Re: decision theory papers

```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.

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.

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.

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

Why choosing an arbitrary sequence of noise ?

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".

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

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