On the Dynamic Qualitative Behaviour of Universal Computation

We explore the possible connections between the dynamic behaviour of a system and Turing universality in terms of the system's ability to (effectively) transmit and manipulate information. Some arguments will be provided using a defined compression-based transition coefficient which quantifies the sensitivity of a system to being programmed. In the same spirit, a list of conjectures concerning the ability of Busy Beaver Turing machines to perform universal computation will be formulated. The main working hypothesis is that universality is deeply connected to the qualitative behaviour of a system, particularly to its ability to react to external stimulus--as it needs to be programmed--and to its capacity for transmitting this information.Comment: forthcoming in Complex Systems vol. 2

A Behavioural Foundation for Natural Computing and a Programmability Test

What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical system to compute based on this notion. It proposes a behavioural characterisation of computing in terms of a measure of programmability, which reflects a system's ability to react to external stimuli. The proposed measure of programmability is useful for classifying computers in terms of the apparent algorithmic complexity of their evolution in time. I make some specific proposals in this connection and discuss this approach in the context of other behavioural approaches, notably Turing's test of machine intelligence. I also anticipate possible objections and consider the applicability of these proposals to the task of relating abstract computation to nature-like computation.Comment: 37 pages, 4 figures. Based on an invited Talk at the Symposium on Natural/Unconventional Computing and its Philosophical Significance, Alan Turing World Congress 2012, Birmingham, UK. http://link.springer.com/article/10.1007/s13347-012-0095-2 Ref. glitch fixed in 2nd. version; Philosophy & Technology (special issue on History and Philosophy of Computing), Springer, 201