# Re: decision theory papers

```Dear Matthieu:

At 4/19/02, you wrote:
>On 18 Apr 2002, at 20:03, H J Ruhl wrote:
>
> >
> > 5) I do not see universes as "splitting" by going to more than one next
> > state.  This is not necessary to explain anything as far as I can see.
> >
> > 6) Universes that are in receipt of true noise as part of a state to state
> > transition are in effect destroyed on some scale in the sense the new state
> > can not fully determine the prior state.
> >
>
>"The new state can not fully determine the prior state" only means that the
>application that give the next state from the prior state is not bijective.```
```
I do not agree.  You seem to have missed what I said.  Post the true noise
event there is no T that can determine [deterministically extract] the
prior state from just the info in the current state [because the true noise
has no identifying tags].

>Let's call S the set of all possible states of universes.
>T is the application that give the next state from a prior state.
>
>Without "true noise" T is an application from S to S
>                   T
>       S       -------->       S
>prior state   -------->  next state
>
>If the application T is not bijective (There is no reason that it should
>be) then the new state can not fully determine the prior state.

All that seems to say is that some computational universes are also severed
from their history when using a fixed T.  Some other T may be able to make

>Now with the mysterious "true noise", the prior state alone can not
>determine the next state. T is not an application from S to S.
>T is an application from SxN to S.
>                              T
>     S   x    N          ---------->       S
>(prior state, noise)    ---------->  next state.

I see it as:

T + N
S(i)  -------------------------> S(i +1)

>In your system universes are sequences s(t) defined by a given initial
>state s(0) and a given application T. Without "true noise" the sequence
>follows the rule: s(t+1) = T(s(t))

I usually write my Type 1 [no internal rules allowing external true noise]
more like T(i) acting on P(i) where P(i) is the shortest self delimiting
program that computes S(i) [not necessarily from S(i -1) in fact there may
be no S(i -1)]. This allows derivation of a cascade with naturally
increasing information in the P(i) as i counts up.

P(i + 1) always contains P(i) plus T(i) plus the self delimiter.

T(i) may change given the requirement for true noise regardless of the
nature of T

>But with the "true noise", s(t+1) = T( s(t), noise(t)).

I usually write my Type 2 [internal rules allow external true noise] as
T'(i) acting on P'(i) where P'(i) is the shortest self delimiting program
that computes S(i) from some S'(i - 1).  S'(i - 1) is not necessarily the
actual S(i - 1) but can be deterministicly proposed from S(i) using some
deterministic T.

>What is noise(t) ? Is it true random ? I would like to know your definition
>of true random.
>I suppose noise(t) is an arbitrary sequence in the N set.

I define it as new information from an external source [from the
Everything/Nothing boundary].  The closest model I can think of in our
universe is to attach a radiation counter to a computer input and use the
event data to create strings that are then used in the computer's
computations.

>Why choosing an arbitrary sequence of noise ?

That is a little longer story and is addressed in my draft paper at:

http://home.mindspring.com/~hjr2/model01.html

I am still editing this work.   The root reason is to avoid information
generating selection in the Everything.

>I prefer to consider the application T' from S to the set of subset of S.
>T'(s) is the union of { T(s,n) } for all n element of N.
>T' is the application that give all possible next state for a given prior
>state.
>
>This means that when we consider a starting state s(0) there is not only a
>sequence of successive states but a tree of all possible histories starting
>from s(0).
>In other words, "true noise" causes the universes to "split".

As you can see I consider the process like one makes soup [the T'] and then
right at the end adds a random sprinkle of salt.  The result is one
finished soup.  No more is needed.

>If you say your universes don't split and are affected by a "true noise",
>you are choosing an arbitrary sequence of noise.

Well what other kind of true noise is there?

>This is a kind of physical
>realism.

Actually I do not see a need for a "physical" reality.  The S(i) strings
can have more than one interpretation but these interpretations need not be
"physical"

>On this list, we are mathematic realist (some even think only algebra has
>reality), and we think physical reality is a consequence of math reality.

In that sense I see no need for anything "mathematic", just a lookup table
[a rather large but finite one in our case] active at each of a number of
discrete cells plus some degree of external noise in some of them [a
cellular automaton + some noise].  For example I suspect that our universe
is a cellular grid organized as face centered cubic in its ground
state.  This is a 12 about 1 structure with interesting symmetry.  Each
cell would contain a single point that can be at any of say 1000 locations
within its cell.  The "with external noise" look up table would need to
have more than 14 columns [column 14 contains the "deterministic" next
state of the central cell as a function of its current state and that of
its 12 neighbors and the ones above 14 are where part of the noise goes]
and [10^3]^13 rows.  The rest of the noise determines which column above 13
is selected as the next state of the central cell

This is below any formal system in that it is all axiom [the [10^3]^13]
rows plus external noise.

>Don't say again "my" system is too complex, I just tried to define clearly