The Machine as Data: A Computational View of Emergence and Definability

TL;DR

This paper explores how classical computation models inform our understanding of information emergence, complexity, and control, emphasizing the balance between informational structure and computational means to manage it.

Contribution

It offers a novel mathematical framework for analyzing the computational structure of information, bridging classical computation and information theory.

Findings

Insights into the emergence of higher-order information from classical computation

A mathematical model for balancing informational complexity and computational control

Implications for understanding chaos, randomness, and data in computational systems

Abstract

Turing's (1936) paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure comprehensively hosting causality at the physical level and beyond. On the other (the main point of Turing's paper), it can give an insight into the way in which higher order information arises and leads to loss of computational control - while demonstrating how the control can be re-established, in special circumstances, via suitable type reductions. We examine the classical computational framework more closely than is usual, drawing out lessons for the wider application of information-theoretical approaches to characterizing the real world. The problem which arises across a range of contexts is the characterizing of the balance of power between the complexity of informational structure (with emergence, chaos, randomness and 'big data' prominently on the scene) and the means available (simulation, codes, statistical sampling, human intuition, semantic constructs) to bring this information back into the computational fold. We proceed via appropriate mathematical modelling to a more coherent view of the computational structure of information, relevant to a wide spectrum of areas of investigation.