2 research outputs found
Compression is Comprehension, and the Unreasonable Effectiveness of Digital Computation in the Natural World
Chaitin's work, in its depth and breadth, encompasses many areas of
scientific and philosophical interest. It helped establish the accepted
mathematical concept of randomness, which in turn is the basis of tools that I
have developed to justify and quantify what I think is clear evidence of the
algorithmic nature of the world. To illustrate the concept I will establish
novel upper bounds of algorithmic randomness for elementary cellular automata.
I will discuss how the practice of science consists in conceiving a model that
starts from certain initial values, running a computable instantiation, and
awaiting a result in order to determine where the system may be in a future
state--in a shorter time than the time taken by the actual unfolding of the
phenomenon in question. If a model does not comply with all or some of these
requirements it is traditionally considered useless or even unscientific, so
the more precise and faster the better. A model is thus better if it can
explain more with less, which is at the core of Chaitin's "compression is
comprehension". I will pursue these questions related to the random versus
possibly algorithmic nature of the world in two directions, drawing heavily on
the work of Chaitin. I will also discuss how the algorithmic approach is
related to the success of science at producing models of the world, allowing
computer simulations to better understand it and make more accurate predictions
and interventions.Comment: 30 pages. Invited contribution to Chaitin's festschrift based on an
invited talk delivered at the Workshop on 'Patterns in the World', Department
of Philosophy, University of Barcelona on December 14, 201
Estimations of Integrated Information Based on Algorithmic Complexity and Dynamic Querying
The concept of information has emerged as a language in its own right,
bridging several disciplines that analyze natural phenomena and man-made
systems. Integrated information has been introduced as a metric to quantify the
amount of information generated by a system beyond the information generated by
its elements. Yet, this intriguing notion comes with the price of being
prohibitively expensive to calculate, since the calculations require an
exponential number of sub-divisions of a system. Here we introduce a novel
framework to connect algorithmic randomness and integrated information and a
numerical method for estimating integrated information using a perturbation
test rooted in algorithmic information dynamics. This method quantifies the
change in program size of a system when subjected to a perturbation. The
intuition behind is that if an object is random then random perturbations have
little to no effect to what happens when a shorter program but when an object
has the ability to move in both directions (towards or away from randomness) it
will be shown to be better integrated as a measure of sophistication telling
apart randomness and simplicity from structure. We show that an object with a
high integrated information value is also more compressible, and is, therefore,
more sensitive to perturbations. We find that such a perturbation test
quantifying compression sensitivity provides a system with a means to extract
explanations--causal accounts--of its own behaviour. Our technique can reduce
the number of calculations to arrive at some bounds or estimations, as the
algorithmic perturbation test guides an efficient search for estimating
integrated information. Our work sets the stage for a systematic exploration of
connections between algorithmic complexity and integrated information at the
level of both theory and practice.Comment: 33 pages + Appendix = 44 page