmed by QM (without
collapse).
Then for the math, there is a need to see well the difference between
all points of view, and thanks to incompleteness, we get the
difference from the very classical definition of belief, knowledge,
sensations, already provided by the greeks (notably Theaetetus).
But I prefer to be sure people get the uda, before embracing auda,
which needs more background in logic (good book for helping auda is
Boolos 1979, Smorynski 1985, but they requires "Mendelson").
Hope this help a little bit. If you grasp that uda makes comp
extending Everett's imperative, you got the main thing. The rest
consists in using computer science and mathematical logic to make the
physics, or its logic, technically precise, notably the difference
between the points of view. Those are more subtle than a frog/bird
scaling difference. It is more akin to the difference between seeing
someone tortured and being tortured. It is very different.
Bruno
http://iridia.ulb.ac.be/~marchal/
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