Two philosophical applications of algorithmic information theory

We show that real-value approximations of Kolmogorov-Chaitin (K_m) using the algorithmic Coding theorem as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols), is in agreement with the number of instructions used by the Turing machines producing s, which is consistent with strict integer-value program-size complexity. Nevertheless, K_m proves to be a finer-grained measure and a potential alternative ap...

In order to find out the limiting speed of solving a specific problem using computer, this essay provides a method based on information entropy. The relationship between the minimum computational complexity and information entropy change is illustrated. A few examples are served as evidence of such connection. Meanwhile some basic rules of modeling problems are established. Finally, the nature of solving problems with computer programs is disclosed to support this theory and ...

This is a very basic introduction to some notions related to logic and complexity.

This is an alternative version of the course notes in chao-dyn/9407003. The previous version is based on measuring the size of lisp s-expressions. This version is based on measuring the size of what I call lisp m-expressions, which are lisp s-expressions with most parentheses omitted. This formulation of algorithmic information theory is harder to understand than the one that was presented in chao-dyn/9407003, but the constants obtained in all theorems are now less than half ...

I describe my path to unconventionality in my exploration of theoretical and applied aspects of computation towards revealing the algorithmic and reprogrammable properties and capabilities of the world, in particular related to applications of algorithmic complexity in reshaping molecular biology and tackling the challenges of causality in science.

We reminisce and discuss applications of algorithmic probability to a wide range of problems in artificial intelligence, philosophy and technological society. We propose that Solomonoff has effectively axiomatized the field of artificial intelligence, therefore establishing it as a rigorous scientific discipline. We also relate to our own work in incremental machine learning and philosophy of complexity.

We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic information theory. We investigate the properties of these quantities by means of program-size complexity from the point of view of algorithmic randomness. It is then discovered that, in the interpretation, the temperature plays a role as the ...

In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the conventional approach to computation. Then we explain how new models of algorithms turned the classical closed algorithmic universe into the open world of algorithmic constellations, allowing higher flexibility and expressive power, supporting ...

I present my viewpoint on complexity, stressing general arguments and using a rather simple language.

There is a cognitive limit in Human Mind. This cognitive limit has played a decisive role in almost all fields including computer sciences. The cognitive limit replicated in computer sciences is responsible for inherent Computational Complexity. The complexity starts decreasing if certain conditions are met, even sometime it does not appears at all. Very simple Mechanical computing systems are designed and implemented to demonstrate this idea and it is further supported by El...