A contrast: my approach vs Schmidhuber's

From: Hal Ruhl <hjr.domain.name.hidden>
Date: Tue, 28 Nov 2000 23:09:00 -0800

The following may assist in generating commentary on my model.

In my approach Rj is primarily just a comparator. It decides whether one
string [a chance encounter] is an acceptable successor to another string
[the existing state].

I make no restriction on the nature of Rj except that it be one of the
counting numbers in the "Everything" I describe and that it and its
interpretation is fixed for a given universe.

The number that is the initiating axiom Aj and the number that is Rj
encounter each other and Rj arbitrates the successors to Aj in a recursive
process thus forming a universe.

In my approach - by appealing to Chaitin's work - the string Uj must
progressively increase in length to accommodate the information it
contains, and the length of its compression Pj - which contains the
operative fc-FAS - must do likewise without changing the axiom base Aj or
the rules Rj leaving just additions to the alphabet as the change engine.

The same Rj could arbitrate successors for any Aj in a variety of different
ways. A given combination is fixed and defines a particular universe.

In my approach Rj can have a degree of "Do not care." [randomness] in its
arbitration process. This is one way to add bits to the string Uj.

It can be fully deterministic, it can be partially deterministic and
partially random in all combinations and permutations, it can be fully random.

The fully random case is just the same as an empty Rj so Pj is empty which
is just the "Everything" back again.

My approach if run JUST over all the completely deterministic subset of Rj,
AND ignoring the Chaitin imposed necessary increases in complexity of the
fc-FAS as the recursion progresses looks just a little bit like a universal
dove-tailer except its one where the execution slot assigned to a
particular universe is in constant flux. This substantial substantive
down selection from my approach is - I believe - close to the deterministic
portion of Schmidhuber's approach if I read his paper correctly.

In my opinion his treatment of the introduction of "noise" and similar
issues is also quite considerably different from mine.

All in all however, our two models seem to bring us into agreement on many
consequences which I will discuss in a later post.

Hal
Received on Tue Nov 28 2000 - 20:19:48 PST