12,644 research outputs found
The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications
The principle goal of computational mechanics is to define pattern and
structure so that the organization of complex systems can be detected and
quantified. Computational mechanics developed from efforts in the 1970s and
early 1980s to identify strange attractors as the mechanism driving weak fluid
turbulence via the method of reconstructing attractor geometry from measurement
time series and in the mid-1980s to estimate equations of motion directly from
complex time series. In providing a mathematical and operational definition of
structure it addressed weaknesses of these early approaches to discovering
patterns in natural systems.
Since then, computational mechanics has led to a range of results from
theoretical physics and nonlinear mathematics to diverse applications---from
closed-form analysis of Markov and non-Markov stochastic processes that are
ergodic or nonergodic and their measures of information and intrinsic
computation to complex materials and deterministic chaos and intelligence in
Maxwellian demons to quantum compression of classical processes and the
evolution of computation and language.
This brief review clarifies several misunderstandings and addresses concerns
recently raised regarding early works in the field (1980s). We show that
misguided evaluations of the contributions of computational mechanics are
groundless and stem from a lack of familiarity with its basic goals and from a
failure to consider its historical context. For all practical purposes, its
modern methods and results largely supersede the early works. This not only
renders recent criticism moot and shows the solid ground on which computational
mechanics stands but, most importantly, shows the significant progress achieved
over three decades and points to the many intriguing and outstanding challenges
in understanding the computational nature of complex dynamic systems.Comment: 11 pages, 123 citations;
http://csc.ucdavis.edu/~cmg/compmech/pubs/cmr.ht
Universal Intelligence: A Definition of Machine Intelligence
A fundamental problem in artificial intelligence is that nobody really knows
what intelligence is. The problem is especially acute when we need to consider
artificial systems which are significantly different to humans. In this paper
we approach this problem in the following way: We take a number of well known
informal definitions of human intelligence that have been given by experts, and
extract their essential features. These are then mathematically formalised to
produce a general measure of intelligence for arbitrary machines. We believe
that this equation formally captures the concept of machine intelligence in the
broadest reasonable sense. We then show how this formal definition is related
to the theory of universal optimal learning agents. Finally, we survey the many
other tests and definitions of intelligence that have been proposed for
machines.Comment: 50 gentle page
Design of engineering systems in Polish mines in the third quarter of the 20th century
Participation of mathematicians in the implementation of economic projects in
Poland, in which mathematics-based methods played an important role, happened
sporadically in the past. Usually methods known from publications and verified
were adapted to solving related problems. The subject of this paper is the
cooperation between mathematicians and engineers in Wroc{\l}aw in the second
half of the twentieth century established in the form of an analysis of the
effectiveness of engineering systems used in mining. The results of this
cooperation showed that at the design stage of technical systems it is
necessary to take into account factors that could not have been rationally
controlled before. The need to explain various aspects of future exploitation
was a strong motivation for the development of mathematical modeling methods.
These methods also opened research topics in the theory of stochastic processes
and graph theory. The social aspects of this cooperation are also interesting.Comment: 45 pages, 11 figures, 116 reference
Algorithmic complexity for psychology: A user-friendly implementation of the coding theorem method
Kolmogorov-Chaitin complexity has long been believed to be impossible to
approximate when it comes to short sequences (e.g. of length 5-50). However,
with the newly developed \emph{coding theorem method} the complexity of strings
of length 2-11 can now be numerically estimated. We present the theoretical
basis of algorithmic complexity for short strings (ACSS) and describe an
R-package providing functions based on ACSS that will cover psychologists'
needs and improve upon previous methods in three ways: (1) ACSS is now
available not only for binary strings, but for strings based on up to 9
different symbols, (2) ACSS no longer requires time-consuming computing, and
(3) a new approach based on ACSS gives access to an estimation of the
complexity of strings of any length. Finally, three illustrative examples show
how these tools can be applied to psychology.Comment: to appear in "Behavioral Research Methods", 14 pages in journal
format, R package at http://cran.r-project.org/web/packages/acss/index.htm
- …