Re: Jurgen Schmidhuber

From: Eliezer S. Yudkowsky (
Date: Fri Dec 01 2000 - 15:03:42 MST wrote:
> I am not sure how many people have every visited this fellows webiste, but he
> has a newly published article, that has been released on the
> website (55-pages .PDF format). It seems to impact much of what sl4 examines.
> His personal website is at

People posting article references: Please include at least the title,
rather than just the blind link. (Sorry for not stating this earlier.)




We make the plausible assumption that the history of our universe is
describable, and sampled from a formally describable probability
distribution on the
possible universe histories. To study the dramatic consequences for
observers evolving
within such a universe, we generalize the concepts of decidability,
halting problem,
Kolmogorov's algorithmic complexity, and Solomono 's algorithmic
probability. We
describe objects more random than Chaitin's halting probability of a
Turing machine,
show that there is a universal cumulatively enumerable measure (CEM) that
previous measures for inductive inference, prove that any CEM must assign
low proba-
bilities to universes without short enumerating programs, that any
describable measure
must assign low probabilities to universes without short descriptions, and
several sim-
ilar \Occam's razor theorems." Then we discuss the most ecient way of
all universes based on Levin's optimal search algorithm, and make a
natural resource-
oriented postulate: the cumulative prior probability of all objects
incomputable within
time t by this optimal algorithm should be inversely proportional to t.
sequences for inductive inference, physics, and philosophy, predicting
that whatever
seems random is not, but in fact is computed by a short and fast algorithm
which will
probably halt before our universe is many times older than it is now.


It seems fairly obvious to me that our Universe's laws of physics are not
minimally efficient. The Game of Life is minimally efficient. Our laws
have a great deal of internal functional complexity. Personally, I
predict that state-vector reduction will turn out to be really and truly
fundamentally random - noncausal, acausal, a gap in the causality of the

Still, it's a great line of reasoning, and if any characteristics of our
Universe show signs of having minimal informational complexity, I'd be

-- -- -- -- --
Eliezer S. Yudkowsky
Research Fellow, Singularity Institute for Artificial Intelligence

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