Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability

Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and the associated Universal Distribution are (or should be) of the greatest importance in science. Here we investigate the emergence, the rates of emergence and convergence, and the Coding-theorem like behaviour of AP in Turing-subuniversal models of computation. We investigate empirical distributions of computing models in the Chomsky hierarchy. We introduce measures of algorithmic probability and algorithmic complexity based upon resource-bounded computation, in contrast to previously thoroughly investigated distributions produced from the output distribution of Turing machines. This approach allows for numerical approximations to algorithmic (Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a computational hierarchy. We demonstrate that all these estimations are correlated in rank and that they converge both in rank and values as a function of computational power, despite fundamental differences between computational models. In the context of natural processes that operate below the Turing universal level because of finite resources and physical degradation, the investigation of natural biases stemming from algorithmic rules may shed light on the distribution of outcomes. We show that up to 60\% of the simplicity/complexity bias in distributions produced even by the weakest of the computational models can be accounted for by Algorithmic Probability in its approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity calculator: http://complexitycalculator.com

Apperceptive patterning: Artefaction, extensional beliefs and cognitive scaffolding

In “Psychopower and Ordinary Madness” my ambition, as it relates to Bernard Stiegler’s recent literature, was twofold: 1) critiquing Stiegler’s work on exosomatization and artefactual posthumanism—or, more specifically, nonhumanism—to problematize approaches to media archaeology that rely upon technical exteriorization; 2) challenging how Stiegler engages with Giuseppe Longo and Francis Bailly’s conception of negative entropy. These efforts were directed by a prevalent techno-cultural qualifier: the rise of Synthetic Intelligence (including neural nets, deep learning, predictive processing and Bayesian models of cognition). This paper continues this project but first directs a critical analytic lens at the Derridean practice of the ontologization of grammatization from which Stiegler emerges while also distinguishing how metalanguages operate in relation to object-oriented environmental interaction by way of inferentialism. Stalking continental (Kapp, Simondon, Leroi-Gourhan, etc.) and analytic traditions (e.g., Carnap, Chalmers, Clark, Sutton, Novaes, etc.), we move from artefacts to AI and Predictive Processing so as to link theories related to technicity with philosophy of mind. Simultaneously drawing forth Robert Brandom’s conceptualization of the roles that commitments play in retrospectively reconstructing the social experiences that lead to our endorsement(s) of norms, we compliment this account with Reza Negarestani’s deprivatized account of intelligence while analyzing the equipollent role between language and media (both digital and analog)

Different Approaches to Proof Systems

The classical approach to proof complexity perceives proof systems as deterministic, uniform, surjective, polynomial-time computable functions that map strings to (propositional) tautologies. This approach has been intensively studied since the late 70’s and a lot of progress has been made. During the last years research was started investigating alternative notions of proof systems. There are interesting results stemming from dropping the uniformity requirement, allowing oracle access, using quantum computations, or employing probabilism. These lead to different notions of proof systems for which we survey recent results in this paper

Normalized Information Distance

The normalized information distance is a universal distance measure for objects of all kinds. It is based on Kolmogorov complexity and thus uncomputable, but there are ways to utilize it. First, compression algorithms can be used to approximate the Kolmogorov complexity if the objects have a string representation. Second, for names and abstract concepts, page count statistics from the World Wide Web can be used. These practical realizations of the normalized information distance can then be applied to machine learning tasks, expecially clustering, to perform feature-free and parameter-free data mining. This chapter discusses the theoretical foundations of the normalized information distance and both practical realizations. It presents numerous examples of successful real-world applications based on these distance measures, ranging from bioinformatics to music clustering to machine translation.Comment: 33 pages, 12 figures, pdf, in: Normalized information distance, in: Information Theory and Statistical Learning, Eds. M. Dehmer, F. Emmert-Streib, Springer-Verlag, New-York, To appea

Normalized Web Distance and Word Similarity

There is a great deal of work in cognitive psychology, linguistics, and computer science, about using word (or phrase) frequencies in context in text corpora to develop measures for word similarity or word association, going back to at least the 1960s. The goal of this chapter is to introduce the normalizedis a general way to tap the amorphous low-grade knowledge available for free on the Internet, typed in by local users aiming at personal gratification of diverse objectives, and yet globally achieving what is effectively the largest semantic electronic database in the world. Moreover, this database is available for all by using any search engine that can return aggregate page-count estimates for a large range of search-queries. In the paper introducing the NWD it was called `normalized Google distance (NGD),' but since Google doesn't allow computer searches anymore, we opt for the more neutral and descriptive NWD. web distance (NWD) method to determine similarity between words and phrases. ItComment: Latex, 20 pages, 7 figures, to appear in: Handbook of Natural Language Processing, Second Edition, Nitin Indurkhya and Fred J. Damerau Eds., CRC Press, Taylor and Francis Group, Boca Raton, FL, 2010, ISBN 978-142008592