Physics and Computation

2009

September 7-11th 2009

Ponta-Delgada, Azores, Portugal

## Main.JozefGruska History

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Faculty of informatics Masaryk University Brno, Czech Republik

Faculty of informatics

Masaryk University

Brno, Czech Republik

## Talk from Jozef Gruska

Faculty of informatics Masaryk University Brno, Czech Republik

### Title

Physics and informatics as two windows to see/explore the world(s)

### Abstract

In the first part of the talk a new perception of informatics, much nature information processing motivated, is introduced and analysed. This new perception see informatics as also bringing a new, third, fundamental methodology for science and society.

In the second part of the talk physics and (new) informatics are analysed and demonstrated, in several ways, as two windows to explore the world.

In the last part of the talk a new, informatics-based, methodology is discussed in more details, especially the existing and potential impacts of this methodology to physics and informatics itself. This new methodology may be also a way to (start to) deal with some of the key problems of the current science in a new way.

## Talk from Mathieu Hoyrup

### Title

Dynamical systems: unpredictability vs incomputability.

### Abstract

The long-term forecasting of chaotic dynamical systems is generally not possible, because of the so-called "sensitivity to initial conditions": if you do not know exactly the initial state of a system, you cannot predict its long-range evolution. For this reason, the mathematical theory of dynamical systems is more focused on the understanding of the global, asymptotic behaviour of dynamical systems than the prediction of individual trajectories. In particular, several notions of entropies of a system are defined in order to quantify its unpredictability.

Computability theory provides another perspective on the problem of unpredictability: a system is unpredictable if its evolution cannot be computed by a machine. Unpredictability is then understood as incomputability, or difficulty to compute.

I will present some works that connect these two approaches: the classical one from the mathematical theory of dynamical systems, the recursion-theoretic one using concepts from computability theory, especially Kolmogorov complexity.

## Talk from Mathieu Hoyrup

### Title

Dynamical systems: unpredictability vs incomputability.

### Abstract

The long-term forecasting of chaotic dynamical systems is generally not possible, because of the so-called "sensitivity to initial conditions": if you do not know exactly the initial state of a system, you cannot predict its long-range evolution. For this reason, the mathematical theory of dynamical systems is more focused on the understanding of the global, asymptotic behaviour of dynamical systems than the prediction of individual trajectories. In particular, several notions of entropies of a system are defined in order to quantify its unpredictability.

Computability theory provides another perspective on the problem of unpredictability: a system is unpredictable if its evolution cannot be computed by a machine. Unpredictability is then understood as incomputability, or difficulty to compute.

I will present some works that connect these two approaches: the classical one from the mathematical theory of dynamical systems, the recursion-theoretic one using concepts from computability theory, especially Kolmogorov complexity.