Saibal Mitra writes:
> I agree with the notion of OMs as events in some suitably chosen space.
> Observers are defined by the programs that generate them. If we identify
> universes with programs then observers are just embedded universes. An
> observer moment is just a qualia experienced by the observer, which is just
> an event in the observer's universe.

I can agree with the thrust of this, but let me break it down a bit.

I agree that, "Observers are defined by the programs that generate them."
One complication is that any output, including an observer, may be
produced by multiple programs, which leads to Bruno's first-person
indeterminacy.  But that's not important here.

I pretty much agree that, "If we identify universes with programs then
observers are just embedded universes."  However I think the terminology
is being stretched quite a bit here, calling observers embedded universes.
What I would say is, programs produce every possible kind of information
structure.  We could call all of these structures "universes", although
the word is going to be more applicable in some cases than others.
For example, there is a program which outputs the sequence of integers.
Is that sequence a "universe"?  It's a stretch, but okay, we can call
it that.

But there are also programs which output the dynamic information patterns
that recognizably correspond to observers.  The structure of such programs
is a key part of the "book" which Lee Corbin suggests I have been in
effect writing.  If we stick to the definition that all outputs are
(in some sense) "universes" then yes, I agree with your statement that
observers can be thought of as embedded universes.

Actually I'm not sure I fully agree about the "embedded" part.  I'm not
sure what you mean by that.  Maybe you mean that the observer (whom we
have defined as a universe) is himself embedded in a larger universe,
the world we see around us.  I agree that this will often be the case.

"An observer moment is just a qualia experienced by the observer,
which is just an event in the observer's universe."  I think I see what
you're saying here.  If we focus on the observer as a "universe" we can
think of him as being sort of self-contained.  Yes, in practice he is
probably embedded in a larger world, but we can restrict our attention
to the observer himself, as an abstract process that is going through
a sequence of states.  These momentary states are what you are calling
the "events" of the observer "universe", and these would correspond
to observer-moments.

In our space-time we have a notion of "events" as the four dimensional
points out of which space-time is built.  But you are saying that the
internal structure of an observer as a sort of self-contained universe is
not really four-dimensional.  Maybe it's trillion-dimensional.  It is an
abstract structure which, while embedded in our space-time, exists on its
own terms with its own internal data representation.  You are defining
"events" within that data structure, that self-contained universe.
They don't have a direct correspondence with four dimensional space-time
events in the larger universe that the observer is embedded in.

This reminds me of Jesse Mazer's conjecture about consciousness as a
causal pattern.  I asked whether he could imagine an abstract causal
network as capturing the essence of a given moment of consciousness.
I could see that concept as being closely related to your idea of the
observer as a universe, embedded in a larger structure.  However I may
be merely projecting both of your ideas into my own framework.

> I don't think that Hal's idea of identifying brain patterns with OMs will be
> successful. The brain is just the hardware that runs a program (the
> observer).

I don't think we necessarily disagree about this.  In I wrote:

"To apply this concept to observers, we first need to think of an observer
as an information pattern.  I adopt a block universe perspective and think
of time as a dimension.  Then we can see the dynamic activity that is
part of an observer's thinking as producing a pattern in space and time."

So I have an observer as being a *dynamic* pattern in space and time.
It is not just the hardware, it is the temporal pattern of activation of
the neural network.  I then went into painstaking albeit crude detail in
the rest of that message to try to estimate just how much information
it would take to capture a certain number of seconds of firing of the
neural network.  Again, this is a pattern of activity, a series of
related events, not just a static snapshot.

I also discussed in detail in that message how an observer as a self
contained information pattern could be considered to be embedded in a
larger universe, and how that would affect the measure of the observer.
That seems very much like your conception above, if I understood it

> If I run a simulation of our solar system on a computer, then the
> relevant events are e.g. that Jupiter is in such and such a position. This
> is associated with the state of the transistors of the computer running the
> program. But that same pattern could arise in a completely different
> calculation. You would have to extract exactly what program is running on
> the machine to be able to define OMs like that. To do that you need to feed
> the program with different kinds of input and study the output, otherwise
> you'll fall prey to the famous ''clock paradox'' (you can map the time
> evolution of a clock to that of any object, including brains).

I'm not sure I fully understand this, but I'll make two comments.  First,
a simulation of the solar system is vastly simpler than the calculation
needed to create an observer.  Intuitions based on the first case will
fail when applied to the other.  It may be plausible that two different
calculations could create matching representations of Jupiter's orbit.
But it's completely implausible that two calculations could accidentally
both create the same sequence of observer moments.  I estimated in the
message above that the chance of that happening would be one in 2^(10^18).
No human alive can even begin to grasp the impossibility of such an event.
Think of the most absolutely, totally, completely impossible event you
could ever imagine, and you won't be anywhere near as improbable as that.
It is beyond human comprehension.

Second, this clock paradox has been discussed before.  Years ago Jacques
Mallah on this list pointed out that algorithmic complexity disposes of
it neatly.  Sure, you can map any two calculations together, but if the
map becomes bigger than the calculations, then all the correspondence
is in the map and none in the calculations.

In measure terms, it still comes down to how short a program you can
write to produce the output that corresponds to an observer.  Go ahead
and write your clock or counter program, but its output does not match my
canonical representation of an observer moment.  The challenge is to write
a translation program that turns the output of your clock into the OM's
canonical representation (which is 10^18 bits in size!).  Such a program
is going to be as big as the OM data itself.  The clock is of no help.

On the other hand consider a program which (we would agree) really
does output or create the observer-moment, but perhaps not in the nice
canonical representation I might have defined.  Then we can write
a mapping program which will be relatively short, to turn one data
representation into another.  Even though we have 10^18 bits of data,
the mapping program will still be much smaller than this, because its
complexity does not depend on the size of the data to be translated.
This shows that the program really did create the observer-moment, because
there was little extra data in the map program.  The correspondence was
in the calculation, not in the map.

With such large data sets as observer-moments, the point becomes
very clear.  There is effectively no ambiguity about whether a given
calculation instantiates an OM or not.  Clocks don't do it; neural network
simulations can do it (with proper input); universe simulations can do it
(using a subset of their output).

Hal Finney

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